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:Zz LIBRARY
Michigan State
University

This is to certify that the
dissertation entitled

Soft Computing for Damage Prediction and Cause
Identification in Civil Infrastructure Systems

presented by

Zhe Li

has been accepted towards fulfillment
of the requirements for the

PhD degree in Civil Engineering

 

 

 

 

 

MSU is an affirmative-action, equal-opportunity employer

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5/08 KrlProilAcosPreleIRCIDateDue mdd

 

Soft Computing for Damage Prediction and Cause Identification in
Civil Infrastructure Systems

By

Zhe Li

A DISSERTATION
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
In Civil Engineering

Department of Civil and Environmental Engineering

2008

ABSTRACT

Soﬁ Computing for Damage Prediction and Cause Identiﬁcation in Civil Infrastructure
Systems

By

Zhe Li

The deterioration of civil infrastructures is a serious problem for society and a
considerable challenge for civil engineers. To alleviate and prevent such degradation,
manual inspections are carried out for continuous monitoring and records are saved in
structural inventory databases. Structural damage prediction models that use an
integration of statistical and artiﬁcial intelligent algorithms were developed based on an
evidential database extracted and organized from a structural inventory database. Damage
in the abutment walls of highway bridges was used as an example problem where the
goal was to identify the sources of damage and predict their structural condition with
time. Unbalance, complexity, subjectivity, and incompleteness are major deﬁciencies in
the evidential database, which obstruct the development of prediction models. Novel data
organizing schemes were thus developed to overcome these obstacles and make full use
of the database in the training of an ensemble of neural networks. The damage
identiﬁcation performance of such an ensemble of networks reached 86%, which
exceeded the performance the best-trained single networks in the ensemble by 18%. Also
contributing to the development of successful prediction models were other soft
computing methods, statistical analyses, ﬁeld inspection and monitoring, and ﬁnite
element analyses. A virtual database was created through ﬁnite element analyses to

analyze the behavior of structures with different design parameters. The combination of

an evidential database and a virtual database in ensembles of neural networks was found
to be a promising innovation to improve the performance of the developed damage

prediction models.

© Copyright by Zhe Li 2008

All Rights Reserved

ACKNOWLEDGMENTS

At this moment of ﬁnishing the dissertation, I would like to thank my advisor, Dr.
Rigoberto Burguefio for his exceptional and patient guidance, warm-hearted
encouragement, and ﬁrm support. His broadness and depth of knowledge, hard working,
interest and passion to explore the unknown ﬁelds embodied a spirit to seek excellence. I
learned a great deal of technical knowledge from Dr. Burgueﬁo. However, the most
important thing he taught me is the importance of creative thinking in the training and
development of a Ph.D student. I still remember vividly the moment of our discussion
and his words, “Sit at the table with a few pieces of white paper and a pencil, no books,
no references. Think about the problem.” Such encouragement helped me to overcome
the obstacles in my Ph.D research and will continue to encourage me to use critical

thinking, innovation to solve problems in my future career.

I thank professors in my Ph. D guidance committee: Dr. Ronald S. Harichandran, his
in-depth understanding of structural engineering and sense of humor help me a lot; Dr.
Pradeep Rarnuhalli, I learn a lot from his expertise in state-of-the-art issues of soft
computing; Dr. Lyudmila Sakhanenko, her knowledge in statistics, patience, and

encouragement help me to keep high efﬁciency in the face of difﬁculties.

I grateﬁrlly acknowledge the ﬁnancial support from the Michigan Department of
Transportation and the Department of Civil and Environmental Engineering of Michigan
State University. The suggestions and help from MDOT engineers Messrs. Roger Till,

Steven Beck, Chuck Occhiuto, Dave Juntunen, and Eric Burns are really appreciated.

Thanks to Messrs. Sia Ravanbakhsh and Brian Zakrzewski for their help in the ﬁeld work.
Thanks to Mr. Craig Gunn for his patient help and guidance in my English writing. My
sincere appreciation goes to my English Tutor Anne Dykema, who helped me

considerably to improve my spoken English.

Thanks to the help of my friends and colleagues: Jun Wu, Wei Zhao, Zhan Chen,
Martin Law, Yuan F an, Xuejian Liu, Ryan Donaghy, Kyung Hoon Sun, Andrew Pauly,
David Bendert, Mahmood Haq, Golrokh Nossoni, Benjamin Pavlich, Ian Mccullough,

Richard McClary, and Janelle Musch.

I want to express my sincere appreciation to my parents and my aunt. Their love,
encouragement and conﬁdence in me support me to work hard with perseverance and
self-discipline. Their attentions on me never changed from the time I was little boy until

now, even though that attention needs to cross the Paciﬁc.

vi

TABLE OF CONTENTS

 

 

 

 

 

LIST OF TABLES x
LIST OF FIGURES xii
1 INTRODUCTION 1
1.1 Motivation ........................................................................................................... 1
1.2 Speciﬁc Research Problem: Structural Damage in the Abutment Walls of
Highway Bridges ............................................................................................................ 2
1.3 National Bridge Inventory System Database ...................................................... 8
1.4 Research Objective ........................................................................................... 11
1.4.1 Database Processing and Statistical Analyses .......................................... 12
1.4.2 Field Instrumentation ................................................................................ 12
1.4.3 Finite Element Simulation ........................................................................ 13
1.4.4 Soft Computing ......................................................................................... 13
1.4.5 Ensemble of Neural Networks and Combination of Databases ................ 14
1.5 Causes of Structural Damage in Abutment Walls ............................................ 15
1.5.1 Pavement Pressure .................................................................................... 15
1.5.2 Transverse Temperature Effect ................................................................. 19
1.5.3 Longitudinal Temperature Effect .............................................................. 21
1.6 Research Contributions ..................................................................................... 21
1.7 Dissertation Overview ...................................................................................... 22
2 STATE-OF-THE-ART RESEARCH 24
2.1 Introduction ....................................................................................................... 24
2.2 Structural Damage in the Abutment Wall of Highway Bridges ....................... 25
2.3 Artiﬁcial Neural Networks and Fuzzy Logic ................................................... 27
2.4 Handling Missing Values in Data Analysis and Neural Network Application 31
2.5 Ensemble of Neural Networks .......................................................................... 33
2.6 Data Organization for an Ensemble of Neural Networks ................................. 36
2.7 Discussion ......................................................................................................... 38
3 DATABASE CREATION AND STATISTICAL ANALYSES 40
3.1 Introduction ....................................................................................................... 40
3.2 Evidential Database .......................................................................................... 41
3.2.1 Deﬁnition of parameters ........................................................................... 41
3.2.2 Initial data screening ................................................................................. 43
3.2.3 Database creation ...................................................................................... 45
3.2.4 Deﬁciencies of MDOT NBI database ....................................................... 47
3.3 Signiﬁcance of Design and Operation Parameters ........................................... 48
3.3.1 Frequency Analyses .................................................................................. 48
3.3.2 Correlation Analysis ................................................................................. 50
3.3.3 Analysis of Factorial Effects ..................................................................... 57
3.3.4 Hypothesis Test ......................................................................................... 61

vii

3.4 Regression Analysis .......................................................................................... 65

 

 

3.4.1 Linear regression using ﬁrst order of explanatory variables .................... 68
3.4.2 Linear regression analysis using ﬁrst and second order of explanatory
variables ................................................................................................... 72
3 .5 Discussion ......................................................................................................... 8 1
4 FIELD MONITORING 84
4. 1 Introduction ....................................................................................................... 84
4.2 Bridges Selection .............................................................................................. 84
4.3 Field Inspection ................................................................................................. 88
4.3.1 U-shape pull out ........................................................................................ 88
4.3.2 Vertical cracks between girders ................................................................ 89
4.3.3 Vertical cracks underneath girder through the dowel ............................... 89
4.4 Field Instrumentation ........................................................................................ 90
4.4.1 Instrumentation Strategy and Implementation .......................................... 90
4.4.2 Deployment of measuring points .............................................................. 92
4.4.3 Variables Measured .................................................................................. 93
4.4.4 Measurement schedule .............................................................................. 96
4.5 Data Interpretation ............................................................................................ 97
4.5.1 Distribution of Strains ............................................................................... 97
4.5.2 Peak strain vs. time and temperature in region around girders ................. 98
4.5.3 Peak strain vs. time and temperature in spans between girders .............. 103
4.6 Evaluation of Potential Damage Causes ......................................................... 106
4.6. 1 Pavement pressure .................................................................................. 106
4.6.2 , Transverse temperature effect ................................................................. 111
4.6.3 Longitudinal temperature effect .............................................................. 1 12
4.7 Discussion ....................................................................................................... 1 12
5 FINITE ELEMENT SIMULATIONS 114
5. 1 Introduction ..................................................................................................... 1 14
5.2 Finite Element Simulation Strategy ................................................................ 115
5.2.1 Steel bridges ............................................................................................ 1 17
5.2.2 Concrete bridges ..................................................................................... 121
5.2.3 Boundary conditions ............................................................................... 123
5.3 Case Matrices and Analytical Models ............................................................ 124
5.3.1 Simple/cantilevered steel bridge ............................................................. 124
5.3.2 Continuous steel bridge .......................................................................... 124
5.3.3 Prestressed concrete bridge ..................................................................... 126
5.4 Damage scenarios ........................................................................................... 126
5.4.1 Pavement growth .................................................................................... 126
5.4.2 Temperature ﬁeld .................................................................................... 127
5.5 Result Variables .............................................................................................. 130
5.6 Result Interpretation and Parametric Analyses ............................................... 130
5.6.1 Simple/cantilevered steel bridges ........................................................... 131
5.6.2 Continuous steel bridges ......................................................................... 139
5.6.3 Prestressed concrete bridges ................................................................... 140

viii

5.7 Discussion ....................................................................................................... 141

 

6 SOFT COMPUTING 143
6.1 Introduction ..................................................................................................... 143
6.2 Multilayer Perceptron Network ...................................................................... 144
6.3 Radial Basis Function Network ...................................................................... 149
6.4 Support Vector Machine ................................................................................. 153
6.5 Supervised Self-Organizing Map .................................................................... 157
6.6 Evaluation of ANN Models for Abutment Distress Problem ......................... 159

6.6.1 Input variables and structure of the ANN models .................................. 159
6.6.2 Evaluation of ANN models ..................................................................... 161
6.6.3 Deterioration curves for highway bridge abutment walls ....................... 167
6.7 Fuzzy Neural Network Model ........................................................................ 170
6.7.1 Fuzzy Sets ............................................................................................... 171
6.7.2 Fuzzy-Neural Network ........................................................................... 1 73
6.7.3 Back transforming scheme ...................................................................... 175
6.7.4 Results ..................................................................................................... 176
6.7.5 Bridge abutment deterioration curve ...................................................... 178
6.8 Discussion ....................................................................................................... 1 80

7 ENSEMBLE OF NEURAL NETWORKS AND COMBINATION OF

 

 

DATABASES 182
7.1 Introduction ..................................................................................................... 1 82
7.2 Data Organization ........................................................................................... 186
7.3 Voting Scheme ................................................................................................ 188
7.4 Results ............................................................................................................. 190

7.4.1 Ensemble and network structure ............................................................. 190
7.4.2 Evaluation of Voting Schemes ............................................................... 191
7.4.3 Bridge Abutment Deterioration Curves .................................................. 195
7.5 Combination of Databases for Soft Computing .............................................. 201
7.5.1 Introduction ............................................................................................. 201
7.5.2 Concept and Methodology ...................................................................... 203
7.5.3 Networks trained on virtual database ...................................................... 203
7.5.4 Improvement in damage identiﬁcation ................................................... 207
7.5.5 Diagnosis of possible causes for structural damage ............................... 209
7.6 Software Development: Bridge Abutment Damage Diagnosis (SbNet) ........ 210
7.7 Discussion ....................................................................................................... 21 1

8 FUTURE RESEARCH AND CONCLUSION 213

8.1 Further Research ............................................................................................. 213
8.1.1 Prediction models for other structures .................................................... 213
8.1.2 Improved combination of databases ....................................................... 213
8.1.3 Prediction model with online updating capacity ..................................... 214

8 .2 Conclusions ..................................................................................................... 2 1 6

REFERENCES 218

 

ix

LIST OF TABLES

Table 1-1 Bridge ratings and physical conditions of structural members .......................... 9
Table 3-1 Deﬁnition of parameters ................................................................................... 42
Table 3-2 Criteria for data extraction ............................................................................... 44
Table 3-3 Criteria to reﬁne the data set ............................................................................ 46
Table 3-4 Common characteristics of bridges with poor abutments ................................ 50
Table 3-5 Type III Model ANOVA .................................................................................. 60
Table 3-6 Test of factorial effects (covariates values are Os) ........................................... 61
Table 3-7 Frequency analysis by girder type and abutment condition ............................. 64

Table 3-8 Chi-square Test for H0: no association between abutment condition and beam

type ............................................................................................................................ 64

Table 3-9 Frequency analysis by approach surface type and abutment condition ........... 65

Table 3-10 Chi-square Test for H0: no association between abutment condition and
approach surface type ............................................................................................... 65

Table 3-11 Subset of explanatory variables for simple/cantilevered steel bridges ........... 69

Table 3-12 Explanatory variable subsets of simple/cantilevered steel bridges and their

Mallow’s Cps ............................................................................................................. 71
Table 3-13 Mean and standard deviation of the quantitative variables ............................ 75
Table 3-14 Results of Mallow’s Cp Selection Method (Top 7 rows) ............................... 77
Table 4-1 Criteria for simple/cantilevered steel bridge selection (in both phases) .......... 85
Table 4-2 Criteria for continuous steel bridge selection (Phase 1) ................................... 85
Table 4-3 Criteria for simple prestressed concrete bridge selection (Phase 1) ................. 86
Table 4-4 Criteria for continuous steel bridge selection (Phase 2) ................................... 86
Table 4-5 Simple/cantilevered Steel Bridges Field Assessment Result (Phase 1) ........... 87

Table 4-6 Final instrumentation list .................................................................................. 91

Table 5-1 Element details used to simulate the structural members ............................... 1 16
Table 5-2 Material properties ......................................................................................... 117
Table 5-3 FEA case matrix for simple/cantilevered steel bridges .................................. 125
Table 5-4 FEA case matrix continuous steel bridges ..................................................... 125
Table 5-5 FEA case matrix for prestressed concrete bridges ......................................... 126

Table 5-6 Temperature Ranges (Part of Table 3.12.2.1-1 of AASHTO Speciﬁcation). 128

Table 5-7 Temperature values for linear temperature gradient in the deck .................... 130
Table 6-1 Parameters of MLP ......................................................................................... 148
Table 6-2 Confusion matrix of abutment rating prediction using an MLP ANN ........... 163
Table 6-3 Confusion matrix of abutment rating prediction using an RBF ANN ........... 164
Table 6-4 Confusion matrix of abutment rating prediction using an SVM ANN .......... 165

Table 6—5 Confusion matrix of abutment rating prediction using an SSOM ANN ........ 166

Table 6-6 Conﬁdence level for the conﬁdence bands of deterioration curves ............... 169
Table 6-7 Confusion matrix of an FNN .......................................................................... 177
Table 7-1 Collection algorithm for subjective voting ..................................................... 192
Table 7-2 Evaluation of different voting schemes .......................................................... 194

Table 7-3 Confusion matrix of an ensemble of neural networks using modiﬁed majority
voting ...................................................................................................................... 196

Table 7-4 Parameters of networks based on virtual database ......................................... 207

Table 7-5 Confusion matrix for the ensemble of networks with combined databases 208

xi

LIST OF FIGURES

Figure 1-1 Structural components and design parameters of a highway bridge ................. 3
Figure 1-2 Structural members of a highway bridge (in site view) .................................... 3
Figure 1-3 Concrete spalling in the abutment wall ............................................................. 4
Figure 1-4 Pull-out of concrete block in the abutment wall under girder support .............. 4
Figure 1-5 Vertical cracks between girders ........................................................................ 5
Figure 1-6 Vertical cracks underneath girders .................................................................... 5
Figure 1-7 Repair of damage in abutment walls ................................................................. 6
Figure 1—8 Corroded pin-hanger assembly ......................................................................... 7
Figure 1-9 Water leaked to the abutment wall underneath a girder .................................... 8
Figure 1-10 Interaction of research methods .................................................................... 12
Figure 1-11 Generation of pavement pressure .................................................................. 17
Figure 1-12 Concrete pullout caused by pavement pressure ............................................ 18
Figure 1—13 Bridge abutment damage with their possible causes .................................... 20
Figure 3-1 Scatter plot matrix of simple/cantilevered steel bridges ................................. 45
Figure 3-2 Frequency analysis of highway bridge inspections ......................................... 49
Figure 3-3 Ratio of poor abutment rating ......................................................................... 49
Figure 3-4 Schematic representations of the correlation of two random variables .......... 53
Figure 3-5 Scatter plot for abutment rating and average daily total trafﬁc ...................... 54
Figure 3-6 Database Sub-Division for Statistical Correlation Analyses .......................... 56
Figure 3-7 Scatter Plot for Abutment Rating and Age at Inspection ................................ 57
Figure 3-8 Residual plot for the model of simple/cantilevered steel bridges ................... 72

xii

Figure 3-9 Leaf and stem plot and box plot of residuals for simple/cantilevered steel
bridge ........................................................................................................................ 73

Figure 3-10 Normal probability plot for the model of simple/cantilevered steel bridges 74

Figure 3-11 Mallow’s Cp against p .................................................................................. 76
Figure 3-12 Plot of Residual against predicted values ..................................................... 78
Figure 3-13 Plot of Residual against “deck width” .......................................................... 78
Figure 3-14 Stern and leaf plot and box plot of residuals ................................................. 79
Figure 3-15 Normal Probability Plot of the residuals ....................................................... 80
Figure 4-1 Abutment Distress and Pavement for Bridge A1.7 ......................................... 88
Figure 4-2 Location of bridge and instrumentation region ............................................... 92
Figure 4-3 Brass cylinders installed on the abutment wall ............................................... 92
Figure 4-4 Measuring points with contact seats screwed on brass cylinders ................... 93

Figure 4-5 Deployment of measuring points on half of the abutment wall of bridge A1.7

................................................................................................................................... 94
Figure 4-6 Measurement of girder end displacement (unit: mm) ..................................... 95
Figure 4-7 Temperature measuring points on bridge abutment wall ................................ 95

Figure 4-8 Horizontal strains, control joints and cracks on abutment wall of bridge A1.7

................................................................................................................................... 99
Figure 4-9 Distribution of horizontal strains and cracks on backwall of bridge C2.1 ...... 99
Figure 4-10 Horizontal strains on abutment wall of bridge A1.7 using moving average

method ..................................................................................................................... 100
Figure 4-11 Division of measuring points on bridge A1.7 by regions ........................... 101
Figure 4-12 Peak strains in region 2 of bridge A1.7 ....................................................... 102
Figure 4-13 Peak strains in region 5 of bridge A2.1 ....................................................... 102
Figure 4-14 Division of measuring points on bridge A1.7 by spans .............................. 104

xiii

Figure 4-15 Peak strains in span 2 of bridge A2.l .......................................................... 105

Figure 4-16 Peak strains in span 3 of bridge A1.7 .......................................................... 106
Figure 4-17 West abutment of bridge B2.1 .................................................................... 107
Figure 4-18 West approach pavement of bridge B2.1 .................................................... 107
Figure 4-19 East abutment of bridge B2.1 ...................................................................... 108
Figure 4-20 East approach pavement of bridge B2.1 ..................................................... 108
Figure 4-21 Abutment distress in bridge A1.7 ............................................................... 109
Figure 4-22 Approach pavement of bridge A1.7 ............................................................ 1 10
Figure 4—23 Pin-and-hanger assembly of bridge A1.7 .................................................... 1 10
Figure 5-1 Bridge plan (unit: mm) .................................................................................. 1 17
Figure 5-2 Bridge side View (unit: mm) ......................................................................... 1 18
Figure 5-3 Bridge Model ................................................................................................ 119
Figure 5-4 Modeling details of one transverse span of bridge ....................................... 1 19
Figure 5-5 Modeling of back wall and abutment wall .................................................... 120
Figure 5—6 Modeling of pin-and-hanger assembly ......................................................... 120
Figure 5-7 Pin-and—hanger detail in model built in ABAQUS ....................................... 121
Figure 5-8 Mesh of prestressed concrete I girder ........................................................... 122
Figure 5-9 Prestressed concrete bridge model ................................................................ 122
Figure 5-10 Boundary condition at the bottom surface of the abutment wall ................ 123
Figure 5-11 Boundary condition at the pier cap ............................................................. 123

Figure 5-12 Diagram for simple/cantilevered steel bridges with 2 spans (unit: mm) 125
Figure 5-13 Diagram for continuous steel bridges with 4 spans (unit: mm) .................. 125

Figure 5-14 Positive vertical temperature gradient in concrete and steel structures (units:
mm, Figure 3.12.3-2 of AASHTO Speciﬁcation) ................................................... 128

xiv

Figure 5-15 Simpliﬁcation of temperature gradient for steel bridges (unit: mm) .......... 129

Figure 5-16 Simpliﬁcation of temperature gradient for concrete bridges (unit: mm) 129

Figure 5-17 Principal tensile stresses in the abutment wall ............................................ 131
Figure 5-18 Maximum principal strain in a simple/cantilevered steel bridge model ..... 132
Figure 5-19 Maximum principal strain on the surface of the abutment wall ................. 133

Figure 5-20 Horizontal strain at a level 0.305 m below the top of the abutment wall 133

Figure 5-21 Maximum stress of bridges under pavement pressure (with ﬁ'ee moving pin-

and-hanger assembly, width = 17.8 m) ................................................................... 134
Figure 5-22 Maximum horizontal strain for bridges under pavement pressure (with free
moving pin-and-hanger assembly, width = 17.8 m) ............................................... 134
Figure 5-23 Maximum stress of bridges under pavement pressure (with locked pin-and—
hanger assembly, width = 17.8 m) .......................................................................... 135
Figure 5—24 Maximum horizontal strain for bridges under pavement pressure (with
locked pin-and-hanger assembly, width = 17.8 m) ................................................. 136
Figure 5-25 Maximum stress of bridges in summer (with ﬁ'ee moving pin-and-hanger,
width = 22.7 m) ....................................................................................................... 137
Figure 5-26 Maximum stress of bridges in summer (with locked pin-and-hanger, width =
22.7 m) .................................................................................................................... 137
Figure 5-27 Maximum horizontal strain of bridges in winter (with free moving pin-and-
hanger, with = 22.7 m) ............................................................................................ 138
Figure 5-28 Maximum horizontal strain of bridges in winter (with locked pin-and-hanger,
width = 22.7 m) ....................................................................................................... 139
Figure 6-1 Diagram of MLP ........................................................................................... 145
Figure 6-2 Sigrnoid activation function (a = 1) .............................................................. 146
Figure 6-3 Gaussian function in two-dimensional space ................................................ 150
Figure 6-4 Diagram of RBF ............................................................................................ 151
Figure 6-5 Optimal decision boundary decided by SVM ............................................... 153

XV

Figure 6-6 Transformation of feature space [Law 2006] ................................................ 155

Figure 6-7 Performance of ANN models ........................................................................ 167
Figure 6-8 Scatter plot of abutment rating vs. age at manual inspection ........................ 168
Figure 6-9 Abutment deterioration curve for bridge A1.5 .............................................. 169
Figure 6-10 Membership ﬁmction of fuzzy sets ............................................................. 172
Figure 6-11 Membership function of ﬁrzzy sets after modiﬁcation for ANN ................ 172
Figure 6-12 Schematic of an FNN model ....................................................................... 174
Figure 6-13 Abutment deterioration curve of a prestressed concrete bridge .................. 179

Figure 6-14 Deterioration curve developed by an FNN for the bridge in Figure 6-9 ..... 180

Figure 7-1 Diagram of ensemble of MLPs ..................................................................... 183
Figure 7-2 A novel data organization scheme: bagging with categories ........................ 187
Figure 7-3 Example of subjectivity voting scheme ........................................................ 190
Figure 7-4 DIR versus number of networks in an ensemble of neural networks ........... 193
Figure 7-5 FAR versus number of networks in an ensemble of neural networks .......... 194
Figure 7-6 Abutment deterioration curve of a continuous steel bridge .......................... 195
Figure 7-7 A deterioration curve with long ﬂat range .................................................... 198
Figure 7-8 A deterioration curve with spike in the middle ............................................. 199
Figure 7-9 A deterioration curve shows increase of abutment rating ............................. 200

Figure 7-10 Deterioration curve developed by an FNN for the bridge in Figure 6-9 ..... 201

Figure 7-11 Scheme of database combination ................................................................ 204
Figure 7—12 Deterioration curve shown in Figure 7-6 with smoothed curve .................. 211
Figure 8-1 Online update scheme for soft computing model ......................................... 215

xvi

1 INTRODUCTION

1.1 Motivation

Problems can happen in every area in the world. In the scope of medicine, a person
might suffer a heart attack; in the ﬁeld of meteorology, a storm might arise; in the area of
the economy, inﬂation might happen, etc. Although they are different phenomena in
diverse ﬁelds, some characteristics are common. First, something goes wrong and there
are some causes behind the problem. Second, the past records and current observations of
the problem are available. Third, a set of potential causes might lead to the problem. The
relationship between causes and effect is highly nonlinear; and, thus, the prediction of the
problem and the identiﬁcation of potential causes are complex inverse problems. How to
predict the problem and identify its potential causes has been the constant interest of the

academic world as well as the industry in the past decades.

In the ﬁeld of structural engineering, one of such problems is the degradation of civil
infrastructure, such as the corrosion in bridges, cracks in concrete buildings, pavement
blow-ups, etc. Degradation of civil infrastructure threatens the prosperity of the economy
and the quality of life. The American Society of Civil Engineers (ASCE) assessed 15
categories of America’s infrastructure in 2005 and concluded that the average condition
of the country’s infrastructure is poor. It has been estimated that sixteen trillion dollars
are needed to address these infrastructure problems [ASCE 2005]. In an effort to monitor
and alleviate these problems in a timely manner, manual inspections of transportation
inﬁastructure are documented as Structural Inventory System Databases (SISD). For

instance, in a structural inventory system database for highway bridges, an inspection

record of a bridge documents the design parameters, such as the length, width, and skew
angle; the conditions of structural members, such as bridge decks and abutment walls;

and operation parameters, such as average daily truck trafﬁc.

In this research, a structural damage prediction procedure is developed through the
integration of different tools, including soft computing, statistical analyses, ﬁeld
instrumentation, and ﬁnite element simulations. Such a procedure can be used to develop
prediction models given an SISD. Civil engineers can use such a tool to predict structural
damage; identify potential causes of the damage, and thus repair and maintain civil
inﬁastructure more cost—effectively. A cornerstone in such a procedure is the advanced
exploration of an SISD using an ensemble of neural networks with a novel data

organizing scheme.

1.2 Speciﬁc Research Problem: Structural Damage in the Abutment Walls
of Highway Bridges

An example of the degradation of civil inﬁ'astructure is the distress in the abutment
walls of highway bridges in the State of Michigan. Structure and design parameters of a
highway bridge are illustrated in Figure 1-1. The abutment walls of a bridge (Figure 1-2)
are the two walls that provide the end supports for the bridge superstructure and contain
the backﬁll soils. Highway bridges in the State of Michigan are suffering from distress in
the form of cracks and concrete spalling in their abutment walls (Figure 1-3). The forms
of abutment distress are on the front side of the abutment wall and are of the following
types: U-shape concrete spalling under the girder supports (Figure 1-4), vertical cracks

between girders (Figure 1-5), and vertical cracks underneath girders (Figure 1-6).

 

 
   

To end of

 

Structural components: CDsteel girder, ®deck, ©cross-frame, @approach pavement,
©abutment wall, ©pier, @pin—and-hanger, .bearings, ©expansion joint, @railing.
Design parameters: (a)structura1 type, (b)bridge length, (c)skew angle, (d)bridge
width, (e)sparr length, (ﬂapproach pavement type.

 

Figure 1-1 Structural components and design parameters of a highway bridge

Abutment wall

—.

 

Figure 1-2 Structural members of a highway bridge (in site view)

 

 

Figure 1-3 Concrete spalling in the abutment wall

 

Figure 1-4 Pull-out of concrete block in the abutment wall under girder support

 

Vertical crack in abutment
wall (between girders,
ampliﬁed in the right ﬁgure)

 

(a) General view of abutment wall (b) Detailed view of the vertical
cracks between girders

Figure 1-5 Vertical cracks between girders

ertic a1 cracks in
abutment wall
(underneath girder) ”'

 

Figure 1-6 Vertical cracks underneath girders

The distress seems to be incremental, with cracks and concrete spalling growing with
time as a consequence of factors not yet fully understood. Additional effects from
corrosion due to leaky joints worsen or increase the damage. Thus, While initially the
cracks are cosmetic, with little effect on serviceability or safety of the bridge, with time
they can severely degrade the integrity of the abutment wall. In some cases, the
degradation due to damage under girder supports can be extensive and thus compromise
the system’s structural integrity. The Michigan Department of Transportation (MDOT)
has traditionally been addressing this problem by continuously monitoring the condition
of this distress and then acting on repairs to restore the integrity of the abutment wall.
The repair cost of damaged abutment walls is high. Figure 1-7 shows a picture of a
repaired abutment wall. It is of interest to improve the understanding of the causes behind
this damage, to develop strategies to alleviate it, and to create models that predict the

damage in the ﬁrture.

 

Figure 1-7 Repair of damage in abutment walls

The causes of the mentioned damage in the abutment walls are not clearly known.
Possible sources include corroded, or “frozen,” bearings and expansion details, e.g., pin-
and-hanger assemblies (Figure 1-8), underperforming expansion joints, the pressure
generated by the thermal movement of pavement approaches (or “pavement growth”), the
leak of expansion joints in the superstructure, and the water and salt leaked to the
abutment wall (which lead to the degradation of concrete, as shown in Figure 1-9),

temperature effects, heaVy vehicle trafﬁc, design quality, construction quality, etc.

While the factors mentioned above are potential contributors for the damage in bridge
abutment walls, the relative importance of these causes is not well understood. Focused
and effective strategies for relieving the structural distress in the abutment walls can only
be developed after a better understanding of the different causes and their relative
importance. Furthermore, the ability to forecast potential problems in abutment walls and
knowing how to avoid such problems will improve the management of maintenance and

future design of highway bridges.

 

Figure 1-8 Corroded pin-hanger assembly

 

Figure 1-9 Water leaked to the abutment wall underneath a girder

1.3 National Bridge Inventory System Database

In order to keep bridges in good condition, the Michigan Department of
Transportation (MDOT) maintains an SISD, which is a bridge inspection database in the
National Bridge Inventory (NBI) system [Hartle et a1. 1991]. The database is based on
manual inspections of structural members at a time interval of no more than two years. A
0-9 scale rating is used to record the conditions of structural members, where the larger
number means better condition and 0-4 means different distress levels in the structural
member. The Michigan Structure Inventory and Appraisal Coding Guide [MDOT 2003]
describes the inspection ratings and corresponding physical conditions of structural
members of highway brides. BIR #12 Abutrnents (SI & A item 60, Substructure) of the
Michigan Structure Inventory and Appraisal Coding Guide [MDOT 2003] is reproduced

in Table 1-1.

Table 1-1 Bridge ratings and physical conditions of structural members

 

Rating Condition

Description

 

9 New

8 Good

7 Good

6 Fair

5 Fair

4 Poor

3 Serious

2 Critical
Imminent

1 .
farlure

0 Failed

No deﬁciencies in any of the structural components that will
affect the long term performance.

All structural components are sound and functioning as
designed. There may be superﬁcial cracking or weathering of
protective coatings and/or dirt contamination on structural
components.

All members retain ﬁrll section properties and ﬁmction as
designed. There may be minor cracking in structural
components.

All members retain ﬁrll section properties and function as
designed. There may be some deterioration affecting structural
members such as minor cracking, scaling, small scattered
spalls, or shallow scour. Some protective coating failures.

Moderate deterioration affecting structural members such as
cracking, scaling scattered spalls, minor settlement or shallow
scour. Minor section loss in low or no stress areas. All
members continue to function as designed.

Considerable deterioration affecting structural members such
as cracking, scaling, scattered spalls, partial settlement or,
scour. . All members continue to function as designed.

Considerable deterioration affecting structural members.
Structural, hydraulic, and/or load analysis may be necessary to
determine if the structure can continue to function without
restricted loading or immediate repairs.

Deterioration has progressed to the point where the structure
will not support design loads and must be posted for reduced
loads.

Bridge is closed to trafﬁc, but corrective action may put the
bridge back in service.

Bridge closed.

 

Use of the SISD poses several challenges, which need to be addressed through
innovations in the development of a prediction model for structural damage. An SISD
documents the condition of the infrastructure with design and Operation parameters, and
thus provides information for scheduling maintenance and repair. However, further
exploration and the advanced use of these evidential databases are constrained by some
inherent difﬁculties:

. The database can be highly scattered and no conspicuous trend or correlation can
be extracted. For the bridge abutment problem, there is no obvious one to one
relationship between cause and effect of structural damage, which means that
many causes can lead to the damage of the abutment. Moreover, the relationship
can be highly nonlinear and thus very hard to be extracted, if not impossible, by
current methods.

. Subjectivity exists in the manual inspection methods, and there is large variance
in the adopted structural evaluation ratings. For the NBI system, it has been
found that for the same structural component, its ratings assigned by 49 bridge
inspectors from 25 state departments were dispersed, with only 68 percent of
them within il (in a scale of O to 9) around the mean and 95 percent of them
falling in i2 around the mean [Phares et a1. 2001]. Even if all the bridges with
the same design and operation parameters were inspected by the same structure
inspector, the ratings might still be different because construction quality can not
be identical.

0 The values of some variables in some observations are missing or subject to

error. For instance, the approach pavement type (a parameter of importance to

10

the damage in highway bridge abutments) for some highway bridges in the
database is missing.

. The distribution of the inspection records is unbalanced. Cases of severe damage
are relatively rare in comparison to the large number of structures in relatively

good condition.

1.4 Research Objective

The purpose of this research is to develop a procedure to predict structural damage in
civil infrastructure and identify causes of damage within the context of structural damage
in bridge abutment walls. This research was based on the research project Identification
of Causes and Development of Strategies for Relieving Structural Distress in Bridge
Abutments, which was ﬁrnded by the MDOT. However, applications of the
methodologies are not limited to the scope of the abutment walls or bridges. It is a
generalized approach to help researchers and civil engineers alleviate the degradation of
civil infrastructure. Given structural design and operation parameters, such a procedure is
able to predict damage in structures and evaluate the contributions of potential damage
causes through in the depth exploration of an SISD and the interaction of a series of tools.
The research methods are shown in Figure 1-10. The methods in Figure 1-10 are not
independent from each other or work in a sequential or linear manner. They are used
interactively to help each other in the process of identifying the potential causes and

developing prediction models. These methods are described in the following subsections.

ll

FEA Statistical Field
Simulations Analyse' Monitoring

'

Soft \
Computing —.| Causes of Damage I

 

 

ll

I Damage Prediction Model I

 

 

Figure 1-10 Interaction of research methods

1.4.1 Database Processing and Statistical Analyses

Generally, a structural inventory system database includes a great deal of information,
and only part of it is relevant to the research goal. Thus, the database is ﬁrst investigated,
processed, and organized in a way that it could be analyzed. Statistical analyses were
performed to identify the cause-effect association between structural damage in bridge
abutment walls and bridge design and operation parameters, develop regression models to
predict structural condition, and provide information and guidance for other analyses,

simulations, and ﬁeld instrumentation.

1.4.2 Field Instrumentation

Based on the results of the statistical analyses, a set of typical structures (bridges)
were identiﬁed and inspected. Suitable ones among them were instrumented and
monitored to evaluate the contribution of the identiﬁed parameters and assist the

execution and validation of the analytical studies. Assuming that the number of structures

12

being monitored was adequate, ﬁeld instrumentation also provided an additional source

of information for the soft computing models.

1.4.3 Finite Element Simulation

Finite element analyses (FEA) were used to investigate the behavior of structures
(bridges) with different design parameters under different damage scenarios. A virtual
database created from the FEA was used in a parametric study and served as an

additional information source to an ensemble of neural networks.

1.4.4 Soft Computing

Multilayer perceptron (MLP) network, radial basis function network (RBF), support
vector machine (SVM), supervised self-organizing map (SSOM), and ﬁrzzy—neural
network (FNN) models were exploited interactively to overcome the difﬁculties with the
database mentioned above and build damage-prediction models. An MLP model can
“learn” from data patterns and map nonlinear relationships in the data [Haykin 1999]. It
is robust to erroneous or incomplete data. MLP was applied in this research considering
the difﬁculties mentioned in Section 1.3, especially the complexity, incompleteness, and
erroneousness data. An RBF is a good tool for curve ﬁtting. It is used to ﬁt the
relationship between explanatory variables and structural conditions in this research. An
SVM model optimizes the decision boundary between data categories and avoids local
rrrinima [Taylor & Cristianini 2004]. It is a powerful tool to overcome the difﬁculties
mentioned in Section 1.3, especially the complicated nonlinear relationship between
explanatory variables and structural conditions. An SSOM is a tool for feature extraction

and feature mapping. It was used in this research to identify the features of this

13

complicated problem. An FNN model is a combination of ﬁrzzy logic and artiﬁcial neural
networks. It was applied to process the discrete and highly subjective manual damage
evaluation ratings as well as to overcome the subjectivity and imprecision in manual

inspection and data collection.

1.4.5 Ensemble of Neural Networks and Combination of Databases

A single artiﬁcial neural network (ANN) model might suffer from local minimum and
misrepresent relationships that might be correctly mapped by other ANN models [Guo
and Luh 2004]. The sources behind structural damage are highly scattered; and thus it is
hard for a single neural network to catch all the damage sources and derive a good
prediction model. An ensemble of neural networks (ENN) is composed of a series of
individual ANN models in parallel and makes predictions by collecting and combining

predictions of individual neural networks through a voting process.

An ENN was used in this research to alleviate the local minima problem suffered by
individual ANN models and anneal the effects of all damage sources together in the
development of a prediction model. More importantly, a novel data organizing and voting
scheme enabled the ensemble of neural network to overcome the unbalance of the SISD
and identify the structural damage with higher accuracy. A virtual database created
through ﬁnite element simulations was combined with the evidential database in an effort

to improve the prediction power of an ensemble of neural network.

14

1.5 Causes of Structural Damage in Abutment Walls

Among the a series of potential causes for structural damage in abutment walls
mentioned in Section 1.2, three of them were identiﬁed as major causes to the damage.
The identiﬁcation was based on the statistical analyses, ﬁeld inspection, ﬁeld
instrumentation, and ﬁnite element simulations. As introduced in Section 1.4, these
methods were used interactively, the identiﬁcation of causes for structural damage also
provide valuable guidance for statistical analyses, ﬁeld instrumentation, and ﬁnite
element simulations. Pavement pressure is identiﬁed as the most signiﬁcant cause.
Transverse and longitudinal temperature effects also proved to be important contributors.

The evidence for the identiﬁcation of these causes is presented in the following chapters.

1.5.1 Pavement Pressure

The interface between the bridge superstructure and embankments is a well-known
source of large maintenance problems [Briaud et al. 1997, Long et al. 1998]. A relevant
problem at this interface is the so-called “pavement growth” phenomena, which refers to
the movement and expansion of pavements against the bridge deck. The causes for
pavement growth are complex, encompassing pavement motions due to temperature
effects, incorrect design of approach slabs, improper design of sleeper slabs, expansive
soils, soil consolidation, soil embankment movement, drainage, etc. Burke [1998, 2004]
found that pavement growth was generated through years of temperature variation cycles
and failure of expansion joint sealing. The process is illustrated in Figure 1-11. Concrete
slabs were connected with expansion joints with sealing at the end of the pavement

construction process. During the winter season, temperature decreases and concrete slabs

15

contract, thus increasing the gap at joints. Debris falls into the expansion joint gaps if the
joint sealing doesn’t work well. With temperature increase during the summer period
concrete slabs expand closing the expansion joint gaps and compacting the deposited
debris inside of it. The compacted debris thus takes part of the space in the expansion
joint gap. With the next winter cycle the pavement joints will again open allowing more
debris to deposit in the joint gaps, which will later be once again compacted when the gap
closes during the summer season. The repetition of this process over the years will ﬁll
and compact the space in the expansion joints. The reduction of ﬁee space in the
expansion joint gaps generates compressive pressure between adjacent pavement slabs.
The pressure can be large enough to mobilize the slabs or can result in upwards buckling

of the pavement, or pavement blowup.

The mechanism and force ﬂow behind the damage caused by pavement pressure are
shown in Figure 1-12. In Figure 1-12, hollow arrows composed by solid lines represent
forces generated by pavement growth. At the beginning the pavement slabs move
towards the approaches of a bridge and the expansion joints at the pavement/
superstructure interface was not be able to accommodate the pavement movement. Then
the generated pavement pressures against the bridge deck will transfer forces to the
girders and these will subsequently transfer the loads to their bearing or anchorage detail
on top of the abutment wall. If the bearings or anchorage detail are not designed to
accommodate such a large pressure, or are locked due to corrosion, the pavement
pressure will be transferred to the abutment wall. When the pressure transferred to the

abutment wall is large enough, cracks underneath the girder through the position dowel

16

will occur in the abutment wall. In serious cases, complete concrete segments will be

pulled out from the abutment wall, as shown in the in-site picture in Figure 1-12.

Sealing Expansion joint
\ /

 

r/

 

 

 

 

 

 

Concrete pavement (New)

Debris fell into opened space

l—_'—" ‘—
Contracted____

Sealing opened

 

 

 

   

In winter

Debris compacted

 

 

 

 

in the sealing Pressure generated
\ \
-. $ Expanded 3L; .-
In summer

Years of cycles

Huge pressure accumulated
in concrete slabs

15 to 30 years later

 

 

 

 

Figure 1-11 Generation of pavement pressure

17

 

lPush by pavement

 

 

 

l
7 ‘ :> ‘ :ﬁ>ﬁ DeCk Slab‘
Dependent ] ::>.l

BaCkwall H» '::::::::::

 
     
     
      
     
   
  
   

Approach pavement
transmitted

B .
earrng from slab

l
l
l
Force Generation ; 1
l

 

Index:
r:>—

Steel girder

Pavement growth

Forces
transimitted

structure combined ﬁom girder

with lock of pin and
hanger

In-site

Figure 1-12 Concrete pullout caused by pavement pressure

1.5.2 Transverse Temperature Effect

Temperatures in bridge superstructure and substructure could be different
signiﬁcantly in summer and winter. The sunshine in summer time heats up the bridge
deck, and thus makes the temperature of superstructure to be higher than substructure.
The soil around substructure keeps them warm in winter time, and thus makes the
temperature of superstructure lower than substructure. The details of temperature proﬁle
can be found in Section 5.4.2. Transverse effects of this temperature difference can lead

to vertical cracks in abutment walls at locations between girder supports.

The mechanism and force ﬂow behind the damage caused by the transverse
temperature effect are shown in Figure 1-13. In summer, the temperature in the bridge
superstructure is higher than substructure. Thus, the superstructure has a trend to expand
relatively to the substructure. In Figure 1-13 hollow arrows represent forces generated by
the transverse thermal expansion of the superstructure. At the beginning, the deck heats
up and expands. The expansion of the deck will lead to an increase of the transverse
distance between girders. At the same time, the abutment wall, which has less expansion
than the deck, will restrain the girders from transverse movement. If the bearings, or
anchorage details, are not designed to accommodate such transverse movement, or are
locked due to corrosion, tensile stresses will be generated in the abutment wall. When the
tensile stresses generated in the abutment wall are large enough vertical cracks will occur
in the abutment wall at locations between girder supports, as shown in the in—site picture

in Figure 1-13.

19

Thermal expansion in transverse direction

 

 

J

 

 

 

 

<): :>—
Deck slab fall: Connection‘bolt\‘££y
H
<: :>—
ll
7 Forces. Vertical crack}: , T
:nsméttidb of concrete H Backwall Steel girder
t 011g S a ll Bearing
H H E. if iUﬁ—/
<: H ::>
Force transmitted ii Abutment Wall
from girder l Connection bolt

kVertical crack of concrete

 

 

 

Figure 1-13 Bridge abutment damage with their possible causes

20

1.5.3 Longitudinal Temperature Effect

When the pin-and-hanger assemblies of a steel bridge are rusted and can not
accommodate the longitudinal movement of the girders longitudinal forces are generated
at the bearings and then transmitted to the abutment wall. Figure 1-12 illustrates the
mechanism and force ﬂow behind the damage caused by longitudinal temperature effects.
In Figure 1-12, hollow arrows composed by dashed lines represent forces generated by
longitudinal temperature effects. If the deck and girders are contracted due to a
temperature decrease then girder ends will move away from their supports (bearings or
anchorage). If the bearings, or anchorage details, are not designed to accommodate such a
longitudinal movement or are locked due to corrosion, stresses will be generated in the
abutment wall. When these stresses are large enough, damage will occur due to the
pulling forces transmitted from the girder through position dowels cast inside the

abutment wall.

1.6 Research Contributions

The most important contribution of this research is the innovative application of an
ensemble of neural networks to overcome inherent difﬁculties of an SISD in developing a
prediction model for structural damage. Such a contribution advanced the state-of-the-art
of knowledge in diagnosing structural damage using artiﬁcial intelligence in the
interdisciplinary ﬁeld between civil engineering and computer science. Details of the
innovation and contribution in this research are listed below:

0 A comprehensive procedure to develop prediction models for damage in civil

infrastructures through the integration of a series of tools.

21

0 New data organizing and voting schemes in an ensemble of neural networks to
identify the damage of structures.

. Concept and methodology for the combination of evidential and virtual databases
in an ensemble of neural networks to solve a complex inverse problem.

. Identiﬁcation of potential causes for the distress through the interaction of ﬁeld

inspections, analyses and simulations.

The procedure designed in this research can predict damage in structures and evaluate
the potential causes of damage. Use of this procedure and tools for the prediction of the
structural condition and the identiﬁcation of potential causes of damage can allow for

more efﬁcient maintenance and repair of civil infrastructure.

1.7 Dissertation Overview

This dissertation includes eight chapters. The ﬁrst chapter is an introduction,
including the motivation, challenge, and objective of the research and introduction of a
speciﬁc research problem: distress in abutment walls of highway bridges. The state-of-
the-art research in related ﬁelds and the application and innovations of similar research
methods are reviewed in Chapter 2. Chapter 3 presents the processing of a structural
inventory system database, the creation of evidential database for the research, and a
series of statistical analyses: frequency analysis, correlation analysis, analysis of factorial
effects, and regression analysis. Chapter 4 illustrates the ﬁeld monitoring plan executed
for this speciﬁc research problem. The ﬁeld monitoring work consisted of bridge
selection, ﬁeld inspection of typical bridges, ﬁeld instrumentation, data collection, and
data interpretation. Chapter 5 introduces the ﬁnite element analyses in this research.

Seven hundred and eighty three (783) highway bridges were simulated, and the results

22

were used in two ways: parametric studies to identify the inﬂuence of design parameters
on the behavior of bridges and the creation of a virtual database to be used in an
ensemble of neural networks.

Chapter 6 documents the development of soft computing models to predict structural
damage in abutment walls of highway bridges. Five models were applied: MLP, RBF,
SVM, SSOM and FNN. Chapter 7 presents the development of an ensemble of neural
networks in predicting structural damage. A novel data organizing scheme for ensemble
of neural networks enabled it to overcome the unbalance present in the evidential
database and reach good accuracy in identifying damage in civil infrastructures. The
combination of an evidential and a virtual database in the context of an ensemble of
neural networks could improve the performance of the prediction model; it is a bright
direction for future research. Chapter 8 looks forward to future research needs on this

topic and presents conclusions from this research.

23

2 STATE-OF—THE-ART RESEARCH

2.1 Introduction

In order to identify effective strategies to solve the problem introduced in Chapter 1, a
thorough review of the state-of-the—art research is presented in this chapter. In predicting
structural damage most neural network applications used simulated or tested structural
dynamic characteristics to decide the location and magnitude of damage in the structure
[Chen 2005, Fang 2005, Huang et a1. 2003, Park et a1. 2006, Song et a1. 2005, Taha and
Lucero 2005, Zhao et a1. 1998]. The features of these problems are very different from
the inverse problem in this research. Thus instead of focusing on research in structural
engineering, the literature review emphasizes the similarity in the nature of the problems
no matter to which ﬁelds the problems belonged. The nature of the problems is that even
though the symptoms in individuals are known, the causes of those symptoms are not
clear. Symptoms and parameters of individuals are recorded historically and compose an
evidential database. An inverse problem thus needs to be solved in order to identify the

causes of the problem and develop effective prediction models.

The relevant research on the example problem, damage in bridge abutment walls, is
investigated at the beginning. Then, a literature review summarizes the application and
innovation of artiﬁcial neural networks and fuzzy logic in solving inverse problems and
developing prediction models based on evidential databases. Since one of the difﬁculties
in the NBI manual inspection database is the issue of missing values, methodologies and

techniques in handling missing values in the database are discussed. The state-of-the-art

24

research on neural networks ensembles and the organization of training data sets for

ENNs are reviewed in the later part of this chapter.

2.2 Structural Damage in the Abutment Wall of Highway Bridges

Uncertainties on the causes behind the observed abutment damage motivated the need
for a more extensive literature review with the attempt to learn more about this type of
distress. Continuous literature review throughout the length of this research failed to
identify any published document that described a problem similar to the one being
addressed by this study. Attention then focused on trying to identify literature related to
the causes hypothesized as the sources of damage. Yet, while some information was
found on the suspected sources of damage, these did not contain information or direct

correlation to the distress in abutment walls. A brief overview follows.

Several research projects focused on evaluating the negative effects of rusted or
“locked” pin-hanger assemblies on steel girder bridges. Yet, little documentation exists
on the distress induced by this effect on other elements of the bridge system and most of
the work focuses on the potential danger of hanger fracture or pin slip (due to pushing
forces ﬁ'om the rust buildup). Nonetheless, some analytical work has provided evidence
that the reaction forces due to locked pin-hangers can be signiﬁcant at the abutments.
Analyses suggest values as high as 2.5 times the stress level to initiate yield when full

ﬁxity is assumed [Elewa 2004].

Recent publications [Burke 1998, 2004] indicate that pavement growth is one of the
possible causes of abutment damage, which is consistent with the expectations of MDOT

bridge engineers. The phenomenon consists of the gradual movement of pavement slabs

25

as joint gaps between them are reduced due to debris. This generates substantial pressures
and, consequently, movement, upon thermal expansion of the slabs. From the information
provided by Burke [1998, 2004], Richards [1979] and Shober [1997], the magnitude of
the induced compressive stress on bridge deck slabs by the movement of pavement slabs

towards bridge abutments is estimated to be approximately 7 MPa (1 ksi.)

While the literature review process failed to identify any published work directly
addressing abutment distress, the related information on the possible sources of damage
provided ideas for the systematic organization of database used in this research. It also
helped to clarify the mechanisms that could lead to abutment distress. The identiﬁcation
of important parameters in the damage of bridge abutments was necessary in order to
extract relevant data and predictive parameters from the National Bridge Inventory (N BI)
database, which was to be used as an evidential database of damage for statistical
analyses and diagnosis model development. While the NBI rating has provided a good
mechanism to constantly evaluate the state of highway infrastructure, its use for statistical
and predictive model development posed considerable problems because the data are
highly scattered and clear patterns were not easily identiﬁable. The subjectivity and large
deviation of the visual inspection for highway bridges used in the NBI database are
discussed in a research report by the Federal Highway Administration [FHWA 2001] and
a paper by Phares et a1. [2001]. The inspection process was found to be subjective and
with large deviation, which supported initial struggles in this research in interpreting the

data and later provided justiﬁcation to assess its variability.

26

2.3 Artiﬁcial Neural Networks and Fuzzy Logic

Cattan and Mohamrnadi [1997] applied a multilayer perceptron network to predict
subjective condition ratings for railroad bridges using bridge design parameters. The
subjective bridge condition rating used numerical values between 1 and 5. When applied
to an MLP, the subjective bridge condition rating was transformed to four binary
variables, and twelve input design parameters were transformed to 45 binary variables.
An MLP network model was developed using a database containing 405 railway bridges
in the Chicago metropolitan area. The input layer and output layer of the MLP included
45 and 4 neurons, respectively. Two hidden layers were deployed in the MLP with 45
hidden neurons in each layer. In the testing phase, the MLP network obtained a correct
ratio of 73%. Since no operation or environmental information was incorporated in the
training of the MLP, the network can not retrieve the degradation history or predict the
future degradation trend of a railway bridge. An attempt was made in using analytical
data as one of the input parameters to improve the performance of the MLP. However,

the trial failed because the analytical data only used a few design parameters.

Shyur et a1. [1996] and Luxhoj et al. [1997] applied MLP networks in predicting
safety performance indicators of aircraft using operation parameters. The database used
in developing prediction models is the combination of part of the service difﬁculty
reporting database and the aircraft utilization database. The database is only for one type
of aircraft monitored over a l6-year period; and thus the data is less unbalanced, less
noisy, and less complicated compared to the database used in this research. Performance

of the MLP networks was good in predicting safety performance indicators of aircraft.

27

In order to improve the performance of an MLP, Roberts and Attoh-Okine [1998]
applied a quadratic function ANN model to predict the international roughness index of
pavements. A quadratic function ANN uses an evolutionary mechanism to develop a
near-optimal structure. The database included 105 records documented by the Kansas
Department of Transportation. The output variable of the network was the international
roughness index for the pavement, which uses three integer numbers for severity. The
input variables were severity values for different distresses and values for loading. The

quadratic function ANN model showed a better performance than a conventional MLP.

Pleune et al. [2000] predicted the fatigue life of carbon and low-alloy steels
successfully using an MLP trained with test data. Researchers had more control on test
data than ﬁeld data and thus the test data had less noise and were easily learned by the
MLP network. The fatigue life of smooth cylindrical specimens was determined through
tests under fully reserved axial strain control loading. The records of 1036 fatigue tests
were used as training data. The input variables of the MLP were a series of environmental,
compositional, and structural parameters. The output variable of the MLP network was
the fatigue life of steel component. The MLP network provided insights into the fatigue

trends of steel.

Pande and Abdel-Aty [2005] applied MLP and RBF networks to classify the types of
accidents on highways. The database used for developing the prediction model was
collected ﬁ'om highway loop detectors. Four thousand crashes were included in the
database; 52% of them were rear—end crashes. The response variable was binary: the

crash is a rear-end collision or not. The MLP in the research had one hidden layer with 12

28

hidden neurons. The RBF in the research used unequal width. The performance of the

MLP and RBF was reported to be worse than a decision tree.

In the paragraphs above, the applications of MLP and RBF networks are discussed.
With regard to SVM networks, they have been used in the diagnosis of breast cancer
based on historical clinical data with reasonable performance [Land, et a1. 2003]. The
database included about 2,500 samples. There are enough cases of breast cancer in the
training database. Evolutionary programming was used to ﬁnd the optimal structure of
the SVM. It was proved that SVM could be used to develop software to assist in breast

cancer detection.

In addition to MLP, RBF, and SVM, SSOM is also a promising tool in developing
prediction models. Xiao et a1. [2005] applied an SSOM network to classify compounds
using a dihydrofolate reductase inhibition data set. The data set included 135 compounds:
80% of them were used as training data and the remaining 20% were used for testing.
SSOM models were trained through two approaches: training with a k-means clustering
limit with a zero neighborhood radius and training until the neighborhood radius
decreased to zero. The SSOM model outperformed models using multiple linear

regression, partial least squares, genetic functional algorithm, and the k-NN algorithm.

By combining a fuzzy set with one or several MLPs, an FNN is expected to have a
better tolerance of imprecise and subjective data in building prediction models. Pal and
Mitra [1992] applied an FNN in speech recognition. They applied the FNN to a database
consisting of 871 Indian Telugu vowel sounds. Input vectors with a dimension of nine

were obtained from a spectrum analysis on the speech data. The resultant variable was

29

the classiﬁcation of vowels. The fuzzy-neural network model achieved a better result

than conventional neural networks and a Bayes classiﬁer.

Juang et al. [1999] applied an FNN to solve uncertainty in the input and output
parameters in a geotechnical engineering problem and showed that the performance of
the FNN was superior to that of conventional neural networks. Quantitative variable
collapse potential was the target variable of the FNN. The input variables for the FNN
were seven soil parameters. The database used in training the network was ﬁeld recorded

data.

Mitra and Hayashi [2000] conducted a survey on neuro-fuzzy algorithms and
categorized various neuro-fuzzy models used for rule generation. The fuzzy neural
network model was applied to diagnose hepatobiliary disorders. The database consisted
536 patient cases of various hepatobiliary disorders. Nine of the input parameters were
biochemical test results and one parameter was the gender of the patients. The neuro-

fuzzy model achieved more reﬁned results.

An MLP with back propagation algorithm and an FNN were used to predict the root-
mean-square pressure coefﬁcients and the time series of wind-induced pressures on a
large gymnasium roof [Fu et a1. 2007]. Data from a wind ttmnel test were used as training
sets. Performance of both the MLP and FNN models was satisfactory for engineering

applications. Nonetheless, the FNN was found to have better accuracy than the MLP.

30

2.4 Handling Missing Values in Data Analysis and Neural Network

Application

As mentioned in section 1.3, one of the difﬁculties in using a structural manual
inspection database is that there are missing values for some variables in some records.
Two approaches are commonly used to handle missing values in a database. One
approach is to delete the missing values [Little and Rubin 2002], either by deleting the
records that include variables with missing values or by deleting the variables with
missing values ﬁom all records. The other one is to utilize records with missing values
after estimating those missing values [Chan et a1. 1976, Dixon 1979, Wagstaff and

Laidler 2005].

Granger et al. [2000] applied fuzzy ARTMAP [Carpenter et a1. 1992], which is a
neural network architecture based on Adaptive Resonance Theory, in the classiﬁcation of
radar pulse data. Incomplete data included a limited number of training cases, missing
components, missing class labels, and missing classes. Fuzzy ARTMAP obtained a high

accuracy in the classiﬁcation.

Juszczak and Duin [2004] proposed an ensemble of one-class classiﬁers trained on
each individual explanatory variable to handle missing values in the database. The
ensemble could still make a prediction with the rest of classiﬁers when the value for a
variable, by which one classiﬁer was trained, was missing. This approach was used
together with two commonly used methods to solve a missing value problem on several
of UCI data sets. UCI database is a series of data sets maintained by University of

California—Irvine to serve the machine learning community [Blake and Merz 1998]. At

31

present, UCI database is consists of 171 data sets. It was shown that an ensemble of one-
class classiﬁers had a better performance than a classiﬁer trained by either deleting

records with missing values or estimating missing values.

Wagstaff and Laidler [2005] applied a clustering analysis algorithm, “K-means with
Soft Constraints” (KSC) to handle missing data in astronomy to separate stars from
galaxies based on the Sloan Digital Sky Survey database. In the KSC algorithm, fully
observed features were used for clustering, and records with missing values were used to
create soft constrains on the clustering algorithm. The KSC algorithm achieved up to

90% improvement in the correct separation of stars and galaxies.

Lim et al. [2005] presented a hybrid neural network to handle missing features in
training data for pattern classiﬁcation. The hybrid network was FAM-FCM. FAM is an
acronym for fuzzy ARTMAP [Carpenter et al. 1992], which is a neural network
architecture based on Adaptive Resonance Theory. FCM is an acronym for Fuzzy C-
Means Clustering. Two stages were included in the training of the hybrid neural network.
In the ﬁrst stage, FAM was trained using data with complete features. In the second stage,
a number of FCM-based strategies were applied to estimate and replace missing features.
Then, data with estimated features were combined with data with complete features to
retrain the FAM. The hybrid network was applied to two benchmark problems (the Iris
problem and the Pima Indian Diabetes problem in the UCI database) and an acute
coronary syndrome problem. In the acute coronary syndrome problem the database
included 118 records of suspect heart attack patients. The performance of the hybrid

neural network was found to be promising.

32

In this research, the features of the NBI manual inspection database were different
from those used in research methods mentioned above. The NBI manual inspection
database includes a large number of inspection records. About one third of the records
had missing values for the qualitative variable “approach pavement type”. The number of
records with missing or erroneous values for other variables was relatively small. The
loss would be too large if all the records with missing values for “approach pavement
type” were discarded. Furthermore, estimating that large portion of missing values could
hardly be reasonable and would harm the prediction model rather than improve it. Thus,
the qualitative variable “approach pavement type” was transformed to three dummy
variables: one code sequence of dummy variables represented those cases with missing
values. Records with missing or erroneous values for the other variables were deleted

from the database.

2.5 Ensemble of Neural Networks

An ensemble of neural networks can be trained separately for a problem and their
predictions can be combined through a certain voting scheme. Such an ensemble of
neural networks can overcome the local minima and explore the database from multiple
perspectives. The concept of combining estimators to achieve better performance has
been applied in a variety of ﬁelds for some time [Sharkey 1999]. Hansen and Salamon
[1990] proved theoretically that an ensemble of neural networks could improve
prediction accuracy. They applied an ensemble of neural networks to classify a number of
regions in a 20-dimensiona1 hypercube. The regions were deﬁned by 10 “pure” patterns

chosen randomly. Both plurality and majority voting rules were evaluated. It was proved

33

that an ensemble of neural networks could outperform a single neural network even
though each individual neural network in the ensemble was less accurate than that single

network.

Hansen et a1. [1992] applied neural network ensembles in the recognition of
handwritten digits. The database included 6973 handwritten digits written by 280 people.
An ensemble of neural networks outperformed the best individual neural network in the
ensemble by 20-25%. The authors also observed that the improvement of performance of
an ensemble by adding more neural networks was not signiﬁcant after more than 15

neural networks were included in the ensemble.

Zhou et al. [2002] applied neural network ensembles in lung cancer cell identiﬁcation.
Images of specimens were used as input, and cancer diagnoses were used as output. By
using the ‘bagging’ approach in data organization and two stages with full voting in the
ﬁrst stage, the network ensembles were shown to have better performance than individual

networks.

Based on trafﬁc accident records, Sohn and Lee [2003] predicted the severity of road
trafﬁc accident using driving environmental factors as predictors. The database was
composed of accident records and thus no unbalance problem existed. The accuracy of
prediction was improved with the application of an ensemble of networks with a normal

bagging algorithm.

Yun et al. [2003] and Lee et al. [2004] applied an ensemble of neural networks for

structural health monitoring. Modal parameters were used as input for the network and

34

element level damage indices were used as output. The ensemble of networks was found

to signiﬁcantly improve the identiﬁcation of damage.

In predicting market clearing prices, Guo and Luh [2004] proposed an ensemble of
networks using a weighted voting scheme. The weighting coefﬁcients of individual
neural networks were decided based on their possibility to map an input-output
relationship correctly. The method was applied in predicting the market clearing prices in
New England power markets and was proved to outperform both individual neural

network and an ensemble of networks using ensemble-averaging voting.

Yang and Browne [2004] proposed a multistage ensemble of neural networks in
which another neural network was applied to collect voting and produce ﬁnal results.
Data sets used for developing prediction models included “breast cancer,” “iris,” “Pima-
diabetes,” etc. The training data sets were organized through distributing sample
presentation sequences randomly, noise injection, bagging, boosting, etc. After the
training of individual neural networks, the whole training data was applied to individual
neural networks and their outputs were used as inputs to the voting neural network.
Compared with majority voting, voting through another neural network improved the

performance of the ensemble of neural networks.

Yu et al. [2008] applied an ensemble of neural networks with a reliability-based
voting scheme in credit risk assessment. Prediction models were developed based on two
databases. One involved with Japanese consumer credit card application approval, which
included 653 records with 357 granted cases and 296 refused cases. The other database

concerned a UK corporation credit that included 60 records: 30 of them were failed ﬁrms

35

while the other 30 were non-failed ﬁrms. The records in the database were balanced.
However, the databases suffered from insufﬁcient records. The bagging algorithm was
applied to make full use of insufﬁcient data. The ensemble of neural networks

outperformed fuzzy-SVM, SVM, MLP, and logit regression models.

2.6 Data Organization for an Ensemble of Neural Networks

Two major approaches in organizing data sets are bagging [Breiman 1996; Duda et al.
2001; Sharkey 1999] and boosting [Duda et a1. 2001; Schapire 1990]. Bagging is a
procedure to produce multiple training sub-sets by drawing samples randomly from the
original training set with replacement. Boosting is a procedure to produce multiple
training sub-sets in a manner that the subsequent selection is focused on the samples that

are not recognized well by the classiﬁers training on the previous training sub-sets.

Breiman [1996b] introduced bagging theory and its application in the real-world and
simulated data sets. The real-world data sets included breast cancer, waveforms, letters,
etc. It was shown that the bagging algorithm can signiﬁcantly improve the accuracy of
predictions. Bagging is effective in making full use of small data sets; and Breiman
[1996a, 1996b] also proved that bagging can improve the accuracy of unstable prediction

models, such as neural networks.

Opitz and Maclin [1999] evaluated these two methods using a series of data sets,
which included breast cancer, credit, diabetes, iris, letters, vehicles, etc. Explanatory
variables, target variables, and the number of records in each data set were all varied
from one set to another. Bagging proved to be more stable than boosting even though

boosting was sometimes more accurate than bagging. It was also concluded that most of

36

the improvements in performance was achieved when the ﬁrst few classiﬁers were added

to the ensemble.

Quinlan [1996] compared bagging with boosting by testing both techniques on a
collection of representative data sets, which included letters, vote, waveforms, etc. Both
algorithms improved the performance of the prediction model. Bagging proved to be
more resilient to noise and more stable, which was also a major difﬁculty in using a
structural inventory system database. Boosting had a better accuracy for some data sets,
while it suffered from severe degradation on others. Boosting was modiﬁed slightly to

alleviate the setbacks and a better performance was achieved.

Parasurarnan et al. [2006] applied two ensembles of neural networks in predicting the
saturated hydraulic conductivity of soils. Data sets from two ﬁeld tests were used to build
prediction models respectively. One data set included 126 records; the other data set had
78 records. The input parameters were sand content, silt content, clay content, and bulk
density. The training data for neural networks in two ensembles were organized using a
bagging algorithm and a boosting algorithm, respectively. It was shown that the
ensembles of neural networks trained on ﬁeld-scale data outperformed the general
purpose neural network, which was trained on a larger-scale database. The ensemble of
neural networks using training data organized through the boosting algorithm performed

better than its counterpart using training data organized through the bagging algorithm.

Chen and Yu [2007] proposed a new bagging algorithm for an ensemble of neural
networks. The training subsets of individual networks were distilled based on Euclidean

distances between two arbitrary samples. Weighted averaging was used as the voting

37

scheme for the ensemble. The algorithm was applied to regression data sets and a real-

world problem of measuring ethylene yield with good performance.

2.7 Discussion

No information was found on research that directly analyzed the problem of structural
damage in the abutment walls of highway bridges. Literatures that discussed issues
related to the damage in bridge abutment wall were reviewed. That related research
provided implications in evaluating the causes of damage in bridge abutment wall even

though none of them presented a direct analysis of the problem.

Only a few works were found on the use of ANNs to develop prediction models for
structural damage based on a historical inspection database. In other areas, several types
of ANN models were applied to solve inverse problems with good performance. The
applied ANN models included MLP, RBF, SVM, SSOM, and FNN. None of that
research encountered an evidential database with a highly unbalanced distribution of
records. Methods used to handle missing values in data analysis and artiﬁcial neural
network were evaluated. The Fuzzy ARTMAP and an ensemble of one-class classiﬁers
showed good performance. Since the characteristics of the NBI database in this research
were different from the research found in that literature, a different strategy was applied

to handle missing values in this research.

An ensemble of neural networks was applied successfully in different areas to
develop prediction models and solve inverse problems. However, none of them was
developed based on a highly unbalanced database. Bagging and boosting are two widely

used methods in organizing training data sets for an ensemble of neural networks. Both of

38

them have been successfully used. In this research, a novel training data organization
strategy was devised through bagging within categories to overcome the unbalance in the
training data. Modiﬁed majority voting, subjectivity voting, and evaluation voting
schemes were applied to overcome subjectivity in the training data. An ensemble of
networks was then developed using the novel data organization strategy and voting

schemes.

39

3 DATABASE CREATION AND STATISTICAL ANALYSES

3.1 Introduction

As mentioned in Section 1.1, the design parameters and manual inspections of
infrastructure are documented in Structural Inventory System Databases (SISD). SISDs
should be exploited and used at an advanced level to identify the causes and develop
prediction models for structural damage. By extracting raw data from an SISD, screening,
preprocessing, and organizing the raw data; an evidential database can be subsequently
created. This chapter shows the statistical analyses’on an evidential database consisting of
frequency analyses, correlation analyses, analysis of factorial effects, hypothesis tests,
and regression analyses. They serve three major functions:

. Identify cause-effect associations between structural damage in bridge abutment
walls and bridge design and operation parameters.

. Develop regression models to predict structural condition given design and
operation parameters.

0 Provide information and guidance for other analyses, simulations, and ﬁeld

instrumentation.

Details on each type of the statistical analyses are only partially shown in this chapter
due to space considerations. A complete review of all the statistical analyses made on this
example problem can be found in the ﬁnal research report on this project for MDOT
[Burgueﬁo and Li 2008]. The commercial statistical software SPSS 13.0 [SPSS 2004] and

SAS 9.1 [SAS 2004] were used in the analyses.

40

3.2 Evidential Database

An example of an SISD is the National Bridge Inventory (NBI) system database
[Hartle et al. 1991], which is based on manual inspections of bridge structural members at
an interval of no more than two years. For the sample bridge abutment problem, an
evidential database was created to directly identify the potential causes of damage in
bridge abutment walls and provide an information data bank for the other analyses and
simulations. The evidential database consisted of data ﬁ'om the NBI bridge inspection
records, which document design and operation parameters as well as abutment inspection
ratings for highway bridges. The information database provided important information
for the subsequent simulations and analyses, as well as for the ﬁeld inspections and
instrumentations in this research. The commercial software Infomaker 10.0 [Sybase Inc.

2004] was used to retrieve data from the raw bridge inventory database.

3.2.1 Deﬁnition of parameters

The deﬁnition of structural design and operation parameters in the bridge abutment
problem is listed in Table 3-1. The average daily truck trafﬁc (ADTT) is the product of
the average daily trafﬁc and the corresponding truck percentage for each bridge. The
average daily trafﬁc data was not always measured in the same year for all bridges, and
direct application of average daily trafﬁc data without accounting for the year in which it
was measured would introduce additional errors. Thus, all of the ADTI‘ retrieved for
individual bridges were converted to the ADTT measured at the time of inspection by the

following procedure.

41

Table 3-1 Deﬁnition of parameters

 

Parameter Deﬁnition

 

Annual temperature difference at the location

Matdiﬂ‘f] of a bridge
A geinsp *2 Age of a bridge at the time of inspection
Apprsurstif*3 Approach surface type
Average daily truck trafﬁc at the time of
ADTT inspection
Maxspan Maximum span (m)
Length: Total length (m)
Deck width Total deck width(m)
Pin type Whether has pin-and-hanger assembly
Skew Skew angle (°)
Materialmain *4 Main structure type

 

*l: The difference between mean annual maximum temperature and mean annual minimum

temperature for each county in Michigan, which were estimated from corresponding graphs.

*2: Obtained by subtracting built year from inspection date (months and days are converted to

years after dividing by 12 and 365 respectively.)
*3: It was converted to three indicator variables in the statistical analyses and ANN models.

*4: It was transformed to four indicator variables in the artiﬁcial neural network application.

First, the ADT'T increasing rate (ADTTinc) was estimated with equation (3-1) for

each bridge:

ADTT .
ADTTinc = ”Wed —1 <3-1>
ADTT

measured

 

42

where ADTTmmsmd is the ADTT in the year in which it was measured; ADTTpmdicted is

the predicted ADTT in the future; 7. is calculated using equation (3-2).

1
— Yearm

 

— (Yearp (3-2)

redicted easured )

Where Yearmeasmd is the measured year for ADTTmmsmd (months and days were
converted to years by dividing by 12 and 365, respectively); Yearpredicwd is the year in

which the ADTT is predicted. The ADTT at the time of inspection (ADTTinsp) is then

calculated as:

ADTT

i nsp

=ADTT

measured

~(ADTTinc +1)“ (3-3)

K‘ = (Yea — Yearm (3-4)

rinsp easured )

3.2.2 Initial data screening

Raw inventory data retrieved from the MDOT NBI database was initially screened to
exclude outliers and erroneous observations. The criteria for this initial screening are
shown in Table 3-2. Most of the MDOT highway bridges are of one of three
structural/material types: simple/cantilevered steel, continuous steel, and prestressed
concrete. A scatter plot matrix of abutment rating for simple/cantilevered steel bridges
and ﬁve design and operation parameters is shown in Figure 3-1. Each cell in the matrix
is a scatter plot and describes the distribution of observations concerning two parameters
on the abscissa and ordinate. It can be seen from Figure 3-1 that the database is highly

complicated and that no clear trend can be observed. Some observations had almost

43

identical predictor values but with abutment rating differing each by more than 1. Those
confusing observations could cause a problem of node proliferation, which was highly
detrimental to the development of prediction models as well as the identiﬁcation of
causes for abutment damage. Thus, they were deleted from the database. The deleted

observations accounted for less than 3% of all the observations.

Table 3-2 Criteria for data extraction

 

 

# Parameters 2 Criteria

1 userbrdg_legal_cd * l

2 abutment rating 0~9

3 built year >0

4 maximum span >0

5 deck area >0

6 deck width >0

7 skew angle >=

8 average daily total traﬂ‘ic >0

9 truck percentage not equal -1

10 type of design/construction >=0 & not equal 18 & not equal 19
11 inspection year no earlier than built year
12 year at which daily traﬁfc was measured >=0

 

* userbrdg_legal_cd is MDOT Legal system, 1=MDOT, 2=County Primary, 3=County Local,
4=City Major, 5=City Minor, 6=Other. Userinsp_abut_rtg_cd is abutment rating.

 

 

Abut_Rating

Length_m

Width_m

Skew_degree

AgeInsp_y

ADTTInsp_ln

 

 

 

0.86

Figure 3-1 Scatter plot matrix of simple/cantilevered steel bridges

3.2.3 Database creation

Raw data extracted from MDOT’s NBI database were organized into a consistent
evidential database to be used in statistical analyses, ﬁeld inspection and instrumentation,
numerical simulation, soft computing, and an ensemble of neural networks. After

examining the NB] database, it was found that the longest bridge is up to 5,866.7 m:

45

however, more than 99.8 % of them have their lengths less than 1,000 m. Thus, in this
research bridges with lengths of more than 1,000 m have been removed as outliers from
the evidential database. A skew angle of a bridge should be a value between 0 and 90
degrees. Since “99 degrees” in the record indicates a major variation in the skew of the
substructure units and “90 degrees” doesn’t make sense in reality, inspection records of
bridges with a skew angle equal 90 or 99 were removed from the database. Since more
than 99.8 % of the bridges have average daily truck trafﬁc less than 30,000, the
inspection records for the bridges with average daily truck trafﬁc greater than 30,000
were removed from the database. The criteria for creating the evidential database are
shown in Table 3-3. After ﬁltering by the mentioned criteria, 905 inspection records were

deleted and the evidential database was composed of 19,615 inspection records.

Table 3-3 Criteria to reﬁne the data set

 

 

# Parameters Criteria

1 Length > 0 ft and < = 1000 m
2 Deckwidth > 0 ft

3 skew angle >= 0° and < 900

4 Age at inspection >= 0

5 Approachtype >= 0

6 Average daily truck traﬁ‘ic at inspection > 0 and <= 30, 000

 

46

3.2.4 Deﬁciencies of MDOT NBI database

Further exploration and advanced use of the MDOT NBI database is constrained by
these inherent difﬁculties:

. The database is highly complicated and no conspicuous trend or correlation can
be extracted. There is no one-to-one relationship between the cause and effect of
structural damage, which means many causes can lead to the damage of the
abutment wall. Moreover, the relationship can be highly nonlinear and thus very
difficult to be extracted if not impossible, by current means.

0 Subjectivity exists in the manual inspection methods and a large variance results
in the adopted structural evaluation ratings. For the NBI system, it has been
found that for the same structure its ratings assigned by 49 bridge inspectors from
25 state departments were dispersed, with only 68 percent of them within il (in a
scale of 0 to 9) around the mean, 95 percent of them fall in i2 around the mean
[Phares et al. 2001]. Even if all the bridges with the same design parameters were
inspected by the same engineer the ratings might still be different because
construction quality can not be identical.

. The values of some variables in some observations are missing or subjected to
error. For instance, the approach pavement type (a parameter of importance to
the damage of bridge abutments) for some bridges in the database is missing.

. The distribution of inspection records is unbalanced. Cases of severe damage are
relatively rare in comparison with the large number of bridge abutments in

relatively good condition.

47

. The abutment rating is a general condition rating but the details of the damage
are unknown.

0 Some important factors are not available, such as soil type and pavement type.

3.3 Signiﬁcance of Design and Operation Parameters

3.3.1 Frequency Analyses

Frequency analyses in this research aimed at ﬁnding out the distribution of highway
bridge populations to reveal common features of highway bridges that were susceptible to
damage in abutment walls. The analyses concerning approach pavement surface type is

presented here as an example.

Pavement pressure was one of the susceptible causes of damage in bridge abutment
walls. Its frequency analyses are shown in Figure 3-2. In Figure 3-2, each column
represents one structural type, where “simstl” means inspections of simple/cantilevered
steel bridges, “constl” denotes inspections of continuous steel bridges, and “prscrt”
represents inspections of prestressed concrete bridges. Each row represents one type of
approach surface type, where “Bimcon” means ﬁeeway designed bituminous concrete on
aggregate base, and “Concret” denotes concrete pavement. The label “unknown” means
that the corresponding value in the database is missing. The ratios of poor abutment for

each category in Figure 3-2 are shown in Figure 3-3.

48

 

 

H

Unknown q/QV g
7273 ‘ 1570

0mm“ '/ LJ HQ

7399 2811

Bitumen E
6089 2911

 

 

 

 

 

 

 

 

 

 

Abutment Condtion CZ] Good
— Poor

3mm" H C/ Q
776 / 10 281
simstt oonsti prscrt

 

 

Figure 3-2 Frequency analysis of highway bridge inspections

 

 

 

 

 

 

 

 

)
U k
n nown . ..
I'm; - ~17
)I'r '- bit
‘ ll. I-n"
. p .. )1
:‘ '.j :,:&
. . . I Y
1.»? 10 '16 .-,
Viv: .‘H
751‘, J."
{kl-)- ‘1'};
n2; :._.
)‘y‘: til-r
"/.‘ _i_,
Cm UEt - .r.’
wre- .b 7
’92-. r.

 

Bitumen

Brncon .2049
.0000 .0214
Mars

Figure 3-3 Ratio of poor abutment rating

 

 

 

 

49

 

After a detailed evaluation of Figure 3-2 and Figure 3-3 it can be concluded that steel
bridges with concrete approach pavement and “unknown” approach pavement have a
high percentage of poor abutment rating. For prestressed concrete bridges the ratio of
poor abutment rating does not seem different for any of the approach pavement types.
Frequency analyses revealed common characteristics of bridges that were susceptible to

abutment damage. These common features are summarized in Table 3-4.

Table 3-4 Common characteristics of bridges with poor abutments

Structural type Simple or Continuous Prestressed
Design parameters cantilevered steel steel concrete

 

Length (m) [76.2, 1000] [121.9, 1000] [45.7, 91.4]
Maximum span (m) [24.4, 46.7] [30.5, 54.9] [18.3, 30.5]
Deck width (m) [18.3, 24.4] [9.1, 18.3] [18.3, 21.3]
Skew angle (degree) [0, 60] 0 [0, 45]
Approach pavement type concrete concrete bitumen, concrete
ADTT [5000, 30000] [5000, 30000] [5000, 30000]
Year built before 1980 before 1980 before 1980
Age at inspection (year) 30 30 30

 

3 .3 .2 Correlation Analysis

Correlation analysis is an important statistical tool to draw inferences about the
strength of the relationship between two or more variables. That is, it is a measure of the
degree to which the values of these variables vary in a systematic manner. In this manner,
it provides a quantitative index of the degree to which one or more variables can be used

to predict the values of another variable. Correlation analyses were used for bridge

50

abutment problem in an attempt to reveal the association between bridge abutment rating

and explanatory parameters, such as design and operation variables.

3.3.2.1 Statistical theorem about covariance and correlation

The degree of linear association between two variables X and Y was reﬂected by
value of Pearson product-moment correlation coefﬁcient R [Snedecor and Cochran 1989].
The conception of the Pearson correlation coefﬁcient is to separate the variation of values
of random variable Y into two parts: linear variation with random variable X and
nonlinear variation. The correlation coefﬁcient is deﬁned as the ratio of linear variation to
the total variation. That is, the fraction of the total variation that is explained by the linear
relationship between Y and X. Based on the concept mentioned above, Equation (3-5) was

used to calculate the correlation coefﬁcient R.

 

R—

n 2 1 n 2 n 2 1 n 2 (3-5)
Ext __ in Zyi __ Zyi
i=1 n i=1 i=1 n i=1
where x,- is the ith value of random variable X, i=1, 2, , n; and yi is the ith value of
random variable Y, i=1, 2, , 11. If the linear variation of values equals the total variation,

the correlation coefﬁcient will equal 1. If the relationship between X and Y is inverse and
the linear variation equals the total variation in magnitude, R will equal -1. These
conditions represent the extremes, but both values indicate a perfect association, with the

sign only indicating the relationship. A correlation coefﬁcient of zero, which is

.51

sometimes called the null correlation, indicates no linear association between the two

variables X and Y [Ayyub and McCuen 1997].

The physical characteristics of the correlation coefﬁcient are elaborated in Figure 3-4.
The schematic in Figure 3-4a indicates that there is no linear relationship between the two
random variables; as the value of X increases it is not certain whether Y will increase or
decrease. The correlation coefﬁcient is expected to be close to zero; and the two random
variables can be considered to be uncorrelated. Figure 3-4b indicates a positive
correlation between X and Y, that is, Y increases as X increases. However, the
relationship is not perfectly linear, indicating that R is expected to be between 0 and 1.0.
Figure 3-4c shows an example of perfectly positive correlation between the two random
variables X and Y; Y increases linearly as X increases. Data points (X, Y) form a straight
line with a positive slope rate in the X, Y plane; the correlation coefﬁcient is expected to
be close to one. Figure 3-4d illustrates a case of perfectly negative correlation between
the two random variables; that is, Y decreases linearly as X increases. Data points (X, Y)
form a straight line with a negative slope rate, indicating that R is negative one. Figure
3-4e and f indicate that there could be some nonlinear relationship between the two

random variables; however, since the relationship is not linear, R is expected to be zero.

If the correlation coefﬁcient needs to be calculated from observed sample values, it is
rare to obtain values of precisely zero, +1 or -1. Two random variables can be considered
to be statistically independent if the absolute value of correlation coefﬁcient is less than
0.3; and they can be considered to be perfectly correlated if the absolute value of

correlation coefﬁcient is greater than 0.9 [Haldar and Mahadevan 2000].

52

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20-

 

150'

100'

 

 

 

mo 0 so
X
(b)O<R<1

100
80 ~
60 .
40

20

 

 

 

100~

50~

Figure 3-4 Schematic representations of the correlation of two random variables

 

5o

(c)R=1

 

‘mo 0

 

160-
140»
120»
>
/ 100]

801

 

60

 

 

so
X
(e)R=0

Mo 0 5o
X
(0R=O

53

3.3.2.2 Analysis on entire database

Efforts were made to discover a correlation between bridge abutment rating and
explanatory variables by analyzing the whole database. However, the correlation
coefﬁcients were less than 0.3. Figure 3-5 is one of the scatter plots generated in these
analyses. It can be seen that the data are highly scattered in the graph, which means the
two random variables can be considered to be uncorrelated. A series of similar analyses
showed that this kind of calculation throughout the whole database would provide very

limited information about which parameters correlated with abutment rating.

 

 

 

 

 

 

 

 

10—
mmoo (no 0
8— _CD on) o O 0
20000000 000 o o o o
co
g 6~ ZEGDCDCI) (DCOO o oo o
E ”000 on o
a
34-— nmoooooo oo o o 0
<1
mom 0 oo o
2— amour o coo o
o
0— mm o o
0 5000 10000 15000 20000 25000
Average total daily traffic

Figure 3-5 Scatter plot for abutment rating and average daily total trafﬁc

54

3.3.2.3 Division by main structure type, maximum span, skew and approach type

Since the correlation obtained from the analyses on the entire database provided
limited information, the database was sub-divided into categories to evaluate the
correlation coefﬁcients based on each individual data group. Data with common features
were categorized in the same division (Figure 3-6). This rationale for dividing the
database followed from the consideration that for bridges with common features, the

mechanism that caused degradation of abutment walls would be similar.

Figure 3-7 shows the scatter plot for abutment rating and age at inspection. The
abscissa and ordinate are abutment rating and age at inspection respectively. It can be
seen that there seems to be some degree of negative correlation between the two
parameters; with the correlation coefﬁcient expected to be a value between -0.3 and -0.9.
The analysis showed that the correlation value was —0.555. Thus, for this category of
bridges, with a maximum span between 18.3 m and 30.5 m, skew angle greater than 45°
and ﬂexible surface approach, the age at inspection is, to some extent, negatively

correlated with abutment rating.

Analyses on all the data sub-divisions identiﬁed in Figure 3-6 were carried out in a
similar manner as described throughout this section. In general, no clear association
between the abutment rating of highway bridges and the explanatory variables could be
found through simple correlation analyses. Deck width, pin condition, age at inspection,
built year, average daily total trafﬁc, and average daily truck traﬁic were all shown to

have some degree of correlation to abutment rating. The correlation coefﬁcients varied

55

according to the different data categorizations and subdivisions and evidence was not

strong enough to support a more general positive conclusion.

 

[ All Bridge Inspection Records ]

 

 

l
till

 

 

 

 

 

 

 

 

 

 

. . Simple or . Simple Continuous
Simple Continuous cantilevered Continuous Prestressed Prestressed
Concrete Concrete Steel
Bridges Bridges BSLeel Bridges CBorzicrete CBondcrete
n ges n ges n ges
(MM1) (MM2) (MM3) (MM4) (MM5) (MM6)
f v 1
Maximum Span M 1.8'3 m < 30.5 m <
= axrmum Span . . . .
< 18.3 m G 30 5 m Maxrmum Span

 

 

 

 

i w l

 

 

15 degree <
<S_l<r=1.-\:5vdAngle Skew Angle 45 degree < . . .
— egree <= 45 degree Skew Angle

 

 

1

Flexible Approach
Surface (F)

Rigid Approach
Surface (R)

   

Figure 3-6 Database Sub-Division for Statistical Correlation Analyses

56

 

Abutment rating
‘i‘

2—

 

 

O
0000 000 00
O O 0 0001!!) (III) 00
OO 0 GD 0 CG!!!) OCIIID O CIDO
00 0330 O O
O CIID
CD 0
(DO
I | l l l l
0 20 40 60 80 100
Age at inspection

Figure 3-7 Scatter Plot for Abutment Rating and Age at Inspection

3.3.3 Analysis of Factorial Effects

Factorial effects were analyzed through a two-way analysis of variance (ANOVA).

ANOVA is a statistical method to divide the variation in response variable into several

components contributed by different factors and error. In ANOVA, linear regression

models are used to explain and separate the variation in the response variables. The

model is shown in equations (3-6)-(3-9) [Rice 1995].

Yijk = ,u+a,.+,6j +50. +5.31.

57

(3-6)

 

1
. = 0 <3-7)

J
2 '61 = 0 (3-8)

I J
25,]. =26, =0 (3-9)

In the above equations Y 1],. is the kth record in the group with ith level of factor A and jth
level of factor B; at is the differential effect of ith level of factor A; ,6,- is the differential
effect of jth level of factor B; 5,; is the effect of interaction between ith level of factor A
and jth level of factor B; and em, is the random error in the kth record for the group with
ith level of factor A and jth level of factor B. The total sums of squares can be partitioned

using equation (3-10):
SSW =SSA+SSB+SSAB+SSE (340)

where SSTOT is the total sums of squares; SSA, SS3, 55,43, and SSE are sums of squares for
factor A, factor B, interaction between A and B, and error, respectively. Using the sums
of squares, F tests can be carried out to evaluate the signiﬁcance of the factors, as shown
in equation (3-11). In equation (3-11), dﬁq means the degree of freedom for factor A, (if);
represents the degree of freedom for error. The F statistics can be calculated for the

effects of the other factors and interactions between factors in a similar manner. The F

58

statistics can be evaluated using either a sequential sum of squares (Type I) or by fully

adjusted sums of squares (Type III.)

F_ SSA/de

_ (3-11)
555 Mfg

The analyses of factorial effects was aimed at verifying the signiﬁcance of the
qualitative variables “pin type” and “approach type” in the development of damage in
bridge abutment walls. The analyses were conducted using generalized linear regression
model procedure “SAS PROC GLM” [SAS 2004]. In the factorial design, the qualitative
variable “pin type” had two levels “without pin-and-hanger assembly” and “with pin-and-
hanger assembly”. The qualitative variable “approach type” had three levels: “rigid,”
“ﬂexible,” and “unknown.” Six covariates were added to this model: “length,” “deck

99 6‘

width,” “age at inspection, average annual temperature difference,” “ADTT at

inspection,” and “maximum span.”

Table 3-5 shows one of the Type III analysis of variance (ANOVA) models derived
in the analyses of factorial effects. It can be seen from Table 3-5 that the interaction term
between “pin type” and “approach type” was signiﬁcant under a type I error rate of
0.01%. Thus, the effect of the levels of one factor within the levels of another factor
needed to be explored. It can also be seen that “approach type” was also signiﬁcant under
a type I error rate of 0.01 %. Even though “pin type” was signiﬁcant under type I error
rate of 5 %, the evidence was not very strong. This justiﬁes the model selected in section

3.4, in which the dummy variable “pin type” was excluded by Mallow’s Cp criterion.

59

Table 3-5 Type 111 Model ANOVA

 

 

Source DF Type 111 SS Mean Square F Value Pr > F
Pin type 1 4.44 4.44 3.88 0.0487
Approach Type 2 213.36 106.68 93.28 <.0001
Pm type x 2 68.30 34.15 29.86 <.0001
Approach type

 

The tests of difference in factorial effects were carried out based on the results shown
in Table 3-5. All the covariate values in the model were set to be constant in each test.
Three scenarios were considered according to covariate values “0,” “-1,” and “1.” It can
be seen from the residual plots in Section 3.4 that these three values encompassed the
samples that were most frequent. The factorial effects when covariates had a value of “0”

are shown in Table 3-6.

It can be seen from Table 3-6 that the effect of “pin type” was not signiﬁcant for
bridges with ﬂexible approach. However, for the bridges with the rigid approach or
unknown approach, the effect of “pin type” was signiﬁcant. For bridges with unknown
approach the abutment rating of bridges with pins was signiﬁcantly higher than those
without pins. However, for bridges with rigid approach pavement, the abutment rating of
the bridges with pins were signiﬁcantly lower than those without pins under a type I error
rate of 0.01 %. The difference of the effect of approach types was always signiﬁcant
under the type I error rate of 0.01 % no matter whether pins were present or not. The
abutment ratings of bridges with ﬂexible approach pavement were signiﬁcantly higher
than those for bridges with the other two types of approach pavements, irrespective of
whether pins were present or not. For bridges with pins, the abutment ratings of those

with unknown approach pavement type were signiﬁcantly higher than bridges with rigid

60

approach type. Conversely, for bridges without pins, the abutment rating of bridges with

rigid approach pavement type was signiﬁcantly higher than those with unknown

approach pavement type.

Table 3-6 Test of factorial effects (covariates values are Os)

 

 

Parameter Estimate Standard Error tValue Pr > |t|
Drfference of prn wrtlnn ﬂexrble 0.041 0.033 _1 .24 0.21 57
approach
D‘ﬁerence ofpm “mm“ 0.133 0.033 4.06 <0.0001
unknown approach
Difference ofprn wrthrn r1g1d 0.201 0.029 -6.92 <0.0001
approach
Difference of ﬂexible and
unknown approach for bridges 0.147 0.031 4.82 <0.0001
with pin
D‘fference 0f ﬂfx‘ble a.“ “.g‘d 0.335 0.029 1 1.52 <0.0001
approach for bridges wrth prn
D‘ﬁerence Of "momentum 0.187 0.029 6.43 <0.0001
approach for bridges wrth pin
Difference of ﬂexible and
unknown approach for bridges 0.322 0.033 9.83 <0.0001
without pin
D‘ﬁerenc" 0f ﬂfx‘ble ind mg“. 0.175 0.031 5.66 <0.0001
approach for bridges wrthout prn
D‘ﬁerence 0f ““kmwn and “9“ 0.147 0.031 -4.81 <0.0001

approach for bridges without pin

 

3.3.4 Hypothesis Test

Hypothesis test is a statistical algorithm to evaluate the possibility of an assumption
to be untrue based on the gathered data. The assumption under consideration is called

null hypothesis, H0. A test statistic needs to be deﬁned in a hypothesis test. Assuming H0

61

is true, the distribution of test statistic can be derived. The result of a test is expressed in
the possibility of obtaining a statistic if the null hypothesis is true. The values of a test
statistics can be calculated based on the gathered data, and the possibility to get that value
if H0 is true can be compared with a signiﬁcance level, a. If the possibility is less than 01,

H0 can be rejected. Otherwise, H0 can not be rejected.

A series of statistics can be used in hypothesis test, such as 2, t, )6, etc. In this
research, x2 test of goodness of ﬁt [Snedecor and Cochran 1989] was applied. Chi-square
distribution is the sum of squares of independent standard normal variables. The value of
x2 statistics can be calculated by equation (3-12). In equation (3-12)ﬁ means the observed
frequency in a class; F ,- represents the expected frequency from theoretical distribution;

and k signiﬁes the number of classes in consideration.

$02-12):

2_
F.

1

(3-12)

 

Z

Hypothesis tests were applied to investigate the contribution of beam type and
approach pavement type in the development of abutment damage of prestressed concrete
bridges. Speciﬁcally, chi-square hypothesis tests were applied. At ﬁrst, the abutment
conditions were divided into 10 classes: 0-9. Four beam types were considered in the
analyses: adjacent box girder, spread box girder, I-girder, and others. The inspection
records of prestressed concrete bridges were categorized into 40 cell groups considering
all combinations of beam types and abutment conditions. It should be pointed out that 53
% of the cells had expected counts less than 5; and thus, the chi-square test was not a

valid test. Similarly, for associations between the approach pavement type and abutment

62

condition, four approach pavement types were considered: bitumen concrete mixed,
bitumen, concrete, and unknown. Again, 47.5 % of the 40 cells had expected counts less

than 5 and thus the chi-square test was not valid.

In further analyses, abutment conditions of prestressed concrete bridges were
categorized in two groups: “with abutment distress” (abutment rating less than 5) and “no
abutment distress” (abutment rating larger than 4). Two reasons accounted for the
regrouping of the inspection records. First, of primary concern was whether the bridge
had abutment distress instead of differentiating between a rating of 7 or 8. Thus,
frequency analyses and hypothesis tests on whether the bridge had abutment distress were
more rational. Second, after converting the 10-category abutment ratings to 2-category

abutment conditions each cell would have enough counts to facilitate the hypothesis tests.

Results of the frequency analyses concerning abutment condition and beam type are
shown in Table 3-7. Results of the corresponding chi-square hypothesis test are shown in
Table 3-8. The null hypothesis H0 is: “no association between abutment condition and
beam type.” It can be seen from Table 3-8 that the null hypothesis test can be rejected
under a type I error rate of less than 0.01 %. The conclusion was that for prestressed

concrete bridges there is association between abutment condition and beam type.

63

Table 3-7 Frequency analysis by girder type and abutment condition

 

 

 

 

Beam utrnent Condition Good Poor Total

Frequency

~39:th Percentage
Row Percentage

Frequency

Spread Box Percentage
Row Percentage

Frequency

I-Girder Percentage
Row Percentage

Total Frequency

Percentage

 

 

Table 3-8 Chi-square Test for H0: no association between abutment condition and beam

type

 

Statistic

Chi-Square

Degree of Freedom Value Probability
2 18.7403 <.0001

 

Similarly, for approach surface type, the frequency analysis is shown in Table 3-9.

Results of the corresponding chi-square hypothesis test are shown in Table 3-10. The null

hypothesis H0 is: “No association between abutment condition and approach surface

type.” It can be seen from Figure 3-10 that the null hypothesis can not be rejected even

under type I error rate of 50 %.

Table 3-9 Frequency analysis by approach surface type and abutment condition

 

 

  

 

 

Abutment Condition
Approach Surface GOOd Poor Total
Frequency 29 3
Bitumen and Percenta

concrete mixed ge
Row Percentage

Frequency

Bitumen Percentage
Row Percentage

Frequency

Concrete Percentage
Row Percentage

Frequency

Unknown Percentage
Row Percentage

Frequency

Total
Percentage

 

 

Table 3-10 Chi-square Test for H0: no association between abutment condition and

 

 

approach surface type
Statistic Degree of Freedom Value Probability
Chi-Square 3 1.1198 0.7723

 

 

3.4 Regression Analysis

Regression analysis is an area of statistics that deals with methods for investigating
the association, and, if present, the characteristics of the associations among various
observable quantities [Graybill and Iyer 1994]. These associations can further be

expressed in the form of mathematical expressions, which may allow the prediction of the

65

unobservable value of a variable based on the observed value of one, or more, associated
or related variables. These models may also help to determine how to manipulate a given
variable to control the value of an associated or related variable. Thus, regression analysis
offers a sensible and sound approach for examining associations among variables and for
obtaining good rules for prediction. Regression models are widely used in engineering
analysis and have been successfully applied in a project to evaluate the causes behind

precast I-girder end cracking [Myers et. al. 2001].

The linear regression models are linear combination of ﬁrst order of the regression
coefﬁcients, no higher order or cross product of coefficients is involved in the model
[Montgomery et. al. 2006, Myers et. a1. 2002, Weisberg 2005]. A linear regression model
can use the ﬁrst order of the explanatory variables or a higher order of the explanatory
variables. While multiple linear regressions with the ﬁrst order of explanatory variables
are adequate for modeling a wide variety of relationships between response variables and
predictor variables, many situations require terms of higher order to be considered.
Equations (3-13)—(3-17) [Montgomery et al. 2006] deﬁne a multiple linear regression
model. In these equations, y is a vector of values of a response variable, X is a matrix of
levels of explanatory variables; ,6 is a vector of regression coefﬁcients; and e is a vector
of residuals. The underlying assumption in the process of ﬁtting a regression model is
that the residuals are NIID, which means the residuals are normally, independently and

identically distributed.

y = X13 + 8 (3-13)

66

 

y]
Y2

 

y”;

 

,8]
A

 

 

1 x1,

1 x2,

1 x

 

 

3‘12

x22

x122

67

 

(3-14)
,
xlk
X
i" (3-15)
xnk _
(3-16)
(3-17)

3.4.1 Linear regression using ﬁrst order of explanatory variables

3.4.1.1 Selection of explanatory variables
(a) Automatic search Procedures

Stepwise regression based on an iterative procedure was applied in this research. The
procedure considers a sequence of t-tests on the explanatory variables at each stage. It
can be classiﬁed as forward stepwise regression, backward stepwise regression, etc,
depending on the iteration scheme. It may be initiated with no variables in the model and
variables can be added later on; or it could be started with all the variables in the model
and variables can be later deleted from it [Kutner et. al. 2005]. A forward stepwise
procedure was used to search for a proper subset of explanatory variables to build a

model to predict abutment condition in highway bridges.

The subset of explanatory variables for simple/cantilevered steel bridges selected by
the forward stepwise procedure is shown in Table 3-11. It can be seen from Table 3-11
that eight variables were included in the subset, each of them with a signiﬁcance value of
less than 0.0015. Even though this can not ensure that the subset is optimal, it can still
provide a valuable reference for the identiﬁcation of key parameters, especially after the

models were veriﬁed.

68

Table 3-11 Subset of explanatory variables for simple/cantilevered steel bridges

 

 

1 Matdiff 0.0343 0.0343 729.06 <.0001
2 Ageinsp 0.0282 0.0625 615.94 <.0001
3 Deckwidth 0.0301 0.0925 679.06 <.0001
4 Apprsurstif 0.0054 0.0979 121.93 <.0001
5 ADTTinsp 0.0015 0.0994 34.22 <.0001
6 Maxspan 0.0014 0.1008 31.22 <.0001
7 Pin type 0.0005 0.1013 12.05 0.0005
8 Skew 0.0004 0.1018 10.08 0.0015

 

(b) Criterion based on all combinations

There are many criteria for the selection of proper models from all combinations,
such as RP), Rap) , Cp , AICp , SBCP and PRESSp [Kutner et. al. 2005]. Mallow’s Cp

[Kutner et. al. 2005] criterion was used in this research. Mallow’s Cp is computed as

SSE

C : p — "—2
P MSE(X,,X,,...,XP_,) ( p) (348)

 

where SSEp is the sum of the square error of the model in consideration, and MSE is the
mean squared error of the full model that included all the explanatory variables. SSEp is
the summation of two terms. One error is that due to bias; that is, the model does not
properly reﬂect the relationship between dependent and independent variables. The
second component is due to variation, which is a sampling error. Thus, when C p is plotted

against p and a line Cp = p is drawn on the plot, the CPS of models with little bias will fall

69

in the vicinity of the line, the Cps of models with signiﬁcant bias will fall high above the
line, and the Cps of models without bias will fall below the line. The assumption
underlining the calculation of Mallow’s Cp factor is that the full model, including all the

explanatory variables, has no bias. That is, MSE is an unbiased estimator of the variation

02.

In the application of Mallow’s Cp criterion, a Mallow’s Cp that is small and close to
the p value is sought. A small Q, value means a small total square error. A Cp value close
to p ensures the bias term to be small. A small Cp value itself can not ensure a small bias,
so the model with a larger subset of explanatory variables with only a slightly larger Cp
value is preferable in comparison with models with slightly smaller Cp values and smaller
p values. The Cp value for the full model (including all the explanatory variables) is p

[Kutner et. al. 2005].

The subsets of explanatory variables for simple/cantilevered steel bridges seem to be
good as tested by Mallow’s Cp criterion and shown in Table 3-12. It can be seen from
Table 3-12 that the most suitable subset is the ﬁrst one, since its Cp value is small and
close to the number of variables p. It is reassuring to ﬁnd out that the ﬁrst subset exactly
matches the subset obtained by the stepwise automatic selection, as seen by comparing

with Table 3-11. Thus, the ﬁrst subset was selected and tested.

70

Table 3-12 Explanatory variable subsets of simple/cantilevered steel bridges and their

 

 

Mallow’s Cps
Number Of Cp Variables in Model
varrables p
8 7 812 Deckwidth Skew Matdiff Apprsurstif Maxspan Pin
. Ageinsp ADTTinsp
9 9 291 Length Deckwidth Skew Matdiff Apprsurstif
' Maxspan Pin Ageinsp ADTTinsp
9 9 588 Deckwidth Skew Matdiff Apprsurstif Maxspan Pin
' Desi grrload Ageinsp ADTTinsp
10 11 Length Deckwidth Skew Matdiff Apprsurstif
Maxspan Pin Designload Ageinsp ADTTinsp

 

 

3.4.1.2 Regression analysis and validation

A regression model developed for the abutment degradation of simple/cantilevered
steel bridges is presented in this section. The ﬁrst order of the variables listed in Table
3-11 were used as predictors and the abutment rating was the response variable. The plot
of predicted values versus residuals is shown in Figure 3-8. It can be seen from Figure
3-8 that the variance of the residuals is not constant and the magnitude of the residual is
large. The stem-and-leaf plot and box plot are shown in Figure 3-9. It can be seen from
Figure 3-9 that the distribution of the residuals is not normal and that the distribution is
skewed. The normal probability plot is shown in Figure 3-10. Again, it can be seen from
Figure 3-10 that the plot is close to the reference line, but the distribution is skewed.
Based on the evaluation of Figure 3-8, Figure 3-9 and Figure 3-10, it can be concluded

that the residuals of the regression model for simple/cantilevered steel bridges are not

71

NIID. Thus, the regression model is not valid. It follows that linear regression models

using the ﬁrst order of explanatory variables can not reﬂect the relationship between

explanatory variables and the abutment ratings for this research problem.

 

Residual

 

 

 

 

Pred cted Value

Figure 3-8 Residual plot for the model of simple/cantilevered steel bridges

3.4.2 Linear regression analysis using ﬁrst and second order of explanatory variables

Multivariate linear regression models were developed considering quadratic and cross
interaction terms of explanatory variables. In general, multivariate linear regression

models were also found not to be adequate for predicting abutment damage.

72

H st ogr am
4. 75+*

*
i
*
******
*****************
********************************************
************************************************
****************************
****************

_1. 25.._***********
******
*****
***

****

-7.25+*
----#---+—---+~---+—---+----+~---+---—+----+---
* may represent up to 111 counts

371
113

NOD-{>00

3)pr 0t

__OOO

+~—---+
*-—'+b-*
+b----+

I"CDCDOCD'—'—'_

‘-

Figure 3-9 Leaf and stem plot and box plot of residuals for simple/cantilevered steel

bridge

3.4.2.] Data preparation

In order to avoid a possible multi-colinearity problem, and the severe round off error

caused by it, the seven quantitative variables were normalized using equation (3-19)

before quadratic and cross interaction terms were added. The corresponding mean and

standard deviation of the variables are shown in Table 3-13.

73

*

|
I
I
| H"
| -I-H+ *
I IIIII*******
I +4j*******
I *t*******
I ********
I *****++
I ****++

_1 25+ ****
I +++***
I I'll ***
I+++ ***
I *****
I***
I*
I*
I
I*
It
I*

-7.25+*
+.---+_---+.---+.---45---+..---+.---+.-_-+.---+.---+

-2 -1 0 +1 +2

Figure 3-10 Normal probability plot for the model of simple/cantilevered steel bridges

* _ .
xi _ (3-19)
The qualitative variable “approach type” was coded by two dummy variables: “appl ”

and “app2,” where appl = 0 and app2 = 0 for bitumen approach pavement; appl = l,

app2 = 0 for bitumen and concrete mixed approach pavement; and appl = 0, app2 = 1 for

74

concrete pavement. The qualitative variable “pin type” can be deﬁned as a dummy

variable itself, so no recoding was needed for it.

Table 3-13 Mean and standard deviation of the quantitative variables

 

 

Parameter Mean (u) standard deviation (0)
Length (m) 64.796 38.001
deckwidth (m) ' 15.394 6.957
Skew (°) 19.265 18.078
Ageinsp 36.46 12.127
Matdiff (°C) 10.8 0.79
ADTTinsp 2762.1 3388.200
Maxspan (m) I 24.977 9.241

 

Quadratic and cross interaction terms were added after the covariates were recoded.
No quadratic term for the dummy variables was added. No interaction term was added
between dummy variables “appl” and “app2” since they are derived from the same
qualitative variables. After adding quadratic and interaction terms, the explanatory
variables included 7 covariates, 3 dummy variables, 7 quadratic terms of the covariates,
and 44 cross interaction terms; that is, 61 explanatory variables in all. The response

variable was the abutment rating.
3.4.2.2 Selection of the optimal explanatory variables subset

The commercial statistical software SAS [SAS 2004] was used to search for the
optimal subset of explanatory variables using Mallow’s Cp criterion. The regression

analysis module “SAS PROC REG” [SAS 2004] procedure evaluated 4151 regression

models developed with different combinations of explanatory variables. Figure 3-11

75

shows a plot of “p” versus “Mallow’s C ”. It can be seen that most of the points fall
under the CI, = p line in this plot. The top seven models are shown in Table 3-14 ordered
by the Cp value. Considering parsimony, the subset that contained 40 explanatory

variables with the smallest Cp value (the last row in Table 3-14) was chosen.

+++DP¢P
'— DP =P .
anr full model) +1

 

Figure 3-11 Mallow’s Cp against p

3.4.2.3 Regression analysis and validation

A regression model considering the ﬁrst and second order of explanatory variables
was developed for abutment degradation of simple/cantilevered steel bridges and is
presented in this section. The explanatory variables were listed in the last row of Table
3-14 and abutment rating was used as the response variable. In order to verify the model,
residuals are plotted against predicted values and explanatory variable “deck width” in

Figure 3-12 and Figure 3-13, respectively. Both plots feature fan-shape patterns and the

variances of the residuals are not constant. There are also some outliers in both plots.

76

Table 3-14 Results of Mallow’s Cp Selection Method (TOp 7 rows)

 

Cp

Variables in the model

 

44

43

45

43

42

40

37.18

37.43

37.44

37.52

37.56

37.6

length deckwidth ageinsp matdiff ADTTins maxspan pintype appl
app2 Len2 Dew2 Ske2 Age2 Adt2 MasZ LenAge LenMat LenAdt
LenMas LenApl DewSke DewAge DewMat DewAdt DewMas
DewPin DewApl SkeMat SkeMas SkePin SkeApl SkeAp2
AgeMas AgeApl AgeAp2 MatAdt MatMas MatApl MatAp2
AdtMas MasPin MasApl PinApl PinAp2

length deckwidth ageinsp matdiff ADTTins maxspan pintype appl
app2 Len2 Dew2 Ske2 Age2 Adt2 Mas2 LenAge LenMat LenAdt
LenMas LenApl DewSke DewAge DewMat DewAdt DewMas
DewPin DewApl SkeMat SkeMas SkePin SkeApl SkeAp2
AgeMas AgeAp2 MatAdt MatMas MatApl MatAp2 AdtMas
MasPin MasApl PinApl PinAp2

length deckwidth ageinsp matdiff ADTTins maxspan pintype appl
app2 Len2 Dew2 Ske2 Age2 Adt2 Mas2 LenAge LenMat LenAdt
LenMas LenApl DewSke DewAge DewMat DewAdt DewMas
DewPin DewApl SkeMat SkeMas SkePin SkeApl SkeAp2
AgeMas AgeApl AgeAp2 MatAdt MatMas MatApl MatAp2
AdtMas Athpl MasPin MasApl PinApl PinAp2

length deckwidth ageinsp matdiff ADTTins maxspan pintype appl
app2 Len2 Dew2 Ske2 Age2 Adt2 LenAge LenMat LenAdt
LenMas LenApl DewSke DewAge DewMat DewAdt DewMas
DewPin DewApl SkeMat SkeMas SkePin SkeApl SkeAp2
AgeMas AgeApl AgeAp2 MatAdt MatMas MatApl MatAp2
AdtMas MasPin MasApl PinApl PinAp2

length deckwidth ageinsp matdiff ADTTins maxspan appl app2
Len2 Dew2 Ske2 Age2 Adt2 MasZ LenAge LenMat LenAdt
LenMas LenApl DewSke DewAge DewMat DewAdt DewMas
DewPin DewApl SkeMat SkeMas SkePin SkeApl SkeAp2
AgeMas AgeAp2 MatAdt MatMas MatApl MatAp2 AdtMas
MasPin MasApl PinApl PinAp2

length deckwidth ageinsp matdiff ADTTins maxspan appl app2
Len2 Dew2 Ske2 Age2 Adt2 LenAge LenMat LenAdt LenMas
LenApl DewSke DewAge DewMat DewAdt DewMas DewPin
DewApl SkeMat SkeMas SkePin SkeApl SkeAp2 AgeAp2
MatAdt MatMas MatApl MatAp2 AdtMas MasPin MasApl
PinApl PinAp2

 

77

Residual

Residual

 

 

 

 

 

Predicted value

Figure 3-12 Plot of Residual against predicted values

 

 

 

++ g
i” ﬁfﬁg t a
3;. at? if- ..............
§ 4»
3
1
4 + 1 +
4, + 4” +++
-8 +1 V I T T I T j ﬂ
-2 0 2 4 6
Deck width (Normalized)

Figure 3-13 Plot of Residual against “deck width”

78

 

 

A check of the residual distribution is also an important procedure to validate the
regression model. The stem-and-leaf plot and the box plot of residuals are shown in
Figure 3-14. It can be seen from the stem-and-leaf plot on the left that the distribution of
the residuals is skewed. After observing the box plot on the right, some outliers are
detected in addition to the skew. The normal probability plot of the residuals is shown in

Figure 3-15. The skew problem stands out again.

H st ogram # BDXPI ot
3. 25+* 8 O
.* 18 0
.* 102 0
.a-a-«na 438 I
.**************** 1W1 I
.******************************it 3737 +_____+
.********i*************************************** 57% *—-+s-*
'0'25+.************************** 3103 +,___--+
.**************** 1844 I
_........ 968 I
.***** 531 l
,**** 416 0
,*** 316 0
_*** 251 0
-3_ 75+* 104 0
t w *
4 1 *
.* 1 *
,* 10 *
-7.25+* 1 *

----+~---+~---+----+~---+~---+~---~I~---+----+—--
* nay represent up to 121 counts

Figure 3-14 Stern and leaf plot and box plot of residuals

79

3. 25+ *

I +*
I lllll *
I ++++peetttt
I +*********
I *******
I *********
'0 25+ *****++
I *****++
I ****+
I H***
I I'llliit
I“ ***
I ****t
-3. 75+“
It
|*
|
I*
|*
If
-7. 25+*
+~---+~---+~---+~---+~---+~---+~---+~---+~---+~---+
-2 -1 0 +1 +2

Figure 3-15 Normal Probability Plot of the residuals

Based on the residual diagnosis discussed above, it can be concluded that the NIID
distribution of residuals could not be conﬁrmed, and thus the regression models were not
valid. Furthermore, none of the regression models developed in this research could be
proved to be adequate after a model checking process. Thus, regression analyses are not
suitable tools to develop prediction models based on a complicated and unbalanced

database as is the case in this research.

80

3.5 Discussion

An evidential database was created from the SISD (NBI database for the sample
problem.) Statistical analyses based on the evidential database were carried out for the
example problem to evaluate the signiﬁcance of design and operation variables in the
development of structural damage and provided valuable information for the subsequent

analyses and simulations in this research.

As expected, frequency analyses revealed that older bridges have higher incidences of
poor abutment performance. The higher number of bridges with poor abutment for stiff
approaches (asphalt on concrete base or concrete) supports the assumption of pavement
grth on abutment damage. Finally, poor performance of expansion joints was also
clearly related to abutment performance. This could be indicative of abutment forces due
to restrained temperature movements, poor bearing performance, and pavement growth

problems.

Exploration of correlation coefﬁcients between abutment rating and different
parameters was performed. The search for the key parameters by different paths was
represented by sorting the bridge population in the database in sub-divisions or sub-
categories. Generally, deck width, pin condition, age at inspection, built year, average
daily total trafﬁc, and average daily truck trafﬁc are all shown to have some degree of
correlation to abutment rating. The correlation coefﬁcients differ according to the

different data categorization and subdivision.

In the analysis of factorial effects of simple/cantilevered steel bridges, two factors

(pin type and approach surface type) were considered. The factorial effects were

81

evaluated for the different levels of factors. Since the interaction term between them was
signiﬁcant, the difference between the effects of levels of one factor is considered within
certain levels of the other factor. It was found that when the covariates were zero, the
effect of pin type was not signiﬁcant for ﬂexible approaches; while for the other approach
types, the effect was signiﬁcant. The effects of different levels of approach type were
always signiﬁcant regardless of whether the bridge had a pin or not. Some of the factorial

effects also changed with the variation of covariates.

Hypothesis tests concerning the association between design parameters and abutment
condition for prestressed concrete bridges showed that there was an association between
beam type and abutment condition. Proper linear regression models can not be developed
by only considering the ﬁrst order of explanatory variables. The linear regression model
using 40 covariates was a relatively good regression model for the current research
problem. Covariates consist of the design parameters of the bridge and their quadratic and
cross interaction terms. However, it was still not appropriate to reﬂect the complex
problem of abutment distress. Evaluation of the residual plots shows that most of them
have fan-shaped patterns and outliers. The NIID assumption concerning the distribution

of residuals can not be satisﬁed by regression models, and thus the models are not valid.

Another generalized linear regression model that can be developed is a multivariate
logistic regression model. A multilayer perceptron using sigmoid activation function
without hidden layer is equivalent to a logistic regression model [Bishop 1995, Dreiseitl
and Ohno-Machado 2002, Hastie et al.2001]. The multivariate logistic regression model

can not be expected to have a better performance than the multilayer perceptron using

82

sigmoid activation function with two hidden layers developed in section 6.2. Thus, the

logistic regression model was not further explored in this research.

83

4 FIELD MONITORING

4.1 Introduction

Chapter 3 presented an approach to the structural damage problem from a statistical point
of view, which was very helpful for evaluating the signiﬁcance of different design
parameters. However, it was shown that mechanisms for the development of damage and
speciﬁc damage patterns can not be obtained through statistical analyses on the evidential
database. Field monitoring in this research aims at evaluating the contribution of the
identiﬁed parameters and to assist the execution and validation of the analytical studies.

This chapter introduces ﬁeld monitoring for the example research problem, which
includes the bridge selection process, the ﬁeld inspection of typical bridges, ﬁeld
instrumentation, data collection, and interpretation of the ﬁeld data. Key processes and
important observations of ﬁeld monitoring are presented in this chapter; a complete
description of the ﬁeld monitoring and analyses of the ﬁeld data in the example problem are

provided in the ﬁnal research report for MDOT [Burgueﬁo and Li 2008].

4.2 Bridges Selection

Typical bridges inspected in this research were chosen based on the common features of
those susceptible to abutment distress identiﬁed through statistical analyses. Table 4-1, Table
4-2, and Table 4-3 list the selection criteria in inspection Phase 1 for simple/cantilevered
steel bridges, continuous steel bridges, and prestressed concrete bridges, respectively. In
order to solve the issues remaining from the Phase 1 inspection, and to make the ﬁeld
evaluation representative and effective, inspection Phase 2 was carried out. The selection

criteria for simple/cantilevered steel bridges were not changed, as shown in Table 4-1. Since

84

urrrepaired continuous steel bridges were not enough according to the original criteria, the
criteria for selection of continuous steel bridges were changed to that shown in Table 4-4 in
inspection phase 2. For prestressed concrete bridges, Phase 2 focused on bridges with I-
girder beams or spread box beams, whose population was small, thus no additional criterion
was applied except for the beam type. The selection of bridges to be inspected focused on the

counties less than 240 kilometers away from Lansing, MI.

Table 4-1 Criteria for simple/cantilevered steel bridge selection (in both phases)

 

 

# Parameters Criteria

1 Length >=76.2 m

2 deck area >=1393.6 m2

3 average daily total trafﬁc >30,000

4 deck width >18.3 m

5 approach surface type “Concrete” or “Unknown”

 

Table 4-2 Criteria for continuous steel bridge selection (Phase 1)

 

 

# Parameters Criteria

1 Length >=121.9 m

2 deck area >=1393.6 m2

3 Skew <20°

4 skew multply deck width <1 82.9 °m

5 approach surface type “Concrete” or “Unknown”

 

85

Table 4-3 Criteria for simple prestressed concrete bridge selection (Phase 1)

 

 

# Parameters Criteria

1 Length 45.7 m — 91.4 m

2 deck area 929.0 m2 - 1393.6 m2

3 deck width <61 m or 18.3 m - 24.4 m

 

Table 4-4 Criteria for continuous steel bridge selection (Phase 2)

 

 

# Parameters Criteria

1 Length >=121.9 m

2 deck area >=1 393.6 m2

3 Skew <20°

4 approach surface type “Concrete” or “Unknown”

 

Bridges were assigned simple ID labels for easy identiﬁcation in the inspection planning
as well as in ﬁeld evaluation. The ID nomenclature was in the form “Xm.n”, where X is a
capitalized letter indicating the structural type of the bridge, “A” means simple/cantilevered
steel bridges, “B” represents continuous steel bridges, and “C” signiﬁes prestressed concrete

66199

bridges. The “m” is a number identifying the inspection phase, where means Phase 1 and
“2” means Phase 2. The “n” represents the number of the bridge within list selected for
inspection in each phase.

Forty-four highway bridges were selected for ﬁeld inspection. Nine simple/cantilevered
steel bridges, eight continuous steel bridges, and nine prestressed concrete bridges were
selected for inspection Phase 1. Two simple/cantilevered steel bridges, six continuous steel

bridges, and ten prestressed concrete bridges were inspected in Phase 2. Table 4-5 shows the

list of simple/cantilever steel bridges inspected in Phase 1.

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87

4.3 Field Inspection

Three major damage patterns in abutment walls of highway bridges were observed:
U-shape pull out, vertical cracks between girders, and vertical cracks underneath girders

through the positioning dowels.

4.3.1 U-shape pull out

The abutment of bridge Al .7 with U-shape pull out damage is shown in Figure 4—la.
Figure 4-lb shows the concrete approach pavement of the bridge, which would generate
much larger compression pressure due to “pavement growth” with time. The inspection
process provided compelling evidence that this type of damage was induced by the
compression forces generated by pavement expansion, or pavement growth. Pressure
seems to be transferred from the integral backwall through the girder anchor bolts down

to the abutment wall.

   

(a) U — shape pull out underneath girder (b) Concrete approach pavement

Figure 4-1 Abutment Distress and Pavement for Bridge A1.7

88

4.3.2 Vertical cracks between girders

Another typical damage pattern observed were vertical cracks in the abutment wall
located between girders, as shown in Figure 1-5. Figure 1-5a shows a general View of the
abutment wall and part of the superstructure of bridge A1.4. The vertical cracks in the
abutment wall can be seen in the close-up view in Figure 1-5b. The inspections provided
compelling evidence that this type of damage pattern is mainly caused by the restrained

support forces generated due to transverse thermal expansion of the superstructure system.

4.3.3 Vertical cracks underneath girder through the dowel

The third important observed damage pattern was in the fornr of vertical cracks in the
abutment wall located underneath the girder, such as the damage was observed in
abutment wall of bridge Bl.1 (Figure l-6.) It can be seen from Figure 1-6 that the bearing
of this bridge has been seriously corroded, thus, providing unintended ﬁxity at the girder
supports. Displacements or rotations of the superstructure will cause additional stress in

the abutment due to the increased stiffness of the bearing.

Bridges visited during both phases of the ﬁeld inspections were representative for
major types of MDOT highway bridges and were selected with parameters that
categorized them to be susceptible to abutment distress. The ﬁeld inspection and
assessment was very helpful in identifying typical damage patterns and their possible
causes. Detailed inspection records and photographs for each inspected bridge were
documented as part of the information database and served as a basis for the selection of

bridges for ﬁeld instrumentation.

89

4.4 Field Instrumentation

Field instrumentation in this research focused on the deployment of a strategic ﬁeld
monitoring scheme on four bridges with and without signs of abutment distress. Of the 44
inspected bridges (Section 4.3), four bridges were selected for ﬁeld instrumentation as
shown in Table 4-6. In addition to the factors already considered in the selection of
bridges for ﬁeld inspection and the additional information from damage patterns and
observations noticed during the inspections, the accessibility to the bridge abutment and
the overall bridge site were also taken into account. Two bridges were selected for each
superstructure type for comparison; one of them already showed abutment distress and
the other one showed minor abutment distress but with the potential, since they shared

parameters, to develop damage.

4.4.1 Instrumentation Strategy and Implementation

The objective of the ﬁeld instrumentation is to obtain the strain distribution on the
abutment walls and backwalls, relative movements of the superstructure to substructure,
and the temperature ﬁeld on bridge structures. Since the instrumented bridges can be
considered approximately symmetric about the trafﬁc centerline, only one-half of one of
the abutment walls for each bridge was provided with measuring points (see “shaded
area” in Figure 4-2.) In this way, the number of instrumented bridges was doubled with
the available resources. As shown in Figure 4-2, trafﬁc direction was toward the
instrumented part of the abutment wall. This abutment side was selected for monitoring
because it might be able to capture any effects caused by truck braking. The location of
the instrumented bridges and information on the instrumented abutment is given in Table

4-6.

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Direction Road B I
@ Length
_'__________________L.
RoadA _j _ _ Temperature r_n_ea_slrrgne_nt pginL _ ﬂ _ _ L Road A
I _______________ .
2__ _______ oi _______ 6 t
_ _ Abatrngrtﬂal _________
L —————— —-3— ————— 14‘
Road B Bridge girder
Instrumentation region

 

Figure 4-2 Location of bridge and instrumentation region

4.4.2 Deployment of measuring points

The measuring points consisted of brass cylinders (Figure 4-3) embedded into the
abutment wall. The brass cylinders have a threaded end where a screw-in seat that can be
attached (Figure 4-4). For the girder ends, target discs were glued to the beam surface
using an epoxy adhesive. The deployment of measuring points on bridge Al.7 is shown

in Figure 4-5.

 

Figure 4—3 Brass cylinders installed on the abutment wall

92

 

Figure 4—4 Measuring points with contact seats screwed on brass cylinders

4.4.3 Variables Measured
Variables measured in the ﬁeld monitoring plan are listed as follows:
. The deformation of the backwall and the abutment wall: determined ﬁ'om the
distance between the measuring points deployed on the backwall and the

abutment wall (Figure 4—5.)

The longitudinal displacement of the girder end: the location of measuring points

to measure displacements of girder ends is shown in Figure 4-6.

Temperature of the bridge: temperatures of the bridge deck as well as on the
abutment wall were recorded at the start of the measurement process for each
bridge. Temperatures at ﬁfteen locations were taken using a Raynger ST non-
contact thermometer. Six of the locations were on the deck (Figure 4-2) and nine

of them were on the abutment wall (Figure 4-7).

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94

 

 

 

 

 

 

 

 

 

 

—-L

3

O
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Figure 4-6 Measurement of girder end displacement (unit: mm)

Half of the width of the bridge

 

 

 

Til
7. 8. 9 O I
Instrumented half of the abutment wall I
10 11 12
O \ O
13 Temperature measurement point 1 5
o 14o 0

Figure 4-7 Temperature measuring points on bridge abutment wall

95

 

Two approaches were applied in calculating the strain distribution along the abutment
wall. One approach was to calculate strain value as the ratio of variation of the distance
between measuring points to its initial value, as given by equation (4-1):

dijk —dijO
81.11, = d

IJO

(4-1)

 

where 89k means the jth strain in the ith line under the top of the abutment wall calculated
for the kth month; dU-k is the jth distance between adjacent measuring points in the ith line
calculated for the kth month; and dijo is the jth distance between adjacent measuring

points in the ith line calculated for the initial measurement (in December 2006.)

The position of the calculated strain is in the middle of two adjacent measuring points.
The second approach is a moving average method that calculates the strain value in the
middle of four consecutive measuring points using the sum of variations of the distance
between those points divided by the sum of the initial distances, as given in equation

(4-2):

di.j—l.k _ di.j-l,0 + d',j,k _ d d

l

', '+l,k :
‘1 d... o +d

+d.

i,j,O t,j+l.k _

+d.

i,j,0 r,j+l,0

i,j+l,0 (4-2)

 

8

4.4.4 Measurement schedule

The ﬁeld monitoring data was collected over a period of one year at one-month
intervals. Continuous monitoring or more ﬁequent measurements was not required
because the effects leading to abutment distress occur slowly over a long period. A major

cause of the abutment distress was believed to be thermal movements, which can be

96

assessed by measuring extreme temperatures. Furthermore, the ﬁeld monitoring was not
intended to provide precise measure of bridge response but to reveal the overall behavior
of bridges under different circumstances over time. During the ﬁrst eight months of
measurements, two sets of readings were made in each round for the backwall and the
abutment wall of each bridge. One set of the readings was taken directly on the anchored
brass cylinders (Figure 4-3.) The other was done on the contact seats (Figure 4-4)
screwed on the brass cylinders. It was found that the data collected directly ﬁom the brass
cylinders were more reliable. Thus, measurements were taken only on the brass cylinders

for the remaining ﬁve rounds.

4.5 Data Interpretation

Data from the ﬁeld measurements were plotted in three different perspectives to help
identify the relations among horizontal strain (target variables), longitudinal and
horizontal girder end movements (bridge behavior), and temperature at the deck and the
abutment wall (environmental variables.) The calculated variations were determined by

using values measured in December 2006 as reference.

4.5.1 Distribution of Strains

The distributions of strains along the abutment wall and backwall together with girder
end movements were plotted. Examples are shown in Figure 4-8 and Figure 4-9. The
legend “Al” represents the horizontal line 152 mm below the top of the abutment wall.
Similarly, “A2” represents the horizontal line 457 mm below the top of the abutment wall.
“GM” means girder end movement, which is the average of the values measured at the

side of the girder and the bottom of the girder. A positive value means that the girder end

97

moved away from the abutment wall and vice versa. “MiC” signiﬁes minor cracks in the
abutment wall, “MaC” signiﬁes major cracks, and “CJ” means control joints. “Mic,”
“MaC,” or “Cl” plotted on the upper level means that they are at the level of “A1,” while

when plotted on the lower level means they are at the level of “A2”.

From the strain proﬁles in Figure 4-8 and Figure 4-9, it can be observed that wall face
in the vicinity of girder pull-out was subjected to tension, while the region in the vicinity
of girder inward motion was subjected to compression (Figure 4-8.) Similar trends can be
observed in the backwall (Figure 4-9.) In general, cracks and control joints induced local
peak horizontal strains in the abutment wall (Figure 4-8,) which is to be expected. It can
be seen from Figure 4-8 that the data are noisy. Reasons include the accuracy of the
digital caliper, the errors of measurements taken in a difﬁcult environment, the large gage
length used. To help ﬁlter this noise, the moving average method was used to interpret
the data (Figure 4-10.) Average strain values were calculated at three point intervals. It

can be seen from Figure 4-10 that variation trends of horizontal strains are clearer.

4.5.2 Peak strain vs. time and temperature in region around girders

The second approach to explore the ﬁeld instrumentation data is to divide the
instrumented abutment wall into regions around girders. The division of the abutment
wall of bridge Al.7 is shown in Figure 4-11 as an example. The regions for the other
three bridges were divided in the same manner. The maximum and minimum horizontal
strains in each region were plotted together with changes of average temperatures in

decks and abutment walls.

98

 

 

Longitudinal movement of girder end (mm)

 

 

 

 

 

 

 

Honzontal strain
0
" $;g _
“<25
/
3
3

 

 

 

_5 i : l :. z“ . . .
0 2 4 6
Distance from the left most measuring point (m)

 

 

Figure 4-8 Horizontal strains, control joints and cracks on abutment wall of bridge Al .7

 

 

* GM - —A- Backwall
----- MiC

 

 

 

 

 

Honzontal strain
a»
Mgr-er
a .
" \29
K

 

 

l nnnitl Idinnl mnvnment nf nirrler and (mm)

.4l . 4 . . ,4
0 2 4 6 8 10

Distance from the left most measuring point (m)

Figure 4-9 Distribution of horizontal strains and cracks on backwall of bridge C2.l

99

0

Longitudinal movement of girder end (mm)

 

 

 

 

 

 

 

 

 

 

Horizontal strain

 

 

 

 

 

 

_5i 1 I I r i r 1 l 1 l I _2
0 2 4 6 8 10
Distance from the left most measuring point (m)

 

Figure 4-10 Horizontal strains on abutment wall of bridge A] .7 using moving average
method

Peak strains in region 2 of bridge A1 .7 is shown in Figure 4—12. Peak strains in region
5 of bridge A21 is shown in Figure 4-13. In Figure 4-12 and Figure 4-13 “TK” indicates
the change of average temperature (°C) in the deck; “TA” means the change of average
temperature (°C) in the abutment wall. “Max Str” represents the maximum horizontal
strain in the region; sinrilarly; and “Min Str” represents the minimum horizontal strain in

the region.

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l'

 

lOl

Peak horizontal strain

Peak horizontal strain

 

 

 

 

l — -A — -TK*3e-5

   

 

 

 

 

Longitudinal movement of girder and (mm)

 

 

 

 

 

 

  

 

 

—Ar ~TA*3e-5
+ Max Str
‘3 Min Str
-2 I -2
0 2 4 6 8 1O 12
Month in 2007
Figure 4-12 Peak strains in region 2 of bridge A1 .7
—4
8" 1° . . ,4 . . 10.6 a
--A-~TK*3e-5 x” +GM 3:;
6- —-4 -TA*3e-5 ,1 z... _‘a.\ 04 g
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i “v / E
-4— \\ / I -0.6 E
r- \fwﬁ/ “tore
,- or
8 r L 1 r i 1 g
o 2 4 6 8 1o 12 "

Month in 2007

Figure 4-13 Peak strains in region 5 of bridge A21

102

It can be seen from Figure 4-12 that the girder end movement varies in an opposite
way to the change of average deck temperature. The trend is reasonable since the
expansion of the deck tends to push girders toward the abutment wall and vice versa. This
trend only exists for part of the regions, so there must be some other reasons, such as
pavement growth, that contribute to the longitudinal movement of girder ends. It can be
seen from Figure 4-13 that the maximum and minimum horizontal strains in the region
have their biggest change with the longitudinal movement of the girder ends. Only part of
the bridges showed this matched pattern between peak strains and longitudinal
movements of the girder ends. Some other bridges showed this matched pattern for a few
months, and others showed cases in which value changes in these two variables didn’t
match at all. Longitudinal movements of girder ends can explain part of the strains in the
abutment wall. No obvious relationship between temperature and horizontal strains in the

abutment wall could be observed.

4.5.3 Peak strain vs. time and temperature in spans between girders

The third approach to explore the ﬁeld instrumentation data was dividing the
instrumented abutment wall into spans between girders. These spans for the abutment
wall of bridge Al.7 are shown in Figure 4-14 as an example. The spans for the other
three bridges were divided in the same manner. The maximum and minimum horizontal
strains in each span were plotted together with the changes of average temperatures in the

decks and abutment walls.

103

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104

In some spans the variation of peak horizontal strains approximately matched the
change of transverse distances between girder ends, as shown in Figure 4-15. “SC” in the
ﬁgure represents the change of transverse distance between girder ends (unit: millimeter.)
In other cases, the match between variation trends was not so good. For a few bridges, the
transverse distance between girder ends varied with the change of average temperature in
the deck (Figure 4-16). However, contrary to the expectation, this trend was not true for
the majority of cases. Thus, no direct association between average temperature variation

and peak strain in the spans could be observed.

 

 

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l
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l - -A - - TK*3e-51 ?
+ Max Str l I

-€+ Min Str

Peak horizontal strain

 

 

 

 

O 2 4 6 8 10
Month in 2007

Change of transverse distance between girder ends

Figure 4-15 Peak strains in span 2 of bridge A2.1

105

 

 

 

 

 

   

 

 

 

 

 

 

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'1-5 I ‘ ‘ 1 l '-1.8
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Month in 2007 g
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Figure 4-16 Peak strains in span 3 of bridge Al .7

4.6 Evaluation of Potential Damage Causes
4.6.1 Pavement pressure

. Evidence A: comparison of different bridges

The conditions of two abutment walls of bridge B2.1 were found to be different from
each other signiﬁcantly during the ﬁeld inspections in the summer of 2006. The west
abutment was rated as “7” (see Figure 4-17 and [Burgueﬁo and Li 2008].) It can be seen
from Figure 4-17 that its approach ended by a “T” intersection nearby (Figure 4-18) and
that consequently little pavement pressure can be accumulated. The cast abutment was
rated as “3 or 4” (see Figure 4-19 and [Burgueﬁo and Li 2008].) Its approach extended to
a road (see Figure 4-20) and consequently very large pavement pressure can be generated

along the approach of the road.

106

 

Figure 4-17 West abutment of bridge B2.l

 

Figure 4-18 West approach pavement of bridge B2.1

107

 

Figure 4-20 East approach pavement of bridge 82.1

108

. Evidence B: investigation of different structural members of the same bridge

Bridge 82182291000S110 had distress in the abutment walls as shown in Figure 4—21.
The approach pavement of the bridge was concrete (Figure 4-22.) A large pavement
pressure could thus be accumulated. The pin-and-hanger assembly is in good working
condition (Figure 4-23) and thus only small forces can be transferred to the abutment wall

through longitudinal temperature effects on the bridge superstructure.

 

Figure 4-21 Abutment distress in bridge A1 .7

109

 

Figure 4—23 Pin-and-hanger assembly of bridge A1 .7

110

. Evidence C: Analyses of ﬁeld instrumentation

The analyses of ﬁeld instrumentation results (Section 4.5) indicate that the horizontal
strain in the bridge abutment wall is related to the longitudinal movements of the girders.
However, temperature effects can only explain these movements for some of bridges.
Thus, pavement pressure must be a high contributor to the longitudinal movement of the

girders together with temperature effects.

4.6.2 Transverse temperature effect

. Evidence A: In-site observation

Many of the vertical cracks in the abutment walls were consistently located in
between the girders (Figure 1-5). Furthermore, it was noticed from the ﬁeld
measurements that the vertical cracks occurred in the parts of abutment wall where no
control joint existed or the intervals between control joints were too long. These
observations mean that transverse temperature effect is a direct cause of those vertical

cracks located in between the girders.

. Evidence B: Field instrumentation

Analyses of ﬁeld instrumentation results indicated that the strains on the abutment
wall had a peak variation that approximately matches the change of transverse distance

between the girder ends.

111

4.6.3 Longitudinal temperature effect

Data from ﬁeld instrumentation support for longitudinal temperature ﬁelds as a
source of damage in the following ways:

. The outer face of the abutment wall and backwall in the vicinity of girder pull-
out was subjected to tension while that in the vicinity of girder inward movement
was subjected to compression.

. For some bridges, regions around girders showed that the girder end movement
varied opposite to the change of average deck temperature.

. Maximum and minimum horizontal strains in the region around girders changed

with the longitudinal movement of the girder ends for some cases.

4.7 Discussion

Field monitoring in this research focused on revealing the mechanisms behind the
development of structural damage. For this example research problem, four MDOT
highway bridges were instrumented during a one-year period. Two of them were
simple/cantilevered steel bridges; the other two were prestressed concrete bridges. They
were selected based on the result of statistical analyses of the NBI manual inspection
database in the State of Michigan and the ﬁeld inspection of forty-four bridges. All of the
instrumented bridges had features that were found to be common to bridges with
abutment damage. One steel bridge and one concrete bridge had poor abutment, the rest

two bridges had good abutments.

112

Variables measured for each bridge were deformations of the abutment wall and

backwall, longitudinal displacements of the girder ends, and temperatures on the bridge

deck and abutment wall. Analyses of the collected data can be summarized as follows:

On the abutment wall and backwall, concrete in the vicinity of girder pull-out
was subjected to tension and the concrete in the vicinity of girder inward
movement was subjected to compression.

Cracks and control joints in the abutment wall and backwall induced local peak
horizontal strains.

In some regions around girders, the girder end movement was found to vary
opposite to the change of average deck temperature. For the cases where this
trend didn’t exist, pavement pressure might play an important role in the girder
movement.

Maximum and minimum horizontal strains in the regions around girders changed
with the longitudinal movement of girder ends for some cases.

In some areas between girder spans the peak horizontal strains varied in the same
trend with the change of transverse distance between girder ends.

Some distances between adjacent girder ends varied in the same trend with the
change of the average temperature in the deck.

No direct association between average temperature variation and peak strain in

areas between girder spans could be observed.

113

5 FINITE ELEMENT SIMULATIONS

5.1 Introduction

Field monitoring was very helpful in recording the behavior of structures and
understanding mechanisms in the development of structural damage. Due to limitations
of funding, human resources, time, trafﬁc conditions, environmental conditions, etc., it
was difﬁcult for a ﬁeld monitoring program to cover a large number of structures and
thus create a database that is representative of major structures in the system. Simulation
of virtual structures using ﬁnite element analysis (FEA) on high performance computer
servers is relatively free ﬁ'om these limitations. Nonetheless, ﬁnite element simulations
also have disadvantages, such as the simpliﬁcation inherent in the modeling process and
that its results are not easily of the same type as what can be measured in the ﬁeld. Thus,
ﬁnite element simulation and ﬁeld monitoring should complement each other to evaluate

structural behavior and the mechanisms behind structural damage.

Finite element simulations served three principal purposes in this research: predicting
the effects of different assumed damage scenarios, performing parametric analyses to
investigate the behavior of structures with different design parameters, and creating a
virtual database for soft computing models. In the example problem, bridges of three
structural types were simulated: simple/cantilevered steel bridges, continuous steel
bridges, and prestressed concrete bridges with I-girders. The ﬁnite element program
ABAQUS 6.6.1 [ABAQUS 2006] was used in the simulations. The number of models
simulated for simple/cantilevered steel bridges, continuous steel bridges, and prestressed

concrete bridges were 450, 225, and 108, respectively. This chapter presents the major

114

steps and representative results of the ﬁnite element analyses for the example research
problem. More details on the ﬁnite element simulation studies can be found in the ﬁnal

research report for MDOT [Burgueﬁo and Li 2008].

5.2 Finite Element Simulation Strategy

Highway bridges are complicated 3-dimensiona1 structures. The effects of damage
scenarios, such as temperature ﬁeld, are also phenomena in 3-dimensional spaces. Thus,
three-dimensional ﬁnite element models were developed in this research to simulate the
behaviors of bridge structures under different damage scenarios. The elements and mesh
details used in the FE simulations are summarized in Table 5-1. The material properties

used in the FEA models are given in Table 5-2.

The girders are critical members for the ﬁnite element models in this research
because they directly connect to the bridge abutment wall. All forces from superstructure
needed to be transferred to the substructure through the girders. Geometrically, girders
could be modeled using 3-dimensional beam elements since its length is much larger than
cross-sectional dimensions. In this research, shear lag and cross-sectional deformation of
the girders are very important for correct simulation of forces transformed to the
abutment wall. However, a 3-dimentiona1 beam element can not simulate these two
phenomena. Thus, shell elements were used to simulate the steel girders and solid
elements were used to simulate the concrete girders. The abutment walls are members
from which the response variables were extracted and thus the foci of the ﬁnite element
analyses. They were simulated using solid elements to model the bending and shear

behavior under different damage scenarios.

115

Table 5-1 Element details used to simulate the structural members

 

 

Average
Structural Material Element type element Geometry
member . (mm)
srze (mm)
S4R: 4-node doubly curved thin
or thick shell, with reduced 229
Slab Concrete integration, hourglass control, and 508 (thickness)
ﬁnite membrane strains.
S4R: 4-node doubly curved thin
Girder top Steel or thick shell, with reduced 127 19
ﬂange integration, hourglass control, and (thickness)
ﬁnite membrane strains.
84R: 4-node doubly curved thin
. or thick shell, with reduced 13
Girder web Steel integration, hourglass control, and 127 (thickness)
ﬁnite membrane strains.
S4R: 4-node doubly curved
Girder bottom Steel thin or thick shell, with reduced 127 22
ﬂange integration, hourglass control, (thickness)
and ﬁnite membrane strains.
S4R: 4-node doubly curved
thin or thick shell, with reduced 610
Backwall Concrete integration, hourglass control, 127 (thickness)
and ﬁnite membrane strains.
. . 762
Abutment wall Concrete C3 D8: 8-node11near brick 127 .
(thickness)
. B31: 2-node linear beam in 1067 (width)
Pier cap Concrete space 153 991 (height)
. . u. . . ,, height of web 229 (width)
Link plate steel Sprrngs. pornt to pomt minus 203 13
spring element mm (thickness)
Prestressed
concrete I Prestressed C3D8: 8-node linear brick 127 Ewe IR]?
girder concrete ype

 

* Refer to prestressed concrete I—beam details in [MDOT 1999].

116

Table 5-2 Material properties

 

 

Material Modulus of Poisson's Coefﬁcient of thermal
elasticity E (GPa) ratio expansion (l/°C)
Concrete 24 0.2 11.7><10*S
Presuessed 33.9 0.2 11.7><10'6
concrete
Steel 200 0.3 11.7><10'6

 

5.2.1 Steel bridges

A two-span simple/cantilevered steel bridge was used as an example to describe the
models. The geometry of the bridge was the combination of the ﬁrst values of each of the
design variables in Table 5-3. The plan and side views of the bridge are shown in Figure

5-1 and Figure 5-2, respectively.

 

 

 

 

 

 

 

% 24380 .2
F—nzso—‘I [F910 12190
If.#I’EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEéﬁEEEEEEEEEEEEEEEEEEEEEEEEEEEEEI}... I
I IEXPaDSiOD bearing ' I IExpansion bearing Fixed bearing E I §
I: l l (\I
l
l
l
l
l
I I
I 1
l

 

 

 

Figure 5-1 Bridge plan (unit: mm)

117

 

 

 

 

 

 

 

 

 

 

 

r
11 Deck slab
Dependent i j
Backwall —— I . ..
_. 610 I ._ Steel girder a
Bearing \_h I I!
I -
1- I
Connection
O
8

Bolt

~— 760 —«—~

Abutment
wall

     

 

 

 

Slope 1:2

 

 

Figure 5-2 Bridge side view (unit: mm)

Three-dimensional ﬁnite element (FE) models (see Figure 5-3) were built using the
general-purpose ﬁnite element program ABAQUS 6.6.1 [ABAQUS 2006] with an
attempt to simulate the behavior of different bridges under possible damage-inducing
demands. The concrete deck and the backwall were modeled by shell elements, and the
cross frames were modeled by beam elements (Figure 5-4). The girders were modeled
based on a baseline design provided by the MDOT. For steel bridges, the ﬂanges and

webs were modeled using shell elements.

118

 

Figure 5-3 Bridge Model

Girder ﬂange overlapped with concrete slab \

\\ /
\ /
l \ \ / / Slab
/ / / \ \ (Shell elements)
/ \
/ \
— *— — — — — Steel Girder
Stiffener (beam elements) overlapped Cross frame (Shell elements)
with girder web (shell elements) (Truss elements)

Figure 5—4 Modeling details of one transverse span of bridge

The abutment walls were simulated by eight-node linear solid elements (Figure 5-5).
The height of the abutment wall was taken to be 2.6 m. The girders were tied to the
backwall by the web end and constrained to the top of the abutment wall by a single point
(the center node of the bottom ﬂange). The pin-and-hanger assembly was simulated by a
“point to point” spring element (Figure 5-6 and Figure 5-7). The spring element only has
stiffness in the direction of the two linked points, so the girders connected by it can move
or rotate freely in other directions. The stifﬁiess of the spring element was taken to be the
elastic modulus of the steel times cross-sectional area of two link-plates. The cross

section of two vertical plates in the cross frame was taken to be 89.2mm X 10.2 mm to

119

simulate the stiffeners. A standard shape L 4X4><5/ 16 deﬁned by the Steel Construction

Manual (AISC 2006) was used for other members of the cross ﬁ'ame.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Node of
girder
connected
with
abutment
wall
(SOhd K Girder web
elements) (Shell elements)
The region ﬁom which
to extract the
maximum horizontal
Vertical strain along transverse
and direction
longitudinal
displacement . _
ﬁxed Vertrcal displacement
ﬁxed

 

 

 

 

 

 

 

 

 

 

Figure 5-5 Modeling of back wall and abutment wall

Girder ﬂange connected
with concrete slab

Girder web
(Shell elements)

 

Pin and Hanger
(Spring Connection)

Figure 5-6 Modeling of pin-and-hanger assembly

120

I ~I i ‘1 .....
_ I ............

Figure 5-7 Pin-and-hanger detail in model built in ABAQUS

5.2.2 Concrete bridges

The concrete compression strength for the prestressed concrete bridges was assumed
to be 48 MPa. The unit weight of concrete was taken as 2355 kg/m3. The modulus of
elasticity for the prestressed concrete I-girder can be estimated by equation (5-1)
[AASHTO 2007]. Eight node linear solid elements were used to model the prestressed

concrete I-girder. A typical mesh of a prestressed concrete I—girder is shown in Figure 5-8.

A prestressed concrete bridge model is shown in Figure 5-9.

E. = 0-043wl'5I/7; = 33900MPa = 33.9GPa (5-1)

121

   

 

~
“22
a

s
\
a
~

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if“

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IV" ‘
If?”

$
a“

\

:0» '
a“
JI"

%

41,00 1
I i
11"“

  

61'

Figure 5-8 Mesh of prestressed concrete I gird

“u.
u

.I...
I.“...,::“

h

if?“

:“mumn

If
mm

In II“‘\‘\‘
'

1
“§

 

Figure 5-9 Prestressed concrete bridge model

122

5.2.3 Boundary conditions

The vertical displacements at the bottom of the abutment walls and pier cap were set
to be zero. The horizontal boundary condition at the bottom surface of the abutment wall

is shown in Figure 5-10. The boundary condition at the pier cap is shown in Figure 5-1 1.

Bottom surface of the abutment wall u = 0

 
   
   

OOOOOOOOO‘OIOOOOOOOOQII
O O. O

 

v (longitudinal
A direction) v = 0

u (transverse

direction)
:—-—

 

 

Figure 5-10 Boundary condition at the bottom surface of the abutment wall

v (longitudinal
4 direction) u = 0

u (transverse

direction)
*-

 

 

Figure 5-11 Boundary condition at the pier cap

123

5.3 Case Matrices and Analytical Models

Case matrices for FE simulations were deﬁned for three types of superstructures
representative of MDOT highway bridges. The bridge models covered the most frequent
range of the primary design parameters. The simulation cases were ﬁrrther reﬁned in the
range of the parameters within which the bridges were more susceptible to abutment

distress according to the results of statistical analyses.

5.3.1 Simple/cantilevered steel bridge

For simple/cantilevered steel bridges, the simulation cases were the combination of
the values in the last column of Table 5-3. Seventy-ﬁve structural models were created.
The damage scenarios were pavement pressure, summer temperature increase and
gradient, and winter temperature drop and gradient. The conditions of a pin-and-hanger
assembly in good condition and the rusted (locked) pin-and-hanger assembly were
simulated under each damage scenario. Thus, there were six simulations for each
geometric bridge model and 450 simulations for this structural type. The analytical
diagram for the simple/cantilevered steel bridge model depicting the assumed boundary

conditions is shown in Figure 5-12.

5.3.2 Continuous steel bridge

For continuous steel bridges, the simulation cases were the combination of the values
in the last column of Table 5-4. The pin-and-hanger assembly were modeled as “new” for
pavement pressure and modeled as “rusted” (locked) for the temperature effects. Seventy-
ﬁve structural models and 225 simulations were done for this structural type. The

analytical diagram for continuous steel bridges is shown in Figure 5-13.

124

Table 5-3 F EA case matrix for simple/cantilevered steel bridges

 

 

 

Desi arameters Most frequent Features indicate Values taken in the
gn p interval potential distress simulation
number of spans <=4 >=2 and <=4 [2]
Maximum 3 an (m) >=12.2 and >=24.4 and [12.2, 24.4, 30.5,
p <=36.6 <=42.7 36.6, 42.7]
deck width (m) >=6.1 and <=30.5 >i18'3 and [13.0, 17.9, 22.7]
<—24.4
skew (degree) <= 60 <= 60 [0, 15, 30, 45, 60]
WW

 

O ' 9
2:; 2:.
/ / / / /7777/

Figure 5-12 Diagram for simple/cantilevered steel bridges with 2 spans (unit: m)

Table 5-4 F EA case matrix continuous steel bridges

 

 

 

 

Desi ararneters Most frequent Features indicate Values taken in the
gn p interval potential distress simulation
number of spans <=4 >=4 and <=7 [4]
. : = = = [30.5, 36.6, 42.7,
maxrmum span (m) > 12.2 and < 36.6 > 30.5 and < 54.9 48.8, 54.9]
deck width (m) >=6.1 and <=36.6 >=9.1 and <=18.3 [13.0, 15.4, 17.9]
Skew (degree) <= 60 0 [0, 15, 30, 45, 60]
W76 W76
Q, T Q Q Q U :3.

Figure 5-13 Diagram for continuous steel bridges with 4 spans (unit: mm)

125

5.3.3 Prestressed concrete bridge

All of the prestressed concrete bridges with I-girders inspected in the summer of 2006
were simple supported. Thus, the number of spans in the case matrix was taken to be one,
as shown in Table 5-5. The damage scenarios were pavement pressure, summer
temperature increase and gradient, and winter temperature drop and gradient. Thirty-six

structural models and 108 simulations were done for this structural type.

Table 5-5 FEA case matrix for prestressed concrete bridges

 

 

Desi arameters Most ﬁequent Features indicate Values taken in the
gn p interval potential distress simulation
number of spans <=4 >=2 and <=4 [1]
. >=12.2 and >= 18.3 and <=
Maxrmum span (m) (=3 6. 6 30.5 [18.3, 24.4, 30.5]
. >= 6.1 and <= >= 18.3 and
deck wrdth (m) 30.5 <=21.3 [13.0, 17.9, 20.3]
skew (degree) <= 60 >= 0 and <= 45 [0, 15, 30, 45]

 

5.4 Damage scenarios

After evaluating possible damage scenarios and the feasibility of simulating them
through F EA, three scenarios were simulated: pavement growth, temperature ﬁeld during

summer, and temperature ﬁeld during winter.

5.4.1 Pavement grth

While pavement growth is a physical phenomenon that seems to be well accepted, a
quantiﬁable measure of the pressure generated by pavement grth is an elusive issue.

Richards [1979] conducted ﬁeld testing to determine the stresses in concrete pavements

126

and instrumented six sites (three of them adjacent to a bridge). A stress level of 7 MPa
was observed. Burke [1998, 2004] estimated the pavement pressure to be greater than 7
MPa. Shober [1997] estimated the pavement pressure to be 7-14 MPa. Richards and
Burke did their studies in Ohio, while Shober performed his evaluation in Wisconsin.
Since both states neighbor Michigan and have similar climatic conditions, it was
reasonable to assume that the pavements of Michigan may behave in a similar manner.
Thus, their results provide a valuable reference in deﬁning a magnitude for the pressure
due to pavement growth. Based on the noted research studies, the pavement growth

pressure was set at 7 MP3 for these simulations.

5.4.2 Temperature ﬁeld

Two other damage scenarios simulated in the FEA were temperature ﬁelds in the
summer and winter seasons. The temperature variation speciﬁed in the AASHTO LRFD
Bridge Design Speciﬁcations [AASHTO 2007] is a piecewise linear temperature proﬁle.
Use of this proﬁle in the simulation is too complicated especially considering the large
number of models needed to be simulated. After evaluating different simpliﬁcation
approaches, a linear temperature gradient through the bridge deck. was found to be a good

approximation to the piecewise linear temperature ﬁeld.
5.4.2.1 Temperature variation

Temperature ranges for bridge design purposes are given in the AASHTO LRFD
Bridge Design Speciﬁcations [AASHTO 2007]. Data from this source is reproduced in

Table 5-6. Here, the temperature range was taken to be -34.4 to 48.9 °C for steel bridges

and -l7.8 to 37.8 °C for concrete bridges.

127

Table 5-6 Temperature Ranges (Part of Table 3.12.2.1-1 of AASHTO Speciﬁcation)

 

CLIMATE STEEL OR ALUMINUM (° C) CONCRETE (° C)

 

Cold -34.4 to 48.9 -l7.8 to 37.8

 

The temperature gradient deﬁned by the AASHTO LRFD Bridge Design
Speciﬁcations [2007] is reprodqu in Figure 5-14. In Michigan, T1, T2 and T3 can be
taken to be 5.0 °C, -11.7 °C, and -17.8 °C, respectively for concrete pavement surfaces.

The value of “A” is taken to be 305 mm.

 

 

 

 

 

 

3
i All
E I / T2 §

I. g < / l
g *5 j— l Steel Girder
*g. g i_ I Structures Only
Q m m I

a N.

 

 

1

Figure 5-14 Positive vertical temperature gradient in concrete and steel structures (units:
mm, Figure 3.12.3-2 of AASHTO Speciﬁcation)

5.4.2.2 Simpliﬁcation approach

The temperature distribution in the deck was simpliﬁed as linear, and the temperature
ﬁeld in other parts of the bridge was simpliﬁed as constant. Thus, the temperature
gradient for steel bridges in Figure 5-14 was transformed to the simpliﬁed gradient

shown in Figure 5-15 by equating the areas under the temperature curves for both ﬁgures.

128

Similarly, the temperature gradient for concrete bridges in Figure 5-14 was transformed

to the simpliﬁed gradient shown in Figure 5-16. The temperature values for the

simulations are summarized in Table 5-7.

 

 

 

 

 

 

 

a) ‘ T1: 5.0 0C

H I

g a
g T T2= -11.7 °C or
i
3 Average

“-4 ::>-
o

5

8 _ 0

Q T6 — -14.2 C

T4 = -3.10C

l/

Deck

 

 

 

—.1 T5 = -14.2 0C

Figure 5-15 Simpliﬁcation of temperature gradient for steel bridges (unit: mm)

 

 

 

 

 

 

 

 

 

 

 

N
O
E * T1=5.O C i T4=O.1 C
o 8}
g In I T.=-11.7°C N
a i
m I—‘ Average
‘5 : Deck
it
5 T3=-17.8°C . T5=-17.4°C

Figure 5-16 Simpliﬁcation of temperature gradient for concrete bridges (unit: mm)

129

Table 5-7 Temperature values for linear temperature gradient in the deck

 

 

Structures (Members) conifc‘g‘)‘: tron Winter (°C) Summer (°C)
Top of the deck 15.6 -38.8 63.6
Steel Bridge
Other members 15.6 -35.5 52.4
Top of the deck 15.6 -23.2 44.6
Concrete
Bndge Other members 15.6 -179 27.0

 

5.5 Result Variables

Two responses were extracted ﬁom each simulation: the largest value of the
maximum principal stress along the top of the abutment wall and the maximum
horizontal strain from the elements in the ﬁ'ont top corner of the abutment wall (Figure
5-5). Contour images of the principal tensile stresses on the abutment wall are shown in
Figure 5-17. The location of the extracted maximum principal stress is the point where
the girder is connected to the abutment wall (Figure 5-5). At this location, the model
results are mesh sensitive. Thus, the maximum horizontal strain from the elements in the

front top comer of the abutment wall was also extracted (Figure 5-5).

5.6 Result Interpretation and Parametric Analyses

Results from the FE simulations were plotted using skew angle as abscissa and result
variables as ordinate. Most of the maximum principal stresses exceeded the tensile
strength of the concrete by a large margin because the analyses assumed a linear elastic
response. Extreme assumptions in the modeling process also contributed to the large

stress values. For example, the pin-and-hanger assembly could still allow some

130

movement even though they were rusted, and the abutment wall could have slightly
displacement and rotation. Also, the simulated damage-causing loads are conservatively
high. Thus, interpretation focused on the variation trends of the resultant variables to the

change of design parameters and damage scenarios.

 

 

 

 

 

423.;
(a) Top view of the abutment wall (b) Ampliﬁed view

Figure 5-17 Principal tensile stresses in the abutment wall

5.6.1 Simple/cantilevered steel bridges

Figure 5-18 shows the distribution of maximum principal strain in a
simple/cantilevered steel bridge model. The corresponding damage load is pavement
pressure applied at the cross section of the deck on the left side of the bridge. It can be

seen that the principal strains in the girders are largest at the region around the connection

131

points to the abutment wall (on the left). This indicates large forces transmitted to the

abutment wall through bridge girder and connection bolts.

 

Figure 5-18 Maximum principal strain in a simple/cantilevered steel bridge model

Figure 5-19 shows the distribution of maximum principal strains on the face of the
abutment wall. As expected, the positions of peak values are the connection points
between the girder and the abutment wall. Comparing with Figure 1-4, the shape of strain
contours are very similar to the shape of concrete spalling in the bridge abutment wall.
The distribution of horizontal strain at a level 0.305 m bellow the top of bridge abutment
wall is shown in Figure 5-20. The abscissa is the distance from leﬁ end of the abutment
wall in meters; the ordinate is the horizontal strain. It can be observed that the horizontal
strain reaches peak values at the positions where the girders connected with the abutment
wall. This is to be expected as these are the locations of force transfer between these two

elements.

132

 

 

 

 

 

.1
‘ '-
Hu—A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5-19 Maximum principal strain on the surface of the abutment wall

 

0.00004

0.00002:

Horizontal strain

\

rlerlrl

0 5.1 10.2
Distance from the left end of the abutment wall (111)

-0.00002!

 

 

 

 

 

Figure 5-20 Horizontal strain at a level 0.305 m below the top of the abutment wall

For bridges subjected to pavement pressure, as shown in Figure 5-21, the maximum
stress increases signiﬁcantly with the increase of the skew angle. The maximum
horizontal strain does not change much when the skew angle is between 0 and 30 degrees

and increases signiﬁcantly when the skew angle is larger than 30 degrees (Figure 5-22.)

133

300 r

 

--G--Span12.2 m
_ —B Span 24.4 m
_.,L Span 30.5 m
——*— Span 36.6 m
i + Span 42.7 m

N
U1
0

N
O
O

 

 

 

 

Maximum principal stress (Mpa)

 

l J

00 10 20 30 40 50 60
Skew angle (Degree)

Figure 5-21 Maximum stress of bridges under pavement pressure (with free moving pin-
and-hanger assembly, width = 17.8 m)

.4

x10

--G--Span12.2 m
12” —8 Span 24.4 m
11_ -—v Span 30.5 m
“ﬁe—Span 36.6 m
10- +Span 42.7 m

 

 

 

 

Maximum horizontal strain

CD‘ICDCD

 

 

50 10 20 30 40 50 60
Skew angle (Degree)

Figure 5-22 Maximum horizontal strain for bridges under pavement pressure (with free
moving pin-and-hanger assembly, width = 17.8 m)

134

Bridges analyzed in Figure 5-21 and Figure 5-22 have free moving pin-and-hanger
assembly. For comparison, analyses of same bridges with locked pin-and-hanger
assembly are shown in Figure 5-23 and Figure 5-24. It can be observed that bridges with
locked pin-and-hanger assembly have less demand on the abutment walls. For these
bridges, a portion of pavement pressure can be transferred to girders in the adjacent span
through locked pin-and-hanger. Thus, the locking of pin-and-hanger assemblies due to
corrosion may actually alleviate the maximum demands on the wall. Span length and

width of the bridge didn’t have a signiﬁcant effect on the maximum wall demands.

 

 

 

 

 

 

 

160 —
A --G--Span12.2m
3140— —B Span24.4m
g —F Span 30.5 m //,’
3 120 —*—Span 36.6 m ’
g. —&— Span 42.7 m
To 100 -
.9
O
E 80 —
Q _
E
3 _
g 60
X
‘2“ 40»

2 1 r 1 1 1 1
0 10 20 30 40 50 60

Skew angle (Degree)

Figure 5-23 Maximum stress of bridges under pavement pressure (with locked pin-and-
hanger assembly, width = 17 .8 m)

For demands due to summer temperatures, the locking of pin-and-hanger assembly
has a signiﬁcant effect on the maximum stresses on the abutment wall, as shown in
Figure 5-25 and Figure 5-26. The maximum stresses in the abutment wall for bridges

with a locked pin-and-hanger were much larger than when the assembly is working

135

properly. When the pin-and-hanger is locked, both skew angle and span length have a
signiﬁcant inﬂuence on the maximum stress. Longer bridges and bridges with larger
skew angles are subjected to larger stresses. The maximum horizontal strain demands
follow similar trends. Horizontal strains increased with an increase of skew angle and
span length. They also increased slightly with the increase of bridge width. Finally, result
show that a locked of pin-and-hanger only increases the maximum horizontal strain by a
moderate amount. Comparison of Figure 5-25 and Figure 5-26 also proved that when pin-
and-hanger assemblies are locked, the temperature effects could be a signiﬁcant

contributor to the damage in the abutment wall.

 

7x104
--e--Span12.2 m
6-5- A} Span 24.4 m

  
   
  
  
  
  
 
   

—v Span 30.5 m
-—*— Span 36.6 m
_ —£~— Span 42.7 m

0)

 

 

S”
or

 

:‘i‘
or

A

Maximum horizontal strain
01

 

9°
01

l l J

0 10 210 310 40 50 60
Skew angle (Degree)

Figure 5—24 Maximum horizontal strain for bridges under pavement pressure (with
locked pin-and-hanger assembly, width = 17.8 m)

136

10¢

 

--G-Span12.2 m
~43 Span 24.4 m
8’ —V Span 30.5 m
+Span 36.6 m
+ Span 42.7 m

 

 

 

 

Maximum principal stress (Mpa)

 

 

 

0 1 0 20 30 40 50 60
Skew angle (Degree)
Figure 5-25 Maximum stress of bridges in summer (with ﬁee moving pin-and-hanger,
width = 22.7 m)
120 -
--G--Span12.2 m
—v Span 30.5 m

~—a— Span 36.6 m
80 i —e— Span 42.7 m

 

 

 

 

 

 

Maximum principal stress (Mpa)

 

 

0 110 210 50 410 50 60
Skew angle (Degree)

Figure 5-26 Maximum stress of bridges in summer (with locked pin-and-hanger, width =
22.7 m)

137

For bridges subjected to winter temperature variations, the trends of maximum
stresses developed in the abutment wall are similar to those in summer, except that the
values are negative. As shown in Figure 5-27 and Figure 5-28, when pin-and-hangers are
in proper working condition, the inﬂuence of design parameters to maximum horizontal
strains is trivial. When the pin-and-hangers are locked, bridges with longer spans tend to

have less horizontal compressive strain in the abutment wall.

 

 

 

 

 

 

 

 

.4
43.0055 10
--G-Span12.2 m
C 4501* —e Span 24.4 m /
'5 —-v Span 30.5 m a —
Z) 6015 -—*—Span 36.6 m /
g -6.02 _ +Span 42.7 m
.E
g-6.025~ /-/_v\\\‘
E \ v—~ _ ~
-6.03- - e
g 3" "‘ ’€\ \ v
a? 43.03 ,I, \S _ __ .8
E x”” ,0
-6.04 - ,-
.0 -
-6.045 1 1 1 1 J ,
0 10 20 30 40 50 6O
Skew angle (Degree)

Figure 5-27 Maximum horizontal strain of bridges in winter (with ﬁee moving pin-and-
hanger, with = 22.7 m)

138

3(10‘

 

 

 

 

-2
is --G-Span12.2m
: -2.5~ —Er Span 24.4m
'5 W“ —V Span 30.5m
:5 -3- —*—Span 36.6m
*2 I, -A:Span 42.7m ’ /,
S-3.5— ‘\1\~\ /,/
-: ‘ \ v _____ v
o /B
E \ \ \a —— —- -—Et
.2 .5. '0
«1 c9 ________ ,----'
2 ——~e __________ O _________ {I ,
-5-
'5.5 l 1 L 1

 

 

0 10 20 30 40 50 60
Skew angle (Degree)

Figure 5-28 Maximum horizontal strain of bridges in winter (with locked pin—and-hanger,
width = 22.7 m)

Comparing the effects of the three damage scenarios, the stresses generated by the
pavement pressure were larger than those generated by the winter temperature ﬁeld and
the summer temperature ﬁeld in that order. As mentioned at the beginning of Section 5.6,
the absolute value of the resulting variables deviate from reality by a large margin due to
the assumption of linear elastic response. Thus, the observation on the relative
magnitudes of response caused by different damage scenarios should only be used as a

reference.

5.6.2 Continuous steel bridges

The results of the ﬁnite element simulation for continuous steel bridges are
summarized in this section. Plots and more details can be found in the ﬁnal report to the

research sponsor, MDOT [Burguefio and Li 2008].

139

For bridges with good pin-and-hanger assemblies subjected to pavement pressure,
stresses in the abutment wall increased signiﬁcantly with an increase of the skew angle.
They also increased slightly with the increase of the deck width. The effect of span length
on the abutment wall demand was trivial. For bridges under summer temperature load
with locked pin-and-hanger, maximum abutment stresses increased with skew angle. The
bridge width had trivial inﬂuence on the abutment wall demands. Generally, demands on
the abutment wall increased with span length. For bridges under winter temperature
loading with locked pin-and—hanger assemblies, variation trends for maximtun demands
were similar to those under summer temperature loads, although the magnitude of the

horizontal strain was much smaller.

Comparing the effects of three damage scenarios, the maximum stresses generated by
the pavement pressure were larger than those generated by summer and winter
temperature effects. As mentioned before, these comparisons of magnitudes of response

variables can only serve as a reference.

5.6.3 Prestressed concrete bridges

The results of the ﬁnite element simulation for prestressed concrete bridges are
summarized in this section. Plots and more details can be found in the ﬁnal report to the

research sponsor, MDOT [Burgueﬁo and Li 2008].

For bridges under pavement pressure, maximum stress in the abutment wall increased
with skew angle. When the skew angle was less than 30°, the effect of skew on the
maximum horizontal strain was trivial. When the skew angle was larger than 30°, the

maximum horizontal strain increased signiﬁcantly with the increase of skew angle. The

140

effects of span length and bridge width on the demands in the abutment walls were trivial.
For bridges under summer temperature ﬁelds, the maximum principal stress and
maximum horizontal strains increased with an increase in skew angle when up to a value
of 30 degrees. In general, demands on the abutment wall increased slightly with the
increase of span length. The effect of bridge width was trivial. The variation trends of
abutment wall demands due to winter temperature loads were similar to those due to

summer temperatures.

Since the bearing condition on one side of the bridge was pin connected and the other
side allowing horizontal movement, the demands induced by pavement growth were

much larger than those induced by temperature effects.

5.7 Discussion

The behaviors of highway bridges with three different structural types were simulated
using ﬁnite element analyses. The structural types were: simple/cantilevered steel bridges,
continuous steel bridges, and prestressed concrete bridges with I-girders. Each of these
bridge systems was evaluated under three damage scenarios: pavement growth, summer
temperature ﬁeld, and winter temperature ﬁeld. Four hundred and ﬁfty
simple/cantilevered steel bridges, 225 continuous steel bridges, and 108 prestressed
concrete bridges were analyzed. A virtual database was created using these FE
simulations and will be ﬁrrther exploited in the development of prediction models for
structural damage in Section 7.5. It was observed through the FE simulations that:

0 Stress demands in the abutment wall increased with an increase of skew angle.

This pattern is more pronounced when the skew angle is larger than 30 degrees.

141

o For bridges under pavement pressure, the effect of span length is trivial. When
considering summer or winter temperature ﬁelds, the effect of span length is
moderate.

0 Generally, the effect of bridge width to the stress demands in the abutment wall

is trivial.

142

6 SOFT COMPUTING

6.1 Introduction

The discussion in Chapter 1 presented how the mechanism behind the development of
structural damage is highly complicated. The deﬁciencies in an SISD make the work in
developing damage prediction models even more difﬁcult. In order to overcome the
complexity and difﬁculties in the problem, soft computing was used as the main approach

to develop predictive tools for the current research problem.

Soft computing is a collection of methodologies that permits the creation of
prediction models by learning from data and mimicking human intelligence [Kecman
2001]. In comparison with hard computing (which is based on precise, deﬁnite, and
rigorous data,) soft computing utilizes a tolerance for imprecise, uncertain, incomplete,
and subjective data. The three principal types of soft computing are: neural networks,

fuzzy logic and probabilistic reasoning [Zadeh 1994, Mathworks 2007b].

An artiﬁcial neural network is a network composed of one or more layers of
computing units connected by synaptic weights. It can “learn” knowledge from the
environment (data) and store the learned knowledge in synaptic weights for future use,
such as a prediction [Aleksander and Morton 1990]. An ANN has a high capacity for
nonlinear input-output mapping and is robust to faulty, incomplete or imprecise data. The
application of four types of neural networks: multilayer perceptrons (MLP), radial basis
function (RBF), support vector machine (SVM), and supervised self-organizing map
(SSOM) were evaluated for the problem in this research. Considering the subjectivity in

manual inspections, a fuzzy neural network (FNN) was developed to combine the

143

advantages of fuzzy logic and artiﬁcial neural networks and overcome the difﬁculties in

the SISD.

6.2 Multilayer Perceptron Network

A multilayer perceptron (MLP) model is a network composed of several layers of
neurons. Each neuron is a computation unit, which, given an input value, calculates an
output value through an activation function. The multilayer perceptron model is then
composed of neurons assumed to be organized in layers, each consisting of one or more
neurons. An input vector enters the MLP through an input layer, which is followed by
one or several hidden layers. The computation result is given through an output layer.
The output of the previous layer contributes to the input of the next layer after being

modiﬁed by synaptic weights. A typical structure of an MLP ANN is shown in Figure 6-1.

The data set for developing an MLP model can be divided into two subsets: training
data and test data. Training data are used in training of an MLP. Test data are used in
evaluating the performance of the MLP. The relationship between input variables and
output variables is stored in synaptic weights after training, such that a trained network
can predict the output values from novel inputs. The training process consists of a series
of iterations (epochs) In each epoch, input vectors enter the MLP through input layer and
information ﬂows to the output layer in a forward manner. Then, synaptic weights are
updated using a back propagation algorithm, which minimizes the sum of the squares of
the error computed at the output layer (comparing the computed output to actual known

data). Thus, the back propagation algorithm seeks global optimization of the network

144

[Haykin, 1999]. After the training process, an MLP can predict the output values given

novel input vectors, which is called a generalization process.

If designed for the prediction of damage in bridge abutments, as shown in Figure 6-1,
the input layer with p neurons would input p bridge design and service parameters and
the output layer would have k neurons to represent k condition levels of the bridge

abutment. Two hidden layers are shown in the model schematic of Figure 6-1.

Structural Synaptic Activation Structural
parameters weight function Condition

 

 

 

Input layer Two hidden layers Output layer
(p neurons) (n neurons each layer) (r neurons)

Figure 6-1 Diagram of MLP

A commonly used nonlinear activation function for individual neuron is the sigmoid

function, as shown in equation (6-1) and Figure 6-2:

1
V001) = (00001)) = _,,,I(,,, (64)
1+ 6 '

 

145

where v0(n) is the output value of a neuron in nth training iteration; v,-(n) is the input
value of a neuron in nth training iteration; and a is a constant that modiﬁes the shape of

the sigmoid curve. The value of vi(n) can be calculated using equation (6-2):

vI(n) = z ijxJ. + bI (6-2)
j=1

where m is the number of neurons in the previous layer, w”, wig, , w,-,,, are synaptic
weights connect the neuron with neurons in previous layers, x 1, x2, ..., xm are inputs

applied to the neuron (which are outputs of the neurons in the previous layer,) and b,- is a

bias applied to the neuron.

 

 

0.8~ -

0.6 r -

9(V)

0.4- .

0.2 ~ .

 

 

 

 

Figure 6-2 Sigmoid activation function (a = 1)

The error at the ith output neuron, e,-(n), after the nth iteration is calculated using equation

(6-3):

146

91°07) = d; _ yi(n) (6'3)

where d,- is the target value for the neuron and yI-(n) is the output of the neuron after nth

iteration. The sums of squares of the error at the output layer after the nth iteration can be

calculated using equation (6-4):
_ i Z 2 (6-4)
501) — 2 6,. (n)
i=1

After the nth iteration, the weights of a network are adjusted in a back propagation
process according to equation (6-5); where wy-(n) and w,~j(n+1) are the jth weights in the
ith layer in the nth and (n+1 )th iterations, respectively; and n is the learning rate of the

network [Ramuhalli 2005].

68(n)
8w

wIJ.(n+l)= wij(n)-77 (6'5)

Several factors are important for good generalization of an MLP network:

Architecture of the network, such as the number of hidden layers (m), and the
number of neurons in each hidden layer (n).

0 Selection of input variables and preprocessing of the input data.

. Network parameters. A set of important MLP parameters are listed in Table 6-1.
0 Danger of overﬁtting, which refers to a phenomenon that the MLP learns too

much from the training data and memorizes them. When this happens, the MLP

147

extracts the speciﬁc feature (which might be noises) of the training data instead

of the underlying input-output relationship of the problem.

Table 6-1 Parameters of MLP

 

Parameter Description

 

Activation function of A function through which the input value to a neuron is
neurons (40) transferred to a output value.

Changing rate of synaptic weights and biases during the back

Learrrrng rate ('7) propagation process in the training of an MLP.

Number of calculation cycles including presenting the
Number of epochs in training vector to the network in a feed forward manner and

training (ne) calculating the new weights and biases in a back propagation
process.

Mean square error Average squared error between the network outputs and the

(me) target outputs at the output layer of a neural network.

 

It has been proved that an MLP network with one hidden layer and any continuous
sigrnoidal nonlinear activation function for hidden nodes can approximate arbitrary
decision regions [Cybenko 1989, Homik et al. 1989, 1990, White 1990]. Theoretically,
only MLP networks with one hidden layer need to be used. However, it might be difﬁcult
to obtain the optimal scenario for the MLP with one hidden layer to approximate the
complicated nonlinear input-output relationship. So MLPs with one, two, and three layers

of hidden neurons were applied in searching for an optimal network structure.

Overﬁtting should be avoided because the paramount goal of a prediction model is to
make predictions for novel data instead of training data. In order to avoid overﬁtting and,
thus, improve the prediction power of the network, the number of epochs (71.) during

training shall not be too large and the mean square error (mse) to stop the training process

148

shall not be too low. The speciﬁc values for maximum n. and me should be set

considering the characteristics of the problem.

The Matlab® neural network toolbox [Mathworks 20070] was used to develop the
MLP ANN models. Matlab built in functions (newfj: Sim, etc.) were used for training and
testing of the networks. Custom programs were developed for setup of the neural

networks and preparation of the training and testing data.

6.3 Radial Basis Function Network

The radial basis function network is based on the basic idea of curve ﬁtting, which is
searching for a hyper surface in a multidimensional space that best ﬁts the training data.
The hyper surface is composed of the combination of a set of basis functions, as shown in
equation (6-6). In equation (6-6), F (x) is the target function, w,- is the weight for ith basis
function, and (o is a basis function [Haykin 1999]. Gaussian functions are commonly used
basis function for RBFs and were thus used in this research as shown in equation (6-7),
where a is the width of the basis function. Figure 6-3 shows a Gaussian ﬁrnction in a two-
dimensional space. The parameters of the basis functions and their combination weights
can be derived through the training process. Two important parameters in RBF networks
are the number of basis functions (N) and the width of the basis functions (a). The
diagram of RBF in a three-dimensional space is shown in Figure 6-4. The value the
output variable can be calculated from the hyper surface given new input values. This

approach is called an “exact” RBF.
F (x) = Z ngoqlx — xI") (6'6)
i=1

149

2

 

20'2

r
(p(r) = exp(— J, 0' > O, r E SR (6-7)
An “exact” RBF is susceptible to overﬁtting because the number of basis functions (N)

might be much larger than the underlining dimension of the function F (x). This problem

can be solved by using regularization theory to develop a generalized RBF network, as

shown in equations (6-8) and (6-9):

 

0.8I

0.5. -

9(0

0.4t ~

 

 

 

-10 35 0 5 10

Figure 6-3 Gaussian ﬁrnction in two-dimensional space

F*(x) = Z WIGQIX — ti”) (6-8)
i=1
_ C(xntr) C(xvtz) G(x1atm)-

G— G(x29t1) G(x2,t2) G(x2,tm)
"' (6-9)

_G(xN9tl) G(x1vat2) Got/vat»: )_

 

 

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151

where F *(x) is an approximated solution and t,- is the center of ith basis function. The

number of basis functions is thus reduced from N in an “exact” RBF to m in a generalized

RBF. Equation (6-8) can be solved by minimizing the cost functional {(F') deﬁned by

equation (6-10), where d,- is the target value of the ith response variable and )t is a

constant. Custom programs for a generalized RBF network were developed for this

research.

 

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152

2

§(F*) = i dl. - ‘2 wiGQIxi — ti”) + A||DF*
i=1 j=l

G(tl 9 tm )—
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G(tm 9 tm )_.

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(6-11)

(6-12)

(6-13)

6.4 Support Vector Machine

Support vector machine (SVM) has become an important technique in soﬁ computing
in recent years. The SVM is related to statistical learning theory [Vapnik 1999]. The
concept is that a series of separation boundaries might be able to separate two different
classes of data in a hyper space. The basis of the SVM is to search for the decision
boundary that maximizes the marginal distance between the boundary and the closest
points in each data class that it separates (Figure 6-5 [Law 2006]). In Figure 6-5, sub-
optimal decision boundaries (dashed lines) separate circles from squares (i.e., two data
classes) for the training data. However, compared to the optimal (max-margin) decision
boundary, sub-optimal boundaries provide a better chance for the test patterns to fall on
the other side of the boundary and thus be misclassiﬁed. Nonetheless, sub-optimal

decision boundaries can not be expected to have a good generalization performance.

 

 

 

 

 

Figure 6-5 Optimal decision boundary decided by SVM

Equation (6-14) deﬁnes a decision surface to separate two classes; where w is a
weight vector, x is a data vector, and b is a bias. The decision rules are described in
equations (6-15) and (6-16). Data vectors that are closest to the decision boundary are
support vectors, as shown in Figure 6-5. The search for the optimal decision boundary

can then be transformed to a mathematical optimization problem.

wa + b = 0 (6-14)
wa + b 2 0 for dz. = +1 (6-15)
wa + b < O for a". = —1 (6-16)

Most real world problems will not be linearly separable; however, the non-linearly
separable vectors x,- might be linearly separable after being transformed to vectors (”(3%) in
a higher dimensional space (Figure 6-6.) The notation “(00” represents the nonlinear
transformation from input space to a higher dimensional feature space. This
transformation is facilitated through the application of a “Kernel Trick”. The “Kernel
Trick” calculates the inner product of input vectors in a feature space instead of mapping
input vectors to a feature space explicitly, as shown in equation (6-17). The use of a
kernel ﬁmction saves the calculation of transforming (pf) for each vector explicitly and

thus reduces the calculation load of an SVM.

154

 

 

 

 

 

Input space Feature space
(lower dimension) ( higher dimension)

Figure 6-6 Transformation of feature space [Law 2006]
K(X»X.)= <0T(X)<0(x.) (6—17)

There are two main approaches to design an SVM for a general multi-class
classiﬁcation problem where the number of classes is greater than two. One is to
construct and combine several binary classiﬁers, and the other is to consider all data in
one optimization formulation. The formulation to solve multi-class SVM problems in one
step has variables proportional to the number of classes. Therefore, for multi-class SVM
methods, either several binary classiﬁers have to be constructed or a larger optimization
problem is needed [Hsu and Lin 2002]. The two methods based on constructing and

combining several binary SVM classiﬁers are:

A) One-against-all method: this method establishes k SVM models where k equals the
number of classes. Each SVM is trained separately. In the training of the ith SVM, all of
the training data in the ith class were labeled as positive and training data in other classes

were labeled as negative [Hsu and Lin 2002]. In the training stage, the input data is put

155

into each of the k models. A weight w is deﬁned for each model and k decision ﬁmctions
are obtained. In the testing stage the test vector will be classiﬁed to the class 1' if the ith

SVM model yield the maximum of decision functions.

B) One-against-one method [Hsu and Lin 2002, Knerr et al. 1990]: this method
constructs k(k-1)/2 classiﬁers and each classiﬁer is trained on data from two classes.
Using training data from the ith and the jth classes, the binary problem is solved such that
data in the ith class falls on one side of the decision hyper plane and data in the jth class
falls on the other side. The input data are applied to each of the k(k-I)/2 classiﬁers. If it is
decided by one single SVM that the input vector x belongs to the ith class the count for
the ith class is increased by one. Otherwise, the count for the jth class is increased by one.
After counting the predictions from all the single SVMs the class with the largest count is
then the predicted class. The voting approach described above is also called the
“MaxWins” strategy. In the case that two classes have identical votes, the one with the

lower class index is selected.

A ﬁ'eely distributed SVM toolbox [Gunn 1997] with a radial basis function as a
kernel function was used as a single SVM classiﬁer for this research. The one-against-
one method was used to solve the multi-class classiﬁcation problem based on a series of
single SVM classiﬁers. Two important parameters are the width of the radial basis
function d, and trade off parameter c between the error and the separation margin.
Custom programs for constructing multi-classes classiﬁcation models ﬁom single SVM

classiﬁers were pro grarnmed for this research.

156

6.5 Supervised Self-Organizing Map

The development of self-organizing map (SOM) networks was motivated by the
structure and function of the human brain in which neurons of different regions are
responsible for different tasks: vision, hearing, smelling, etc. Different neurons in the
SOM identify features of data in different classes. Neurons in the map usually lay on a
one or two-dimensional lattice. After initializing the synaptic weights the formation of an
SOM can be ﬁnished in three steps, which are: competition, cooperation, and adaptation

[Haykin 1999, Kohonen 1990].

In the competition process, the index i(x) identiﬁes the neuron for input vector x and

is calculated using equation (6-18):

, j=1,2,...,l (648)

 

 

i(x) = arg minllx — W].
I

where x is an input pattern, Wj is the synaptic weight vector for neuron j, and I is the
number of neurons in the SOM. The winning neuron in the competition process deﬁnes
the location of a topological neighborhood (kl-1m) of the excited neurons using equation
(6-19) through a cooperation process:

2

h “M = exp 201:2 (6-19)

 

where 0 represents the effective width of the topological neighborhood, and (1],,- represents

the distance between the winning neuron i and the excited neuron j, as shown in (6-20).

7

h

 

 

d f 2 Hr]. — r, (6-20)

157

Finally, in the adaptation process, the weights of the neurons are updated using equation

(6-21):

wj(n+1)= wj(n)+77(n)hj’,(x)(n)(x—wj(n)) (6-21)

where wj(n) and wj(n+1) are the weights of the jth neuron in the nth and the (n+1)th
iterations, respectively; ”(n) is the learning rate in the nth iteration. After training, an
SOM is organized in a way that the feature of the training patterns are captured and
stored in the synaptic weight vectors. Two important parameters for an SOM are the

number of rows and columns in the original lattice (m, nc).

A self-organizing map is a kind of unsupervised learning network by nature. By
providing proper supervised training it can also be transformed into a supervised learning
network. Several steps are needed to achieve this:

. Create and train an ordinary SOM. The topology of the map and its weight
vectors will represent the features of the training data. Each neuron in the map
will win certain number of training vectors in a way that the weight vector of this
neuron represents their common features.

0 Count the number of training vectors that each neuron has won. The class of
training vectors that is most populous among all won by a neuron is assigned to
that neuron.

. In testing there will be a single winning neuron for each test vector and the class

of the winning neuron will be assigned to it as the predicted value.

158

6.6 Evaluation of ANN Models for Abutment Distress Problem

None of the ANN model is inherently superior to the other without knowing the
nature of the problem [Duda et al. 2001]. Four ANN models were applied to the bridge
abutment problem and their ﬁtness in solving the problem was evaluated. These four

ANN models were introduced in previous sections: MLP, RBF, SVM, and SSOM.

6.6.] Input variables and structure of the ANN models

The selection of a proper set of input variables is a key issue in building a good
predictive model. The nature of a complex problem typically cannot be captured with
only a few input variables. At the same time, redundant variables will cause overﬁtting,
non convergence, and high computational costs. Thus, it is necessary to identify the
variables that signiﬁcantly contribute to the conditions of structures. Processes based on
three different rationales were combined in the selection of prediction variables:
knowledge-based evaluation (i.e., the subjective selection of variables based on principles

of structural engineering) statistical analyses (Section 3.4.1.] ,) and trial and error.

Incorporating the statistical analyses, the knowledge of bridge engineering, and trial
and error, input variables for ANNs were decided to be: length, deck width, skew,
Ageinsp, ADTT, Matdiff, Apprsurstif. Abut_Rating was designated as the response
variable. The ﬁrst six variables are quantitative and they were normalized before input to
network models. ApprSur_type is a qualitative variable with four major classes,
bituminous, bituminous concrete, unknown, and concrete. It was transformed to three
indicator variables: v1, v2, and v3. “v1” takes 1 if the approach surface is bituminous, 0

otherwise. Similarly, “v2” takes 1 if the approach surface is bituminous concrete, 0

159

otherwise; “v3” takes 1 if the approach surface is unknown, 0 otherwise. Two ﬁfth of the
records in the NBI manual inspection database were randomly selected as the training
data for the MLP networks and the rest were used as testing data. For RBF, SVM, and
SSOM networks, a quarter of the records in the data set were randomly selected as

training data and the rest were used as testing data.

Proper setting of an ANN structure is one of the key issues to build a good prediction
model. Rules of thumb have been developed for the different ANN models and no
rigorous theoretical procedure was available at the time of this research. Parameters for
the ANNs were thus determined by the combination of rules of thumb and trial and error.
It was impossible to test every possible parameter combinations since multiple
parameters existed for each ANN with inﬁnite possible values for each parameter. Thus,
the approach used in this study was as follows: for parameters x and y, k values that
spread over their ranges, respectively, were selected and build ANN models for each of kz
combinations between [x1, x2, ...xk] and [y], y;, ...y, ] were built. Model parameters with
minimum testing error would be the center of next trial (xi, yj). In a similar procedure, k
values that spread over [x,--1, xm] and [VJ--1, yj+[], respectively, were selected and ﬁnd the
reﬁnement of the optimal combination was found. This search process was reﬁned until a
satisfactory testing error was reached. While this approach is susceptible to a local
minimum effect, it was a practical way to solve the problem due to the lack of a

rigorously theoretical method.

160

6.6.2 Evaluation of ANN models

For the MLP ANN models, a network with 2 hidden layers, 130 neurons in each
hidden layer and a learning rate r; = 0.05 had the best performance. For the best model, n.
= 10,000, and mse = 0. 05, and a sigmoid ﬁmction was used as the activation function.
Predictions ﬁom the trained MLP ANN are tabulated in the conﬁrsion matrix shown in
Table 6-2 together with the manual inspection (i.e., true) values. A confusion matrix
[Kohavi and Provost 1998] contains information about actual and predicted
classiﬁcations and can thus be used as a measure of the model performance [Silva et a1.
2004]. In Table 6-2 the columns are the predicted values and the rows are the manual
inspection (or true) value. The numbers in the cells with row and column numbers
between 0 and 9 are the numbers of observations that fall into those categories.
Accordingly, the diagonal elements (darker gray cells) are the number of correct
predictions. Thus, cells far from the diagonal imply that the predictions are away from the
actual response. The row labeled correct ratio (CR) gives the ratio of the number of
correct predictions to the number of all instances for that given level of response (given
in the “True Sum” row). Subjectivity in the rating of structural members is well
recognized and a margin of error of i1 has been found to be representative [Phares et a1.
2001]. Thus, an acceptable prediction band width can be deﬁned within the confusion
matrix by considering a prediction acceptable if it is within :tl of the true response value.
The expanded band width in the confusion matrix is shown by a lighter gray shade along
the main diagonal in Table 6-2. Considering all records that fall within the acceptable
bandwidth, an acceptable ratio (AR) can be used as another criterion to evaluate the

performance of the network. Additionally, a distress identiﬁcation ratio (DIR) was

161

deﬁned as the number of inspection cases whose inspection (or true) value is less than 5
and was predicted to be less than 5. The DIR is calculated by summing the top left 5X5
square sub-matrix of Table 6-2 and dividing by the sum of the ﬁrst half of the row “True

,9

Sum.

The RBF network with parameters N = 3 and o = 290 had the best performance. For
the SVM networks, the best performance was obtained when its parameters were d = 4
and c = 50. The SSOM with parameters n, = 16 and nc = 19 had the optimal performance.
The confusion matrices for the RBF, SVM, and SSOM predictions are shown in Table

6-3, Table 6-4, and Table 6-5, respectively.

162

 

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The performance of the best prediction models (MLP, RBF, SVM, and SSOM) are
compared in Figure 6-7. The MLP and SVM showed better performance among the four.

Performance of the RBF network is not considered good because of a low DIR value,

even though it had the highest AR value.

 

 

 

 

 

 

 

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Figure 6-7 Performance of ANN models

6.6.3 Deterioration curves for highway bridge abutment walls

Since the national bridge inspection (NBI) program was created not very long ago
[Hartle et al. 1991], inspection records for each bridge in the database only covers a short
life span, as shown in Figure 6-8. It is thus very difﬁcult, if not impossible, to ﬁnd the life
cycle trend of abutment condition from these inspection records. However, ANN models
can extract and combine useful information to generate a deterioration curve for the

abutment wall throughout the life cycle of a highway bridge.

167

 

 

 

 

 

 

 

 

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0 10 20 30 40 50 60

Age at Manual Inspection (year)

Figure 6-8 Scatter plot of abutment rating vs. age at manual inspection

The MLP and the SVM network models were applied to retrieve and predict the
conditions of the abutment walls of a simple/cantilever steel bridge in the State of
Michigan (bridge A15). The deterioration curves for this bridge are shown in Figure 6-9.
The abutment ratings predicted by the ANN models are shown by the stepwise lines. The
stepwise shape follows from the integer 0 to 9 rating scale. Data points corresponding to
the manual ratings currently available in the database for this bridge are also shown as
dotted-connected triangles. Conﬁdence bands for the deterioration curves are also shown
in the ﬁgure as dashed curves. The width of the stepwise conﬁdence band is two times
the standard deviation of each of the predicted values. The center of the band is biased
from the predicted value to account for the asymmetrical deviation of the model. The
amount of bias is decided by the ratio of those manual ratings above the predicted value

to those below it. Therefore, both the width and bias of the conﬁdence band change with

168

the predicted value. Since abutment condition is predicted to degrade gradually, the
stepwise conﬁdence bands were smoothed to curves through the Lowess method using a
ﬁrst-degree polynomial. Since ANN models are non-parametric models, the conﬁdence
levels for the conﬁdence bands are difﬁcult to derive through statistical methods.
However, the conﬁdence level can be obtained through testing results (summarized in
Table 6-2 and Table 6-4.) The conﬁdence levels of the deterioration curves in Figure 6-9

are shown in Table 6-6.

9\
80—

 

 

  
 

 

 

 

\

 

Abutment Rating

 

 

 

 

 

0 1 O 20 30 40 50 60 7O 80
Age of Bridge (year)

Figure 6-9 Abutment deterioration curve for bridge A1.5

Table 6-6 Conﬁdence level for the conﬁdence bands of deterioration curves

 

Predicted
value

MLP(%) 100 47.8 23.0 49.0 49.4 94.3 70.6 93.0 70.4
SVM(%) 5.6 72.7 58.6 46.8 49.9 94.1 82.8 87.6 20.5

0 2 3 4 5 6 7 8 9

 

 

 

169

It should also be noted that not all of the deterioration curves have the same shape as
seen in Figure 6-9. Development of different deterioration curves has shown that for
some bridges abutment deterioration was predicted to occur earlier than others and/or
degrade at different rates. There are also some deterioration curves that show abnormal
behavior and their validity is thus suspected. Further discussion about this issue is given

in Section 7.4.3.

6.7 Fuzzy Neural Network Model

Arr artiﬁcial neural network can map complicated input-output relationship and fuzzy
sets can account for the subjectivity in manual inspections using vague decision
boundaries. By combining them, a fuzzy-neural network was developed to predict
structural condition using design and operation parameters. In the training phase, integer
structural ratings were transformed to membership values of fuzzy sets. In the testing
phase, predicted membership values were back transformed to integer structural ratings
through another neural network. Samples that can be used in training the back transform
neural network were limited. Duplications and noise vectors were utilized to improve the

generalization capacity.

A fuzzy set (FS) is a collection of members whose relationship with the set is deﬁned
by a membership function. The key feature of a fuzzy set is its continuous and gradual
boundary, contrary to the rigorous and sharp boundary of an ordinary set. This feature is
close to the thinking and decision making process of a human being [Zadeh 1965]. It thus
enables an PS to address uncertainties in a database [Yao 1980]. ANN and FS can be

combined to develop a fuzzy-neural network models [Jain and Martin 1999, Pal and

170

Mitra 1999] to map a nonlinear relationship using a data set with uncertainty and

subjectivity.

6.7.1 Fuzzy Sets

Fuzzy sets are often deﬁned by linguistic variables [Zadeh 1975a, 1975b, 1975c,
1994]. The membership function value of a linguistic variable means the degree to which
the output belongs to that linguistic variable. The membership function value is in the

6‘1”

range of [0, l], where means the highest degree of membership and “0” means lowest
degree. Thus, a membership ﬁrnction enables an PS to account for the imprecision or

subjectivity exists in real world problems.

FS is a suitable tool for damage assessment of structures considering the subjectivity
of manual inspections and the large variance in structural ratings. Transforming discrete
integer ratings to continuous membership values of linguistic variables, such as
“damaged”, “poor”, “moderate”, “good”, and “excellent ”, can reﬂect the thinking
process of structure inspectors better than discrete integer ratings. It is thus more

reasonable to use these linguistic variables as the output variable of an ANN.

A Gaussian function was used as the membership function of the FS as shown in
Figure 6-10. The activation function used in the ANN was a sigmoid function, it is most
effective when the input values are distributed in the range [-1, 1]. Values of membership
functions were thus transformed to the [-l, 1] range by multiplying them by 2 and

subtracting l, as shown in Figure 6-11.

171

Membership Grade

Membership Grade

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a, ----- Excellent
L, — Good
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8 9
Abutment rating

Figure 6-10 Membership function of fuzzy sets

A
----- Excellent
——Good
_-___ ~Moderate
— - - Poor
—— Damaged

'_l -\__.

8 9

 

 

 

 

Abutment rating

Figure 6-11 Membership function of fuzzy sets after modiﬁcation for ANN

172

6.7.2 Fuzzy-Neural Network

An FNN can be developed by incorporating a fuzzy output processing module into a
conventional neural network, as shown in Figure 6-12. The ANN in an FNN will use the
membership values of linguistic variables as outputs. A fuzzy output transform module
includes two transformation processes. One process is to transform “vague” structural
rating into “linguistic” variables to serve as output variables in the training of an MLP
ANN. The other process is to transform the “linguistic” output of the MLP ANN back to
the form of structural ratings that directly indicate conditions of structures in the
prediction phase. Another MLP ANN model needs to be developed for this back

transformation.

The structure of the ANN is illustrated in Figure 6-12. The parameter values for the
best performance were: p=13, n=145, and k=5. One third of the records in each abutment
rating category were selected and combined as test data. The remaining records were
used as training data. If the number of remaining records in any category was larger than
1500, those extra records were excluded from the training data to provide some level of
balance. In the training of the neural network, the mean square error and the maximum

number of epochs to stop were set at 0.05 and 30000, respectively.

173

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174

6.7.3 Back transforming scheme

Sparseness of the training points was a major difﬁculty in the development of a neural
network to transform membership values of linguistic variables back to structural ratings.
For instance, seven integral structural ratings were transformed to ﬁve linguistic variables
in the training of the neural network. Thus, only seven known points (seven integral
ratings) were available in the 5-dimensional space (ﬁve linguistic variables) in the
training of the back transform ANN. A neural network can not be properly trained using
such sparse training data. By duplicating each training point and adding a random noise
vector to each of the duplications, the seven known points would be expanded to seven
clusters of points; and thus cover the space better and improve the generalization of the
back transforming ANN. The magnitude of the random noise to reach the optimal
generalization depends on the distance of the training points, the structure of the neural
networks, etc. The ratings that showed structural damage were duplicated more than the
other ratings to improve the probability of identifying structural damage after being

processed by the fuzzy transform module.

The structure of the back transformation MLP ANN had 1 hidden layer (see Figure
6-12,) and its parameters were k = 5, m = 100, and r = 7. In the training of the back
transformation module, 9400 vectors were included in the training data set. For abutment
ratings of 3 and 4 there were 4200 vectors for each. For ratings of 5 to 9 there were 200
vectors for each of them. The components in the random vector were random values in
the range of [-0.1, 0.1]. The mean square error and the maximum number of epochs to

stop training were set at 0.02 and 1000, respectively.

175

6.7.4 Results

In addition to the DIR performance metric a false alarm ratio (FAR) was used as an
indicator to evaluate the performance of prediction models. FAR is deﬁned as the ratio of
“good structures” identiﬁed as damaged to all “good structures.” The DIR and FAR were

calculated using Equations (6-22) and (6-23), respectively:

DIR=ﬁix100% (6-22)
"d
"rd 0
FAR = — x100 A) (6-23)
n
8

where nd is the number of records in which the abutment rating from the manual
inspection was “3” or “4,” among the nd records, nid is the number of records in which the
predicted rating was also “3” or “4,” 22,. is the number of records in which the abutment
rating from the manual inspection was greater than “5” among ng records, and nfd is the

number of records in which the predicted rating was “3” or “4.”

The DIR and FAR of the fuzzy neural network were 82.31 % and 14.61 %,
respectively. Compared to the DIR and FAR of a conventional MLP ANN, which are
65.84 % and 2.65 %, respectively (Section 6.6), the FNN model showed a 16.47 %
improvement of DIR at the cost of an 11.96 % increase in the FAR. The confusion matrix
of the fuzzy neural network is shown in Table 6-7. It can be seen from Table 6-7 that the

FNN model can identify damage in bridge abutments with satisfactory accuracy.

176

 

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177

It should also be pointed out that the model could not give a prediction for the rating
“5”. This might be caused by the noise vectors added for training of the back
transformation model. It can also be noticed that most of the test patterns with manual
inspection rating “5” were predicted as “4” or “6.” The deviation is considered acceptable
given the large variance in the manual inspection data. Table 6-7 is presented in a manner
slightly different from Table 6-2 to Table 6-5 because it was found through ﬁeld
inspection that the bridges with abutment rating less than 3 were closed and thus not in
normal operation. Thus, those inspection records were deleted from the database in the

later stages of the study.

6.7.5 Bridge abutment deterioration curve

The FNN model was applied to predict the abutment condition of one prestressed
concrete bridge in the State of Michigan. Its abutment deterioration curve is shown in
Figure 6-13. A conﬁdence band was evaluated through the confusion matrix of the
prediction model (Table 6-7). The conﬁdence level was 82.3 % for the case that abutment

damage exists and 81.4 % for a 75-year life span for the bridge.

It should also be noted that not all the deterioration curves are in the exactly same
shape as Figure 6-13. The abutment walls of some bridges deteriorate at earlier times,
some are predicted to degrade faster, and some of them show abnormal (and suspect)
trends due to the improper prediction of the model or the inherent complexities of the
structural inventory database. Figure 6—14 shows the deterioration curve developed using
the FNN for the bridge shown in Figure 6-9 (bridge A15) for comparison. Compared

with predictions of the MLP and SVM (Figure 6-9,) the prediction of the FNN (Figure

178

6-14) is more precise in matching the manual inspections. However, the deterioration
trend developed by the FNN is not as reasonable as those of the MLP and SVM. Figure
6-9 is the one selected among several bridges for which the MLP and SVM developed
deterioration curves that show reasonable trends. For the FNN, the bridge was deﬁned for
comparison, so the above comparisons can not be generalized without further and more
comprehensive comparisons and evaluations. There are also some deterioration curves

exemplify unreasonable deterioration trends. Further discussion about this issue can be

referred to section 7.4.3.

 

 

 

 

 

 

 

 

 

 

9 _
— deterioration curve
8 A manual inspection
----- confidence band
7 ‘
0)
.E
E 6
E
z
5 t
4 -
3 1 1 I ‘ _ -. _. 1... ........,.a., ..
O 20 4O 60

age of the bridge (year)

Figure 6-13 Abutment deterioration curve of a prestressed concrete bridge

179

 

 

 

 

 

 

 

 

 

 

— deterioration curve
8 _ A manual inspection
. ----- confidence band
7
a) ,
.E
E 6
E
z
5
4 t
3 1 ‘ ‘
O 20 4O 60

age of the bridge (year)

Figure 6-14 Deterioration curve developed by an FNN for the bridge in Figure 6-9

6.8 Discussion

Four major types of neural network models were developed for the present research
problem to predict the condition of highway bridge abutment walls based on the NBI
database. These four neural network models were: multilayer perceptron (MLP), which is
based on recursive learning; radial basis ﬁrnction network (RBF), which is based on
curve ﬁtting; support vector machine (SVM), which is based on optimization of a
decision boundary; and supervised self-organizing map (SSOM), which is based on

feature extraction and feature mapping.

Since the primary goal for developing the ANN models was to predict abutment
distress, SVM seemed to be the optimal ANN model since it had the highest ratio of

damage identiﬁcation (DIR). The MLP model also had good performance as it had the

180

second highest DIR indicator with high acceptable ratio (AR) and correct ratio (CR) at
the same time. The SSOM model was inferior to the MLP model for all three
performance indicators. The RBF model did not seem to perform well for this problem
because its DIR was too low. Thus, it couldn’t identify abutment distress even though its
acceptable ratio was the highest among the four. For the problem of abutment damage
identiﬁcation and prediction the SVM and MLP models were identiﬁed as the suitable

ones to build degradation prediction models.

A fuzzy neural network was also developed to identify damage in bridge abutment to
account for the subjectivity in the manual inspections. A fuzzy transform module was
designed to alleviate the negative effect of subjectivity by using linguistic variables and
membership functions instead of integer structural ratings. A Gaussian function was used
as the membership function of the ﬁrzzy sets. In the training of the back transform
network of the fuzzy transform module, the Sparseness of the training data set was
alleviated by duplicating the training data and adding noise to the duplications. The
accuracy in identifying structural damage was improved by focusing on damage patterns
in the training of back transform network. An FNN model was used to predict structural
damage in abutment walls and the DIR of the FNN model reached 82.31 %, which

exceeded the conventional network by 16.47 %.

181

7 ENSEMBLE OF NEURAL NETWORKS AND COMBINATION
OF DATABASES

7.1 Introduction

ANN models have shown reasonable performance in predicting damage in abutment
walls of highway bridges as presented in Section 6.6. However, those models can hardly
be further improved considering the complexity of the problem and the difﬁculties with
the database. In this chapter, an ensemble of networks (ENN) was explored to develop a
damage prediction model with improved accuracy. An ensemble of neural networks is a
set of individually trained neural networks ﬁom which predictions for novel inputs are
obtained through the combination of individual predictions by certain voting schemes
[Opitz and Maclin 1999]. The concept of an ensemble of neural networks follows from
the principle of “divide and conquer,” which means that a complicated task can be
decomposed into a series of simpler tasks and the solution to the complicated problem
can be arrived at by combining the solution of the simpler problems [Haykin 1999]. The
accuracy of an ensemble of neural network is expected to be improved by combining the
knowledge learned by each individual neural network, even though those individual
networks are trained on subsets of data and do not have the optimal performance for the
complete problem. A diagram for the concept of an ensemble of neural networks is

shown in Figure 7-1.

182

 

Structural parameters

l
r l r

network] network2 . - - networkn

l l l

Voting scheme

l

Structural condition

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 7-1 Diagram of ensemble of MLPs

The motivations for using an ensemble of neural networks (ENN) in this research are:
. An individual neural network is susceptible to be trapped into local minima and
to overﬁtting. Combining the predictions of individual neural networks, the
performance of an ENN will not be inﬂuenced when a few of the individual
networks are trapped into different local minimal.

. An individual neural network might misrepresent part of the training data. Since
different network might misrepresent different features of the data, the negative
effects of the misrepresented data can be minimized by combining individual
neural networks to help each other.

. The source of the damage in the abutment walls for the present research problem
is highly scattered, including mechanical processes, environmental factors, trafﬁc

conditions, weather conditions, construction qualities, corrosion, etc. It is thus

183

very difﬁcult for a single neural network to capture all these factors from the
training data.

. A novel data organization scheme applied in an ensemble of neural network can
help to overcome the unbalance in the manual inspection database.

. An ensemble of neural network provides the opportunity to combine the
evidential database with a virtual database to improve the accuracy of the

prediction model.

Theoretically, an ENN can overcome the bias/variance dilemma [Duda et al. 2001,
Haykin 1999] of an ANN and thus improve the performance of the prediction model. The
bias/variance dilemma refers to the interdependence of the bias and the variance of a
neural network. Bias refers to the accuracy of a neural network. A neural network with
large bias will produce a wrong prediction. Variance refers to the precision of a neural
network. A network with a large variance can not be reliable even though its bias might
be small. Given a certain amount of training data the bias of a neural network can not be
reduced signiﬁcantly without the increase of the variance, and vice versa. The error of a

neural network can be expressed using equation (7-1):

E(F(x)— E[DlX = x])2 = B(F(x))+ V(F(x)) (7-1)

where F (x) is the input-output ﬁrnction mapped by the neural network; the bias B(F(x)) is
calculated using equation (7-2); and the variance V(F(x)) is calculated using equation

(7-3).

B(F(x))=(E(F(x))—E[DlX=x])2 m

184

V(F(x))= E(F(x)-E[F(x)])2 <7-3>

It has been proved that the prediction made by summarizing the predictions of
individual neural networks in an ensemble will not reduce the bias of the ﬁrnction F (x)
[Haykin 1999]. However, it would help to reduce the variance of the ﬁrnction F (x) and

thus, improve the performance of the prediction model.

In this research, MLPs with a back propagation algorithm (see Section 6.2) were used
to compose an ensemble for two reasons: ﬁrst, an MLP is good at mapping nonlinear
input-output relationships as discussed in section 6.2; and second, an individual MLP is
vulnerable to local minima, which means that the searching for synaptic weights might
stop at a point corresponding to a suboptimal generalization of rules hidden in the
training data. The performance of an ENN is expected to be better when the errors of the
individual neural networks in the ensemble are more independent [Hansen et al. 1992,
Sharkey 1999]. Kolen and Pollack [1990] demonstrated that the accuracy of an MLP
using back propagation algorithm was sensitive to the initial conditions. The effects of
variation in initial conditions to the generalization of the network were not likely to be as
signiﬁcant as the variation of the training data sets [Sharkey 1999]. In this research, both
the training data sets and the initial synaptic weights were different for the different

MLPs in the ensemble.

The Matlab® [Mathworks 2007c] neural network toolbox was used to develop the
individual MLP ANN models. Matlab’s built-in functions were used in training and

testing of the dividual MLP networks. Customer programs were developed to setup the

185

structure of each MLP, organize the training data sets, compose the ensemble of neural
networks, and realize the different voting schemes. A stand-alone executable program
“SbNet” were developed based on the prediction model using an ensemble of neural
networks. Such a program can predict bridge abutment condition and life-time

degradation curves given design parameters or an MDOT bridge identiﬁcation number.

In the following three sections of this chapter, the data organization, voting schemes,
and the results of their application in an ensemble of neural networks for the example
problem are presented. Then, the combination of databases into an ensemble of neural

networks and the development of a program for the example problem is provided.

7.2 Data Organization

The principal motive for devising a novel data organization scheme is to overcome
the unbalanced distribution of structural inspection records in the database, which is a
challenging issue for an individual network. Two major approaches to organize data sets
are bagging [Breiman 1996, Duda et a1. 2001, Sharkey 1999] and boosting [Duda et al.
2001, Schapire 1990]. Bagging is a procedure to produce multiple training sub-sets by
randomly drawing samples from the original training set with replacement. Boosting is a
procedure to produce multiple training sub-sets in a manner that the subsequent selection
is focused on the samples that are not recognized well by the classiﬁers training on the
previous training sub-sets. Compared with boosting, bagging has been proven to be more
resilient to noise [Opitz and Maclin 1999, Quinlan 1996], which is also a major difﬁculty

in using a structural inventory system database. Bagging is effective in making full use of

186

small data sets; and Breiman [1996a, 1996b] proved that bagging can improve the

accuracy of unstable prediction models, such as neural networks.

In this research, the concept of bagging was applied after modiﬁcation-bagging
within each structural condition to alleviate the difﬁculty of rare damage records. Each
network in the ensemble was trained by a different data set. Each data set contained the
same number of records (n 1) for each structural condition and these n 1 records were
randomly selected ﬁom each category with replacement. As a result, the training set for
each individual network was balanced and different from each other and the errors of
these networks had some degree of independence. The procedure of bagging within

categories is schematically shown in Figure 7-2.

 

 

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Damaged . aggmg D1

 

 

  
  
 

 

 

Setl

 

 

 

 

 

 

 

 

 

 

 

Setn
Bagging ,
1:)- Gn / ///

 

 

 

 

 

 

 

 

 

 

Figure 7-2 A novel data organization scheme: bagging with categories

187

Neural networks ensemble can be trained through parallel computing since bagging
within category enabled each individual neural network to be trained and tested
independently. Parallel computation can signiﬁcantly improve the efﬁciency in
developing the ensemble since the training of each individual neural network is time-

consuming.

7.3 Voting Scheme

Voting scheme refers to the way to combine the individual answers of the neural
networks to reach a ﬁnal prediction by the ensemble. The voting schemes applied in this

research were:

(a) Plurality Voting: The ﬁnal prediction of the ensemble is the one that receives
more “votes” from individual networks than other possible predictions [Hansen and

Salamon 1990].

(b) Modified Majority Voting: In a majority voting scheme, the ﬁnal prediction of
the ensemble is the one that receives more than half of the votes ﬁom individual
networks [Hansen and Salamon 1990, Zhou et. a1. 2002]. In this research, a modiﬁed
majority voting scheme was applied. If no structural condition obtains more than half of
the votes, the prediction will be the worst structural condition that receives more than a
quarter of the votes. If no structural condition obtains more than a quarter of the votes,
the prediction will be the worst structural condition that receives more than the average

number of votes for each structural condition.

188

(c)Weight Voting: The predictions of individual networks are modiﬁed by weights
before being combined to reach the ﬁnal prediction. The weights can be determined
through different methods, considering either the training error of individual networks or
their potential to make good predictions in the applications [Guo and Luh 2004, Marwala
2000]. In this study, weights are assigned to neural networks in the ensemble based on
the mean square error from their training phase. As such, a larger training mean square
error results in a lower weight for that neural network. The votes are multiplied by the

corresponding weights before added to the collection boxes.

((1) Subjectivity Voting: This voting scheme takes into account the subjectivity of
the manual inspection ratings. When an individual network “decides” that the structural
rating is x, the voting scheme recognizes that there is a possibility that the actual rating is
x+1 or x-l, and with a smaller possibility for x+2 or x-2. For the example problem, as
shown in Figure 7-3, when a network in the ensemble predicts “7”, the count for “7” will
be increased by 0.7. Counts for “5,” “6,” “8,” and “9” will be increased by 0.02, 0.08,
0.16, 0.04, respectively, based on the subjective bias trend in the manual inspection of

bridges [FHWA 2001].

(e) Evaluation Voting: Instead of combining the predictions of some individual
neural networks, the evaluation voting scheme takes into account the values of all output
neurons of the networks in the ensemble. For output neurons that represent the same
structural condition in different neural networks, their values were summed to obtain a
probability value for that structural condition. The structural condition that has the

highest probability value will be the prediction of the ensemble.

189

 

 

 

 

 

 

 

 

 

 

 

 

Network 1 l: : :: 2 ~ : : :C : -— Collection Box 0
Network 2 j: : :: : - :
Rating 7 + 0.02

 

 

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:::>— Collection Box 8

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l Network ’1 P :- 1: : 1 1:3) Collection Box 9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 7-3 Example of subjectivity voting scheme

7.4 Results

7.4.1 Ensemble and network structure

The structure of each individual neural network can be referred to Figure 6-1. The
parameter values were: p = 13, n = 50 and r = 8. One third of the records in each
abutment rating category were selected and combined as test data and the remaining
records were used as training data. Only 59 records showed an abutment rating of “9” in
the training data. Thus, all of them were used in the composition of training sets for the
individual neural networks. For records with other abutment rating values, 200 were
selected from each rating category through a bagging procedure to be combined to form
one individual training data set. In the training of individual networks, the mean square

error and the maximum number of epochs to stop were set at 0.15 and 10000,

190

respectively. A neural network was excluded from the ensemble when its mean square

error from the training phase was greater than 0.25.

7.4.2 Evaluation of Voting Schemes

For the example research problem, weight w,- for the ith network in the weight voting

scheme was calculated with equation (7-4):

 

w, = J25 — 10 x mse, (7-4)

where me,- is the mean square error of the ith network in the training phase. The report
from the Federal Highway Administration [2001] noted that there was a tendency to
assign a rating lower than it should be for structural members with good condition; and
that, similarly, there was a tendency to assign a rating higher than it should be for
structural members with poor condition. The collection scheme for the subjective voting
considering these tendencies is shown in Table 7-1. The values in the individual cells of
the table mean that when the network predicts the rating noted in the row title, the

collection box in the noted column title will be increased by that value.

The damage identiﬁcation ratio (DIR) and false alarm ratio (FAR) values (see
Sections 6.6.2 and 6.7.4) versus the number of neural networks in the ensembles for
different voting schemes are plotted in Figure 7-4 and Figure 7-5, respectively. From
these ﬁgures it can be seen that the performance of the ensemble of neural networks
improves with the increase of numbers of networks in each ensemble up to a size of
approximately 50 to 60. No signiﬁcant improvement is observed after the number of

networks in the ensemble exceeds 60.

191

Table 7-1 Collection algorithm for subjective voting

 

 

 

Collection box
Prediction 3 4 5 6 7 8 9
3 0.9 0.08 0.02
4 0.15 0.8 0.04 0.01
5 0.04 0.16 0.7 0.08 0.02
6 0.04 0.16 0.6 0.16 0.04
7 0.02 0.08 0.7 0.16 0.04
8 0.01 0.04 0.8 0.15
9 0.02 0.08 0.9

 

The solid squares in Figure 7-4 show the highest DIR of all the 500 individual neural
networks trained in this simulation. It can be seen from Figure 7-4 that the ensemble of
neural networks outperformed the best individual neural network by a large margin even
though most of the neural networks in the ensemble are not as good as the best neural
network. Similarly, the solid squares in Figure 7-5 represent the lowest FAR of all the
500 individual neural networks in the simulation. It can be seen from Figure 7-5 that the
ensembles of neural networks with evaluation voting, plurality voting, and weight voting
schemes have a lower FAR than the best individual neural network. The ensembles of
neural networks with modiﬁed majority voting and subjectivity voting present FARs that

are 3 % to 4 % higher than the best individual neural network. The increase in the FAR is

acceptable for engineering applications.

192

 

 

 

 

 

 

 

 

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O 100 200 300 400 500
Number of networks in the ensemble

Figure 7-4 DIR versus number of networks in an ensemble of neural networks

Because failure to identify a damaged structure will have a more serious impact than
identifying a good structure as damaged, the philosophy in developing a structural
damage prediction model should be to increase the DIR as much as possible without
raising the FAR too much. In this study, the indicator to evaluate the prediction models
was the difference between the DIR and half of the FAR values. The performance of the
best ensemble of neural networks using different voting schemes is shown in Table 7-2. It
can be seen from Table 7-2 that the modiﬁed majority voting scheme led to the highest
DIR, followed by the subjectivity voting scheme. The evaluation voting scheme had the
lowest FAR and a decent DIR, outperforming both the weight and plurality voting

schemes for both indicators.

193

 

 

* + Modified majority + Plurality
—-e— Subjectivity —0— Weight
+ Best network —a— Evaluation

 

 

 

 

 

 

 

 

0.12 _
0 100 200 300 400 500
Number of networks in the ensemble

Figure 7-5 FAR versus number of networks in an ensemble of neural networks

Table 7-2 Evaluation of different voting schemes

 

Number of networks DIR FIR Indicator

Votrng scheme for best performance

majority 51 86.48% 19.89% 0.7654
Subjectivity 58 85.88% 18.78% 0.7650
Evaluation 463 81.71% 12.77% 0.7532
Plurality 56 81.51% 14.54% 0.7424
Weight 59 81.11% 13.90% 0.7416

 

194

7.4.3 Bridge Abutment Deterioration Curves

To illustrate the use of the ANN ensembles in developing life-degradation curves, an
ensemble of 51 networks using a modiﬁed majority voting scheme was applied to predict
the abutment condition of an existing continuous steel bridge in the State of Michigan.
The abutment deterioration curve for this bridge is shown in Figure 7-6. “CB” in the
legend means the conﬁdence band. A conﬁdence band was evaluated through the
confusion matrix of the prediction model, which is shown in Table 7-3. The conﬁdence

level was 91.33 % for the case when abutment damage existed. The conﬁdence level was

74.54 % for 70 years life of the bridge.

 

 

 

 

 

 

 

 

 

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195

 

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In the development of Figure 7-6, the age span for the manual inspection rating is
relatively short because manual inspections according to the NBI system started in
Michigan in the early 19903, as shown in Figure 6-8. This is another difﬁculty in the
exploitation of the structural inventory system database for life-cycle prediction model as
it is very difﬁcult to extrapolate structural member degradation trends from such a short
span of manual inspection records. Furthermore, a major part of the highway bridges in
Michigan was built in the 1960s and 19703. Thus, most of these age spans were
concentrated within 30 years of life of bridges, with very few inspections records for very
“young” or very “old” bridges. The ensemble of neural networks anneals the information
from different structures to predict the conditions of each structure in the future and

retrieve the historical path for the development of structural damage in bridge abutments.

It should also be noted that not all the deterioration curves have the same shape as
shown in Figure 7-6. Figure 7-7 shows a deterioration curve with long ﬂat range before
major distress occurred. It can also be seen that the deterioration curve matches the
manual inspection records well. It may be inferred that this bridge was well design and
maintained and that no major environmental or operational factors caused its abutment

wall to deteriorate seriously before 40 years of its service.

197

 

 

NBI rating

 

 

 

 

 

r_
-—Curve \ / \

4L A Manual —— — — L—
* Current

3» -—— tzs

2 1 a

 

0 10 20 30 40 50 60 70
Age of the bridge (year)

Figure 7-7 A deterioration curve with long ﬂat range

Figure 7-8 shows a deterioration curve with a spike, or jump, in the middle. It can be
seen from Figure 7-8 that the deterioration curve matches the manual inspection records
well before the spike occurs. Probably, the spike point occurs because the ensemble of
neural networks did not generalize that pattern well. The deterioration curve looks
reasonable if the spike point is removed. Figure 7-8 and Figure 7-9 show situations in
which current age of a bridge is smaller than its ages at inspection. This means that the
bridge has been rebuilt in its service life. These rebuilt bridges add another difﬁculty in

developing prediction models and lead to the occurrence of some unreasonable

deterioration curves.

198

 

 

 

 

 

 

 

 

 

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7

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g6 L/ i L _____
a i
E 5-
2 —Curve

4~ A Manual \— —————

‘A' Current
3* ——'CB
2 1 1

0 110 210 310 410 510 60 70
Age of the bridge (year)

Figure 7-8 A deterioration curve with spike in the middle

Figure 7-9 shows a strange looking, and thus suspect, deterioration curve. The
condition of the bridge abutment walls deteriorate dramatically after 20 years of their
service. Then, after remaining in a poor condition for 23 years, the abutment walls of the
bridge are restored back into fair condition. Two reasons might have caused this strange
predictive curve. One is that the ENN does not generalize the patterns well enough and
thus make a wrong prediction. Another is that highway bridges are continuously repaired
and the abutment walls are restored to good condition after damage is observed.
Unfortunately, the prediction model also incorporated the records of restored abutment

walls into the prediction model, which may lead to the abnormal results.

199

 

 

 

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C
'5
S
9
——Curve
4- A Manual
‘A' Current
39 -—— (SB

 

 

 

 

l
0 10 20 30 40 so 60 70
Age of the bridge (year)

 

 

Figure 7-9 A deterioration curve shows increase of abutment rating

Figure 7-10 shows the deterioration curve developed using the ENN for the bridge
shown in Figure 6-9 (bridge A15) for comparison. Compared with the MLP and SVM
(Figure 6-9,) the ENN (Figure 7-10) predicts an earlier beginning of the signiﬁcant
deterioration (20 to 30 years versus about 40 years after the bridge was constructed) and a
worse abutment condition in later life of the bridge (rating 4 versus rating 5.) It is also
noticed that a few small spikes exist in Figure 7-10, which is acceptable for engineering
applications especially considering the subjectivity and large variance of manual
inspections. It should also be pointed out that the deterioration trend developed by the
MLP and SVM (Figure 6-9) is the one selected among several bridges for which the MLP
and SVM developed reasonable deterioration curves. For the ENN, the bridge was

deﬁned for comparison, it can be considered as its standard performance.

200

 

 

 

 

 

 

 

 

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AManual
*Current
a: —'CB
1% i “ii
5 . ii l/L____
25 "l * l/\
3. lt_____
2 1 J 1 1

 

0 10 20 30 40 510 60 70
Age of the bridge (year)

Figure 7-10 Deterioration curve developed by an FNN for the bridge in Figure 6-9

7.5 Combination of Databases for Soft Computing

7.5.1 Introduction

The nature of infrastructure damage is complex. Many factors interact with each other
to cause the damage. Some of these factors are design parameters, someiof them are
environmental effects, and some of them are from inﬂuence of adjacent structures.
Neither an evidential database nor a virtual database alone is sufﬁcient to provide
complete information for solving the problem. The evidential database records the
behavior of the structure under all effects, but suffers from the subjectivity of manual
inspection, incompleteness and imprecision. The virtual database has the advantages of
providing accurate input-output relations for a series of structures, no matter if they exist
in reality or not. At the same time, it has a diminished credibility and applicability due to

the necessary simpliﬁcation and assumptions in building models. In other words, a virtual

201

database can not exactly model the real structure or fully simulate all of the damage

factors, and thus only contains partial information about the problem.

In this research, the evidential database and virtual database were combined to
develop an ensemble of neural networks. ANN models based on evidential databases
have been used to predict the performance indicator of aged aircraft with good accuracy
[Shyur et al. 1996, Luxhoj et al. 1997]. ANN models based on simulated databases have
been used for structural damage detection and localization based on the dynamic
characteristics [Zhao et al. 1998, Fang et al.2005]. However, these two types of databases
have not been used together to solve problems dealing with damage prediction of

infrastructure and identiﬁcation of potential causes of damage.

The major difﬁculty in the combination of evidential database and virtual database in
this research is the large gap between explanatory and response variables of the evidential
database and virtual database. The virtual database is based only on simulated behavior of
the bridge ﬁom the perspective of mechanics and most of the explanatory variables are
bridge design parameters (see Section 5.) On the other hand, the evidential database
records the behavior of bridges through their service life including effects of all factors,
such as mechanics, environmental factors, and human behavior. Its explanatory variables
included not only design parameters, but also operation and environmental factors. The
response variables of the virtual database are stresses and strains in the structure, whereas

the response variables of the evidential database are subjective manual inspection ratings.

202

7.5.2 Concept and Methodology

The methodology for the combination of the evidential database and the virtual
database is shown in Figure 7-11. An ensemble of neural networks based on the
evidential database was trained in the same way as discussed in Section 7.4. The voting
scheme was based on modiﬁed majority voting. It was observed that for about 33 % of
the test vectors, over 50 % of members in the ensemble of networks reached agreement.
For those 33 % of the test vectors, the DIR is as high as 94.24 % and the FAR is as low as
9.43 %. However, for those test vectors the votes were scattered (no more than 25 % of
the members “agreed” on the same prediction,) the accuracy of the ensemble are low. As
discussed in Section 7.5.1, the evidential database and virtual database were created from
completely different sources. Thus, the chance that they share common weakness is low.
Consequently, the concept behind this combination is to use the networks trained based
on virtual database to help make predictions for those structures that were difﬁcult for the

ensemble of networks based on evidential database.

7.5.3 Networks trained on virtual database

One difﬁculty in the combination of databases was the gap between structural
evaluation ratings in reality and the response variables derived ﬁ'om numerical simulation.
The response variables in two databases must be the same so that they can help each
other in making a prediction. For the bridge abutment damage example, as mentioned in
Section 1.2, the response variable in the evidential database is the structural member
rating in a scale of 0 to 9. This rating can not be simulated through F EA models. Instead,
some variables such as maximum principal stress or maximum principal strain can be

derived from FEA simulations.

203

   

Evidential
Database

       

Design parameters ' 7
A Virtual Database

     

Data Organization

 
   

<- ata Organization

    
     

TrainingSubsets
‘ with Causes 7

 

 

[Ei-

Ensemble of Neural
Networks

   

 

   

Virtual Neural Networks

=NN(Cause1) 'l unreauoezj 3
[ liilil((:ai.rsen)1 '

  

 

 

 

 

 

 

 

' <v7

Prediction of Structural Predicljon
Condition "
l\/l

 

 

 

 

 

 

Diagnosis of Causes for
Structural Damage

 

Figure 7-11 Scheme of database combination

The structural member rating is a qualitative evaluation of the condition of the
structure which will be inﬂuenced by the interaction of a series of quantitative or
qualitative variables, such as stresses, strains, temperatures, chemical components in the
environment, and the quality of the construction. Thus, it was not feasible to ﬁnd a
relationship between structural member rating and FEA output. Some assumptions were
thus made and an algorithm to transform the FEA output to virtual structural ratings is

proposed as follows:

For each bridge in the simulation case matrices (see Section 5.3) a single variable
called “response” was deﬁned. For the pavement pressure damage scenario “response” is
the product of the maximum stress and maximum strain. For the temperature variation
scenario the “response” RT is the square root of the sum of the square of the products of
maximum stress, 0mm, and maximum horizontal strain, a ,1, in the summer and winter,

respectively, as shown in equation (7-5).

 

RT : \/( max 8] lmax )iummer + (Umax 8] lmax )irint er (7-5)

The natural logarithm of the “response” values was then calculated. The reason for
calculating the natural logarithm is to compact those extremely large values since they
are induced by the elastic assumption in the FEA. Transformation of responses was done
within each structural type so that they were not inﬂuenced by the deviation induced in
the modeling approaches. At the completion of this step, two virtual databases were

created: a database for pavement pressure effect and a database for temperature effects.

205

Combining and expanding the two data sets through weighted summation of the
“response” by considering different pavement and temperature conditions, the weights
for “bitumen,” “mixed,” “unknown,” and “concrete” pavement were taken to be 0.1, 0.5,
0.5 and 1.0, respectively. The weights for temperature effects are taken to be 0.56 for
bridges in a county with the smallest annual temperature difference in the State of
Michigan and 1.0 for bridges in a county with the largest annual temperature difference.
Weights for bridges in other counties were derived through linear interpolation according
to their annual temperature differences. Each bridge in the case matrix was expanded to
32 bridges according to the combination of pavement and temperature conditions. For
instance, when it has a concrete pavement and a low annual temperature difference, the

comprehensive “response” RC value will be calculated as:

RC :10 x RP + 0.25 x RT <7-6)

Three MLP networks were thus trained using virtual databases: 3 network based on
the pavement pressure scenario, a network based on temperature effect scenario, and a
network that combined those two effects. The parameters of the three networks are shown
in Table 7-4. The response variables in the virtual databases were strains and stresses in
the structure. They were transformed to virtual structural conditions by assigning a rating
3 for structures with largest response values in each structural type and a 9 for structures
with lowest response values. The virtual structural conditions for other structures can be

derived through linear interpolation.

206

Table 7-4 Parameters of networks based on virtual database

 

Network parameters

 

Network n , n ne me 17 mo
Pavement pressure 1 40 2000 0.01 0.1 0.9
Temperature effect 2 40 2000 0.01 0.1 0.9
Combined effects 2 80 10000 0.01 0.1 0.9

 

7.5.4 Improvement in damage identiﬁcation

The confusion matrix of the ensemble of networks with combined evidential and
virtual databases is shown in Table 7-5. The DIR and FAR indices of the ensemble of
networks with combined databases is 86.68 % and 20.02 %, respectively. A 0.2 %
improvement of DIR at the cost of 0.13 % increase of FAR was achieved comparing to
the best performed ensemble of 51 neural networks trained on the evidential database

exclusively.

In order to further evaluate the improvement in prediction power by combining
databases, the networks trained on virtual database was combined with an ensemble of 42
neural networks trained on the evidential database. The ensemble of neural networks
based on combined databases had a DIR of 85.09 % and an FAR of 19.68 %. The DIR
and FAR of the ensemble of neural networks based on the evidential database exclusively
were 84.89 % and 19.76 %, respectively. Thus, the DIR was increased by 0.20 % and
FAR was reduced by 0.08 %. Both performance indicators were thus improved by the

combination of the databases.

207

 

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208

7.5.5 Diagnosis of possible causes for structural damage

The ensemble of neural network based on combined databases could also be applied
to diagnose the possible causes of structural damage, as shown in Figure 7-11. Given the
design parameters of a bridge, the networks trained on pavement pressure scenario and
temperature effects scenario would give two predictions. In case the ensemble of neural
networks based on combined databases predicts that the structure is in poor condition, the
predictions of two networks trained on damage causes can be checked and evaluated. A
prediction closer to the damage condition could signify that the cause has a larger

contribution to the damage of the structure, as shown in equations (7-7) and (7-8).

 

 

C a, 2 RT + 2 _ REC x 100% (7-7)
P R,+R,+4-2me
C = R" + 2 " REC x 100% <7-8)

’6'" R7. +R,,+4—2xR,_.C

where Cpav is the contribution of pavement pressure; Cw," is the contribution of

temperature; REC is the prediction given by the ensemble of neural networks based on
combined databases. As an example, the length, width and skew angle of a
simple/cantilever steel bridge are 40.8 m, 27.3 m,.and 12°, respectively. The approach
pavement of the bridge is concrete. The ensemble of neural networks based on combined
databases predicted its abutment rating as “3.” The pavement pressure network and

temperature effect network predicted its rating as “5” and “4,” respectively. Thus, the

209

system could predict that the contribution of the pavement pressure to the damage is 43

% and the contribution of temperature effect is 57 %.

7.6 Software Development: Bridge Abutment Damage Diagnosis (SbNet)

A program, Bridge Abutment Damage Diagnosis (SbNet), was developed for MDOT
engineers to predict the condition of bridge abutment walls given design parameters.
SbNet is a stand-along executable program compiled from matlab codes of pre-trained
ensemble of networks as described in Sections 7.1, 7.2, 7.3, and 7.4. After the analysis
and evaluation of stepwise deterioration curves derived using soft computing models, it
was found that most of them can be approximated by logistic curves. In SbNet, the
deterioration curves were ﬁtted to logistic curves using equation (7-9) through Matlab’s
curve ﬁtting toolbox [Mathworks 2007a]. SbNet can make predictions either using design
parameters for bridges in design or using MDOT’s Bridge ID for existing bridges. The
output of SbNet includes: bridge deterioration curve based on actual integer values or on
smoothed logistic curves, predictions saved in txt ﬁles, and the bridge abutment rating
given the age of the bridge or current abutment rating if it is an existing MDOT highway
bridge. One of the deterioration curves of a bridge abutment wall is shown in Figure 7-12.
It is a simple/cantilevered steel bridge. The SbNet User’s Manual can be found in the
ﬁnal report to the research sponsor, MDOT [Burguefio and Li 2008].

lb”)
1+m-exp —t——

f(x):a' [b—x]
1+n-exp —t—

(7-9)

 

210

 

 

 

 

 

 

 

 

 

 

 

9. _t
——Stepwise
8~ ‘ \ —-—CB(S)
— ’Logistic
7» \ — -CB(L)
a, \ A Manual
,g 5- * Current
E \\
co 5.
z \
4+ \
3» \\
2 1 i 1 \ AL ; J J
0 10 20 30 40 50 60 70

Age of the bridge (year)

Figure 7-12 Deterioration curve shown in Figure 7-6 with smoothed curve

7.7 Discussion

An ensemble of neural networks with a novel data organizing scheme was applied to
improve the identiﬁcation of damage in abutment walls of highway bridges. The
unbalance of structural inspection databases was overcome by organizing the training
data using bagging within each structural condition. Several new voting schemes were
devised; with modiﬁed majority voting, subjective voting, and evaluation voting schemes
showing good performance. The damage identiﬁcation ratio of an ensemble of networks
reached 81 % to 86 %, which exceeded the performance of the best individual networks
in the ensemble by 13 % to 18 %. An ensemble of networks obtained optimal or close to
optimal performance when 50 to 60 neural networks were included in the ensemble. An
ensemble of neural networks was the optimal prediction model derived through this

research for predicting conditions of abutment walls of highway bridges.

211

 

Previous research [Freund and Schapire 1996, Quinlan 1996, Opitz and Maclin 1999]
has shown that most of the improvement in performance of an ensemble is achieved with
the ﬁrst few (10 to 25) additional classiﬁers (i.e., neural networks). For the structural
damage prediction problem a similar behavior was seen except that considerably more
networks were needed to achieve most of the improvement. The reason for this difference
was the characteristics of the present problem of structural damage prediction and the
corresponding structural inventory database. In order to obtain a balanced training data
set a small part of the records with good structural condition were selected in each round
of bagging. Consequently, more networks were needed to “learn” most of the knowledge
from the records with good structural conditions. Combination of the evidential database
and a virtual database ﬁom FE simulations improved the performance of the ensemble of
networks. However, the improvement was not signiﬁcant because of the signiﬁcant

differences between the evidential database and virtual database for the example problem.

A stand-alone program named SbNet was developed to help MDOT engineers in the
maintenance of existing bridges and in the design of new ones. It was based on a well-
trained ensemble of neural networks and is able to predict bridge abutment condition
given design parameters or MDOT bridge ID. SbNet can be a promising diagnostic tool
so that maintenance and repairs can be more efﬁciently managed with reliable prediction
of future structural condition and the deterioration trend. The software could also be used
as a predictive tool for new designs to evaluate and compare the life-time performance of

the abutment walls for different bridge design options.

212

ll

 

 

8 FUTURE RESEARCH AND CONCLUSION

Conclusions from the presented research work are given in this chapter. Three
promising future research directions are also proposed: predicting structural damage for
other structures, improving the combination of databases, and online updating of soft

computing models.

8.1 Further Research
Developing damage prediction models for other structures, improving the
combination of databases, and online updating of soft computing models are three

promising directions in future research.

8.1.1 Prediction models for other structures

The concept and methodologies developed in this research can be easily applied to
predict damage in other structural component in civil inﬁ'astructures. The soft computing
procedures can be upgraded to a model that can evaluate the condition of a structure
holistically. Another computation model could be developed to evaluate the condition
and reliability of the structure based on the condition of all the individual structural
components. The knowledge of structural engineering needs to be incorporated in this
computation model, such as load path, importance of individual structural members, and

failure mechanism of the structure.

8.1.2 Improved combination of databases

The concept and methodology of database combination is a promising direction to

improve the power of soft computing in damage identiﬁcation for civil infrastructure. In

213

this research, the prediction power did not improve signiﬁcantly through the combination
of evidential database and virtual database due to the limitation of the databases.
However, the combination model can be improved through two approaches in future
research:

. Improve the accuracy of ﬁnite element simulations. Even though there will
always be simpliﬁcation in the ﬁnite element simulation. A better approximation
to the real-world problem can be reached through developing nonlinear structural
models that consider geometric nonlinearity and material nonlinearities.

. Create a dynamic database through online instrumentation of a series of typical
structures. The dynamic database should have the same explanatory variables
with the evidential database and the same response variables as the virtual
database. Such a more representative and precise dynamic database can provide
new information for the computing model and improve the combination of the

evidential database and virtual database.

8.1.3 Prediction model with online updating capacity

The prediction power of soft computing models can be improved continuously if the
neural networks can be retrained with updated evidential and dynamic databases. The
online updating of soft computing models can include a procedure to screen, normalize,
and organize the raw inspection and instrumentation data to ﬁt in the databases and a
procedure to train and test the soft computing models, as shown in Figure 8-1. The
concept of parallel computing based on high performance computer servers can be

implemented to improve the online training and testing of a prediction model.

214

 

 

 

New

 

 

 

        
 

 

 

 

Inspection Yes
Data New
Monitoring Yes
Data

   
 
  

   

  
 

New _
Simulations

  

Update

 

 

 

  

Dynamic \ﬁrtual
Database Database

  
 

Evidential L

 

 

 

 

 

 

New Data \

Available?

 

 

C Design parameters D
’ L Predict Damage in
Infrastructure

Figure 8-1 Online update scheme for soft computing model

 

 

215

8.2 Conclusions

A comprehensive procedure was developed to predict damage in civil infrastructures
through integration of a series of tools. These tools included data processing, statistical
analysis, ﬁeld inspection and instrumentation, ﬁnite element simulation, soft computing,
and ensembles of neural networks. It was shown that a series of soft computing tools,
such as MLP, RBF, SVM, SSOM, and FNN; can be used to develop prediction models,
even if none of them is inherently better than others without knowing the feature of the

problem.

An ensemble of neural networks with a novel data organization scheme was effective
to predict damage in structures based on a complicated and unbalanced database. The
unbalance of structure inspection databases was overcome by organizing the training data
using bagging within each structural condition. The damage identiﬁcation ratio of an
ensemble of networks reached 81 % to 86 % for the bridge abutment distress problem,
which exceeded the best individual networks in the ensemble by 13 % to 18 %. The
ensemble of networks obtained optimal, or close to optimal performance when 50 to 60
neural networks were included in the ensemble. An ensemble of neural network was the
optimal prediction model derived through this research for the prediction of highway

bridge abutment condition.

An evidential database can be developed from SISD through data processing and
statistical analyses. Statistical analyses also provided valuable information for other
analyses and simulations, such as evaluation of the signiﬁcance of explanatory variables,

revealing the common features of the structures that were susceptible to structural

216

damage, and the development of case matrices for ﬁnite element analyses. A virtual
database can be developed through ﬁnite element analyses. Such a virtual database can
reveal the relationship between design parameters and the behavior of a structure and it
can be combined with the evidential database to improve prediction models developed
through an ensemble of neural networks. Additional information about the behavior of

structures can be collected through ﬁeld inspections and instrumented monitoring.

The comprehensive procedure developed in this research can predict damage in
structures and evaluate the potential causes of damage. With the identiﬁcation of
potential causes of structural damage and the accurate prediction of the structural
condition, the human resources and funding in maintenance and repair of civil

infrastructures can be deployed more efﬁciently.

217

REFERENCES

AASHTO (2007). AASHTO LRFD Bﬂge Design Speciﬁcations.
ABAQUS, Inc (2006). ABAQUS/Analysis User’s Manual—version 6.6.1.
American Institute of Steel Construction (AISC 2006). Steel Construction Manual.

Askeland, D. R., Ksslinger, F. and Wolf, R. V. (1987, Nov 15) Investigation of Bridga
Pin Failure. Report to Missouri Highwav and Transportation Commission.

Aleksander, I. and Morton, H. (1990). An Introduction to Neural Cormautiag. London:
Chapman and Hall.

ASCE. (2005). Report Card for America’s Infrastructure. http://wwwascegngz
reportcard/ZOOS/ index2005.cfm.

Ayyub, B. M. and McCuen, R. H. (1997). Probability, Statistics & Relgrbilitv for
Engineers. NY, Boca Raton: CRC Press

Bishop C. (1995). Neural networks for paLttem recognition. Oxford:0xford University
Press.

Blake, C. L. and Merz, C. Z. (1998). UCI Repository of Mﬁhine Learning Databases.
http://www.ics.uci.edu/mleam/MLRepositorv.html. Irvine, CA: Department of
Information and Computer Science, University of California-Irvine.

Breiman, L. (1996a). Heuristics of instability in model selection. Annlals of Statistics:
24(6), 2350-2383.

Breiman, L. (1996b). Bagging Predictors. Machine Leam: 24, 123-140.

Briaud, J. L., Maher, S. F. and James, R. W. (1997, May). Bump at the End of the Bridge.
Civil Engﬁering: 67(5), 68-69.

Burguefio, R. and Li, Z. (2008). Identiﬁcation of CaCuses and Development of Strategies
for Relieving Structural Distress in Bridge Abutments, Final Report for Michigan
Department of Transportation.

Burke, M. P. (1998). Pavement pressure generation: neglected aspect of jointed pavement
behavior. Transportation Research Record: 1627, 22-28.

Burke, M. P. (2004, January). Reducing Bridge Damage Caused by Pavement Forces.
Concrete International. 53-57.

218

Carpenter, G. A., Grossberg, S., Markuzon, N., Reynolds, J. H. and Rosen, D. B. (1992,
September). Fuzzy ARTMAP: A Neural Network Architecture for Incremental
Supervised Learning of Analog Multidimensional Maps. IEEE Transactions on Neural
Networks: 3(5), 698-713.

Cattan, J. and Mohammadi, J. (1997). Analysis of bridge condition rating data using
neural networks. Microcomputers in Civil Engineering: 12(6), 419-429.

Chan, L.S., Gilman, G. A. and Dun, DJ. (1976). Alternative Approaches to Missing
Values in Discriminant Analysis. Journal of the American StaListical Association:
71(365), 842—844.

Chen, C. H. (2005). Structural identiﬁcation from ﬁeld measurement data using a neural
network. Smart Mater. Struct: 14, $104—$115.

Chen, R. and Yu, J. (2007). An hnproved Bagging Neural Network Ensemble Algorithm
And Its Application. Third International Conference on Natural Computation: 5, 730-734.

Cybenko, C. (1989). Approximations by superposition of sigmoid functions.
Mathematics of Control Sigaals and Systems: 2, 303-314.

Dixon, J. K. (1979, October) Pattern Recognition with Partly Missing Data. IEEE
Transactions on Systems, Man and vaemetics: SMC-9(10), 617-621.

Dreiseitl, S. and Ohno-Machado, L. (2002). Logistic Regression and Artiﬁcial Neural
Network Classiﬁcation Models: A Methodology Review. 10ml of Biomedical
Informaticsz35, 352-359.

Duda, R. 0., Hart, P. E. & Stork, D. G. (2001), Pattern Classiﬁcation 2nd editionn. John
Wiley & Sons.

Elewa, MA. (2004, May). Effect of Secondary Structural Components on the
Serviceability of Steel Girder Bridges. Ph.D. Dissertaﬁon. East Lansing, MI: Department
of Civil and Environmental Engineering, Michigan State University.

Fang, X., Luo, H. and Tang, J. (2005). Damage of structures detection using neural
network with learning rate improvement. Computers and Structures: 83, 2150—2161.

Federal Highway Administration (FHWA 2001). Reﬂbilitv of Visual Espection for
Highway Bridges, Volume 1: Final Report.

Freund, Y. and Schapire, R. (1996). Experiments with a new boosting algorithm.
Processings of the Thirteenth International Conference on Machine Learning, 148-156.

Fu, J .Y., Liang, S.G. and Li, Q.S. (2007). Prediction of wind-induced pressures on a large
gymnasium roof using artiﬁcial neural networks. Computers and Structures: 85, 179-192.

219

 

Granger, E., Rubin, M. A., Grossberg, S. and Lavoie, P. (2000). Classiﬁcation of
Incomplete Data Using the Fuzzy ARTMAP Neural Network. IEEE International Joint
Conference on Neural Networks Proceedings: 6, 35-40.

Graybill, F. A. and Iyer, H. K. (1994). Regression Analysis—Concepts and Applications,
Belmont, CA: Dux-bury Press.

Gunn, S. R. (1997). Support Vector Machines for Classiﬁcationﬁand Regression.
Technical Report University of Southampton, Image Speech and Intelligent Systems
Research Group.

Guo, J. J. & Luh, P. B. (2004). Irnproveing Market Clearing Price Prediction by Using a
Committee Machine of Neural Networks. IEEE Transactions on Power Systems. 19(4),
1867-1876.

Haldar, A. and Mahadevan, S. (2000). Probability, Reliability and Statistical Methods in
Engineering Desiga. NY: John Wiley & Sons, Inc.

Hansen, L. K., Liisberg, C. and Salamon, P. (1992). Ensemble Method for Handwritten
Digit Recognition. Proceedings of the IEEE-SP Workshop on le Networks for Signal
Processing, 333-342.

Hansen, L. K. and Salamon, P. (1990). Neural Network Ensembles. IEEE Transactions
on PatternAnalysis and Machine Intelligence. 12(10), 993-1001.

Hartle, R. A., Amrhein, W. J., Wilson, K. E. and Baughman, D. R. (1991). Bridge
insmctor’s training manual 90, Federal Highway Administration. Washington, DC: U. S.

Department of Transportation.

Hastie, T., Tibshirani, R. and Friedman, J. (2001) The elements of statistical learning:
data mining, inference, and prediction. New York: Springer.

Homik, K., Stinchocombe, M. and White, H. (1989). Multilayer Feedforward Networks
Are Universal Approximators. Neural Networks: 2, 359-366.

Housner, G. W. and Vreeland, T. J. (1965). An_alysis of Stress and Deformation. NY:
Macmillan Company.

l-luang, C. S., Hung, S. L., Wen, C. M. and Tu, T. T. (2003). A Neural Network
Approach for Structural Identiﬁcation and Diagnosis of a Building ﬁom Seismic
Response Data. Earthquake Engineering and Structural Dynamics: 32, 187—206.

Homik, K., Stinchcombe, M. and White, H. (1990). Universal approximation of an

unknown mapping and its derivatives using multilayer feedforward networks. Neural
Networks: 3(5), 551-560.

220

 

Hsu, C. W. and Lin, C. J. (2002). A comparison of methods for multi-class support vector
machines. IEEE Transactions on Neural Networks: 13(2), 415—425.

Haykin, S. (1999). Neural Networks: A comprehensive foundation 2“d Edition. Upper
Saddle River, NJ: Prentice Hall.

Jain, L. C. and Martin N. M. (1999). Fusion of neural networks, ﬁrzzy sets, and genetic
algorithms: industrial applications. CRC Press.

Juszczak, P and Duin, R. P. W. (2004). Combining One-Class Classiﬁers to Classify
Missing Data. Multiple Classiﬁer Systems. Proceedings: 3077, 92-101.

Juang, C. H., Ni, S. H. & Lu, P. C. (1999). Training Artiﬁcial Neural Networks with the
Aid of Fuzzy Sets. Computer-Aided Civil and Infrastructure Engineering: 14, 407-415.

Kecman, V. (2001). Learning and Soft Computing: Support Vector Machines. Neural
Networks and Fuzzy Logic Models. Cambridge, MA: MIT Press.

 

Knerr, S., Personnaz, L. and Dreyfus, D. (1990). Single-layer learning revisited: A
stepwise procedure for building and training a neural network. Neurocomputing:
Algorithms, Architectures and Applications NY: Springer-Verlag.

Kohavi, R. and Provost, F. (1998). Glossary of Terms. Machine Learning. 30, 271-274.

Kohonen, T. (1990). The self-organizing map. Proceedmgs of the In_stitute of Electrical
and Electronics Engineers: 78, 1464-1480.

 

Kolen, J. F. and Pollack, J. B. (1990). Back Propagation is Sensitive to Initial Conditions.
Technical Report TR 90-JK-BPSIC.

Kutner, M. H., Nachtsheim C. J., Neter J. & Li, W. (2005). Applied Linear Statistical
Models, 5th edn. New York: McGraw-Hill/Irwin.

Land Jr., W. H., McKee, D., Velazquez, R., Wong, L., Lo, J. Y. and Anderson, F. (2003).
Application of support vector machines to breast cancer screening using mammogram
and clinical history data. Proceedings of SPIE - The Interﬂtional Society for Optical
Engineering. 5032 I, 546-556.

Law, M. (2006). A Simple Introduction to Support Vector Machines. Lecture for CSE
802. East Lansing, MI: Department of Computer Science and Engineering, Michigan
State University.

Lee, J ., Yi, J. D., Kim, J. D., and Yun, C. B. (2004). Health Monitoring Method Using
Committee of Neural Networks Advances in Nondestructive Evaluation. 1983-1988.

221

 

Lim, C. P., leong, J. H. and Kuan M. M. (2005). A Hybrid Neural Network System for
Pattern Classiﬁcation Tasks with Missing Features. IEEE Transactions on Pattern
Analysis and Machine Intelligence: 27(4), 648-653.

Little, R.J.A. and Rubin, p.13. (2002). Statistical Analysis with Missing Data. 2“d edition.
Wiley-Interscience.

Long, J. H., Olson, S. M., Stark, T. D. and Samara, E. A. (1998). Differential Movement
at Embankment-Bridge Structure Interface in Illinois. Transportation Research Record:
1633, 53-60.

Luxhoj, J. T., Williams, T. P. and Shyur, H.-J. (1997). Comparison of regression and
neural network models for prediction of inspection proﬁles for aging aircraft. E

Transactions (In_stitute of Industrial Eng’neers). 29(2), 91-101.

Marwala, T. (2000, January). Damage Identiﬁcation Using Committee of Neural
Networks. J oumal of Engineering Mechanics, 43-50.

Mathworks Inc. (2007a).Curve FittingUser's Guide.

Mathworks Inc. (2007b). Fuzzy Logic Toolbox 2 User’s Guide.

Mathworks Inc. (20070). Nearal NetworkUser's Guide.

MDOT (2001). Bridge Design Guides. Lansing, MI.

MDOT (2003), Michigan Structure Inventory ﬂd Appraisal Codrgrg Guide. Lansing, MI.

Mitra, S., and Hayashi, Y. (2000). Neuro-ﬁrzzy rule generation: survey in soft computing
framework. IEEE Transactions on Neurzg Networks: 11(3): 748-768.

Montgomery, D. C., Peck, E. A. & Vining, G. (2006), Introduction to Linear Reggession
Analysis 4th edition. John Wiley & Sons;

Myers R. H., Montgomery D. C. and Vining, G. G. (2002), Generalized Linear Models
With Applications in Eng'meering and the Science. John Wiley & Sons.

Myers, J ., Nanni, A., Stone, D., Vellore, S.G., and Barney, TR (2001) Precast I-Girder
Crack-ing: Causes and Design Details. Technical Report No. RDT 01-008/RI 97-021,
University of Missouri-Colombia/University of Missouri-Rolla,

Opitz, D. and Maclin, R. (1999). Popular Ensemble Methods: An Empirical Study.
Journal of Artiﬁcial Intelligence Research: 11, 169-198.

Pal, S. K. and Mitra, S. (1992). Multilayer Perceptron, Fuzzy Sets, and Classiﬁcation.
IEEE Trangactions on Neural Networlg: 3(5), 683-697.

222

 

Pal, S. K. and Mitra, S. (1999). Neuro-fuzzyjattem recognition methods in soft
computing. NY: John Wiley & Sons.

Pande A. and Abdel-Aty M. (2005, September). Identiﬁcation of Rear-end Crash Patterns
on Instrumented Freeways: A Data Mining Approach. Proceedings of the 8th
International. IEEE Conference on Intelligent Transportation Systems. Vienna, Austria,
13-16.

Parasuraman, K., Elshorbagy, A. and Si, B. C. (2006). Estimating saturated hydraulic
conductivity in spatially variable ﬁelds using neural network ensembles. Soil Science
Society of America Journal: 70(6), 1851-1859.

Park, S, Yun, C. B., Roh, Y. and Lee, J. J. (2006). PZT-based active damage detection
techniques for steel bridge components. Smart Materials and Structures: 15, 957—966.

Phares B. M., Rolander, D. D., Graybeal, B. A. and Washer, G. A. (2001). Reliability of
Visual Bridge Inspection. Public Roads: March/April, 22-29.

Pleune, T. T. and Chopra, O. K. (2000). Using artiﬁcial neural networks to predict the
fatigue life of carbon and low-alloy steels. Nuclgar Engineer-1g and Desiga: 197(1-2), 1-
12.

Quinlan, J. R. (1996). Bagging, boosting, and C45. Proceedings of the Thirteenth
Natiogrl Conference on Artiﬁcial Intelligence. 725-730.

Rarnuhalli, P. (2005). Course Notes for ECE 885 Artiﬁcial Neural Networks. East
Lansing, MI: Michigan State University.

Rice, J. A. (1995). Mathematical Statistics and Data Aniysis. Belmont, CA: Duxbury
Press.

Richards, A. M. (1979). Measurement Of Stress In Concrete Pavements. Transportation
Research Record: 713, 9-15.

 

Roberts, C. A. and Attoh-Okine, N. O. (1998, September). Comparative analysis of two
artiﬁcial neural networks using pavement performance prediction. Computer-Aided Civil
and Infrastructure Engineering: 13(5), 339-348.

SAS Institute Inc (2004). SAS 9.1 Documentation.

Schapire, R. (1990). The Strength of weak leamability. Machine Learning: 5(2), 197-227.

 

Sharkey, A. J. C. (editor, 1999). Combining Artiﬁcial Neural Nets: Ensemble and
Modular Multi-Net Systems. London: Springer.

223

 

Shober, S. F. (1997). Great Unsealing: A Perspective on PCC Joint Sealing.
Transportation Research Record: 1597, 22-30.

Shyur, H.J., Luxhoj, J. T. and Williams, T. P. (1996). Using neural networks to predict
component inspection requirements for aging aircraft. Computers & Industrial
Engineering: 30(2), 257-267.

Silva, A., Cortez, P., Santos, M.F., Gomes, L., and Neves, J. (2004). Multiple organ
failure diagnosis using adverse events and neural networks. Proceedings of the 6th
International Conference on Enterprise Information Systems. 401-408.

Smith, K. D., Snyder, M. B., Darter, M. I., Reiter, M. J. and Hall, K. T. (1987). Pressure
Relief and Other Joint Rehabilitation Techniques. FHWA, U. S. Department of
Transportation.

Sohn, S. Y. and Lee S. H. (2003). Data fusion, ensemble and clustering to improve the
classiﬁcation accuracy for the severity of road trafﬁc accidents in Korea. Safety Science:
41, 1-14.

Song, H., Zhong, L. and Han, B. (2005). Damage of structures detection by integrating
independent component analysis and support vector machine. Advanced Data Mining and
Applications: First International Conference, Proceedinga. 670-677.

SPSS Inc. (2004). SPSS® 13.0 Base User's Guide.

Snedecor, G. W. and Cochran, W. G. (1989). Statistical Methods, 8th Edition. Iowa State
University Press/AMES.

Sybase Inc. (2004). Gettiag Started InforMak_e_i.

Taha, M. M. and Lucero, J. (2005). Damage identiﬁcation for structural health
monitoring using fuzzy pattern recognition. Eng‘neerinLStructure: 27, 1774-83.

Taylor, J. S. & Cristianini, N. (2004). Kernel Methods for Pattern Analysis, Cambridge
University Press.

Vapnik, V. N. (1999). The Nature of Statistical Learning Theory. 2nd edn. Springer.

Wagstaff, K. L. and Laidler V. G. (2005). Making the Most of Missing Values: Object
Clustering with Partial Data in Astronomy. Astronomical Data Analysis Software and
System XIV: 347, 172-176.

 

Weisberg, S. (2005). Applied Linear Regression, 3rd edition. John Wiley & Sons.

White, H. (1990). Connectionist Nonparametric Regression: Multilayer Feedforward
Networks Can Learn Arbitrary Mappings. Neural Network_s: 3(5), 535-549.

224

 

 

Xiao, Y. D., Clauset, A., Harris, R., Bayram, E., Santago, P. and Schmitt, J. D. (2005).
Supervised Self-Organizing Maps in Drug Discovery. 1. Robust Behavior with
Overdeterrnined Data Sets. Journ_a1 of Chemical Information and Modeling: 45(6), 1749-
1758.

Yang, S. and Browne, A. (2004). Neural Network Ensembles: Combining Multiple
Models for Enhanced Performance Using a Multistage Approach. Expert Systems: 21(5),
279-288.

Yao J. T. P. (1980, August). Damage Assessment of Existing Structures. Journal of the
Engineering Mec_h_anics Division. 785-799.

Yu, L., Wang, S. and Lai, K. K. (2008 February). Credit risk assessment with a
multistage neural network ensemble learning approach. Expert Systems with
Applications: 34(2), 1434-1444.

Yun, C. B., Lee, J. W., Kim., J. D. and Min, K. W. (2003). Damage Estimation Method
Using Committee of Neural Networks. Proceediggs of SPIE - The International Socieg
for Opticaﬂingineering: 5047, 263-274.

Zadeh, L. A. (1965). Fuzzy Sets. Information and Control: 8, 338-353.

Zadeh, L. A. (1975a). Linguistic Variable and Its Application to Approximate Reasoning.
Information Sciences: 8(4), 199-249.

Zadeh, L. A. (1975b). Linguistic Variable and Its Application to Approximate Reasoning.
Information Sciences: 8(4), 301-357.

 

Zadeh, L. A. (1975c). Linguistic Variable and Its Application to Approximate Reasoning.
Information Sciences: 9(1), 43-80.

Zadeh, L. A. (1994). .Fuzzy Logic, Neural Networks, and Soft Computing. Fuzzy
Systems, 77-84.

Zhao, J ., Ivan, J. N. and DeWolf, J. T. (1998). Damage of structures detection using
artiﬁcial neural networks. J ourrial of Infrastructure Systems: 4(3), 93-101.

Zhou, Z., Jiang, Y., Yang, Y. and Chen, S. (2002). Lung Cancer Cell Identiﬁcation Based
onArtiﬁcial Neural Network Ensembles. Artiﬁcial Intelligence in Medicine: 24, 25-36.

225

 

   

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