(It ”
Quarpmfiz.“ was?
.1 in

“mg”. .

«mafia? .
A _ nfiuu. a...
‘ I...‘.I9.8kl
u g. aw .....ufi., 4.1m.
ark n»«.n:.w‘.mmm..uurwnz.m#€

v... a. ti. 1
3.; I!

l. i

. a 1

§

19
x:
a

i
:

Mum
‘ a..."
am.“

.415
1

:30
a:

E
I

 

9

9“...
.1. 3.3.2»! ;
d3
r.
all:
$4an“
..
.5 In \
Emu. ail...
i312: I.
...3.:...uux:.b.lss
.‘isu‘ ‘1 .
J... ‘15:; lilfifiil 10$
.3.v\1.¢.i 5....-
.u»..d u... :
q . ..
.v v.“
I.
1h... v
i .121!
1“:
It 13$

8'!

 

. .2: s. A 1:3. v
..
In

I. l<..l‘

. x
5.3.1.15... . u‘
I». ‘ . . . a L .1!

‘ |||

 

II
t

 

HER/«RY
Michigan State
University

 

This is to certify that the
thesis entitled

STRATEGIES FOR OPTIMIZING HYBRID ELECTRIC
VEHICLE POWERTRAINS AND PROGRESSIVELY
CRUSHING RAILS

presented by

NATHAN CHASE

has been accepted towards fulfillment
of the requirements for the

MS. degree in Mechanical Engineering

 

Major Professor's Signature
5:// 0/2 0/ 0

Date

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

FEB 0 8 2017

O 1 iii 1 g

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5m KthroleccanPrOIlClRCIDatODuohdd

 

 

STRATEGIES FOR OPTIMIZIN G HYBRID ELECTRIC VEHICLE POWERTRAIN S
AND PROGRESSIVELY CRUSHING RAILS

By

Nathan Chase

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Mechanical Engineering

2010

ABSTRACT

STRATEGIES FOR OPTIMIZING HYBRID ELECTRIC VEHICLE POWERTRAINS
AND PROGRESSIVELY CRUSHING RAILS

By
Nathan Chase

In application of automated design optimization methods to complex problems,
often the biggest challenge is to identify an optimization problem statement that will lead
to a design with the desired performance in an efficient and effective manner. In the
current study, the optimization statements of two challenging problems are investigated
and new approaches are introduced to improve the performance of the designs as well as
the optimization process.

Fuel efficient and environmentally friendly ground vehicles require a careful
balance among competing goals for fuel economy, performance, and emissions. Several
optimization approaches are investigated for a series hybrid bus to find the best overall
combination of engine size, battery pack, electric motor and generator with minimum fuel
consumption under specified performance criteria. An alternative to a common
optimization approach for HEV’s is proposed and shown to yield results equivalent to
other common approaches but with greater efficiency for the problem posed.

To increase robustness of the crush mode and to decrease repair costs after a
crash, it is desirable for front and rear structural rails in an automotive vehicle to crush
progressively - where crush initiates near the tip of the rail and progresses rearward in a
controlled fashion. A new strategy is investigated here to achieve progressively crushing
designs during an automated design optimization study. It is demonstrated that high

performing designs with progressive crush can be obtained using the proposed approach.

To my parents for their encouragement, direction, and invaluable advice. And to
my wife for her patience, support, and calming influence. Without them this success

would surely have been unattainable.

ACKNOWLEDGEMENTS

My sincere appreciation to my advisor Dr. Ronald Averill for his guidance and
vision in improving the way optimization is performed and in my understanding of it.
Also I would like to thank my other thesis committee members Dr. Erik Goodman and
Dr. Farhang Pourboghrat. Their support is much appreciated.

I also would like to thank Red Cedar Technology for their support in this
endeavor and specifically Mr. Ranny Sidhu. His advice and aid greatly helped in the
development of the strategies developed for this thesis.

Other key members in the development of this thesis include: Kaushik Sinha and
his aid with the HEV models, as well as the High Performance Computing Center of
Michigan State University (HPCC) and its staff. Without their help and resources this

thesis would not be as complete.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................ viii
LIST OF FIGURES .................................................................................. x
CHAPTER 1
INTRODUCTION .................................................................................. 1
CHAPTER 2
INTRODUCTION TO HYBRID ELECTRIC VEHICLES ................................... 4
2.1 Background .............................................................................. 4
2.2 Literature Review ...................................................................... 6
2.2.1 Overview ..................................................................... 6
2.2.2 Modeling Tools ............................................................. 9
2.2.3 Optimization ............................................................... 10
CHAPTER 3
OPTIMIZATION WITH HEEDS AND ADVISOR .......................................... 15
3.1 Introduction to HEEDS .............................................................. 15
3.2 Introduction to ADVISOR ......................................................... 15
3.2.1 Overview ................................................................... 15
3.2.2 Matlab .m Files ............................................................ 16
3.3 Linking HEEDS to ADVISOR ..................................................... 19
3.3.1 ADVISOR Optimization Preparation .................................. 19
3.3.1.1 optim_control_HEEDS.m ..................................... 19
3.3.1.2 obj_fun__control.m ............................................. 22
3.3.1.3 con_fun_control.m ......................... I .................... 23
3.3.1 .4 indata_control.m ............................................... 24
3.3.2 Running the ADVISOR Simulation from Batch Mode .............. 24
3.3.3 Process Integration Between HEEDS and ADVISOR ............... 25
3.4 Optimization Example: Small Vehicle Parallel HEV ........................... 26
3.4.1 Baseline Model ............................................................ 26
3.4.2 Optimization Problem Statement ........................................ 29
3.4.3 HEEDS Setup .............................................................. 30
3.4.3.1 Starting a New Project ........................................ 30
3.4.3.2 Defining the Evaluation Process ............................. 30
3.4.3.3 Defining the Project Variables and Responses ............ 31
3.4.3.3.1 Defining the Project Variables .................... 31
3.4.3.3.2 Defining the Project Responses .................. 32
3.4.3.4 Tagging the Input and Output Files ......................... 33
3.4.3.4.] Tagging the Input Files ............................ 33
3.4.3.4.2 Tagging the Output Files .......................... 34
3.4.3.5 Assembling the Problem Definition ......................... 34

3.4.4 Running the Project ....................................................... 35

3.4.5 Results and Discussion ................................................... 36
CHAPTER 4
BASELINE ADVISOR MODEL FOR A HYBRID ELECTRIC BUS .................... 38
4.1 Introduction ............................................................................ 38
4.2 ADVISOR Vehicle Model Description ........................................... 39
4.2.1 Vehicle Level Parameters ................................................ 40
4.2.2 Fuel Converter Parameters ............................................... 41
4.2.3 Exhaust Aftertreatment Parameters .................................... 42
4.2.4 Energy Storage System Parameters .................................... 43
4.2.5 Motor Parameters ......................................................... 46
4.2.6 Generator Parameters ..................................................... 49
4.2.7 Transmission Parameters ................................................ 50
4.2.8 Wheel Parameters ......................................................... 51
4.3 Summary .............................................................................. 54
CHAPTER 5
OPTIMIZATION STRATEGY FOR HEV’S USING ADVISOR AS A SIMULATION
TOOL ................................................................................................ 55
5.1 Introduction ........................................................................... 55
5.2 Hybrid Electric Bus Model ......................................................... 56
5.2.1 Component Sizing Procedure ........................................... 56
5.2.2 Control Strategy ........................................................... 58
5.2.3 Driving Cycle .............................................................. 58
5.3 Baseline Designs ...................................................................... 60
5.3.1 Conventional Bus Design ................................................ 60
5.3.2 Baseline Hybrid Bus Design ............................................. 61
5.4 Modeling Concepts for HEV Optimization ....................................... 62
5.4.1 Introduction ............................ ' .................................... 62
5.4.2 SOC Corrections .......................................................... 62
5.4.3 Multiple Initial SOC’s .................................................... 63
5.4.4 Multiple Cycle Repeats ................................................... 66
5.4.5 Corrected Fuel Economy ................................................ 69
5.5 Optimization Strategies and Problem Statements ................................ 70
5.5.1 Strategy 1- Multiple SOC’s and Multiple Drive Cycle
Repetitions ........................................................................ 70
5.5.2 Strategy 2- SOC Correction with Corrected Fuel Economy . .. 72
5.5.3 Strategy 3- A Hybrid Approach .......................................... 77
5.6 Results of the Optimization Studies ................................................ 80
5.6.1 Strategy Comparisons ..................................................... 80
5.6.2 Baseline Hybrid Bus Comparisons ..................................... 94
5.7 Conclusions ......................................................................... 97
CHAPTER 6
INTRODUCTION TO PROGRESSIVE CRUSH ............................................. 98

vi

6.1 Preliminary Information ............................................................. 98

6.2 Literature Review ................................................................... 101
CHAPTER 7
OPTIMIZATION STRATEGY DEFINITION .............................................. 107
7.1 Introduction .......................................................................... 107
7.2 Formal Definition .................................................................... 107
7.3 Implementation of Strategy ........................................................ 111
CHAPTER 8
AXIAL RAIL CRUSH AND ANALYSIS MODEL ........................................ 113
CHAPTER 9
OPTIMIZATION USING THE PROGRESSIVE CRUSH STRATEGY ................ 1 19
9.1 Relation Between Progressive Energy and Total Energy ..................... 119
9.2 Progressive Crush Optimization — without considering mass ................ 122
9.2.1 Conventional Crush Optimization to Maximize Total Energy
Absorbed ......................................................................... 123
9.2.2 Progressive Crush Optimization to Maximize Progressive Energy
Absorbed ........................................................................ 124
9.2.3 Optimization Results .................................................... 124
9.3 Progressive Crush Optimization — accounting for mass ....................... 130
9.3.1 Conventional Crush Optimization to Maximize Total Energy
Absorbed per Unit Mass ...................................................... 131
9. 3. 2 Progressive Crush Optimization to Maximize Progressive Energy
Absorbed per Unit Mass ...................................................... 132
9. 3. 3 Optimization Results .................................................... 133
9.4 Zone 3 Definition Study ........................................................... 138
9.4.1 Introduction ............................................................... 138
9.4.2 Evaluation of the Effect of 5 ........................................... 141
9.4.2.1 Problem Statement ........................................... 141
9.4.2.2 Results ......................................................... 143
9.4.3 Total Stackup Represented by the Sum of Individual Zone
Stackups ......................................................................... 146
9.4.3.1 Problem Definition ........................................... 146
9.4.3.2 Results ......................................................... 147
9.4.4 Conclusions ............................................................... 149
CHAPTER 10
SUMMARY AND CONCLUSIONS ......................................................... 150
REFERENCES .................................................................................. 152

vii

LIST OF TABLES

3.4.1 Baseline model design variable values ................................................... 36
3.4.2 Optimized design variable values ......................................................... 37
4.2.1 Vehicle parameters for the baseline bus model ......................................... 40
4.2.2 Fuel converter parameters for the baseline bus model ................................. 41
4.2.3 Exhaust aftertreatment parameters for the baseline bus model ....................... 43
4.2.4 Energy storage system parameters for the baseline bus model ....................... 45
4.2.5 Motor parameters for the baseline bus model .......................................... 48
4.2.6 Generator parameters for the baseline bus model ...................................... 49
4.2.7 Transmission parameters for the baseline bus model .................................. 51
4.2.8 Wheel parameters for the baseline bus model .......................................... 53
5.2.1 Baseline components of the series hybrid bus for optimization ...................... 57

5.6.] Optimization results obtained from all three strategies. Where three results are
reported for a run, each corresponds with the results from a given initial SOC load case
(0.68, 0.60, 0.52). The highlighted results correspond with the objective value for a
given strategy. *Strategy 2 results were re-analyzed with no SOC correction and run
with the multiple drive cycle iterations and multiple initial SOC analyses used for
Strategy 1. "Strategy 1 results were re-analyzed with the SOC correction settings

of Strategy 2 for one drive cycle .................................................................. 85

5.6.2 Design variable values corresponding with the optimized designs from each
strategy .............................................................................................. 86

5.6.3 Comparison between the optimized designs from Strategy 1 and the baseline hybrid
bus model ........................................................................................... 95

5.6.4 Comparison between the optimized designs from Strategy 2 and the baseline hybrid
bus model ........................................................................................... 95

5.6.5 Comparison between the optimized designs from Strategy 3 and the baseline hybrid
bus model ........................................................................................... 96

viii

8.1.1 Plasticity data for the rail analyses. For different strain rates, the stress vs.
effective plastic strain is defined ................................................................. 114

9.2.1 Comparison of progressive crush and conventional crush optimized results 129

9.3.1 Comparison of progressive crush and conventional crush optimized results when

accounting for mass .............................................................................. 137
9.4.1 Stackup distance 6 allotted for each optimization in the study ...................... 142
9.4.2 Results for each optimization ............................................................ 144

9.4.3 Optimized design from each optimization re-evaluated in terms of PEA for four
different values of 5 .............................................................................. 144

9.4.4 Stackup definitions used to study the relationship between total stackup (8) and the
individual zone stackups (6i) ................................................................... 147

9.4.5 Optimized design from each optimization with energy absorbed calculated for three
different stackup definitions .................................................................... 148

 

LIST OF FIGURES

2.2.1 Series hybrid electric vehicle configuration ................................................ 7
2.2.2 Parallel hybrid electric vehicle configuration .............................................. 7
2.2.3 Combined hybrid electric vehicle configuration A ....................................... 7
2.2.4 Combined hybrid electric vehicle configuration B ....................................... 7
3.3.1 Main input file: optim_control_HEEDS.m .............................................. 21
3.3.2 Objective definition file: obj_fun_control.m ............................................ 22
3.3.3 Constraint definition file: con_fun_control.m ........................................... 23
3.3.4 Input design variable file: indata_control.m ............................................. 24
3.3.5 Process integration performed by HEEDS with ADVISOR ........................... 26
3.4.1 Parallel HEV Configuration in ADVISOR .............................................. 27
5.2.1 Powertrain configuration of the HEV bus (as it appears in ADVISOR) ............ 57
5.2.2 Driving cycle speed/elevation vs. time for the UDDS driving cycle ................. 59
5.2.3 UDDS driving cycle characteristics ...................................................... 59

5.4.1 Optimized design characteristics for one drive cycle of the UDDS (SOC=state of
charge; co=engine speed) with an initial SOC of 0.68 ........................................ 64

5.4.2 Optimized design characteristics (SOC=state of charge; w=engine speed) if re-
evaluated with an initial SOC of 0.60 ........................................................... 65

5.4.3 SOC history plots for an optimized design evaluated for different number of
drive cycles. The period (T) of the cycle corresponds with just less than three cycle
repetitions ........................................................................................... 67

5.4.4 Engine speed history plots for an optimized design evaluated for different number
of drive cycles ..................................................................................... 68

5.5.1 Zero-Delta SOC correction routine. An initial SOC guess is evaluated
(SOCinitial,0) in terms of ASOC. The initial bounds around the zero-A SOC tolerance

are then found (SOCinitia1,1(-) and SOCinitial,l(+)) and linearly interpolated to get
SOCinitial,2(-). This bound (SOCinitial,2(-) and SOCinitial,l(+)) is then linearly
interpolated and the process repeated until an initial SOC is found that gives a ASOC
within the tolerance (SOCinitial,t-zero-delta) [9] .............................................. 74

5.5.2 Logic used to calculate the corrected fuel economy. Scenario 1 occurs when the
fuel penalty is small (or negative) and makes the corrected firel economy equal to: the
drive cycle mi/gal gasoline equivalent for small positive values, and greater than the
drive cycle mi/ gal gasoline equivalent for negative values. Scenario 2 occurs when the
battery equivalent is large but the drive cycle mi/gal gasoline equivalent is not too

large, thus reduces the corrected fuel economy to account for the fuel penalty during

the run. Scenario 3 occurs when the vehicle operates almost entirely as an electric

vehicle (EV) and therefore treats the corrected fuel economy as if the vehicle were
completely EV with all of its fuel used coming from the fuel penalty ..................... 76

5.6.1 Typical convergence plot for the HEV optimizations. The shown optimization
was nearly converged by ~300 evaluations .................................................... 81

5.6.2 Three-dimensional contour plot of the local region surrounding the global
minima locations of the Six Hump Camel Back Function. Note the multiple local
minima and multiple global minima with identical response values ........................ 84

5.6.3 Three-dimensional contour plot of the Rosenbrock’s Valley function for two
variables. Note the similar response values along the valley close to the global
optimavalue .................................. 84

5.6.4 Comparison of the SOC history and engine speed history plots for a typical
optimized design from the Strategy 1 optimizations (Run 1 shown here). With an initial
SOC of 0.68 these optimized designs can run primarily as electric vehicles (EV’s) ...... 87

5.6.5 Comparison of the SOC history and engine speed history plots for a typical
optimized design from the Strategy 1 optimizations with initial SOC = 0.60 (Run 1
shown here) ......................................................................................... 88

5.6.6 Comparison of the SOC history and engine speed history plots for a typical
optimized design from the Strategy 1 optimizations with initial SOC = 0.52 (Run 1
shown here) ......................................................................................... 89

5.6.7 Typical SOC history and engine speed history plots for the Strategy 1 optimized
designs re-analyzed with SOC correction settings from Strategy 2 for a single drive cycle
(Run 1 shown here). Note that due to the Zero-Delta SOC routine, the initial and final
SOC’s are very similar ............................................................................ 90

xi

5.6.8 SOC history and engine speed history plots for typical optimized designs where
maximizing total energy usage is the objective (Run 1 from Strategy 2 is shown).

Note that due to the Zero-Delta SOC routine, the initial and final SOC’s are very

similar ............................................................................................... 91

5.6.9 Comparison of typical SOC history and engine speed history plots (SOC = 0.68)

for the Strategy 2 optimized design of Figure 5.6.8 re-analyzed with no SOC correction
and the settings of Strategy 1 (multiple drive cycle iterations and multiple initial SOC
analyses). Note that the Optimized designs do not act as EV’s .............................. 92

5.6.10 Comparison of typical SOC history and engine speed history plots (SOC = 0.60)
for the Strategy 2 optimized design of Figure 5.6.8 re-analyzed with no SOC correction
and the settings of Strategy 1 (multiple drive cycle iterations and multiple initial SOC
analyses) ............................................................................................. 93

5.6.11 Comparison of typical SOC history and engine speed history plots (SOC = 0.52)
for the Strategy 2 optimized design of Figure 5.6.8 re-analyzed with no SOC correction
and the settings of Strategy 1 (multiple drive cycle iterations and multiple initial SOC

analyses) ............................................................................................. 94
6.1.1 Example of a rail undergoing progressive crush ....................................... 100
6.1.2 Example of a rail undergoing non-progressive crush ................................. 100

6.2.1 Quasi-static axial compression of thin-walled circular aluminum tubes (from

Guillow et a1. [34]) ............................................................................... 102
7.2.1 Specified crush zones in a rail. The tip of the rail corresponds to Zone 1, and the

rear of the rail corresponds to Zone NZ ....................................... ~ ................ 110
7.2.2 Definition of impactor displacements, as used in the calculation of PEA ......... 110
7.3.1 Simple executable used with LS-DYNA to obtain EA(U) ...................... i ..... 112
8.1.1 Analysis model used for the progressive crush strategy .............................. 113

8.1.2 Crush zones and cross—sectional design stations used in the rail analysis and
design model ...................................................................................... 1 15

8.1.3 Section profiles were controlled by 4 independent control points (I through 4).

The other control points were positioned by satisfying vertical and horizontal lines

of symmetry. The cross-section perimeter was scaled to ensure that it was within 2%

of the baseline perimeter ........................................................................ 115

8.1.4 Zone dimensions and impactor displacement specifications in the current
model .............................................................................................. l 17

xii

8.1.5 Reaction force versus time during a typical crush event ............................. 118

9.1.1 Scatter plot of all evaluations performed during the multi-objective optimization.
There are numerous designs with total energy above 15 kJ but with negative

progressive energies. Furthermore, there are designs at 25 k] and above that have
negative or near-zero progressive energies ................................................... 121

 

9.1.2 Scatter plot of good designs in terms of both total energy absorbed and
progressive energy absorbed. Highlighted is the Pareto front of the rank-l designs
from the multi-objective optimization ......................................................... 121

9.2.1 Comparison of the optimized design shapes from the conventional crush
optimization and progressive crush optimization. After 2000 evaluations the
optimization runs were not fully converged but had made significant progress 126

9.2.2 Comparison of the force-displacement curves for the optimized shapes from
the conventional crush optimization (maximize EA) and the progressive crush
optimization (maximize PEA) .................................................................. 127

9.2.3 Crush modes of the Design A optimized designs. At t = t2, the conventional
strategy’s optimized design begins to non-progressively crush ........................... 128

9.2.4 Crush modes of the Design B optimized designs. At t = t2, the conventional
strategy’s optimized design begins to non-progressively crush ............................ 128

9.2.5 Crush modes of the Design C optimized designs. At t = t2, the conventional
strategy’s optimized design begins to non-progressively crush ............................ 129

9.2.6 Crush modes of the Design D optimized designs. Both the conventional strategy
and progressive strategy yielded optimized designs that progressively crushed ......... 129

9.3.1 Comparison of the optimized design shapes fi'om the conventional crush strategy
(maximizing SEA=EA/m) and the progressive crush strategy (maximizing
SPEA=PEA/m). After 2000 evaluations the optimization runs were not fully

converged but had made significant progress ................................................ 134

9.3.2 Comparison of the force-displacement curves for the optimized shapes from the
conventional crush optimization (maximize SEA=EA/m) and the progressive crush
optimization (maximize SPEA=PEA/m) ...................................................... 135

9.3.3 Crush modes of the Design A optimized designs. Both the conventional strategy
and progressive strategy yielded optimized designs that progressively crushed 136

9.3.4 Crush modes of the Design B optimized designs. At t = t1, the conventional
strategy’s optimized design begins to non-progressively crush ........................... 136

xiii

 

 

9.3.5 Crush modes of the Design C optimized designs. At t = t1, the conventional
strategy’s optimized design begins to non-progressively crush ........................... 137

9.3.6 Crush modes of the Design D optimized designs. Both the conventional strategy
and progressive strategy yielded optimized designs that progressively crushed ....... 137

9.4.1 Stackup of a typical rail that progressively crushes. Stackup occurs with a

material buildup of thickness 6 ................................................................. 138
9.4.2 Zone definitions and impactor displacement specifications used within this

study. The material stackup has arbitrarily been set at 83.4 mm ........................... 140
9.4.3 Alternative definition of accounting for stackup: 61 + 62 + 63 = 6 ................. 140

9.4.4 Zone definitions used for the different optimizations performed in the study to
determine the effect of 6 ........................................................................ 142

9.4.5 Optimized designs from the four optimizations with PEA calculated for different
values of 6. The optimized design from optimization B had the highest PEA regardless
of the statement used. This shows that realistic values for the stackup 6 occurring in
crush should be used in the optimization problem statement to encourage the best
progressive crush ................................................................................. 145

9.4.6 Crush modes of the optimized designs from the optimization study of the impact
of the value of U3 on the optimization ......................................................... 145

9.4.7 Progressive energy absorbed by the different optimized designs with the
different optimization definitions .............................................................. 148

9.4.8 Standard deviation of the progressive energy absorbed among the three designs
for the different optimization definitions ..................................................... 149

xiv

CHAPTER 1: INTRODUCTION

Optimization is becoming an essential tool in computer aided engineering,
specifically in the design process. The need for quicker, better solutions in the global
economy that is the reality of today’s world, has made it insufficient to rely solely on an
engineer’s intuition and experience. Optimization allows superior designs to be found
quicker and more robustly in a realm that is not limited to the experience of a specific
engineer working on a project, but rather the search capabilities of the optimization
software in use, and the way the optimization problem is posed.

In the past, optimization has been slow to gain popularity in industry due to the
perceived complexity associated with it. The methods used to perform the optimization
search were largely dependent upon the problem at hand and it was common for one to
need to be an expert in not only the problem being solved but also the search methods
used to solve the problem. Today however, some of the commercial optimization
software packages are improved enough, and user friendly enough, that being an expert
in optimization is no longer a requirement. There are search methods available (e. g.,
SHERPA [29]) that require no knowledge by the user as to the details of the search
strategy employed. Whereas in the past, the user had to specify values of tuning
parameters for a given method, methods like SHERPA require no tuning parameters, only
the number of evaluations allowed. In addition, modern hybrid and adaptive methods
work on broad classes of problems, so the user does not need to know the nature of

design landscape of the problem being solved a priori. These methods adapt to the

landscape of the problem being solved by modifying which search strategies are used,
and how they are used, at various stages of the search process.

Today, it follows that the complexity of search algorithms and their use is no
longer a primary issue. The issue at hand now becomes how to best define the
optimization problem being solved in order to arrive at the desired results. For most
problems this includes only a few decisions by the engineer. He must decide how best to
setup the analysis model of the system he is trying to optimize; this may be deciding on
how best to parameterize a CAD model or choosing the most appropriate settings for a
numerical model, among other things. He then must decide what responses are of interest
to him, and what performance criteria are to be used during the optimization. Finally, he
must decide the allowable design space for his design variables, and what is considered
an acceptable design.

For some applications, the above three decisions by the engineer regarding the
optimization statement may not be sufficient. The way the optimization should be defined
may not be clear to the engineer in that it may be defined in multiple ways. Each
definition possibility may lead the optimization in a different direction and produce
different optimal designs. Defining an optimization problem in one way may lead the
optimization to a design that meets the requirements as defined, but that does not meet
requirements that were undefined — ones that the user may not have thought of before the
optimization was performed, or didn’t know how to define. Once the engineer knows
how to properly define the optimization problem for the specific application he is
interested in, however, not only will he get superior optimal designs, but he also will have

a better understanding of how to define optimization problems for similar applications.

It is the goal of this study to investigate optimization strategies for two specific
applications for which the problem statement is not obvious, and for which multiple
definitions are possible — each that give vastly different results. It is the hope that the
optimization strategies posed here will provide engineers in the respective fields a
“template-like” problem statement to be used in future optimization studies. In addition,
it is hoped that this work will demonstrate the importance of optimization strategies for
complex applications and provide the framework for more application problem

definitions, perhaps even in other fields, to be explored in the future.

CHAPTER 2: INTRODUCTION TO HYBRID ELECTRIC
VEHICLES

2.1 Background

Never before has there been such a concern over the future of the transportation
industry throughout the world. The recent escalation in concerns over global warming
and greenhouse gases, coupled with the depleting supply of the world’s oil reserves and
the growing instability in the regions of the world where these reserves exist, has caused
a heightened awareness in the insufficiency of the standard internal combustion engine
(ICE). It has never been as apparent as in today’s modern world, that the current models
for automobiles and other vehicles that rely on natural reserves are insufficient for a
responsible, realistic firture.

Currently there are many proposals as to the direction the world should take in
changing the dependence on oil. Alternate fuel systems such as fire] cells and bio-diesels
are strong contenders for the next wave of vehicles. However these vehicles, should they
be implemented, would require a major overhaul in the economic and standard landscape
the world has become accustomed to. The shifting agricultural landscape required for
bio-diesels make them an unlikely alternative, while the instability and uncertainty of firel
cells also make them unlikely in the near firture as a replacement for the standard IC
engine. Electric vehicles (EV’s) came into the mainstream of America over a decade ago.
Their prompt failure and unpopularity make them an unlikely alternative for most of the

world anytime soon.

Hybrid electric vehicles (HEV’s) are perhaps the most promising substitute to
conventional vehicles in the near future. HEV’s utilize multiple energy sources; in terms
of this thesis, these energy sources will refer to an energy storage system (such as a
battery or ultra-capacitor), and also an engine. These multiple energy sources allow for
the optimal operation of the engine, thus reducing fuel consumption and emissions. This
proposed alternative to standard vehicles helps reduce the consumption of oil reserves,
while also reducing the emissions of greenhouse gases and not drastically changing the
current landscape of the transportation industry.

The design of hybrid electric vehicles (HEV’s) requires complex optimizations to
account for the intricate interactions among the components, control strategies and the
resulting effects on performance. Due to the size of HEV models and the complexity of
interactions among the many components, it is challenging to properly define an
optimization problem statement that invokes a final design with the desired performance
characteristics. The optimization problem statement (definition greatly affects the
performance of the optimized HEV design, as well as the implications of the design.
While this may seem obvious, the proper problem statement for achieving a particular
performance goal is not always so clear.

In the first section of this thesis, the main characteristics of two optimization
strategies that have been shown to be efficient in optimizing hybrid electric vehicles are
merged into a single and more robust strategy that is shown to have several advantages in
terms of design performance. The main purpose here is to explore these various strategies
and associated optimization problem statements and their effects on the resulting hybrid

vehicle design. As a consequence of this study, a practical and efficient approach is

developed for sizing the components and defining the system control of HEV’s to create

efficient, reliable vehicles.

2.2 Literature Review

2.2.] Overview

Hybrid electric vehicles (HEV’s) include an engine as a fuel converter or
irreversible prime mover, an electric prime mover, and sometimes a generator [1-2]. They
are typically classified into three different categories: series, parallel, or combination.
Series HEV’s utilize an internal combustion engine (ICE) as an auxiliary power unit to
extend the driving range of a purely electric vehicle. These vehicles use a generator to
convert mechanical energy produced by the ICE into electricity that can either charge the
battery or feed the drive motor directly (as shown by Figure 2.2.1). The use of a clutch in
series HEV’s is unnecessary. Parallel HEV’s do require a clutch, and utilize both the ICE
and electric motor to supply tractive power either individually or in combination (see
Figure 2.2.2). Combined HEV’s utilize both a mechanical and electric link, with two

distinct electric machines (as shown by Figure 2.2.3 and Figure 2.2.4).

 

Engine

ll

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Generator
Battery fl Power Converter —— Motor Transmission '— Vehicle
Figure 2.2.1. Series hybrid electric vehicle configuration.
Engine
Battery —- Power Converter fl» Motor Transmission — Vehicle
Figure 2.2.2. Parallel hybrid electric vehicle configuration.
Engine
Generator : Planetary Gear Set ‘ Transmission —i Vehicle
Battery —- Power Converter Motor
Figure 2.2.3. Combined hybrid electric vehicle configuration A.
Generator Engine
Battery Power Converter Motor Transmission _ Vehicle

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.2.4. Combined hybrid electric vehicle configuration B.

 

 

 

Guzzella and Sciarretta [I] as well as Ehsani, Gao, and Miller [3] identify HEV’s
as the most promising alternatives to conventional vehicles. The high energy density of
petroleum fuel and the convenience of current fueling systems make for a long vehicle
operating range, easy refueling, and a smooth transition from conventional vehicles,
while the design of the HEV components provide an improved fuel economy and reduced
emissions. HEV’s can utilize a downsized engine while still fulfilling the maximum
power requirements of the vehicle. They possess the ability to recover energy during
braking (regenerative braking), as opposed to dissipating it in conventional vehicles that
use friction braking. HEV’s can optimize the energy distribution between their prime
movers for maximum efficiency, while also eliminating idle fuel consumption by turning
off the engine when no power is required and eliminating clutching losses by engaging
the engine only when the speeds match. In addition, due to the optimized operation of the
internal combustion engine, the vehicles will need less maintenance than conventional
vehicles currently require, as described by Chan [4].

While the benefits of HEV’s over conventional vehicles are substantial, there are
also some drawbacks as discussed by Chan [4]. Hybrid electric vehicles are typically 10-
30% heavier than conventional vehicles, while costing more due to added motors, energy
storage systems, and power converters. In addition, reliability and warranty related issues
are of concern due to the lack of mechanic training in the electrical aspect of their design.
Safety concerns with HEV’s still need to be addressed due to the presence of high voltage

devices, and the effect of electromagnetic fields on HEV’s is not fully understood.

2.2.2 Modeling Tools

The need for accurate modeling and simulation of hybrid electric vehicles has
been discussed in [5-7]. Gao, et al [5] present an overview of some currently available
methods, and place special emphasis on four modeling tools: ADVISOR [8-9], PSAT
[10], PSIM [11], and VTB [12]. ADVISOR is a steady state model that achieves fast
computation but does not accurately resolve dynamic effects. PSAT is a quasi-steady
state model. PSIM and VTB are dynamic models, in which time integration is performed.
The tool QSS toolbox is introduced by Guzzella, and Amstutz [13] for optimizing and
simulating hybrid powertrains. QSS toolbox uses a backward approach that is faster than
typical approaches due to no feedback loops being used, and rather large time steps being
utilized. There are significant assumptions in this tool, which the authors contend are
small and have negligible effects over an entire drive cycle.

In the current study, ADVISOR was chosen as the modeling tool. An overview of
ADVISOR (advanced vehicle simulator) is provided by Wipke, Cuddy, and Burch [8].
ADVISOR utilizes a combined forward/backward simulation approach to evaluate a
vehicle’s performance. It is used in conjunction with Matlab to simulate the behavior of
Hybrid Electric Vehicles (HEV’s) [9]. An ADVISOR model consists of multiple
components that are evaluated in a l-dimensional manner, often using look-up tables and
efficiency maps to provide fast computation with the backward facing approach. The
force required to accelerate the vehicle through a time step is calculated directly from the
required speed trace. This force is then translated into torque, etc. This process is carried
backward through the HEV drive train, component by component until the entire system

is solved. This backward facing approach is typically more efficient than the forward

facing approach for force calculation. The forward facing aspect of the ADVISOR
solution uses a driver model that considers the required speed and the present speed to
develop appropriate throttle and brake commands, which are in turn translated into
torque, etc. The forward facing approach better takes into account dynamic effects and
maximum effort accelerations, and enables the development of vehicle controllers. By
combining both of these approaches, ADVISOR is able to solve the problem efficiently,
while achieving the desired accuracy. Chapter 3 provides more details on how ADVISOR

works.

2.2.3 Optimization

Three types of HEV optimization are identified by Guzzella and Sciarretta [1].
The first of these is a structural optimization in which the best possible power train
structure is sought. The second type is parametric optimization to find the best possible
parameter values for a fixed power train structure (sizing of components). The third type
of optimization focuses on the control system, where the best possible supervisory
control strategy for a given structure is sought. While these three types of optimization
studies are not necessarily independent, each one represents a meaningful and tractable
suboptimization problem within the overall design process. The current study focuses
primarily on the second type (sizing) while also addressing the role of the control strategy
on the optimization of HEV’s.

The commercial software HEEDS [29] was used as the optimization tool for the
current study. The hybrid and adaptive search method SHERPA [29] was employed

exclusively here because it has been shown to perform well on a wide variety of

IO

problems, including multi-modal, noisy, discontinuous problems. Oh, et al [14]
demonstrated that local search methods such as Sequential Quadratic Programming
(SQP) can be used to find marginal improvement in HEV designs. More often, however,
it has been found that local search methods are not ideal for the optimization of HEV’s.
Montazeri-Gh, et al [15], showed that HEV optimization problems are highly non-linear,
discontinuous, and multi-modal (i.e., multiple local optima exist). Therefore gradient-
based search methods, which require the existence of at least first-order derivatives at
each design point, are often not the ideal choice for HEV design problems. This is
supported by Piccolo, et a1 [16] who concluded that a genetic algorithm is an efficient
search algorithm for identifying optimized control strategy parameters for a design that
meets performance criteria while having low firel consumption. Gao and Porandla [17]
also identified genetic algorithms as a potentially efficient search algorithm for HEV
optimization problems. While optimizing an HEV parallel powertrain with PSAT as the
simulation tool, these investigators benchmarked the use of simulated annealing (SA),
genetic algorithms (GA), and the DIRECT technique to perform the optimization.
DIRECT is a modification to the Lipschitzian approach in which the design space is
represented by a series of shrinking hypercubes for high performing regions of the design
space. It was observed that simulated annealing outperformed the genetic algorithm and
modified Lipschitzian approach in terms of performance for the optimization problem
posed. The response fimctions associated with HEV design problems were found to be
typically multi-modal and sometimes noisy and discontinuous. It was suggested that

stochastic algorithms (such as SA and GA) and deterministic algorithms (such as

11

DIRECT) were insufficient in finding the global Optimum as efficiently as a hybrid
method that mixes stochastic and deterministic algorithms.

It was observed by Montazeri-Gh, et a1 [15] that very different optimized designs
were obtained using different driving cycles. Three different driving cycles were explored
for the same optimization problem, resulting in three very different optimized
configurations for the control strategy of the HEV. The effects of drive cycle were also
studied by Markel and Wipke [18-19], where it was found that the drive cycle greatly
affected the optimized sizing of components in the HEV. It was found that more
aggressive drive cycles yielded designs with smaller battery packs, while less aggressive
drive cycles yielded optimized designs with larger battery packs. It was demonstrated that
the drive cycle not only affects the component sizing of the optimized HEV designs, but
also the energy management strategy of the HEV.

Assanis, et al [20] and Fellini, et a1 [2]] integrated ADVISOR and Turbo Diesel
Engine Simulation Program (TDES) to give greater accuracy in the engine maps being
used for altered hybrid designs. Fellini, et al [21] described an optimization study using
an Object Oriented-CORBA-based environment for the analysis, to optimally size the
engine, motor, and battery of the vehicle. They concluded that optimized engine size is
insensitive to variations in the drag coefficient, shell mass, battery efficiency, and drive
ratio, whereas the battery size and optimized motor are sensitive to these parameters. This
was shown through a sensitivity study following the attainment of optimized values via
an optimization study.

Moore [22] suggested guidelines for specifying performance criteria when

designing components and control strategies for HEV’s. These guidelines specify that

12

the vehicle must be capable of: launching at a given grade road, accelerating to multiple
speeds under given tirnefrarnes, maintaining gradability for a specified time and speed,
achieving a maximum velocity, achieving a minimum fuel economy, meeting emissions
criteria, and being capable of traveling a given distance in a mixed urban and highway
driving environment. In addition, Moore suggested guidelines that are not necessarily
pertinent to optimization of HEV’s, but rather to HEV design in general. These
guidelines include: having refueling times comparable to conventional vehicles, having
noise, vibration, and harshness in travel less than current sedans, having the ability to be
unattended for a given time below freezing temperatures, and meeting safety
requirements.

A common approach to designing HEV’s is to consider some type of battery
state-of-charge (SOC) correction. SOC corrections are routines or methods designed to
ensure that over the tirneframe considered the initial SOC and final SOC are the same.
This provides a meaningful way to compare designs and ensures that a design is less
dependent upon the initial SOC. Wayne, et a1 [23], describe the importance of this
correction in comparing hybrid vehicle performance to conventional vehicle
performance, as described by the SAE Recommended Practice J27117 [24]. Pagerit, et a1
[25] describe how SOC corrections can be used within optimization studies for HEV’s.
Duoba [26] and Senger [27] discuss how a conversion for electrical energy usage can be
used as an alternative to SOC correction, by converting the electrical energy that can be
obtained from gasoline through the efficiency of an average power plant in the United
States in 1996. SOC corrections in some form provide the basis for the vast majority of

all optimization work with HEV’s to date.

13

A review of the existing literature reveals that successful optimizations have been
performed on HEV component, control strategy, and configuration design. However,
despite the magnitude of attention given to the optimization of HEV powertrains, the
roles the Optimization problem statement and SOC correction have in the outcome of the
optimized design has yet to be adequately addressed. In the current study, the HEV
design found with an optimization strategy utilizing an SOC correction method is
compared with the design found utilizing an alternative optimization strategy with no
SOC correction. A comparison between the necessary optimization problem statements
for each strategy and their benefits is presented, and the strategies are merged into a
single and more robust strategy that is shown to have several advantages in terms of

design performance.

14

CHAPTER 3: OPTIMIZATION WITH HEEDS AND
ADVISOR

3. I Introduction to HEEDS

HEEDS (Hierarchical Evolutionary Engineering Design System) is a robust
design exploration and Optimization software package that automates the search for better
and more robust solutions within a given design space and dramatically reduces design
time [29]. HEEDS has a search algorithm SHERPA that is a hybrid adaptive search
method proven to be one of, if not the best search algorithm available today. It has been
demonstrated to outperform other methods on a wide variety of problems (both in terms
of performance and robustness) [28]. For this reason, HEEDS and SHERPA have been
chosen as the optimization tool and search algorithm for this thesis project. All
optimizations performed in this first section utilize HEEDS and showcase the benefits

and power of SHERPA as it relates to the Optimization of hybrid electric vehicles.

3.2 Introduction to AD VISOR

3.2.1 Overview

The advanced vehicle simulator (ADVISOR) is a simulation tool that utilizes a
combined forward/backward simulation approach to evaluate a vehicle’s performance. It
is used in conjunction with Matlab to solve difficult simulations involving Hybrid
Electric Vehicles (HEV’s).

ADVISOR uses Matlab .m files to define the HEV properties along with the

actions to be taken to test the performance of the HEV. It has a graphical user interface

15

(GUI) that correlates all of the .m files needed to run a given problem. However to use
HEEDS with ADVISOR, the GUI cannot be utilized while HEEDS is executing a design
study. As a result the no _gui capabilities specific to ADVISOR must be used to define
and alter the HEV and its performance characteristics during a HEEDS design study. The
baseline model however can be built and tested in the ADVISOR GUI for validation
before time is spent on the no _gui capabilities.

In the next sub-section of this chapter, the different .m files needed for a given
ADVISOR analysis are introduced (for firrther detail, please refer to the ADVISOR
User’s Manual [9]). The no Jgui capabilities are not generally discussed, but are discussed
in detail as they relate to the example problem posed in the following section.

An example problem is presented to demonstrate how to use HEEDS with
ADVISOR. It is representative of a specific problem and the no 3111' utilization will likely

need to be altered for other problems.

3.2.2 Matlab .m Files

To define an HEV and its performance actions in ADVISOR, there are 13 primary
categories of .m files used. These files can be manipulated and managed to represent a

specific HEV. The .m file categories are described below:

Vehicle Description: These .m files describe and load all of the other .m files

needed for a given HEV configuration.

Vehicle: These .m files define all of the parameters associated with

the vehicle such as the coefficient of aerodynamic drag, the

16

Fuel Converter:

Exhaust Aftertreatment:

Energy Storage System:

Motor:

Generator:

Transmission:

mass of the vehicle, etc.

These .m files define all of the parameters associated with
the fuel converter or engine of the vehicle. Examples

include the fuel and torque maps.

These .m files define all emissions data and catalytic

converter data associated with the vehicle.

These .m files define all of the data associated with the

energy storage system such as the batteries, super

capacitors, etc.

These .m files define all of the data regarding the electric

motor.

These .m files define all of the data associated with

generators in the vehicle and devices used for recharging.

These .m files define the transmission for use in the

vehicle.

17

W heel/Axle:

Accessory:

Control:

Drive Cycle:

Test Procedure:

These .m files define the wheels and axles and the

resistances associated with each.

These .m files define the electrical accessories needed for

the vehicle. Air conditioning is included in these .m files.

These .m files define the control system used to define how

the HEV operates.

These .m files define the drive cycle over which the vehicle

is to be tested and evaluated.

These .m files are an alternative category to the Drive
Cycle .m files in that they define a specific test to be
performed on the vehicle rather than a specific route the

vehicle is to take.

18

3.3 Linking HEEDS to AD VISOR
3.3.1 AD VISOR Optimization Preparation

There are four files required with every ADVISOR optimization run. The main
file defines the ADVISOR model to be used and contains the commands for writing the
values of the design variables and responses to an output response file
(outdata_conn'ol.txt in this example). In this example, the main file is named
optim_control_HEEDS.m. Another file identifies the objectives for the run and stores
their values following the simulation (objjitn_control.m for this example). A third file
identifies and stores the values of the constraints for the run (confin_control.m for this
example). The fourth file contains the values of the design variables (indata_control.m
for this example). These files are used by ADVISOR to load and define the entire
problem setup for each HEEDS evaluation. They therefore are unique for every single
optimization which utilizes ADVISOR as an analysis tool. Descriptions of the file

contents follow as they relate to this particular example problem.

3.3. 1.1 optim_control_HEEDS. m

For this example, the file associated with defining the ADVISOR model contains
10 primary sections (see Figure 3.3.1). Section 1 of the code creates a Matlab workspace
where no variables are defined. Section 2 initiates a timer so that the length of the
analysis can be monitored. Section 3 loads the vehicle description .m file
PARALLEL_defaults_in. Section 4 alters the number of battery modules to 14 from the
default value. Section 5 of the code scales the motor to 13.5kW from 75kW. Section 6

defines the variables and responses to be used in the optimization. Section 7 identifies the

19

file containing the design variable information and imports their values into the model.
Section 8 identifies the files containing the Objective and constraint variables and
associates them with the model. Section 9 creates the output file for the analysis
(outdata_control.txt) and writes the objective and constraint data to it. Finally, SectionlO

stops the timer since the analysis is now complete.

20

 

 

% Clear all the variables 1
clear all

 

 

% initiate timer 2
tic
% Load advisor saved vehicle 3

inputinit.saved_veh_file='PARALLEL_defaults_in';
[error_code,resp]=adv_no_gui('initialize',input);

%Alteration to E88 4
input.modify.param={'ess_module_num'};

input.modify.value={14};

[error,resp]=adv_no_gui(‘modify',input);

%Alteration to Motor 5
input.modify.param={‘mc_trq_scale'};

input.modify.value={0.18};

[error,resp]=adv_no_gui('modify',input); 6
% Define variables
dv_names={‘cs_hi_soc','cs_|o_soc','cs_electn'c_launch_spd_lo',‘cs_electric_launch_spd_hi'.
'cs_off_trchrac',‘cs_min_trq_frac',‘cs_charge_trq'};
resp_names={‘combined_mpgge','hc_gpm','co_gpm'.'nox_gpm',
'vinf.accel_test.results.time(1 )','vinf.accel_test.results.time(2)',‘vinf.accel_test.results.time(3)'.
'vinf.accel_test.results.max__speed','vinf.accel_test.results.max_rate',
'vinf.accel_test.results.dist_in__time','vinf.grade_test.results.grade'};

 

 

 

 

% load new design variables 7
indata_control
% Evaluate responses *— 8

 

obj=obj_fun__control(X,dv_names,resp_names);
con=con_fun_control(X,dv_names,resp_names);
% write responses to file 9
fid=fopen('outdata_control.txt','w');
fprintf(fid,'Fuel Economy: %g',obj);

fprintf(fid,'\n');

fprintf(fid,'HC: %g',oon(1));

fprintf(fid,'\n');

fprintf(fld,'CO: %g',con(2));

fprintf(fid,'\n');

fprintf(fid,'NOx: %g',oon(3));

fprintf(fid,'\n');

fprintf(fid.'Aocel 0-60: %g',oon(4));

fprintf(fid,'\n');

fprintf(fid,'Accel 40-60: %g',oon(5));
fprintf(fid,'\n');

fprintf(fid,'Aocel 0-85: %g',oon(6));

fprintf(fid,'\n');

fprintf(fid,'Max Speed: %g',oon(7)):
fprintf(fid,'\n');

fprintf(fid,'Max Accel: %g',oon(8));

fprintf(fid,'\n');

fprintf(fld,‘Distance in 55: %g',oon(9));
fprintf(fid.'\n');

fprintf(fid,'Grade: °/og',con(10));

fprintf(fld,'\n');

fclose(fid);

%end timer 10
too

 

 

 

 

 

Figure 3.3.1. Main input file: optim_control_HEEDS.m

21

3.3. 1.2 obj fln_c0ntrol.m

This file contains six primary sections (see Figure 3.3.2). Section 1 defines a
function. Section 2 initializes the Matlab variables to be used. Section 3 updates the
parameter settings defined by the design variables. Section 4 of the code runs the FTP
driving cycle. Section 5 identifies the objective variable from the driving cycle (gas
mileage). Finally, Section 6 identifies the other objective variables from the driving cycle

(emissions).

 

 

 

function obj=obj_fun(x,varargin) 1

% initialize 2
error=0;

obj=0; 3

 

% update parameter settings
input.modify.param=varargin{1}; % parameter names are stored in the first optional argument
input.modify.value=num20ell(x); % assign corresponding values
[error,resp]=adv_no_gui('modify’,input);
% run FTP driving cycle
if ~error
input.cycle.param={'cycle.name'};
input.cycle.value={’CYC_FTP'};
[error,resp]=adv_no_gui('drive_cycle',input);
end
% assign objective value 5
if ~error '
obj=resp.cycle.mpgge;
end
% assign objective value
if ~error
assignin('base','con‘,[resp.cycle.hc_gpm; resp.cycle.co_gpm; resp.cycle.nox_gpm])
end

4

 

 

return

 

 

 

Figure 3.3.2. Objective definition file: obj_fun_control.m

22

3.3.1.3 con_fun_control.m

This file has four primary sections (see Figure 3.3.3.). Section 1 defines a
function. Section 2 enables additions to the vector where responses are stored. Section 3
runs and defines an acceleration test, as well as obtains constraints from it (acceleration
times, max velocity, max acceleration, distance covered in SS). Section 4 runs and defines

a grade test, as well as obtains the constraint associated with the grade test (grade).

 

 

function [con, con_e]=con_fi1n(x,varargin) 1
con=evalin('base','con‘); 2
3

 

offset=length(con);
% run acceleration test
input.accel.param={'spds','gb_shift_delay','dist_in_time'.‘max_speed_bool'.‘max_rate_bool',};
input.accel.value={[0 60; 40 60; 0 85],0.2,5.0,1,1};
[error, resp]=adv_no_gui('accel_test',input);
if ~error&~isempty(resp.accel.times)
con(offset+1 ,1 )=resp.accel.times(1);
con(offset+2,1 )=resp.accel.times(2);
con(offset+3,1 )=resp.accel.times(3);
con(offset+4,1 )=resp.accel.max_speed;
con(offset+5,1 )=resp.accel.max_rate;
con(offset+6,1 )=resp.accel.dist;
else
con(offset+1 :offset+3,1 )=100;
end
% mn grade test 4
input.grade.param={‘duration','speed'};
input.grade.value={1200,55};
[error, resp]=adv_no_gui('grade_test’,input);
if ~error&~isempty(resp.grade.grade)
con(offset+7.1 )=resp.grade.grade;
else
con(offset+7,1 )=0;
end

 

 

con_e=0;
0/0 itti

return

 

 

 

Figure 3.3.3. Constraint definition file: con_fun_control.m

23

3.3. 1.4 indata_control.m

This file contains only one section which defines all the values for the design

variables referenced in the file optim_control_HEEDS.m (see Figure 3.3.4).

 

X(1 )=0.98
X(2)=0.96
X(3)=10
X(4)=10
X(5)=0.2
X(6)=0.4
X(7)=10

 

 

 

Figure 3.3.4. Input design variable file: indata_control.m

3.3.2 Running the ADVISOR Simulation from Batch Mode

There is an executable located within the gui folder of the ADVISOR files named
advisor_script.exe that is created when ADVISOR is installed. It is this file that allows
ADVISOR to be run from batch mode. To run this file from a command prompt, the

format is:

advisor_script.exe WorkingDirectory ScriptFilename ADVISORRootDirectory SupportDirectory

Where for our optimization problem, this takes the form (if running from the
C:\Temp directory and the ADVISOR root directory is set to

C :\Program F iles\AVL\ADVISOR\ADVISOR2004):

C:\Temp\advisor_script.exe C:\Temp optim_control_HEEDS
C :\PROGRA~1\AVL\ADVISOR\ADVISOR2004 C:\Temp

For use with HEEDS, a batch file needs to be created named RUN_AD VISOR.bat
which contains this command, with the advisor_script.exe copied to the working
directory.

24

3.3.3 Process Integration Between HEEDS and AD VISOR

HEEDS performs the optimization using ADVISOR as the simulation tool by
iteratively performing simulations and searching the design space using the search
method SHERPA. SHERPA is a hybrid adaptive search method that tunes itself for a
given problem [29]. The process of optimizing using HEEDS with ADVISOR will be
described in this sub-section.

As was discussed in Sub-Section 3.3.2, ADVISOR needs to be run from batch
mode for HEEDS to be able to perform a design study. Sub-Section 3.3.1 detailed the
no _gui capabilities of ADVISOR and the files associated with this. How HEEDS uses
this capability is as follows. HEEDS inputs variable values into the input design variable
file (indata_control.m for this example). These design variable values are read into the
main file (optim_control_HEEDS.m for this example), along with data from the objective
definition file (objjim_control.m in this example) and the constraint definition file
(conjun_control.m in this example). The executable advisor_script.exe then launches
ADVISOR using the problem statement defined in the main file
(optim_control_HEEDS.m). The ADVISOR simulation is then run and the output
response file (outdata_control.txt in this example) is written out based upon the
information in the main file. The response values are then read from this output response
file by HEEDS. SHERPA then adapts and tunes its search based upon this information, in
hopes of improving the design. In doing so, it creates new variable values that are again
put into the input design variable file, and this iterative loop begins again. This loop is
continued for a set number of evaluations or until the optimal design is found. Figure

3.3.5 depicts this process integration performed by HEEDS with ADVISOR.

25

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

,. _____________________________
I
: ADVISOR .m Files I
I I
1 Variable .__p Input Objective Constraint I
I Values 0999” Definition Definition I
l variab'e File File I
T FIIe |
' __
l 1 l
' SHERPA I . . I
I f Maln File I
| I
' Response |
| Values I
I I
' ADVISOR '
I 7, v :
I Output - -
I Response File ‘— ADV|SOR 4'! adVIsor_scrlpt.exe :
I
- ———————————————————————————— .I

Figure 3.3.5. Process integration performed by HEEDS with ADVISOR.

3. 4 Optimization Example: Small Vehicle Parallel HE V
3. 4.1 Baseline Model

The vehicle powertrain to be studied in this example problem is that of a Parallel
HEV (see Figure 3.4.1 for this configuration in ADVISOR). Its parameters are defined as
follows (similar to the problem defined by M.Montazeri-Gh, A. Poursamad, and B.
Ghalichi [15]):

0 Body mass: 592 kg

0 Rolling resistance coefficient: 0.009

0 Body aerodynamic drag coefficient: 0.335

0 Vehicle front area: 2m2

26

0 Wheel radius: 0.282 m

0 Gearbox: five speed manual gearbox with the following gear ratios: 2.84, 3.77,
5.01, 7.52, 13.45.

0 IC engine: 41 kW SI engine

0 Electric motor: 13.5 kW AC motor

0 Energy storage system: 14 12V Hawker Genesis valve-regulated lead—acid battery

0 Catalyst converter: close-coupled conventional converter for an SI engine

0 Drive Cycle: FTP

  

I’ T Gasoline \
i

 

Figure 3.4.1. Parallel HEV Configuration in ADVISOR

This vehicle model is provided as a baseline model within the ADVISOR
software. Slight modifications however, do need to be made to the default model (these

modifications are described later). This problem definition correlates to the following

pre-existing .m files:
Vehicle Description: PARALLEL_defaults_in.m

Vehicle: VEH_SMCAR

27

Exhaust A ftertreatment: EX_SI

Energy Storage System: ESS_PB25 with alterations necessary to the number of

battery modules (shown in Sub-Section 3.3.1.1)

Motor: MC_AC75 with alterations to the torque scaling to make
the motor 13.5 kW instead Of 75 kW (shown in Sub-

Section 3.3.1.1)

Transmission: TX_5 SPD
Wheel/Axle: WH_SMCAR
Drive Cycle: CYC_FTP

28

3. 4.2 Optimization Problem Statement

By altering the control system settings of the parallel HEV, this optimization
study attempts to minimize both the fuel consumption and emissions of the vehicle, while
maintaining the performance characteristics of the vehicle. This optimization problem

can therefore be summarized as:

 

+ IC+ ,‘0+ l0x

 

Minimize: J (x) =
mpgge

where:
mpgge is the gas mileage,
HC is the hydrocarbon emissions,
C 0 is the carbon monoxide emissions,
NO): is the nitrous oxide emissions.

Subject to: Grade 2 6.5
Acc_I S 12
Acc_2 S 5.3
Acc_3 S 23.4
V_max 2 85.13
A_max 2 16.1
Dist_5s 2 140.]

where:
Grade is the grade able to be achieved at 88.5 km/hr for 20 min,

Acc_I is the time to accelerate from 0-60 mi/hr,
Acc_2 is the time to accelerate from 40-60 mi/hr,
Acc_3 is the time to accelerate from 0-85 mi/hr,
V_max is the maximum velocity achieved,
A_max is the maximum acceleration achieved,
Dist_5s is the distance achieved in 5 seconds.

 

 

 

29

 

By varying: 0 S DeltaSOC S 0.31
0 S VL S 15
0 S. T _ofl S 0.31
0.25 s T_min s 0.88
4 s T_ch s 35

where:

DeltaSOC is the change in limits on the state of charge of the
system,

VL is the vehicle speed below which the vehicle operates as a zero

emissions vehicle (electric launch speed),

T _ofl is the minimum torque threshold when SOC > LSOC,

T _min is the minimum torque threshold when SOC < LSOC,

T __ch is the torque load on engine to recharge the battery pack

when the engine is on.

 

 

 

3.4.3 HEEDS Setup
This section details the steps necessary to setup the optimization problem in
HEEDS as posed in Sub-Section 3.4.2. Detailed step-by-step instructions are given in this

section as to this setup.

3.4.3.1 Starting a New Project
1. Open the HEEDS Modeler.
2. Open the file menu and click New (or select New from the options displayed on
the screen).
3. Navigate to your working directory.

4. Save the file as parallelHEV.

3.4.3.2 Defining the Evaluation Process
This problem only has one analysis, with 4 input files and one output file.

1. Select the Processes tab.

30

2. Select Analysis__l in the Process Graph. The Analysis Manager will appear
below.

3. Click the Browse button next to the Execution File field and navigate to the
working directory.

4. Select RUN_ADVISOR.bat. This is the file containing the commands and script
necessary to run ADVISOR from batch mode (see above). Delete the path portion
of the field and replace with “.\”.

5. Select the Input Files button to display the Input Files Manager.

6. Right click anywhere in the Input Files Manager and Add Input File.

7. Add the input file indata_control.m.

8. Repeat for the input files optim_control_HEEDS.m, obj_fun_control.m,
con_fun_control.m, and RUN_ADVISOR.bat.

9. Select the Output Files button to display the Output Files Manager.

10. Right click anywhere in the Output Files Manager and Add Output File.

1 1. Add the output file outdata_control.txt

12. Save the Project.

3.4.3.3 Defining the Project Variables and Responses

3.4. 3.3.1 Defining the Project Variables

1. Display the Variables tab.

2. Add 7 design variables and define them as follows:
Name: DeltaSOC; Type: Continuous; Min: 0.0; Baseline: 0.1; Max: 0.31
Name: HSOC; Type: Parameter; Baseline: 0.70

Name: LSOC; Type: Dependent; Formula: HSOC-DeltaSOC

31

Name: VL; Type: Continuous; Min: 0.0; Baseline: 0.0; Max: 15
Name: T_off; Type: Continuous; Min: 0.0; Baseline: 0.0; Max: 0.3]
Name: T_min; Type: Continuous; Min: 0.25; Baseline: 0.40; Max: 0.88

Name: T_ch; Type: Continuous; Min: 4; Baseline: 20; Max: 35

3. Add Internal Variables to the project (to define the path in the

RUN_ADVISOR.bat file).

3.4.3.3.2 Defining the Project Responses
1. Add 13 project responses and define them as:

Name: mppge; Source: File
Name: inv_mppge; Source: File
Name: HC; Source: File
Name: CO; Source: File
Name: NOx; Source: File
Name: J_x; Source: Formula; Formula: inv_mppge+HC+CO+NOx
Name: Grade; Source: File
Name: Acc_l; Source: File
Name: Acc_2; Source: File
Name: Acc_3; Source: File
Name: V__max; Source: File
Name: A_max; Source: File
Name: Dist_SS; Source: File

2. Save the Project.

32

3.4.3.4 Tagging the Input and Output Files
if. 3. 4. 1 T aging the Input Files

1. Display the Tagging tab.

2. For this project, there are two input files that need tagging. The first dealing with
the design variable tagging is indata_control.txt. Select this file in the Processes
tree and the design variable HSOC in the Project Variables window.

3. Tag the file as detailed below (note VL is tagged twice since we want the upper
and lower speeds for which it represents to be identical):

Variable: HSOC; Location: Line 1, Field 3
Variable: LSOC; Location: Line 2, Field 3
Variable: VL; Location: Line 3, Field 3
Variable: VL; Location: Line 4, Field 3
Variable: T_off; Location: Line 5, Field 3
Variable: T_min; Location: Line 6, Field 3

Variable: T_ch; Location: Line 7, Field 3

4. The file RUN_ADVISOR.bat must have the path tagged within it. Select this

input file in the Processes tree and the internal variable Design_Path. Tag the file

as described below:

Internal Variable: Design Path; Location: Line 1, Field 2

33

_3_.:l. 3. 4.2 Tagging the Output File
1. Select the output file outdata_control.txt from the Processes tree and the
response mppge from the Project Responses window.

2. Tag the file as described below:
Response: mppge; Location: Line 1, Field 3
Response: HC; Location: Line 2, Field 2
Response: CO; Location: Line 3, Field 2
Response: NOx; Location: Line 4, Field 2
Response: Acc_l; Location: Line 5, Field 3
Response: Acc_2; Location: Line 6, Field 3
Response: Acc_3; Location: Line 7, Field 3
Response: V_max; Location: Line 8, Field 3
Response: A_max; Location: Line 9, Field 3
Response: Dist_SS; Location: Line 10, Field 4

Response: Grade; Location: Line 11, Field 2

3. Save the Project

3.4.3.5 Assembling the Problem Definition
1. Select the Assembly tab.
2. Select the OPT_Agent_1 button and assign Process_l to the Agent.
3. Select the Methods button and select SHERPA as the optimization technique.
4. Click the Next button and change the number of evaluations to 200.

5. Select the Variables button. Leave the resolution at the default value of 101.

34

6. Select the Responses button. Define the optimization problem as that defined
below:

Response: mppge; Type: Prerequisite
Response: HC; Type: Prerequisite
Response: CO; Type: Prerequisite
Response: NOx; Type: Prerequisite
Response: Grade; Type: Constraint _>_ 6.5
Response: Acc_l; Type: Constraint 5 12
Response: Acc_2; Type: Constraint: 5.3
Response: Acc_3; Type: Constraint _<_ 23.4
Response: V_max; Type: Constraint 3 85.13
Response: A_max; Type: Constraint _>_ 16.1
Response: Dist_5s; Type: Constraint 3 140.1
Response: inv_mppge; Type: Prerequisite
Response: J_x; Type: Objective, Minimize, l

7. Save the project.

3.4.4 Running the Project

To run the HEEDS project, save the project and click on the Run tab and the Run
button in the HEEDS Modeler. The project should run with a HEEDS window popping
“P along with a Matlab window. The Matlab window will close after each evaluation and

a new one pOp up with each new evaluation.

35

3. 4.5 Results and Discussion

The baseline model for this run is defined in Table 3.4.1. This baseline was
chosen somewhat arbitrarily from [15], but was believed to have been a good design to
begin with based upon the paper this problem was adapted from. The resulting response

values for this design are:

mppge = 40.19840
HC = 0.438372
CO = 1.929040
NOx = 0.36759
grade = 8.21989
Acc_l = 10.3826
Acc_2 = 5.3204
Acc_3 = 22.0176
Vmax = 108.788
Amax = 16.2423
Dist_SS = 170.814
J_X = 2.759884

11 variable values

 

Table 3.4.1. Baseline model desi

 

 

 

 

 

 

 

 

Name Baseline
HSOC 0.70
DeltaSOC 0.10
LSOC 0.60
VL 0
T off 0
T min 0.4
T ch 20

 

 

 

 

 

HEEDS was capable of finding within the 200 evaluations specified, a design that

had the following response values:

mppge = 43.75

HC = 0.4266190
CO = 1.910740
NOx = 0.362577
grade = 8.015360
Acc_l = 10.3536

36

Acc_2 = 5.27818
Acc_3 = 21.75
Vmax = 110.045
Amax = 16.2424
Dist_SS = 169.719
J_X = 2.722793

HEEDS found a new design with an 8.84% increase in fuel economy, while
decreasing hydrocarbon emissions by 2.75%, carbon monoxide emissions by 0.96% and
nitric oxide emissions by 1.383% over the baseline design. Also, the design HEEDS
found satisfied all the performance constraints placed upon the problem as defined. This

design corresponds to the values for design variables seen in Table 3.4.2

Table 3.4.2. Optimized design variable values.

 

 

 

 

 

 

 

 

 

 

Name Value
HSOC 0.70
DeltaSOC 0.0206666
LSOC 0.6793333

VL 1.071429
T off 0.0206666
T min 0.4735484

T ch 4

 

37

 

CHAPTER 4: BASELINE ADVISOR MODEL FOR A
HYBRID ELECTRIC BUS

4.1. Introduction

In attempting to develop an optimization strategy for HEV’s, it was necessary to
develop an ADVISOR model that was realistic and representative of a real-world
application. A hybrid bus model was chosen as the baseline model for all work in regards
to optimization. Hybrid buses are becoming commonplace, and work in optimizing their
performance is becoming very important.

An accurate simulation model therefore, had to be created and validated for a
baseline design configuration of a hybrid bus. As mentioned previously, the simulation
software ADVISOR has been chosen for the current study. Therefore, the baseline bus
configuration had to be accurately modeled in ADVISOR by defining the necessary
parameters used in the hybrid electric powertrain model. The baseline bus was modeled
according to early bus specifications and data associated with a joint project between
Michigan State University, Kettering University, and TransTeq [30] with support from
the Michigan Economic Development Corporation. After the baseline model was
validated, the Optimization software HEEDS was used to perform sizing optimization of
the powertrain so as to develop an optimization strategy for hybrid vehicles. The goal of

this chapter is to define the simulation model for the baseline configuration.

38

4. 2. AD VISOR Vehicle Model Description

Since ADVISOR was selected as the simulation tool for this project, each of the
vehicle systems had to be described in detail in terms of the parameters that defined that
system within ADVISOR.

A Series Hybrid Electric Vehicle configuration was chosen for the baseline
simulations of the bus. ADVISOR has a pre-existing model for a bus known as the Orion
VI Low-Floor Transit bus. This vehicle model was used for the simulations, with the
parameters modified to represent the early specifications for the bus in the joint project
discussed briefly above.

While many parameters could be measured or obtained directly, some had to be
estimated based upon assumptions. The height of the vehicle center of gravity
(veh_cg_height) was one of these parameters. TO obtain this vehicle center of gravity, the
bus had to be broken down into components based upon its weight. The curb weight of
the vehicle (the bus weight without passengers) was 26,750 lbs. The tires, axles, and
transmission weight were 4000 lbs, distributed at a location 18.8 inches above the ground
(rolling radius of the wheel). The engine and engine compartment weighed roughly 1300
lbs and had a center of gravity located about 30.8 inches above the ground. The air
conditioning unit was located 80 inches above the ground and weighs 500 lbs. The
remaining weight of the bus (21,150 lbs) was that without components
(veh_glider_mass). The roof of the bus could be estimated as accounting for 15% of the
remaining weight (3,172 lbs) located at 124 inches. The floor accounted for roughly 35%
of the 21,150 lbs (or 7,402 lbs) located at 10.5 inches. The walls accounted for the rest of

the 21,150 lbs, but had the weight evenly distributed so their effect on the center of

39

gravity was insignificant. Assuming 40 passengers at 150 lbs each gave the cargo mass
(veh_cargo_mass = 6000 lbs). If 23 of these passengers were seated, their center of mass
could be assumed to be 2 ft. The other 17 passengers could be assumed to have a center
of mass of 3 ft since they were standing. Standard calculations for the center of gravity

therefore yielded the center of gravity of the bus to be 35.80 inches.

4. 2.1. Vehicle Level Parameters

Table 4.2.1. Vehicle parameters for the baseline bus model.

 

 

 

 

 

 

 

 

 

 

 

ADVISOR Parameter Parameter Source Description
Parameter Value Value
(SI) (English)
. 2 2 Reference Acceleration of
vehgravza 9.81 m/s 32.185 ft/s value gravity
- . 3 3 Reference . .
veh_alr_denszty 1,23 kg/m 0.0768 lb/fi value Arr densrty
Transit Bus Coefficient of
veh_CD 0'79 0'79 Standard aerodynamic drag
2 2 Specific for
veh_FA 9.4732 m 10197 ft Flint Buses Frontal area of bus
. . Specific for Height of vehicle
veh__cg_hezght 0.908304 m 2.98ft Flint Buses center 0 f gravity
Fraction of total
' Specific for vehicle mass
vehfront_wtjrac 0.2785 0.2785 Flint Buses supported by front
axle when at rest
veh wheelbase 7.443m 24.42 ft Sp e crfic for Distance between
— Flrnt Buses front and rear axles
S ecific for Mass Of bus
veh_glider mass 9593.48 kg 657.362 slugs p. without
— F lrnt Buses
components
Vehicle cargo mass
Specific for (assuming 40
veh_cargo_mass 2,721.55 kg 186.486 slugs Flint Buses people at 150 lbs
per persop)

 

 

 

 

 

40

 

4. 2. 2. Fuel Converter Parameters

The fuel converter data corresponded to that of a Detroit Diesel Corp. Series 50

8.5 (205kW) diesel engine. Many of the fuel converter parameters are given as maps.

These maps are defined below in SI units defined in Table 4.2.2.

Map 4.2. l

fc_map_spd = [125.66, 141.37, 157.08, 172.79, 188.50, 219.91]

Map 4.2.2

fc_map_trq =[123.02, 246.04, 369.07, 492.09, 615.11, 738.13, 861.15, 984.18, 1107.20]

Map4.2.3

fc_fuel_map_gpkWh =

[242, 220, 207, 201.5, 198.5, 197, 195.5,
261, 220, 207, 200, 195, 192.5, 190.5,
273, 224, 207, 198, 194.5, 192, 190.5,
288, 228, 209, 200.5, 196, 193.5, 191.5,
288, 238, 217, 207.5, 203, 199.5, 197.5,
290, 244, 222, 210.5, 204.5, 202.5, 199.5,

194.5,
189.5,
189.5,
191.5,
197.5,
199.5,

193.5;
189.5;
189.5;
191.5;
197.5;
199.5]

Table 4.2.2. Fuel converter parameters for the baseline bus model.

 

 

 

 

 

 

 

 

 

 

 

 

Parameter Parameter
33:53:: Value Value Source Description
(SI) (English)
_ ADVISOR
fc_filel_type Diesel Diesel Default Type of fuel
Value
. ADVISOR Engine size
fc_disp 8.5 L 2.245 gal Default (cylinder
Value displacement)
ADVISOR
fc_map_spd Map 4'2'1 Map 4.2.1 Default Speed range Of the
(rad/s) Value engine
ADVISOR .
fc_map_trq ngrfi'z Map 4.2.2 Default Englr: ttérque
Value g
ADVISOR
Map 4.2.3 Fuel use map of
c el ma kWh Ma 4.2.3 Default .
f fl — p _gp (g/kWh) p Value engine
ADVISOR
fc_idle_speed 650 rad/s 650 rad/s Default Idle speed 0f the
Value engrne

 

41

 

4. 2. 3. Exhaust A ftertreatment Parameters
The aftertreatrnent catalyst parameters defined were those for a diesel-powered CI

engine. All of the catalyst parameters are given as maps. These maps are defined below

in SI units defined in Table 4.2.3.

Map 4.2. 4
ex_cat_trnp_range = [-40, 0, 220, 240, 310, 415, 475, 550, 650, 1200]

Map 4.2. 5
ex_cat_hc_frac = [0, 0, 0.04, 0.08, 0.20, 0.57, 0.80, 0.90, 0.91, 0.91]

Map 4.2.6
ex_cat_co_frac = [0, 0, 0.06, 0.20, 0.50, 0.80, 0.90, 0.95, 0.95, 0.95]

Map 4.2.7
ex_cat_nox_frac = [0, 0, 0.01, 0.15, 0.45, 0.30, 0.20, 0.10, 0.01, 0]

Map 4.2.8
ex_cat_pm_frac = [0, 0, 0.04, 0.08, 0.20, 0.30, 0.35, 0.40, 0.40, 0.40]

Map 4.2.9
ex_cat_lim = [1.25, 17.0, 2.0, 0.4]

42

Table 4.2.3. Exhaust aftertreatment parameters for the baseline bus model.

 

 

 

 

 

 

 

 

 

 

 

 

ADVIS OR Parameter Parameter . .
Parameter Value Value Source Descrrptron
(SI) (English)
Map 4.2.4 ADVISOR Catalyst temperature
ex_cat_tmp_range (o C) Map 4.2.4 Default ran e
Value g
Automotive Catalyst HC
Eng. 10/95 conversion efficiency
ex_cat_hcjac Map 4.2.5 Map 4.2.5 p. 42 map (dependent on
(Reference) catalyst temperature)
Johnson Catalyst CO
conversion efficiency
ex_cat_cofrac Map 4.2.6 Map 4.2.6 Matthey (dependent on catalyst
rp. temperature)
ADVIS OR Catalyst NOx
conversion efficiency
ex_cat_noxjrac Map 4.2.7 Map 4.2.7 [33111: (dependent on catalyst
temperature)
ADVISOR Catalyst PM
conversion efficiency
ex_cat_pmfiac Map 4.2.8 Map 4.2.8 12163:: (dependent on catalyst
temperature)
ADVISOR Breakthrough limit of
ex_cat_lim Map 4.2.9 Map 4.2.9 Default converter (5 times the
Value Tier 1 g/mi limits)

 

 

4. 2. 4. Energy Storage System Parameters

The energy storage system was based upon an Ovonic 90Ah NiMH battery. Many
of the catalyst parameters are given as maps. These maps are defined below in SI units
defined in Table 4.2.4.

Map 4.2.10
ess_soc = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]

Map 4.2.11
ess_tmp = [0, 22, 40]

Map 4.2.12
ess_max_ah_cap = [90, 90, 90]

Map 4.2.13
ess_r_dis =

43

0.01*[1.167, 0.631, 0.594, 0.552, 0.541, 0.530, 0.523, 0.536, 0.574, 0.615, 0.585;
1.167, 0.631, 0.594, 0.552, 0.541, 0.530, 0.523, 0.536, 0.574, 0.615, 0.585;
1.167, 0.631, 0.594, 0.552, 0.541, 0.530, 0.523, 0.536, 0.574, 0.615, 0.585]

Map 4.2.14

ess_voc =
[12.5, 12.8, l3.1,13.3,13.4,13.4,13.5,13.6,13.7,13.9,14.2;

12.5, 12.8, 13.1, 13.3, 13.4, 13.4, 13.5, 13.6, 13.7, 13.9, 14.2;
12.5, 12.8, 13.1, 13.3, 13.4, 13.4, 13.5, 13.6, 13.7, 13.9, 14.2]

44

Table 4.2.4. Enem storage system parameters for the baseline bus model.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Parameter Parameter
:DVISOR Value Value Source Description
arame er (SI) (English)
ADVISOR
ess soc Map 4.2.10 Map 4.2.10 Default Range Of the state 0f
— charge of the battery
Value
ADVISOR Temperature range
ess_tmp M21202? '1 1 Map 4.2.11 Default over which data is
Value defined.
Ma 4 2 12 ADVISOR Maximum capacity at
ess_max_ahicap p ' ' Map 4.2.12 Default C/5 rate. (dependent
(A-h)
Value on temperature)
Module’s resistance to
ADVIS OR bemg dlscharged
. Map 4.2.13 (dependent on
ess r drs Map 4.2.13 Default
— _ (Ohms) Value temperature
{vertically} and SOC
{horizontally} )
Module’s Open-circuit
ADVISOR voltage (dependent on
ess_voc M33385” Map 4.2.14 Default temperature
Value {vertically} and SOC
{horizontally})
Storage system
ADVISOR minimum voltage
ess_min_volts 9.135 volts 9.135 volts Default (based upon 10 cells
Value and a 105% safety
factor)
Storage system
1 5.675 1 5.675 ADVISOR maxlmum voltage
ess_maxgvolts volts volts Default (based upon 10 cells
Value and a 95% safety
factor)
ADVISOR .
ess module mass 16.7 kg 1'144313 Default Mass ofa s1ngle 12 V
— r slugs module
Value
ADVISOR .
0.232971
ess module_volume ,006597 m3 3 Default Volume ofa Slngle
r it module
Value
ADVISOR
ess_module_number 25 25 Default Number of modules
Value

 

 

 

45

4.2. 5. Motor Parameters
The motor defined was that of a 58 kW permanent magnet motor/controller.

Many of the motor parameters are given as maps. These maps are defined below in SI

units defined in Table 4.2.5.

Map 4.2.15

mc_map_spd =

[0, 26.2, 52.4, 78.5, 104.7, 130-9, 157.1, 183.3, 209.4, 235.6, 261.8, 288, 314.2, 340.3,
366.5, 392.7, 418.9]

Map 4.2.16
mc_map_trq = [0,25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375,
400]

Map4.2.17

mc_eff_map=

[03,03, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 03,03, 03, 0.3, 0.3, 0.3, 03,03,
0033,07, 0.75, 075,075, 0.73, 071,0.7, 0.7, 0.68, 0.65, 0.63, 0.62, 0.61,0.6, 0.59,
00.55315, 0.8, 0.82, 0.82, 0.82, 0.82, 0.82, 0.81, 0.8, 0.78, 0.77, 0.76, 0.76, 0.75, 0.73,
00.732303, 0.82, 0.84, 0.86, 0.86, 0.85, 0.85, 0.85, 0.84, 0.84, 0.83, 0.82, 0.81, 0.8, 0.77,
00737:075, 0.83, 0.86, 0.87, 0.88, 0.88, 0.87, 0.87, 0.87, 0.86, 0.86, 0.85, 0.84, 084,083,
0($3230.75, 0.84, 0.87, 0.88, 0.88, 0.89, 0.89, 0.88, 0.88, 0.88, 0.87, 0.87, 0.86, 0.86, 0.85,
(30:3;075, 0.84, 0.87, 0.89, 0.90, 0.90, 0.90, 0.89, 0.89, 0.89, 0.89, 0.88, 0.88, 0.88, 0.88,

0.3, 0.75, 0.84, 0.88, 0.89, 0.9, 0.90, 0.90, 0.90, 0.9, 0.90, 0.89, 0.89, 0.89, 0.89, 0.89,
0.89;

0.3, 0.75, 0.84, 0.88, 0.90, 0.9, 0.90, 0.91 , 0.90, 0.90, 0.90, 0.90, 0.90, 0.90, 0.90, 0.90,
0.90;

0.3, 0.75, 0.84, 0.88, 0.9, 090,091,091, 0.91,091,091,0.91,o.91,0.91,0.91.0.91.
0.91;

0.3, 0.75, 0.85, 0.88, 0.9, 091,091,092, 091,091,091,0.91,o.91,0.91,0.91,0.91,
0.91;

00-3, 0.75, 0.85, 0.88, 0.9, 0.90, 0.91, 091,091, 0.91, 0.91, 0.91, 0.91, 0.91, 0.91, 0.91,
.91;

00036 0.75, 0.84, 0.88, 0.89, 0.9, 0.90, 0.90, 0.90, 0.90, 0.90, 0.90, 0.90, 0.90, 0.90, 0.90,

46

0.3, 0.74, 0.82, 0.87, 0.89, 0.89, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9,
0.9; .

0.3, 0.7, 0.82, 0.86, 0.88, 0.89, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9,
0.9;

0.3, 0.7, 0.81, 0.86, 0.88, 0.89, 0.89, 0.89, 0.89, 0.89, 0.89, 0.89, 0.89, 0.89, 0.89, 0.89,

0.892;
0.3,0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3,

0.3]
Map 4.2.18

mc_max_trq=[340, 375,402, 403,401,400, 348, 300, 250, 227, 202, 190, 175, 170, 150,
148, 0]

47

Table 4.2.5. Motor parameters for the baseline bus model.

 

 

 

 

 

 

 

 

 

 

ADVISOR Parameter Parameter . .
Parameter Value Value Source Descrrptron
(SI) (English)
ADVISOR S eed ran e of the
mc_map_spd Map 4.2.15 (rad/s) Map 4.2.15 Default 9 motif
Value
Map 4.2.16 ADVISOR Torque range Of
mc_map_trq Map 4.2.16 Default
(N -m) Value the motor
Motor efficiency
map (dependent on
Ma 4 2 17 ADVISOR speed range of the
mc_eff_map p ' ‘ Map 4.2.17 Default motor {vertically}
Value and torque range
of the motor
{horizontallyD
‘ ADVISOR
mc_max_trq M22413). 18 Map 4.2.18 Default Max Torque Curve
Value
ADVIS OR Maximum current
mc_max_crrnt 480 Amps 480 Amps Default allowed] by th:
Value contro er an
motor
. . 2 0-017333 ADVISOR Rotor’s rotational
mc_mertza 0.0235 kg-m 2 Default . .
slugs-ft Value 11161113
ADVISOR
mc_mass 70 kg 4.80 slugs Default Mass 0f mcfior and
Value contro er
ADVIS OR Minimum voltage
mc_min_volts 120 volts 120 volts Default alloweill by a:
Value contro er an
motor

 

 

 

 

 

 

48

 

4.2. 6. Generator Parameters
Some of the generator parameters were given as maps. These maps are defined
below in SI units defined in Table 4.2.6. For these maps, colons define them. For

example, the torque range is defined by [0252200]. This means that the range is from 0 to

200 in increments Of 5.

Map 4.2.19

gc_map_trq = [0252200]

Map 4.2.20

gc_map_spd = [0:26. 182733.04]

Table 4.2.6. Generator parameters for the baseline bus model.

 

 

 

 

 

 

 

 

 

 

 

 

Parameter Parameter
33:53:: Value Value Source Description
LSI) (English)
Map 4.2.19 ADVISOR Torque range of the
go map trq Map 4.2.19 Default
” " (N-m) generator
Value
ADVISOR
gc_map_spd Map 4'2’20 Map 4.2.20 Default Speed range 0f the
(rad/s) generator
Value
480 Am 3 ADVISOR Maximum current draw
gc_max_crrnt p 480 Amps Default for the motor/controller
Value set
~ ADVISOR Minimum volta e for
gc_min_volts 120 volts 120 volts Default g
the motor/controller set
Value
. . 2 0.007376 ADVISOR , , ,
gc_mertza 0.01 kg-m 2 Default Rotor’s rotatronal 1nert1a
slugs-ft Value

 

 

49

 

4. 2. 7. Transmission Parameters
The transmission in the model was based upon an Allison automatic transmission
for a school bus/transit bus. Some of the transmission parameters are given as maps.

These maps are defined below in SI units defined in Table 4.2.7.

Map 4.2.21
‘gb_ratio=[3.49, 1.86, 1.41, 1.00, 0.75, 0.65]

Map 4.2.22
tx_map_spd=[0, 60.85]

Map 4.2.23
tx_map_trq=[- 1254, 1254]

Map 4.2.24

tx_eff_map= [0.90, 0.90;
0.90, 0.90]

50

Table 4.2.7. Transmission parameters for the baseline bus model.

 

 

 

 

 

 

 

 

 

 

 

Parameter Parameter
33:11:33: Value Value Source Description
(SI) (English)
gb_ratio Map 4.2.21 Map 4.2.21 Filiiilgfrsf: Ratios in gearbox
b ears mm 6 6 Specific for Number of discrete gear
g _g - Flint Buses choices in gearbox
Map 4.2.22 S ecific for Speed of transmission
tx_map_spd (rad/s) Map 4.2.22 p . shaft output (wheel-side
F lrnt Buses . .
of transnussron)
. Torque of transmission
tx map trq Map 4'2'23 Map 4.2.23 SPECIFIC for shaft output (wheel-side
- - (N-m) Flrnt Buses . .
of transmrssron)
Transmission efficiency
(dependent on torque of
ADVISOR transmission shaft
tx_efl_map Map 4.2.24 Map 4.2.24 Default output {vertically} and
Value speed of transmission
shaft output
{horizontally})
ADVISOR 'Final Drive Ratio (5.34
fd_ratio 4.037 4.037 Default is also sited as a good
Value value for transit buses)
ADVISOR . . .
fd_inertia 0 kg-m2 0 slugs-ft2 Default Routgrfi? (1123:“! Of
Value
ADVISOR
gb_mass 283.447 kg 19.42 slugs Default Mass of gearbox
Value
ADVISOR
fd_mass 90.703 kg 6.215 slugs Default Mass of final drive
Value

 

 

 

 

 

4. 2. 8. Wheel Parameters

The wheel parameters were based upon those for a heavy truck (representative of

a transit bus). Some of the wheel parameters are given as maps. These maps are defined

below in SI units defined in Table 4.2.8.

51

 

Map 4.25
wh_axle_loss_mass=[0, 5000, 10000, 15000, 30000]

Map 4.26
wh_slip_force_coeff=[0, 0.3913, 0.6715, 0.8540, 0.9616, 1.0212]

Map 4.27
wh__axle__loss_trq=[0, 15, 30, 45, 90]

Map 4.28
wh_slip=[0.0, 0.025, 0.050, 0.075, 0.10, 0.125]

Map 4.29
wh_fa_dl_brake_frac=[0, 0, 0.5, 0.8, 0.8]

Map 4.30
wh_fa_fric_brake_frac=[0.8, 0.8, 0.4, 0.1, 0.1]

52

Table 4.2.8. Wheel parameters for the baseline bus model.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADVISOR Parameter Parameter . .
Parameter Value Value Source Descnptron
(SI) (English)
ADVISOR .
wh__ax1e_loss_mass Map 4'2'25 Map 4.2.25 Default Veh1cle test mass
(kg) V 1 vector
a ue
Coefficient defined
ADVISOR as thfhtragtrvtefiforce
wh_slipforce_coefl Map 4.2.26 Map 4.2.26 [iffimlt ocliivifledobly this
a ue weight on the front
axle
Ma 4 2 27 ADVISOR Front brake and
wh__axle_loss_trq p ' ' Map 4.2.27 Default axle bearing drag
Value torgme
ADVISOR . .
wh_slip Map 4.2.28 Map 4.2.28 Default Wheel 81") °f dnve
wheels
Value
wh radius 045 111 1.4764 fi Specific for Rolling radius of
— F lrnt Buses wheels
ADVISOR Fraction of braking
whfa_dl_brakefiac Map 4.2.29 Map 4.2.29 Default done by driveline
Value via front axle
ADVISOR Fraction of braking
whjafiicjrakejrac Map 4.2.30 Map 4.2.30 Default done by front axle
Value fiiction brakes
wh Isl rrc 0 00938 0 00938 Reference 18' coefficient of
— r ' ' Value rolling resistance
w h 2nd rrc 0 0 Reference 2nd coefficient of
— - Value rolling resistance

 

53

 

4.3. Summary

A baseline hybrid bus model was developed in ADVISOR based upon early
specifications for a bus in development with a joint project between Michigan State
University, Kettering University, and TransTeq. This was important for early validation
purposes for the project, as well as ensuring that the optimization strategies developed
and explored in this thesis for HEV’s would be valid for real-world hybrid applications.
The development of the baseline simulation model based upon an existing bus also
ensured that the results obtained for simulations were realistic. This chapter gave all of

the details associated with the baseline model.

54

CHAPTER 5: OPTIMIZATION STRATEGY FOR HEV’S
USING ADVISOR AS A SIMULATION TOOL

5.1 Introduction

The design of hybrid electric vehicles (HEV’s) requires complex optimizations to
account for the intricate interactions among the components, control strategies and the
resulting effects on performance. Due to the size of HEV models and the complexity of
interactions among the many components, it is challenging to properly define an
optimization problem statement that invokes a final design with the desired performance
characteristics. The optimization problem statement definition greatly affects the
performance Of the optimized HEV design, as well as the implications of the design.
While this may seem obvious, the proper problem statement for achieving a particular
performance goal is not always so clear.

In this chapter, the main characteristics of two optimization strategies that have
been shown to be efficient in optimizing hybrid electric vehicles are merged into a single
and more robust strategy that is shown to have several advantages in terms of design
performance. The main purpose here is to explore these various strategies and associated
optimization problem statements and their effects on the resulting hybrid vehicle design.
As a consequence of this study, a practical and efficient approach is developed for sizing

the components and defining the system control of HEV’s to create efficient, reliable

vehicles.

55

 

 

5.2 Hybrid Electric Bus Model

5. 2.1 Component Sizing Procedure

For the purpose of the current study, we considered a series configuration hybrid
electric bus as shown in Figure 5.2.1, with the baseline components described in Chapter
4, summarized in Table 5.2.1. The main components of interest for the optimization were
the generator, electric motor, engine, and battery. During optimization, a scaling method
was used to represent the size of each component relative to the baseline size.

By altering these scaling factors (which acted as the design variables during
optimization), different size motors, engines, and generators could be evaluated.
ADVISOR uses the scaling factor specified for a given component to linearly scale the
relative internal parameters of that component. This linear scaling assumption makes for
an easy way to change the size of a component without needing detailed experimental
data for multiple sized components, so long as linear scaling is appropriate for the
different size components in question. This is an approximation for a given component,
but is a common and accepted way to size components of HEV’s [9].

Values of the scaling parameters less than one corresponded to smaller sized
devices, while values greater than one corresponded to larger sized devices. The baseline

model was thus represented by the following parameter values:

Generator Speed Scale (GC SPEED): 1.0
Generator Torque Scale (GC TORQUE): 1.0
Motor Speed Scale (MC SPEED): 1.0

Motor Torque Scale (MC TORQUE): 1.0

56

Engine Speed Scale (F C SPEED): 1.0

Engine Torque Scale (F C T ORQUE): 1.0

Similarly, the battery size was altered using a scaling factor for the capacitance. In

addition, the number of modules for the battery was altered during the study. The

baseline battery was represented as follows:

Battery Capacitance Scale (ESS CAP): 1.0

Number of Battery Modules (ESS MOD NUM): 25

 

 

 

 

 

Figure 5.2.1. Powertrain configuration of the HEV bus (as it appears in ADVISOR).

Table 5.2.1. Baseline com onents of the series h brid bus for o timization.

        

 

 

 

 

 

 

 

 

   
   

 

 

Component Characteristics
Engine Detroit Diesel Corp. Series 50 8.5 (205kW) Diesel Engine
Motor UQ/I 150 kW motor/controller
Generator UQM 150 kW generator
Battery NIMH 90Ah Ovonic, 25 battery modules
Wheel and ACCURIDE, wh_radius = 0.45
Axle
Transmission Single gear, TX ISPD BUS with overall ratio @742 1).
Accessory Mechanical and electrical power scaled of ~ 21.4 kW (29 hp) with
A/C

 

 

57

5.2.2 Control Strategy
A thermostat control strategy was used in the current study. This type of control
strategy allows the user to specify a lower/upper limit for the state of charge (SOC) of the
battery, below/above which the engine turns on/off and the generator charges/discharges
the battery. In a thermostat control strategy, when the engine is on it is run at a constant
speed (ideally that for which the engine operates most efficiently). For all optimization
studies, the lower and upper limits on the state of charge for this thermostat control

strategy were defined as:

Lower Limit on SOC: 0.52

Upper Limit on SOC: 0.68

These values were selected in accordance with an assumed requirement that the

battery of the bus must operate with a state of charge between 52% and 68% in practice.

5.2.3 Driving Cycle

Two different driving cycles were considered the most viable to gauge the
performance of a hybrid electric bus: the Federal Test Provisions Driving Cycle (FTP
Driving Cycle) and Urban Dynamometer Driving Schedule (UDDS). The most
demanding of the two driving cycles was judged to be the Urban Dynamometer Driving
Schedule (UDDS), and therefore it was chosen for all comparative studies. It has the

characteristics of Figures 5,2,2 and 5.2.3.

58

 

 

 

 

 

 

 

 

 

 

 

100 l r I l I I
A
.51
Q.
E
'5
o
o
g N.
50 '
0 * , . . ‘ g 7 - - . m
0 200 400 600 800 1000 l 200 1400
Time (see)
Figure 5.2.2. Driving cycle speed/elevation vs. time for the UDDS driving cycle.
CYC UDDS
25 ,
Tlme: 1369 s
Distance: 7.45 miles
Max Speed: 56.7 mph
A
8\: Avg. Speed: 19.58 mph
go Max Accel: 4.84 ft/ 52
‘3 2
8 Max Decel: -4.84 It] s
a? 2
Avg. Accel: 1.66 it! s
I Avg. Decel: -1.9 fi/s2
Idle Time: 259 s
50 100 No. of Stops: 17
Speed (mph)

 

 

 

 

 

Figure 5. 2.3. UDDS driving cycle characteristics.

59

 

. \IIIIIII .: i .11

 

5. 3. Baseline Designs

5.3.1 Conventional Bus Design

For comparison and validation purposes, an existing baseline conventional (non-
hybrid) bus model was used. Starting with the validated conventional bus model, a,

baseline hybrid bus model was developed and used to gauge the performance of the

different optimization strategies.
The conventional bus had the same basic design characteristics (e. g., engine,
wheel and axle, transmission, and accessories) as the hybrid bus described in Table 5.2.1.
The conventional bus had the following performance characteristics:
fuel economy: 4.7 mpgge

missed_trace: < 5 mph

’60 I 68.6 S

130: 13.3 S

where:

fuel economy is measured in miles per gallon gasoline equivalent (mpgge),
missed_trace is a gauge of how close the bus is to meeting the drive

demands of the cycle (Figure 5.2.2),

1601s the time required for the bus to accelerate from 0-60 mph, and

t 30 is the time required for the bus to accelerate from 0-30 mph.

60

5.3.2 Baseline Hybrid Bus Design

The validated conventional bus model was used as a starting place in designing a

hybrid bus. The baseline hybrid bus model had all of the characteristics of Table 5.2.1,

and the following performance:

where:

A verage fuel economy: 3.71 mpgge
Corrected fuel economy: 4.07 mpgge

missed_trace: 15.7 mph

:60 : 52.67 s

130: 21.22 8

Average fuel economy is a measure of the average fuel economy of the
design evaluated with multiple initial SOC’s over multiple run
cycles of the UDDS with no SOC correction (measured in miles
per gallon gasoline equivalent),

Corrected fuel economy is a measure of the fuel economy over one run
cycle of the UDDS with an SOC correction routine as described by
[23-27] (measured in miles per gallon gasoline equivalent),

missed_trace is a gauge of how close the bus is to meeting the drive
demands of the cycle (Figure 5.2.2),

160 is the time required for the bus to accelerate from 0-60 mph, and

130 is the time required for the bus to accelerate from 0-30 mph.

61

Note that the baseline hybrid bus did not meet the target for missed trace, and
acceleration times, and is thus considered an infeasible design. These performance targets
will subsequently be enforced as constraints during optimization. The fuel economies of
this baseline hybrid design will be used for assessing new designs based on the proposed

optimization strategies.

5. 4. Modeling Concepts for HE V Optimization

5.4.]. Introduction

For the various optimization studies performed in this work, the Optimization goal
was to size the various components of interest in a manner that minimized fuel
consumption while meeting performance characteristics for a given drive cycle. One of
the more challenging and interesting aspects of HEV optimization is identifying an
appropriate definition of fuel economy and subsequently minimizing its sensitivity to
various assumptions in the model and to the drive cycle used during the simulation for
each design. In this section, an overview of why these issues arise is presented as a

prelude to the detailed investigation described in the next section.

5. 4.2 SOC Corrections

SOC corrections in some form are used in the vast majority of optimization work
with HEV’s to date. SOC corrections are important in the design of HEV’s for multiple
reasons. They provide a meaningful way to compare HEV performance to conventional
vehicle performance [23-24], as well as reduce the impact the initial state of charge has

on the performance of the design [9, 25]. By ensuring initial and final SOC over a drive

62

cycle are the same (or nearly the same), SOC corrections alleviate the need for multiple
drive cycles to be performed to see how performance changes with varying initial SOC.
This provides an easy and seemingly robust way to compare designs during optimization

[25].

5.4.3 Multiple Initial SOC ’s

It was desired to see the effects on the results obtained from optimization if an
SOC correction was not utilized. A preliminary optimization was therefore performed
that sized the engine, generator, motor, and battery, such that the fuel economy of the
engine was maximized and certain performance characteristics were met. This
optimization run had an initial SOC of 0.68 and did not utilize SOC correction.

The optimized design found had the SOC and engine speed history plots shown in
Figure 5.4.1. The components for this design were sized such that the design acted almost
entirely as an electric vehicle (EV) over the drive cycle, with the engine not needing to
turn on until the end of the drive cycle. This EV behavior gave a very high performance
during optimization since no battery losses were accounted for. These results are

consistent with the trends seen by Markel and Wipke [18-19].

If however, the Optimized design had an initial SOC less than 0.68, it would not
perform as an EV over the drive cycle. Figure 5.4.2 shows the SOC and engine speed
history plots for the same design found as optimal during the optimization, re-evaluated
in ADVISOR with an initial SOC of 0.60 instead of 0.68. Clearly the design now does

not act as an EV over the drive cycle, and therefore its performance will be drastically

lower than that found during the optimization where it did act as an EV. It was concluded

63

therefore, that if an SOC correction routine is not utilized, multiple initial SOC’s should
be considered when evaluating an HEV’s performance since it is not guaranteed that a

vehicle will always start with a high initial SOC.

 

SOC 0.52
0.6

0.58

0.55

0.54

 

0.52 ~

 

 

 

05 I I I I I l n
0 200 400 500 800 1000 1200 1400 T‘me(5)

 

140 1 f fi U l I

120 .. -.
100 - -l

Engine Speed 80 2 —
(rad/s)
50 l + -

40» -

20- ..

0 200 400 600 1000 1200 1400 mm“)

(b) 01 vs. time.

 

 

Figure 5.4.1. Optimized design characteristics for one drive cycle of the UDDS (SOC=state of charge;
to engine Speed) with an initial SOC 01' 0.68.

 

SOC

 

 

 

 

 

0510 200 400 600 800 1000 1200 1400 Time (s)
(a) SOC vs time.
140
120 _ —.
1CD - ..
Engine Speed 80 b ‘
(rad/s)
60 - + _ 1
40 - ..
20 - -

 

 

 

a? 1 . ' ' Time (5)
0 400 600 800 1000 1200 1400

(b) 0) vs. time.

Figure 5.4.2. Optimized design characteristics (SOC=state of charge; to=engine speed) if re-evaluated
wrth an initial SOC of 0.60.

For a given drive cycle, an HEV performs differently depending upon its initial

SOC [9]. A design’s performance therefore will be skewed depending upon the initial

65

SOC that it is evaluated for (performing well at one initial SOC and poor at another). A
method to overcome the sensitivity to initial SOC is to evaluate a given design for
multiple initial SOC’s and average the performance. One issue with this approach is

selecting which initial SOC ’s to consider in evaluating the average performance.

5.4.4 Multiple Cycle Repeats

If an SOC correction routine is not utilized, evaluating designs based upon the
average performance from multiple initial SOC’s over a single drive cycle may be
inaccurate. Utilizing the optimized design from Sub-Section 5.4.3, a study was performed
to see the effect the number of consecutive UDDS drive cycles has on the responses. The
optimized design was altered so that the initial SOC was 0.60 instead of 0.68 so that it
wouldn’t run as an EV. This design was then run for l, 3, and 20 drive cycles. When
performing multiple drive cycles, a periodic behavior was observed in the SOC and
engine speed time histories, as shown in Figures 5.4.3 and 5.4.4. Thus, as the number of
drive cycle repetitions is increased, the dependency on the initial SOC decreases while
the evaluation time increases. Since the period of the SOC time history for the evaluated
bus appeared to be slightly less than three drive cycles (as seen in Figure 5.4.3), this was
the number of drive cycle repeats used herein whenever an optimization strategy required

multiple drive cycles.

66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

     

 

 

0.6
SOC
0.5 4 . - - . .
0 600 1400 Time (s)
(a) One drive cycle.
0.7 . . . f
l
SOC «
0.6
0.5 l l A; I l 1 1 l
0 2000 . 4500 Time (s)
(b) 3 drive cycles.
07 . . . .
L
soc ' ' I '
0.6 1 '
I .
0.5 '
0 15000 30000 Time (s)
‘.| T ‘—

 

(c) 20 drive cycles.

Figure 5.4.3. SOC history plots for an optimized design evaluated for different number of drive
cycles. The period (T) of the cycle corresponds with just less than three cycle repetitions.

67

 

 

 

 

 

 

 

 

 

140 ' '
, _.
Engine Speed L
(rad/s) 80
+ ..
0 ._ . 1 1 l
0 600 1400 Time (s)
(a) One drive cycle.
140 u f u u v fi-
_ «a _
l
Engine Speed 80 . J
(rad/s)
+
0 L . 1 _——+ .
0 2000 4500 Time (s)
(b) 3 drive cycles.
140 . . . .

.--—--—-----—- ..

Engine Speed 80
(rad/s) . + .

 

 

 

0 15000 30000 Time (s)

(c) 20 drive cycles.

Figure 5.4.4. Engine speed history plots for an optimized design evaluated for different number of
drive cycles.

68

Due to the periodic nature of the SOC history plots with drive cycle repetitions, a
design should be evaluated during optimization for multiple cycle repetitions at multiple
initial SOC’s, in the hopes that this methodology decreases the dependence of a design’s

performance on its initial SOC.

5.4.5 Corrected Fuel Economy

Duoba [26] and Senger [27] discuss how a conversion for electrical energy usage
can be used as an alternative to SOC correction, by converting the electrical energy that
can be obtained from gasoline through the efficiency of an average power plant in the
United States in 1996. The fuel economy values used with the concepts discussed above
base the fuel calculations on the actual volume of fuel used. But in a hybrid vehicle, some
amount of electric energy is also used during the driving cycle. Therefore one could
postulate a ‘corrected fuel economy’ measure as an alternative objective, in which the
equivalent fuel energy of electrical energy used is added to actual fuel energy used. This
approach provides a more consistent comparison among designs and effectively results in

‘perfectly charge sustaining’ vehicle behavior.

69

5. 5 Optimization Strategies and Problem Statements

Three optimization strategies for optimizing HEV’s have been developed and
compared using the concepts discussed in Sub-Section 5.4. The definition of the
strategies, as well as the formal optimization problem statement utilized with each are

discussed in this sub-section.

5. 5.1 Strategy I-Multiple SOC ’s and Multiple Drive Cycle Repetitions

The first strategy utilizes multiple initial SOC’s and multiple drive cycle
repetitions to evaluate the performance of a given design. No state of charge correction is
utilized for this strategy, and a measure of the actual volume of fuel used instead of the
corrected fuel economy. Three analyses are performed for each design, each with a
different initial state of charge (SOC). Two of the analyses use an initial state of charge at
the extremes of the SOC range specified for the thermostat control strategy (High SOC
and Low SOC), while the third analysis uses an initial SOC that is the average of the
extreme SOC’s. By using multiple drive cycle repetitions (three repetitions utilized in this
study) in three different analyses, each with different initial SOC’s, the performance of a
given design should not be highly dependent upon the initial SOC used.

Strategy 1, thus has the following fuel economy performance criterion:

_ 25:] fi
N

f
(5.1)

where:

f is the composite fire] economy (average fuel economy over all analyses),

70

w

 

f,- is the fuel economy for a given analysis, and

N is the number of analyses performed (3 here: each with a different initial SOC).

The optimization problem statement for Strategy 1 as used in this study is

formally expressed as:

 

Maximize: composite file] economy (average miles per gallon of gasoline (mpg) as
defined by Equation (5.1))

Subject to: missed_trace (mph) 5 5.0 (how close the bus was to meeting the drive
demands of the cycle)
minimum SOC 2 0.5175 (lowest state of charge over all initial SOC
loadcases)

t60 S 42.0 s (time to accelerate to 60 mph from start)
t 30 S 10.0 s (time to accelerate to 30 mph from start)

By varying: Number of battery modules = {15,16, .. ,50}

0.3 _<_ Battery capacitance Scale 5 1.5
0.5 3 Engine Speed Scale 3 1.5
0.5 5 Engine Torque Scale 5 l.5
0.5 _<_ Generator Speed Scale 5 1.5
0.5 S Generator Torque Scale _<_ 1.5
0.5 5 Motor Speed Scale 5 3.0
0.5 5 Motor Torque Scale 5 3.0
With: Upper SOC Limit = 0.68
Lower SOC Limit = 0.52
Initial SOC = {0.68, 0.60, and 0.52} (multiple initial SOC

load cases)

 

 

 

71

5.5.2 Strategy 2 — SOC Correction with Corrected Fuel Economy

The second strategy utilizes a SOC correction as well as considers the corrected
fuel economy as opposed to the actual volume of fuel used. Within ADVISOR, there is a
“Zero-Delta SOC correction routine” available [9]. This routine can be set to iterate on
the initial SOC until a tolerance on SOC is satisfied. The routine adjusts the initial SOC
until the simulation run yields either a zero change in SOC +/- a tolerance (making the
initial SOC more or less equal to the final SOC), or until the routine runs for the
maximum number of iterations specified by the user. The default ADVISOR tolerance
and maximum iterations were utilized in this study: 0.5% and 15, respectively. The
algorithm for this routine is described in the following steps (as described in the

ADVISOR User’s Manual [9]) and by Figure 5.5.1 below:

1. An initial SOC is guessed that is the average of the high and

low limits:

SOC high+SOClow

SOC initial.0 = '
2 (5.2)

 

2. The new initial SOC (SOC initial, ,+ 1) is guessed based upon the
previous initial SOC (SOC Min-a], t), the change in SOC achieved

(4900), and a weighting factor (q). The weighting factor is

chosen so that the charge neutral point (zero ASOC) is

bracketed quickly.

72

‘\

 

SOC initial.t+1 = SOC initiaLt +q*A SOCt (5.3)
3. Once the charge neutral state is bracketed (values for the
metrics are known on both the positive ASOC and the negative

ASOC, the new initial SOC is linearly interpolated.

SOC initial.t+l =interp[SOC(ASOCminrHLSOCMSOCminr-D] (5.4)

4. The simulation is then run and the ASOC evaluated, the bracket

size shrinks, and step 3 is repeated until the ASOC is within the

tolerance band or the maximum iterations are run.

5. Final simulation iteration is run at the initial SOC that gives
ASOC within the tolerance, and only those results are reported

from the ADVISOR simulation.

73

 

 

 

SOCinitialJl—l mpg
I I
I I
. /. : : OCinitiaLt-zerocdelta
I
SOCinitiaL2(-) /@ : : ./ SOCinitial,l(+)
SOCinitialJl-l : : .
: r 4
: ; K ASOC
: : SOCinitial,0
fi—fi
Zero-ASOC tolerance

 

 

 

Figure 5.5.1. Zero-Delta SOC correction routine. An initial SOC guess is evaluated
(SOCinitial,0) in terms of ASOC. The initial bounds around the zero-ASOC tolerance are

then found (SOCinitial,l(-) and SOCinitial,l(+)) and linearly interpolated to get

SOCinitial,l(-)- This bound (SOCinitial,2(-) and SOCinitial,l(+)) is then linearly
interpolated and the process repeated until an initial SOC is found that gives a ASOC within

the tolerance (SOCinitial,t-zero-delta) [9]-

While the “Zero-Delta SOC correction routine” attempts to ensure that the energy
input to the battery is the same as the energy output from the battery over the drive cycle,
this is not always the case due to the tolerance and maximum iterations specified for the
routine. For this reason, Strategy 2 also converts the difference in battery energy into
gasoline equivalent energy to obtain the corrected fire] economy. This is done using a
value for the electrical energy that can be converted to gasoline through the efficiency of
an average power plant in the United States (3.11 kWh/liter in 1996). With this method, a
‘fuel penalty’ term (e) is calculated based upon the gasoline equivalence described above

[26-27]. The fuel penalty e is defined as:

74

(essout — essin)*0.000278
e = *0.264172

3.11 (5-5)

 

where:

essou, is the useful energy leaving the batteries over the drive cycle (units of k1),

essm is the energy into the storage system over the drive cycle (units of k1),

0.0002 78 is the conversion factor from k] to kWh,

3.11 is the electrical energy that can be converted to gasoline through efficiency
of an average power plant (units of kWh/L),

0.2641 72 is the conversion factor from L to gallons, and

e is the fuel penalty (units of gallons).

A positive value for the fuel penalty (e > 0) indicates that electrical energy is used
to propel the vehicle and thus acts as a penalty to the fuel economy of the vehicle. A
negative value for the fuel penalty (e < 0) indicates that fuel has been used to charge the
battery and thus acts as additional fuel economy to the vehicle (boosting its performance
value). Figure 5.5.2 shows the logic-loop that evaluates the corrected fuel economy for a

given design using the fuel penalty calculated for that design. For Strategy 2:
0 e will be referred to as the fuel penalty; it is considered as the fuel used to

operate the battery

0 mpgge is the drive cycle mi/ gal gasoline equivalent calculated by

ADVISOR (the same as the fuel economy used in Strategy 1)

75

- dist will represent the distance traveled over the simulation

0 f is the corrected fixel economy

This strategy can also be thought of as calculating the consumed fuel (that of the actual
fuel used during the run (mpgge)), a fuel penalty (e), as well as a corrected fuel economy

(f) (the distance traveled (dist) per consumed fuel).

 

 

 
 
  

@ dist

mpgge>20 Yes H f: —

 

 

 

 

 

 

 

 

 

No No
6) f: —— dISt. @ mpgge
e + drst f = e+1
mppge

 

 

 

 

 

 

 

Figure 5.5.2. Logic used to calculate the corrected fuel economy. Scenario 1 occurs when the fuel
penalty is small (or negative) and makes the corrected fuel economy equal to: the drive cycle mi/gal
gasoline equivalent for small positive values, and greater than the drive cycle mi/gal gasoline
equivalent for negative values. Scenario 2 occurs when the battery equivalent is large but the drive
cYcle mi/gal gasoline equivalent is not too large, thus reduces the corrected fuel economy to account
for the fuel penalty during the run. Scenario 3 occurs when the vehicle operates almost entirely as an
electric vehicle (EV) and therefore treats the corrected fuel economy as if the vehicle were completely
EV with all of its fuel used coming from the fuel penalty.

76

The optimization problem statement for Strategy 2 as used in this study is

formally expressed as:

 

Maximize: corrected fire] economy (accounting for total energy usage with miles per
gallon gasoline equivalent (mpgge) as defined by
Figure 5.5.2 and Equation (5.5))

Subject to: missed_trace (mph) 5 5.0 (how close the bus was to meeting the drive
demands of the cycle)
minimum SOC 2 0.5175 (lowest state of charge achieved)

I60 S 42.0 s (time to accelerate to 60 mph from start)
t 30 S 10.0 s (time to accelerate to 30 mph from start)

By varying: Number of battery modules = {15, 16, .. ,50}

0.3 5 Battery capacitance Scale 51.5
0.5 5 Engine Speed Scale 5 1.5
0.5 5 Engine Torque Scale 5 1.5
0.5 S Generator Speed Scale _<_ 1.5
0.5 S Generator Torque Scale S 1.5
0.5 5 Motor Speed Scale 5 3.0
0.5 5 Motor Torque Scale 5 3.0
With: Upper SOC Limit = 0.68
Lower SOC Limit = 0.52

 

 

Zero-Delta SOC correction routine utilized

 

5. 5.3 Strategy 3 — A Hybrid Approach

The third strategy utilizes multiple initial SOC’s and multiple drive cycle
repetitions to evaluate the performance of a given design, along with the corrected fuel
economy. No state of charge correction is utilized for this strategy. As in Strategy 1, three
analYses are performed for each design, each with a different initial state of charge
(SOC) Two of the analyses use an initial state of charge at the extremes of the SOC
range Specified for the thermostat control strategy (High SOC and Low SOC), while the
third analysis uses an initial SOC that is the average of the extreme SOC’s. In addition,

77

the strategy utilizes multiple drive cycle repetitions (three repetitions utilized in this
study) for each initial SOC analysis, as is done with Strategy 1.

Whereas Strategy 1 utilizes the actual volume of fuel used, Strategy 3 utilizes the
corrected fuel economy as defined by Equation (5.5) and Figure 5.5.2. While Strategy 2
utilizes a SOC correction routine, Strategy 3 does not. Rather than trying to find the
design with the greatest average fuel economy or the design with the greatest corrected
fuel economy, Strategy 3 tries to find the design with the greatest average corrected fuel

economy:

_ 2:1 fi
N

f

(56)
where:

f is the average corrected fuel economy over all analyses,

fl is the corrected fuel economy for a given analysis utilizing Equation (5.5) and

Figure 5.5.2,

N is the number of analyses performed (3 here: each with a different initial SOC).

78

The optimization problem statement for Strategy 3 as used in this study is

therefore formally expressed as:

 

Maximize: average corrected fitel economy (accounting for total energy usage with
miles per gallon gasoline equivalent
(mpgge) as defined by Equation (5.6),
Equation (5.5), and Figure 5.5.2)

Subject to: missed_trace (mph) _<_ 5.0 (how close the bus was to meeting the drive
demands of the cycle)
minimum SOC _>_ 0.5175 (lowest state of charge over all initial SOC
loadcases)

I60 S 42.0 s (time to accelerate to 60 mph from start)
1 30 _<_ 10.0 s (time to accelerate to 30 mph from start)

By varying: Number of battery modules = {15,16, .. ,50}

0.3 5 Battery capacitance Scale 5 1.5
0.5 5 Engine Speed Scale 5 1.5
0.5 S Engine Torque Scale 5 1.5
0.5 S Generator Speed Scale 5 1.5
0.5 S Generator Torque Scale 5 1.5
0.5 5 Motor Speed Scale _<_ 3.0
0.5 S Motor Torque Scale S 3.0
With: Upper SOC Limit = 0.68
Lower SOC Limit = 0.52
Initial SOC = {0.68, 0.60, and 0.52} (multiple initial SOC

 

 

load cases)

 

79

5. 6 Results of the Optimization Studies

5. 6. 1 Strategy Comparisons

The commercial software HEEDS [29] was used as the optimization tool for all
three strategies, and the hybrid adaptive search algorithm SHERPA [29] was employed.
Three independent optimization runs were performed for each strategy to lessen the effect
of the random starting conditions of the search on the optimized design found. Similar to
a genetic algorithm, SHERPA begins with a set of quasi-random initial designs (unless
these designs are otherwise provided) that depend loosely on the value of an arbitrary
number, called a random seed. When the same or similar results are obtained from
multiple optimization runs with different random seeds, there is greater confidence (but
no guarantee) that the results found are at or near a global optimum. In the current study,
each optimization run was allowed to continue for an extended period of time, up to a
maximum of 1000 evaluations. Though all the optimization runs may not have been firlly
converged (something that can never be guaranteed due to the nature of the design
landscapes for these problems), by 1000 evaluations the rate of improvement was very
low in all cases, so the runs were considered to be very nearly converged (see a typical

example in Figure 5.6.1)-

80

Corrected Fuel Economy

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5
4 ' w“, ~ . ,gw.-. . —;,.W
. ‘~ ‘ “"77" 5"“. . ".+ ’ ; . ""‘~""“““’
’ o 0' . 9’.
z 0‘3..."
a O 0.1
...‘. ‘0“. I o
r "--—-——"_‘,J_——_:’; :;‘ ‘r———~""~+-m w-J'; '-- '—-————-—"‘
3 l .000
1
l
2 |
I
1 _ __. :
l
l , I
.. __._ _. _-_ ___+..__._....-_ _--_ _____._-- -._——————————o———> -—+Nr~—-— +2 : e? 4 4 +
l ‘ 4
0 200 400 600 800 1,000

Evaluations

Figure 5.6.1. Typical convergence plot for the HEV optimizations. The shown Optimization was
nearly converged by ~300 evaluations.

The optimized designs from all three strategies are collected in Table 5.6.1 and
Table 5.6.2. Recall that Strategy 1 maximizes the fuel economy from the engine only
(miles per gallon of gasoline), while Strategies 2 and 3 maximize the total energy usage
(miles per gallon gasoline-equivalent). Because the objective functions associated with
each strategy are different, it is difficult to directly compare the solutions obtained from
each strategy. Therefore, the optimized. designs from Strategy 1 and Strategy 2 were re-
analyzed using the criteria from the opposite strategy to facilitate this comparison. In,
other words, the optimized designs from Strategy 1 were re-analyzed with a single drive
CYCle utilizing a SOC correction so that their corrected fuel economy could be calculated.
Likewise the optimized designs from Strategy 2 were re-analyzed with no SOC
correction but rather multiple drive cycles for multiple initial SOC values so that their
average fuel economy could be calculated. Strategy 3 calculates the average fuel
ecoflOmy in terms of the corrected firel economy; therefore its optimized designs did not

need to be re—analyzed for comparative purposes.

81

The fact that each strategy found three different optimized designs with similar
response values is an indication of the difficult design landscapes associated with HEV
design. As Montazeri-Gh, et a1 [15] showed, HEV optimization problems are typically
highly non-linear, discontinuous, and multi-modal (i.e., multiple local optima exist).
Adding discrete variables to the problem statement as was done in this study, only
complicates the optimization search further. The three different optimized designs for a
given strategy would seem to indicate that the optimization is not fully converged. To
check further for the global optima, local search methods could be used around the
optimized designs to see if further improvement could be attained. Local search methods
have been shown to find marginal improvement in HEV designs as shown by Oh, et a1
[14].

The similarity in responses among the three designs for a given strategy could
have multiple explanations. It is possible that multiple local minima with similar
performances exist in the design landscape (see Figure 5.6.2 for an example), or that
many designs with similar performances exist in a flat region in the design space (see
Figure 5.6.3 for an example), among other things. Determining the cause for the
seemingly un-converged similar solutions is beyond the scope of this study.

When considering total energy usage, the optimized designs from Strategies 2 and
3 have a significantly greater corrected fuel economy than the optimized designs from
Strategy 1. Strategy 3 produced designs with a marginally improved corrected fuel
economy over the optimized designs from Strategy 2. Strategies 2 and 3 have consistently
high performing designs for all three Optimization runs. Compared to Strategy 2, Strategy

3 has the added advantage-of improved run-time efficiency. In the current study Strategy

82

3 runs are about 10% more efficient than Strategy 2 runs. This speedup will vary based
on the number of iterations required to perform the SOC correction within Strategy 2.
The speedup would also be affected by the number of initial SOC load cases and drive
cycle repeats utilized within Strategy 3. Overall, Strategy 3 appears to be an effective and
efficient alternative to the commonly used Strategy 2.

When considering only the energy usage from the engine, Strategy 1 produces
designs with the highest average fuel economy, significantly outperforming Strategies 2
and 3. This can be attributed to the very high fuel economies achieved when the initial
SOC is high, corresponding to the 0.68 initial SOC runs. For the three initial SOC’s
chosen for this study (0.68, 0.6, and 0.52) the optimizations with Strategy 1 sized the
components such that they operated almost entirely as an electric vehicle (EV) when the
initial SOC was 0.68. This strategy’s optimized designs had high values for battery
capacitance, a high number of battery modules, and also had less powerful engines than
the optimized designs from Strategies 2 and 3, as shown in Table 5.6.2. Since the average
fuel economy is the average of performance over all initial SOC load cases, the EV
nature of the optimized Strategy 1 designs when the initial SOC is 0.68 gives a very high
overall average fuel economy as well as a high standard deviation. These designs have a
lower performance than those of Strategies 2 and 3 when the relevant measure is overall
energy usage. Nevertheless, in those limited cases where a fixed route can be guaranteed
(as may be the case for some buses) and the fuel usage of the engine is the primary

concern, then Strategy 1 may be very efficient for optimizing such HEV’s.

83

 

Local minima

Figure 5.6.2. Three-dimensional contour plot of the local region surrounding the global minima
locations of the Six Hump Came] Back Function. Note the multiple local minima and multiple global
minima with identical response values.

 

' Figure 5.6.3. Three-dimensional contour plot of the Rosenbrock’s Valley function for two variables.
Note the similar response values along the valley close to the global optima value.

84

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0: NS. dmd Ed is end Ed 2d Gd Gd mod Gd - E 3rd fine—x
dmdm mwdm mmsm flawm mndm vwdm Eém 8.5m 3.: 3.2 M32 v9: - E and “sew
wood wood dwd mood dmwd mmwd wwwd nmwd mwd
ddwd Sod wddd wdwd Swd _dwd :dd ddwd ovwd wvwd Swd wvwd dod
mood Edd mood fed Swd _dwd Swd awd mod 99w. suntaV
fwd fwd dmwd fwd w_wd fwd fwd wfwd Nwd
fwd fwd omwd fwd omwd fwd ded fwd dmwd dmwd omwd omwd dwd
fwd fwd fwd fwd fwd fwd dmwd fwd wed Dew. E=E.E.€<
wed mod 3d wed fd fd fd fd mwd
$.m fd mvd dwN Rd 36 Ed mm...” fd fd fa fa dcd
8d 8a 3% Sam NE E .N N. .N Ed was «issue: 3an
. , .. _. «ca use
. v x 5. one a. one 43“ of” 3m 5.». - names» .55
, . 33% 38.6239 .a:‘
and Q} omen med . .. ._. . .. Nwd
mmé awe of» 5+ .. .3..de 13d 3.2mm :86 odd Swami
Rd med om;V dmé ,. . ,.. wed fieum fink 33.62.39
$2.9 a we awe r2 .8 2.4.8 rows .. .. . - «an 32
3 m E m 3 4 g m *3 m .2 m .8 v .8 m , . «was gem Si a3.
35 ww.m wmd wvw *wwd %wd 39m *www fw f.m 3d am Nwd
oww Ed 86 mwd *Ndd 39m *wdw L 3 3w ftw dmw mw.w odd
m2. cam 84. VS. a; .35 .03 .84. 3.3 $2 3% 3.3. $6 ES :85»:
.msV Mix mi... DOM. om=od8m
@835 w 5i N SQ N 5Q $23.6 m Si N SQ N SQ AmmEhw w 5% m Si N Sex 3.55
m .3235 N 389.5 _ tantrum

 

 

 

 

 

 

.293 91.6 25 he N 3325 we mwitom 558:8 00m 2: .53 dunk—«5-0.— 9.5.; 31.8.. — awed—Em:

._ 63:5

.5. v8: moi—«5 00m 3:... 2.5—2: 2... 25:93: 328 35. 2.51:: 2: 55 E: E.- neuoatoo 00w 2. 5.3 3555.9. Bot 51.8.. N 38.5?
has: 5% a .5 2...: £303.. 2.. 5? 328:3 £22 Bananas 2: .63. .8... .33 83 is 8m Egg 53» a
59—.“ 9:50.— Oflu .3; nUflOa—nOP—Oo 5.0 ofle a kc.“ 3.2.1—0.— 26 3150.- 029. 2053 ggahwn 09:: :6 EOE..— Uofimlunc nu—Buoh fiOflleEmuA—o 219m 23.?

85

Table 5.6.2. Design variable values corresponding with the optimized designs from each strategy.

 

 

 

 

 

 

 

 

 

 

Strategy 1 Strategy 2 Strategy 3
Variable Run 1 Run 2 Run 3 Run 1 Run 2 Run 3 Run 1 Run 2 Run 3
ESS CAP 1.5 1.5 1.5 0.3 0.3 0.3 0.3 1.128 0.312
ESS MOD NUM 50 50 50 29 42 28 40 31 35
FCSPEED 1.15 0.6 0.77 1.14 1.4 0.83 1.28 1.38 1.18
FC TORQUE 0.65 1.31 0.98 0.96 0.69 1.47 1.18 0.76 1.28
GC SPEED 1.32 0.5 0.70 1.05 0.63 0.61 1.05 0.97 0.87
GC TORQUE 0.89 1.5 1.44 1.22 1.39 1.45 0.96 1.3 1.5
MC SPEED 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
MC TORQUE 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

 

 

 

 

 

 

 

 

 

 

 

 

Figures 5.6.4-5.6.6 display the SOC and engine speed history plots of a typical
optimized design from Strategy 1 from this study (the result from Run 1 is shown).
Figure 5.6.7 shows the SOC and engine speed history plots of the same optimized design
when it is re-analyzed with the SOC correction of Strategy 2. Conversely, Figures 5.6.8
displays the SOC and engine speed history plots for the optimized design of Run 1 from
Strategy 2, wherein the objective was to maximize total energy instead of engine fuel
usage only, and Figures 5.6.9-5.6.11 show the same optimized design if it is re-analyzed
With no SOC correction and using the settings from Strategy 1.The trends in Figures
5.6.4-5.6.7 versus those in Figures 5.6.8-5.6.11 are significantly different. When
comparing engine fuel usage only with Figures 5.6.4-5.6.6 and Figures 5.6.9-5.6.11, the
Strategy 1 design runs primarily as an EV for high initial SOC’s whereas the Strategy 2

design does not. The components of the Strategy 1 solution have been designed such that

86

the engine runs continually for long durations of time in order to recharge a nearly
depleted battery. Conversely, the Strategy 2 design has a more evenly distributed load
balance between the engine and electric motor. When comparing total energy usage in
Figure 5.6.7 and Figure 5.6.8, the Strategy 1 design has the engine run around 50%

longer than the Strategy 2 design.

SOC History

 

0.7
0.55

SOC
05

0.55

 

 

 

1 I

0 500 1000 1500 2000 2500 3000 3500 4000 4500 Time (s)

 

0.5

(a) SOC history with initial SOC = 0.68.

Engine Speed History

 

 

 

                 

200 I 7 I I l I l l
_-
150 - _
Engine Speed
(rad/s) 100 - _
+
50 "' .4
U“ ‘ ‘ ":1- -' .. -"- - 93- " '- . ;.‘.'.'.: - :13" ,2; 21.12:; . .
0 500 1000 1500 2000 2500 3000 3500 4000 4500 Tune (5)

0’) Engine speed history with initial SOC=0.68.
Figure 5.6.4. Comparison of the SOC history and engine speed history plots for a typical optimized

design from the Strategy 1 optimizations (Run 1 shown here). With an initial SOC of 0.68 these
optimized designs can run primarily as electric vehicles (EV’s).

87

 

SOC History

 

 

 

 

(a) SOC history with initial SOC = 0.60.

200

150

Engine Speed 100
(rad/s)

50

U,

 

 

 

 

0 500 1 000 1 500 2000 2500 3000 3500 4000 4500
Engine Speed History
_-
_ + a
0 500 1 000 1 500 2000 2500 3000 3500 4000 4500

(b) Engine speed history with initial SOC=0.60.

Time (s)

Time (s)

Figure 5.6.5. Comparison of the SOC history and engine speed history plots for a typical optimized
design from the Strategy 1 optimizations with initial SOC = 0.60 (Run 1 shown here).

88

SOC History
058 l I l l —f l | I

 

0.58 - -

SOC 0.54 ~ ~

0.52 -

 

 

 

U5 1 l l l l l l l .
0 500 1000 1500 2000 2500 3000 3500 4000 4500 Time (s)

(a) SOC history with initial SOC = 0.52.

Engine Speed History

 

 

200
150 .— t. i' * . .7 . :1 ' . ‘1'... . . t ._. 11.1. -
Engine Speed 100 t _
(rad/s)
50 - _
U L

 

 

 

L l I l J l l
0 500 1000 1500 2000 2500 3000 3500 4000 4500 Time (s)
(b) Engine speed history with initial SOC=0.52.

Figure 5.6.6. Comparison of the SOC history and engine speed history plots for a typical optimized
design from the Strategy 1 optimizations with initial SOC = 0.52 (Run 1 shown here).

89

SOC History

 

0.54

SOC 0.53

 

0.52

 

 

 

051 1 J 1 l l -
0 200 400 500 800 1000 1200 1400 Time (s)

(a) SOC history.
Engine Speed History
200 r I T l j l

 

 

1: "In ‘._. .g. .2391 2 =,. - . . .1 2.: _. -7 («a ., l1“. . - '1
1m - ‘

Engine Speed 100 . -
(rad/s) ‘ +

50- _

 

 

I l

0 200 400 500 800 1000 1200 1400 Time (s)
(b) Engine speed history.
Figure 5.6.7. Typical SOC history and engine speed history plots for the Strategy 1 optimized designs

re-analyzed with SOC correction settings from Strategy 2 for a single drive cycle (Run 1 shown here).
Note that due to the Zero-Delta SOC routine, the initial and final SOC’s are very similar.

90

SOC History
0.7 1 . .

 

0.65

SOC (15

0.55

 

 

 

g

o 200 400 500 800 1000 1200 1400 Time (5)

0.5

(a) SOC history.

Engine Speed History
200 . . . .

 

_
150

Engine Speed
(rad/s) 1CD ' .l

a]-

0L . L .
0

200 400 600 800 1000 1200 1400 Time (s)
(b) Engine speed history.

 

 

 

Figure 5.6.8. SOC history and engine speed history plots for typical optimized designs where
maximizing total energy usage is the objective (Run 1 from Strategy 2 is shown). Note that due to the
Zero-Delta SOC routine, the initial and final SOC ’s are very similar.

91

SOC History
0.7 I I l T I I T I

 

0.55 - - ' - __ _
soc * > ‘ --
0.6

I
I

0.55

I
l

 

 

 

 

0'50 51]] 1(0) 1500 2000 2500 III] 350) 4011 4503 Time(s)
(a) SOC history with initial SOC = 0.68.

 

Engine Speed History
m I l I I l I F l
150 _ - -_ - - -- _
Engine Speed
(rad/S) 100 ~ .
+
50 .

+ + + + +
-—l—-———J——1d.+ ' W .
0 500 1000 1500 2000 25001130 3 4000 4500 Time (s)

(1)) Engine speed history with initial SOC=0.68.

 

 

0

 

Figure 5.6.9. Comparison of typical SOC history and engine speed history plots (SOC = 0.68) for the
Strategy 2 optimized design of Figure 5.6.8 re-analyzed with no SOC correction and the settings of
Strategy 1 (multiple drive cycle iterations and multiple initial SOC analyses). Note that the optimized
designs do not act as EV’s.

92

SOC History
0.7 I I I I r I I I

0.65 - _
0.8 ..
0.55 - -

 

SOC

0.5 L e

 

 

 

045 I I I I I I I I
0 500 1000 1500 2000 2500 3000 3500 £1000 4500 Time (s)

(a) SOC history with initial SOC = 0.60.
Engine Speed History

 

 

200 I 7 r I fl I I I

150 _ — — _ _
Engine Speed
(rad/s) 100 - -
+
50 - _
+ +
U.

 

W

0 500 1000 1500 2000 2500 3000 3500 4000 4500 Time (s)
(b) Engine speed history with initial SOC=0.60.

Figure 5.6.10. Comparison of typical SOC history and engine speed history plots (SOC = 0.60) for the

Strategy 2 optimized design of Figure 5.6.8 re-analyzed with no SOC correction and the settings of
Strategy 1 (multiple drive cycle iterations and multiple initial SOC analyses).

93

SOC History
0.7 I I I I I I I I

 

0.55 - I -" _

SOC 05 . - -

I

 

0.55 " -

 

0.5

 

I I l I I I I I
0 500 1000 1500 2000 2500 3000 3500 4000 4500 Time (5)

(a) SOC history with initial SOC = 0.52.
Engine Speed History

 

 

150 - 2

Engine Speed
(rad/s) "30 ' ‘
50 - _

+ + + +

 

 

MW
0 500 1000 1500 2000 2500 3000 3500 4000 4500 Time (s)
(b) Engine speed history with initial SOC=0.52. '

Figure 5.6.11. Comparison of typical SOC history and engine speed history plots (SOC = 0.52) for the
Strategy 2 optimized design of Figure 5.6.8 re-analyzed with no SOC correction and the settings of
Strategy 1 (multiple drive cycle iterations and multiple initial SOC analyses).

5. 6.2 Baseline Hybrid Bus Comparisons

The optimized designs from Strategy 1 significantly outperformed the baseline
non-hybrid bus in terms of engine fuel usage (measured in miles per gallon of gasoline),
as shown in Table 5.6.3. However, when total energy usage is considered (measured in
miles per gallon gasoline equivalence), the optimized designs from Strategy 1 are sub-
par. Again, this is caused by the EV nature of the designs when they start with a high

initial SOC. This demonstrates further the importance of this strategy being utilized only

94

when a fixed route is guaranteed and the starting initial SOC is known to be very high

frequently.

Table 5.6.3. Comparison between the optimized designs from Strategy 1 and the baseline hybrid bus

 

 

 

 

 

model.
Average Fuel Average Fuel Corrected Fuel Corrected Fuel
Economy Econ. Economy Econ.
(mp8) Improvement (mpgge) Improvement
over Baseline over Baseline
Busch“ 3.71 NA 4.07 NA
DeSIgn
Oph'i‘md 13.23 256 % 4.01 -1.5 %
Desrgnl .
Opt‘inmd 12.22 229 % 3.96 -27 %
Des1gn 2
Opufn'z‘d 13.10 253 % 3.86 -5.1 %
Dggn 3

 

 

 

 

 

 

 

The Strategy 2 optimized designs perform better than the baseline non-hybrid bus
design in terms of total energy usage and engine fiiel usage. With Strategy 2 (summarized
in Table 5.6.4), all three optimized designs are a significant improvement in corrected
fuel economy, while two of the three optimized designs are an improvement in the

average fuel economy measure (with the third optimized design being equal).

Table 5.6.4. Comparison between the optimized designs from Strategy 2 and the baseline hybrid bus
model.

 

 

 

 

 

 

Average Average Fuel Corrected Corrected
Fuel Econ. Fuel Fuel Econ.
Economy Improvement Economy Improvement
(mpg) over Baseline (mpgge) over Baseline
Base?“ 3.71 NA 4.07 NA
Design
o"“'.“‘““ 3.90 5.12 % 4.30 5.65 %
Dcsrgnl
Opt'f‘m" 4.03 8.68 % 4.33 6.38 %
Des1gn 2
Opt'fmed 3.70 -0.27 % 4.30 5.65 %
Deggn 3

 

 

 

 

 

95

 

As with the Strategy 2 optimized designs, the Strategy 3 optimized designs
perform better than the baseline non-hybrid bus design in terms of total energy usage and
engine fuel usage. With Strategy 3 (summarized in Table 5.6.5), all three optimized
designs are a significant improvement in average corrected fuel economy, while

marginally better in terms of average fuel economy.

Table 5.6.5. Comparison between the optimized designs from Strategy 3 and the baseline hybrid bus

model.

 

 

 

 

 

 

 

 

 

Average Average Fuel Avg. Corrected
Fuel Econ. Corrected Fuel Econ.
Economy Improvement Fuel Improvement
(mpg) over Baseline Economy over Baseline
(mpgge)
Base?” 3.71 NA 4.07 NA
Design
whim“ 3.84 3.50 % 4.41 8.35 %
Desrgnl
o""'.'““" 4.04 1.09 % 4.30 5.65 %
Desrgn 2
“mime" 3.74 0.81 % 4.42 8.60 %
Design 3

 

 

96

 

\.\.

2*"

11561

1001

2113

for

and

Sir:

5. 7 Conclusions

The main characteristics of two optimization strategies that have frequently been
used in optimizing hybrid electric vehicles have been merged into a single and more
robust strategy that is shown to have some advantages in terms of design performance
and solution efficiency.

If reducing fuel usage is the primary goal, then Strategy lwas shown to work well
for optimizing vehicles with a fixed route, and where a high initial SOC can be
guaranteed a large portion of the operating time. This strategy found optimized designs
for the current problem that run mostly electric in cases where the initial SOC is high.

If total energy usage is more important than fuel consumption, then Strategies 2
and 3 were shown to be superior to Strategy 1 for the problem posed in this study.
Strategy 3 significantly outperformed Strategy 1 in terms of optimized designs with high
corrected fuel economy and marginally outperformed Strategy 2 on this measure.
Strategy 3 was also observed to have an added advantage over Strategy 2 in terms of run-
time efficiency. Strategy 3 has been shown to be a viable alternative to the common

Strategy 2 for optimization of hybrid electric vehicles.

97

CHAPTER 6: INTRODUCTION TO PROGRESSIVE
CRUSH

6.1 Preliminary Information

Axial crush rails are one of the key energy absorbers during frontal and rear crash
of automotive and other transportation vehicles. These components not only absorb a
significant amount of kinetic energy, but also control the maximum forces that are
transmitted to the remaining structure. When designing crush rails, a common goal is to
identify the geometry, gage thickness and material of the rail so as to maximize its energy
absorption while satisfying constraints on mass and the allowable axial force. Using such
a statement within an automated design optimization study can lead to lightweight
designs that absorb large amounts of energy. However, these designs may not necessarily
absorb energy in a progressive manner, in which crush initiates near the tip of the rail and
then progresses rearward in a controlled fashion. Progressive crush here is defined as
crush occurring sequentially through a rail beginning at the front of the rail where impact
occurs and propagating through to the rear of the rail. More formally, ideal progressive
crush would occur when at any place where crush is occurring, there is no place to the
rear of that location where crush has occurred. The propagation of progressive crush can
be thought of as that of an accordion that is fixed at one end and pushed together from the
Opposite end. Figure 6.1.1 shows an example of progressive crush, while Figure 6.1.2

Shows an example of non-progressive crush. Note that the rail in Figure 6.1.1 crushes

98

from front
exaggerate

PIC

A 1
robust cra
both in to:
crash only

limited to

from front-to-back, whereas the rail in Figure 6.1.2 does not. While this is clearly
exaggerated, it demonstrates the point.
Progressive crush is important for several reasons, but the primary ones are
0 to achieve a robust and repeatable crush mode, and

0 to decrease repair costs after a minor crash event.

A rail design with a robust, repeatable crush mode is a key ingredient to achieving
robust crashworthy behavior of the entire vehicle during frontal and rear crash events,
both in terms of crash modality and total energy absorbed. In addition, during a minor
crash only a small portion of the rail may experience crush. If this crushed region is

limited to the tip of the rail, then repair costs can be minimized.

99

 

 

 

 

 

(a) Rail with no impact yet occurring. (b) Rail just after impact.

 

 

(c) Rail midway through crush (11) Rail after crush.

Figure 6.1.1. Example of a rail undergoing progressive crush.

it

(a) Rail with no impact yet occurring. (b) Rail just after impact.

 

 

 

   

(C) Rail midway through crush (11) Rail after crush.

Figure 6.1.2. Example of a rail undergoing non-progressive crush.

100

6.2 Literature Review

DiPaolo et al. [31] describe three major response characteristics for axial energy
absorbing devices. Depending upon such factors as plastic deformation, friction, and
fracture, an energy absorbing device can either undergo axial crush (buckling), inversion,
or splitting when undergoing axial compressive loading. For the purpose of this thesis,
axial crush will be the primary focus.

Extensive research has been performed on the progressive buckling of columns
under axial impact (see Jones [32] for a general overview of the subject). The two
primary collapse modes in columns are global bending and progressive short-column
buckling (folding) (Karagizova and Jones [33]). The latter mode absorbs significantly
more energy than does collapse in bending, or global buckling. The introduction of a
trigger (e.g., a local change in shape or material property) can improve the energy
absorbing characteristics of a column by promoting the initiation of progressive buckling.

When progressive buckling occurs, the force-displacement curve typically follows
a characteristic path (as shown by Guillow et a1. [34]'as well as Zarei and Kroger [35])
(see Figure 6.2.1). The axial load rises until a first buckle is formed, after which the force
decreases significantly. Then folds begin to form, with a small peak in the force-
displacement curve corresponding to each new fold. The values of the force required to
initiate these folds are often significantly less than the maximum force observed at
initiation of the first buckling event. lldeally, the formation of folds occurs sequentially

from the front of the rail progressing toward the rear during progressive crush.

10]

 

 

 

 

 

 

6O .4-“"'" F MAX' maximum or peak load -- lSt fold
.l
50 1
TEST 24A D=97 mm, L=196 mm, t=1.0 mm
‘ 6060-T5 Aluminum
40
E 30 F Av- average post buckling load
5
u] 20
10
0 l I L _I n_ I _L 1 l J I I
0 20 40 6O 80 100 120

DISPLACEMENT (mm)

Figure 6.2.1. Quasi-static axial compression of thin-walled circular aluminum tubes (from Guillow et
a1. I341).

Ku et a1. [36] identify three key aspects in judging how well a column
progressively crushes: geometric efficiency, load efficiency, and energy efficiency.
Geometric efficiency is defined as the effectiveness of the deformation during the
collapse (i.e., the ratio of compression to original length). Load efficiency is a measure of
the load fluctuations between folds in the force-displacement curves. Energy efficiency is
the total amount of energy absorbed.

Many formal definitions have been used to characterize axial crush (DiPaolo et. a1
[31]). The specific energy absorption is defined as the energy absorbed per unit mass of
an axial crush. Similarly, the energy dissipation density is defined as the energy absorbed
per unit volume of material. The structural effectiveness is sometimes used as a means to

compare different materials’ crushing capabilities and is defined as the specific energy

102

divided by the specific true ultimate tensile strength of the material. A load uniformity
parameter is defined as the ratio between maximum and mean crushing forces seen
during crush and indirectly gives an indication of the energy absorbing capabilities. In
addition, there are common characteristics related to the collapse efficiency during crush.
The crush efficiency is defined as the ratio between the maximum displacement and the
total length. The load efficiency is defined as the inverse of the load uniformity parameter
(or as the ratio of the mean load to the maximum load). Finally, the energy efficiency is
defined as the energy absorbed divided by the product of the maximum load magnitude
and the total length of the energy absorbing device.

Gumruk and Karadeniz [37] discuss a common characteristic to progressively
buckling designs of top hat thin-walled sections. When comparing the rigid wall crush
force profiles of progressively buckling designs, designs with mixed modes of
deformation, and globally buckling designs, distinct differences can be seen. For
progressively buckling designs, sharp peaks and valleys are present in the profile. The
mixed modes of deformation designs have the same peaks and valleys present, however
they are much smoother. Finally, global buckling designs have the size of the peaks
decrease substantially.

Through optimization of hexagonal thin-walled columns undergoing axial crush,
Hou et a1. [38] show the effect of a constraint limiting the maximum peak force on the
Optimal design obtained during optimization. By performing identical optimizations of
maximizing specific energy absorption with and without constraints imposed upon the
maximum peak force seen, the authors were able to demonstrate the necessity of the

constraint in crashworthy optimization of rails. Without the constraint, design variables

103

 

determining the thickness of the columns were seen to increase to the extremes of their
allowable values, causing higher energy absorption, weight, specific energy absorption,
and maximum peak forces. Most notably, the peak forces reached values considered
detrimental to passenger safety and vehicle crashworthiness when the reaction force
constraint was not imposed.

Kim [39] performed an optimization of multi-cell aluminium profiles for columns
in which maximizing the specific energy absorption was the objective. The author
defined a unique approach to force progressive crush in his designs by defining a
constraint for the stable progressive collapse of square corner elements in his profile
(based upon a theory for the stable deformation mode of a thin-walled prismatic square
column presented by Abramowicz and Jones [40]). By analytically calculating whether
the profile would progressively buckle based upon the thickness, length, and width of the
corner elements in the profile using this theory, the author was able to enforce the desired
collapse mode and eliminate designs as feasible that had a high specific energy but didn’t
progressively buckle. For simple column buckling this was shown to be an effective way
to optimize for progressive buckling, however for complicated energy absorbing devices
such as front rails where the geometry prevents a simple analytical solution as to whether
progressive crush will occur, the approach is invalid.

The majority of the studies on crashworthy optimization have focused on total
energy absorbed as opposed to progressive crushing. For example, Yamazaki and Han
[41] performed tube optimizations in which they attempted to maximize the total energy
absorbed while constraining the axial reaction force and mass of the tube. Zarei and

Kroger [35] used a weighted multi-objective problem statement which attempted to

104

marimi
satisfyi
optimiz
ineqttal
probler
tetal er
optimi
opttmi
tonstr
Kurtat
forces

absor]

al. [4

maxit

maximize the sum of the total energy and the specific energy absorbed by tubes while
satisfying a constraint on the axial reaction force. Sidhu et a1. [42], [43] used a crush
optimization statement that maximized total energy absorption in a front rail with
inequality constraints on the peak rigid wall force and mass. Cho et al. [44] used a similar
problem statement for optimization of a frontal frame where the goal was to maximize
total energy absorption with constraints on reaction force and volume. A crashworthiness
optimization on an S-frame was performed by Kim et a1. [45] in which they utilized an
optimization problem statement that attempted to minimize the mass of the frame while
constraining not only the energy absorption, but also the sectional bending stiffness.
Kurtaran et a1. [46] presented an optimization statement that attempted to minimize the
forces in the occupant compartment (or the intrusion), while constraining the energy
absorption.

A slightly different crush optimization problem statement was used by Avalle et
al. [47]. They used the load uniformity parameter (LU) defrned as the ratio between the
maximum and mean crushing forces. This load uniformity parameter was then minimized
in the optimization problem statement. By encouraging the design to have an average
force as close as possible to the maximum force, it was assumed the optimization was
attempting to maximize the total energy absorbed. Karbhari and Haller [48] however,
caution that optimizing based upon the load uniformity parameter can give designs with
an extremely good LU at very low overall load levels, and hence at low corresponding
levels of energy absorption. This needs to be considered when determining if the load
uniformity parameter is alone appropriate as an objective for optimization. Hanssen et a1.

[49] define a parameter called the total efficiency as the product of the load efficiency

105

 

(which they call the crush force efficiency) and the relative deformation. This
characteristic accounts for the concern presented by Karbhari and Haller and could be
used in optimization as an alternative to the load uniformity parameter.

None of these common optimization approaches guarantees progressive buckling
of complex structures such as front rails because the buckling failures could initiate

anywhere in the rail and progress in a non-sequential manner.

106

 

pl

of

all

to

CHAPTER 7: OPTIMIZATION STRATEGY DEFINITION

7.1 Introduction

A new strategy for achieving progressively crushing designs during an automated
design optimization study is presented and explored in this chapter. Independent crush
zones are defined along the length of the rail. The main goal of the optimization is then to
encourage maximum energy absorption in a given crush zone to occur prior to any energy
absorption in rearward crush zones. In other words, crush should initiate in the tip and
progress from zone to adjacent zone toward the rear of the rail. Compared to traditional
optimization statements that focus only on total energy, it is demonstrated that the current
approach can produce designs with similar total energy absorption but with a dominant

progressive mode.

7.2 Formal Definition

Traditional crush optimization strategies produce designs that absorb a lot of
energy, but not necessarily progressive crush. The new strategy considered here attempts
to find optimal designs that not only absorb a lot of energy, but also exhibit progressive
crush behavior. The strategy utilizes a measure of the amount and timing of energy
absorbed in different regions of the rail to promote progressive crush.

Figure 7.2.1 displays a rail profile in which different crush zones have been
defined. In an ideal progressive crush scenario, zone N-l will crush almost entirely

before zone N begins crushing (for N > 1).

107

We define a measure called progressive energy absorbed (PEA) as:

NZ-l

PEA = Z PEAN - EANZ

(7-1)
N=1

where PEA N is the progressive energy absorbed in Zone N, NZ is the total number of

zones defined in the rail, and EA NZ is the total energy absorbed by the last zone in the

rail. We define the zone-wise progressive energy absorbed, PEA N, as:

P BAN = EAN(UN) — EAN(UN-l) (7.2)

where EA N (UN) is the total energy absorbed so far by Zone N when the impactor has
displaced an amount U = UN , EA N ( UN_ 1) is the total energy absorbed so far by Zone N

when the impactor has displaced an amount U = UN-1. U is the distance the impactor has

traveled (or in practical terms how far a reference point has moved) after impact (see
Figure 7.2.2 and Section 7.3 for more details).

We assume here that Zone NZ should not crush at all, so the role of the final term
in Equation (7.1) is to penalize PEA for [energy absorption that occurs in Zone NZ. In
system level crash models, often there is a zone such as NZ that must maintain its
integrity during the crash. Further, in component level models such as considered here, it
is common to constrain the rear of the rail at a location beyond which crush is expected

or desired. So crush in Zone NZ is undesirable in both scenarios.

108

The progressive energy as described above does not consider any energy absorbed

in Zone N, afier the impactor has reached a displacement UN. By definition, any energy

absorbed in Zone N before the impactor has reached a displacement UN-1 is also not

considered. Therefore, the impactor displacement range for which the energy absorbed by

Zone N contributes to the progressive energy absorbed is:

UN-l .‘E U 5 UN (73)

A rail design that absorbs significant energy in each zone N (for N = 1 to NZ-l)
while the impactor displacement corresponds to that of Equation (7.3) has a much higher
PEA than a rail design that absorbs the same amount of total energy that is not in
conjunction with the impactor displacement as described in Equation (7.3). The former
design would, by definition, have a crush mode that originates at the front of the rail and
propogates rearward. The latter design could allow energy absorption to occur in a non-
sequential manner, and therefore could have a non-progressive crush mode.

The optimization problem statement for progressive crush optimization can now

be stated as:

Maximize: PEA

Subject to: Constraints on mass, force, etc.

This is contrary to typical crash optimization statements that do not encourage
progressive crush:

109

Maximize: EA

Subject to: Constraints on mass, force, etc.

where EA is the total energy absorbed by the rail during crush. In the latter case, the

optimal solution may find a design that crushes progressively or non-progressively.

 

 

| Zonel E Zone2 I ZoneN Zone NZ

 

 

Figure 7.2.1. Specified crush zones in a rail. The tip of the rail corresponds to Zone 1, and the rear of
the rail corresponds to Zone NZ.

5

 

.1:

 

.13

 

.. _-_____-__-__--!____-

     
 
 
   

.IH- --

\\\§i§i\\\

 

Impactor

Figure 7.2.2. Definition of impactor displacements, as used in the calculation of PEA.

110

7.3 Implementation of Strategy

As was mentioned briefly in the previous section, the impactor displacements are
measured utilizing a reference point (or node) located on the impactor. As the impactor
moves, the relative displacement of the reference point can be measured. Since the
analyses performed in this thesis were performed with LS-DYNA [50], the displacement
of the node or reference point was measured from the nodout file.

The zones were achieved in LS-DYNA by making each zone a separate part. With
different parts making up the rail, the internal energy of each part was written out
independently to the matsum file by LS-DYNA at different times.

As defined by Equation (7.2) the primary interest for the progressive energy
definition is the energy absorption of a specific zone (or part) while the reference point is
at a specific location. However, the displacements of the reference point are reported in
the nodout file and the energy absorptions of the parts in the matsum file. Both are linked
however by the time at which they occur (the nodout file reports the displacements for a
given time and the matsum file reports the energy for a given time). A simple executable
therefore was created that would report the energy absorption for a given part (zone)
given a requested displacement of the reference node. The executable takes the requested
displacement, finds in the nodout file the time at which it occurs, and then obtains from

the matsum file the energy absorption for the part at that time (see Figure 7.3.1). Utilizing

this simple executable, the energy absorbed in zone N at an impactor displacement UN-1

could be obtained along with the energy in zone N at an impactor displacement UN, such

that Equation (7.2) could be used to calculate the PEA of zone N.

111

 

Simple Executable

 

 

nodout time matsum .

 

U, PART ID

 

 

 

 

 

 

 

 

 

Figure 7.3.1. Simple executable used with LS-DYNA to obtain EA(U).

112

CHAPTER 8: AXIAL RAIL CRUSH AND ANALYSIS
MODEL

In this thesis, the following crush scenario and corresponding model were used to
assess the proposed strategy for progressive crush optimization. A tube (rail) of length

500 mm was fixed at its right (rear) end. The tube was made of steel with a density of

7.85e-6 kg/mm3, a Young’s Modulus of 207 GPa, Poisson’s ratio of 0.28, yield strength
of 500Mpa, and the plasticity data of Table 8.1.1. The finite element model for the tube
consisted of 7479 nodes and 7391 shell elements (Belytschko-Tsay with 2 through shell

thickness integration points [50]). A flat rigid impactor with 500 kg mass travelling

initially at 50 kph was used to crush the tube for 25 ms, as shown in Figure 8.1.1.

Impactor (Mass = 500 kg)

\ Encastered

Impactor Velocity = 50 kph

 

Rail profile

ta .
500 mm

Figure 8.1.1. Analysis model used for the progressive crush strategy.

 

 

 

 

///// //f/

113

Table 8.1.1. Plasticity data for the rail analyses. For different strain rates, the stress vs. effective
plastic strain is defined.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Strain Rate (mm/ms
0.005 0.1 10 100 500
Effective Stress Effective Stress Effective Stress Effective Stress Effective Stress
Plastic (MPa) Plastic (MPa) Plastic (MPa) Plastic (MPa) Plastic (MPa)
Strain Strain Strain Strain Strain
0 500 0 500 0 500 0 500 0 500
0.0004 541.65 0.0004 545 0.0005 570.16 0.001 672.62 0.0016 823.46
0.0018 591.96 0.0013 586.24 0.0016 600.13 0.0021 712.03 0.0027 853.28
0.0022 598.91 0.0035 630 0.003 630.85 0.0093 778.56 0.0047 878.03
0.0044 622.32 0.0065 665 0.0056 668.82 0.0122 797.12 0.01 910.59
0.0079 651 0.0086 690 0.0075 689.51 0.0152 817.83 0.0232 934.62
0.0115 678.29 0.011 715 0.0096 712.58 0.0236 853.36 0.0305 945
0.0147 700.93 0.0134 730 0.01 18 738.19 0.0284 871 0.0496 967.48
0.0194 730.46 0.0162 750 0.0143 758.35 0.0379 902.44 0.0567 979.02
0.0242 757.27 0.0214 790 0.019 792.49 0.045 920.14 0.066 990.73
0.0297 784.09 0.0286 815 0.0285 838.85 0.0568 948 0.0753 1003.73
0.0349 806.15 0.0334 833.71 0.0357 867.81 0.0661 967.12 0.0845 1015.92
0.0422 831.51 0.0429 859.62 0.0451 899.89 0.0777 987.85 0.0936 1028.2
0.0475 846.92 0.0477 871.39 0.0569 933 0.0846 998.21 0.1004 1039.41
0.054 862.44 0.0547 887.7 0.0616 941.76 0.1027 1020.37 0.1093 1051.58
0.0601 874.27 0.0617 902.55 0.0685 955.43 0.1072 1026.19 0.1182 1063.55
0.0659 883.51 0.0687 916.09 0.0778 970.7 0.1139 1030.59 0.127 1075.19
0.0722 891.57 0.0871 946.66 0.0892 986.21 0.125 1041.74 0.1357 1084.39
0.0788 898.41 0.0962 959.29 0.096 994.1 0.1293 1044.67 0.1422 1092.42
0.0849 903.66 0.1007 965 0.1073 1005.54 0.1359 1050.66 0.1508 1102
0.0941 910.37 0.1052 970.32 0.1118 1009.62 0.1489 1058.86 0.1594 1110.85
0.0976 912.71 0.1186 983.88 0.1162 1013.46 0.1553 1064.84 0.1678 1116.24
0.1046 917.3 0.1252 989.25 0.1294 1023.43 0.1596 1066.64 0.1763 1119.57
0.111 921.62 0.1318 993.6 0.1338 1026.15 0.1638 1068.96 0.1825 1124.27
0.1 177 926.49 0.1383 996.82 0.1404 1029.53 0.1681 1070.74 0.1908 1 129.38
0.1234 930.99 0.1427 998.28 0.1447 1031.2 0.1723 1075.92 0.199 1133.03
0.1303 937.06 0.1492 999.32 0.1512 1032.62 0.2072 1090.8 0.2072 1136.7
0.2072 969 0.2072 1008.6 0.2072 1044.9

 

 

 

At each iteration during the optimization study, the shape of the rail was varied
according to the following scheme. The cross-sectional shapes at several stations along
the length of the profile (see Figure 8.1.2) were designed independently, thereby allowing
the shape of the profile to vary along the length. Nine independent stations were used
along the length of the rail. Each cross-sectional shape was governed by 12 control points
(only 4 of which were independent due to symmetry). Control points that could move in

the horizontal direction (in Figure 8.1.3) were allowed to vary within 30% of the baseline

114

 

W

coordinate. Control points that could move in the vertical direction were allowed to vary
within 60% of the baseline coordinate. For manufacturability, the total perimeter of all
cross-sections was constrained to vary only within 2% of the baseline perimeter. This was
controlled by scaling of the shape produced for a given cross-section until the perimeter
satisfied the perimeter constraint. Symmetry about vertical and horizontal planes was

maintained in each cross-section.

 

 

 

 

 

 

 

 

 

1234567 8 9

Figure 8.1.2. Crush zones and cross-sectional design stations used in the rail analysis and design
model.

70mm

.512 $1 2_fl

 

 

7|

............ 4+... 175 mm
Lines of Life-H

Symmetry ‘1‘, 9

r
i.

 

 

 

|‘

 

7 £6 1

Figure 8.1.3. Section profiles were controlled by 4 independent control points (1 through 4). The
other control points were positioned by satisfying vertical and horizontal lines of symmetry. The
cross-section perimeter was scaled to ensure that it was within 2% of the baseline perimeter.

“'2.

115

1,7—‘- .- ‘Ih—J
.) _

 

The number of stations along the length of the rail was chosen largely based upon
intuition and experience. Since the goal is to design a rail that progressively crushes, it is
desirable to create more shape variation at the front of the rail, and less towards the rear
of the rail. This helps with crush initiation, as well as creating a crush mode that
propagates rearward. At the same time, it has been observed that too much shape
variation overcomplicates the design and causes complexity in manufacturing as well as
inferior performing designs.

With nine cross sections and five degrees of freedom per cross-section, there were
45 shape design variables for this problem. In addition, the gage thickness was allowed to
vary, so there was a total of 46 design variables.

Figure 8.1.4 displays the zones and impactor displacements used for the majority
of the studies in this thesis (unless noted otherwise). The selection of the location of the
zones was chosen largely based on intuition. In order to emphasize the initial energy
absorption that occurs in the front of the rail, the first two zones were made smaller than
the last two zones which are toward the back of the rail. Attachment locations as well as

stipulations on the size of Zone NZ also should guide the selection of zone locations and

lengths. Note in Figure 8.1.4 that the definition of U3 used in the study does not

correspond with the end of Zone 3. This modification was necessary to account for stack

up in the crushed rail (as will be proven in Section 4 of Chapter 9).

116

U3 = 250 mm

 

 

U: = 166.7 mm!
D1

U1= 100 ,mm
I——’:
E
I

 

-----__-__-_J..___

 

 

 

////7//////

100 mm 66.7 mm 166.? mm 166.7 mm

Figure 8.1.4. Zone dimensions and impactor displacement specifications in the current model.

In rail design, it is commonly required to impose a constraint on the maximum
wall reaction force. A typical crush event is shown in Figure 8.1.5. In the current study,

the first reaction force peak is ignored when calculating the maximum force, as this force

is often artificially high due to numerical inaccuracies. Instead, the highest force after F1

occurs, referred to as F 2, was used as a constraint for optimization.

117

 

 

Reaction Force of Crush
F (W)

400

F1

300

200

100

 

0 0.005 0.01 0.015 0.02 0.025

Time (s)

 

 

 

Figure 8.1.5. Reaction force versus time during a typical crush event.

118

CHAPTER 9: OPTIMIZATION USING THE
PROGRESSIVE CRUSH STRATEGY

9. I . Relation Between Progressive Energy and Total Energy

The advantages of progressive crush would be diluted if the associated total
energy absorbed was less than that for a non-progressively crushing rail. To investigate
this possible trade-off, a multi-objective optimization study was performed in which both
PEA and EA were maximized for the rail model described in Chapter 8. Multi-objective
optimization studies generate multiple optimal solutions representative of the tradeoffs
among the objectives. This is commonly called Pareto optimization. In this study, the

multi-objective crush optimization problem statement used was:

Maximize: PEA and EA

Subject to: F2 S 150 kN

By Varying: Control Points

Rail Thickness

Where PEA is the progressive energy absorbed, EA is the total energy absorbed, F 2 is the

maximum reaction force after initial crush initiation, Control Points refers to the position
of the 45 independent shape control points, and Rail Thickness is the rail gage thickness,

which varies between 1-3 mm.

119

The simulations were performed using the LS-DYNA explicit finite element code
[50] as the analysis solver, and the hybrid and adaptive algorithm SHERPA within the
HEEDS optimization software [29] as the optimizer. The study was performed for 15,000
evaluations, at which stage the results were considered nearly converged. The study was
then repeated to obtain very nearly the same results. Figures 9.1.1 and 9.1.2 illustrate the
resulting feasible designs from this study along with the rank 1 (non-dominated) designs
on the Pareto front. In Figure 9.1.1, it is apparent that many designs with very high total
energy absorption have very poor progressive energy absorption. In some instances, the
progressive energy absorption measure is negative. These designs absorb a significant
amount of total energy, but do so with a very non-progressive crush mode. Contrarily,
there are no designs with high progressive energy and low total energy. Figure 9.1.2
focuses on the local range of best designs found, and better shows the rank 1 designs of
the Pareto front. Within the Pareto front identified here, the EA varies by only 3%, and
this variation appears to be decreasing (note the apparent convergence toward a single
point for maximum PEA and BA in Figure 9.1.1) as the search progresses. These results
indicate that the tradeoff between PEA and EA is very small, if not negligible, for the rail

considered herein.

120

 

 

EA (kJ)

 

 

 

Figure 9.1.1. Scatter plot of all evaluations performed during the multi-objective optimization. There
are numerous designs with total energy above 15 11.1 but with negative progressive energies.
Furthermore, there are designs at 25 In! and above that have negative or near-zero progressive

energies.

 

PEA (kJ)

 

EA (k1)

 

 

 

Figure 9.1.2. Scatter plot of good designs in terms of both total energy absorbed and progressive
energy absorbed. Highlighted is the Pareto front of the rank—1 designs from the multi-objective
optimization.

121

9.2 Progressive Crush Optimization - without considering mass

Two optimization studies were performed — one with a conventional strategy
which maximized total energy absorbed, and one with the proposed new strategy which
maximized progressive energy absorbed. In both strategies, the impact of mass on the
design was ignored. The results of both studies are presented here to assess the ability of
each to produce designs that absorb energy progressively.

For each of the two studies, four optimization runs were performed. Each
optimization run started with the same baseline design with the rail having a constant
rectangular cross-sectional shape along its length, as shown in Figure 8.1.3. Each of the
four optimizations however, started with a different random seed that controlled the
initial set of designs for the optimization. With different random seeds, the four
optimizations started their search in different locations in the design landscape of the
problem. This was done to account for the effects of stochasticity and initial starting
conditions on the search of both strategies. The same four random seeds were used for
both strategies.

In each run, 2,000 crash evaluations were performed using the LS-DYNA explicit
finite element code. The hybrid and adaptive algorithm SHERPA within the HEEDS
optimization software was used for the optimization runs. At 2,000 evaluations, the
optimization runs were not fully converged, but they had made significant progress
toward identifying high performing designs, and their rate of improvement had begun to
decrease significantly. Since in most industrial applications of optimization it is not

feasible to achieve complete convergence due to time constraints, it was deemed more

122

valuable here to compare the results of four nearly converged designs than one fiilly

converged design.

9.2.1 Conventional Crush Optimization to Maximize Total Energy Absorbed

The following conventional crush optimization problem definition was used:

Maximize: EA
Subject to: F2 _<_ 150 kN

By Varying: Control Points

Rail Thickness

Where EA is the total energy absorbed by the rail during crush, F 2 is the maximum

reaction force after initial crush initiation, Control Points are the independent control
points varied in Figure 8.1.3, and Rail Thickness is the rail gage thickness, which varies
between 1 mm and 3mm.

Figure 9.2.1 (a) shows the shapes of the optimized designs found using this design
statement, while Figure 9.2.2 (a) shows their force-displacement curves. The performance

of these designs is summarized in Table 9.2.1.

123

9. 2.2 Progressive Crush Optimization to Maximize Progressive Energy Absorbed

The progressive crush optimization problem statement used was:

Maximize: PEA

Subject to: F2 _<_ 150 kN

By Varying: Control Points

Rail Thickness

Where PEA is the progressive energy absorbed, as defined in Equations (7.1,7.2), F 2 is

the maximum reaction force after initial crush initiation, Control Points are the
independent control points varied, and Rail Thickness is the rail gage thickness, which
varies between 1-3 mm.

Figure 9.2.1 (b) shows the shapes of the optimized designs found using this
design statement, while Figure 9.2.2 (b) shows their force-displacement curves. The

performan'ce of these designs is summarized in Table 9.2.1.

9.2.3 Optimization Results

Based on the optimization results, the following conclusions can be reached.
Three out of four runs using the conventional crush design optimization statement yielded
optimized solutions that did not exhibit progressive crush behavior, while one of the
designs (design D) exhibited very good progressive crush. All of the optimized designs

resulting from the progressive crush optimization statement performed very well in terms

124

of progressive crush. Figures 9.2.3-9.2.6 depict the crushing modes of these designs and
support these conclusions.

On average, the progressive crush strategy yielded designs with over 70% more
PEA and 3.6% less total energy than did the conventional crush strategy. Perhaps more
importantly, the standard deviation of EA and PEA for designs based on the progressive
crush strategy was significantly lower than that for designs based on the conventional
strategy. This indicates that the progressive crush strategy was much more robust in terms

of producing designs that behaved as intended.

125

 

 

 

Design A-top view. Design A-side view.

 

 

 

 

Design B-top view. Design B-side view. Design B-top view. Design B-side view.

I
..»‘ ' ‘ i
7 ' " +- I
' I

 

' I

 

 

 

 

 

 

 

Design C-top View. Design C-side view. Design C-top view. Design C-side view.
, i t
' 1P
i fl If I, t
‘ I
Design D-top View. Design D-side View. Design D-top View. Design D-side View.
(a) Optimized design shapes from the conventional (b) Optimized design shapes from the
progressive crush strategy (maximizing EA). crush strategy (maximizing PEA).

Figure 9.2.1. Comparison of the optimized design shapes from the conventional crush optimization
and progressive crush optimization. After 2000 evaluations the optimization runs were not
fully converged but had made significant progress.

126

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Design A Design A

 

 

 

 

 

 

 

 

 

1m

 

 

Design B Design B

 

 

 

 

 

 

 

 

1w!

 

 

 

 

Design C Design C

 

 

   

 

 

 

 

 

 

Design D Design D
(a) Force-displacement curves of the optimized designs (b) Force-displacement curves of the
from the conventional crush strategy optimized designs from the progressive
(maximizing EA). crush strategy (maximizing PEA).

Figure 9.2.2. Comparison of the force-displacement curves for the optimized shapes from the
conventional crush optimization (maximize EA) and the progressive crush optimization (maximize
PEA).

127

‘ yin-3's.

 

 

 

 

 

 

 

 

 

(a) Conventional strategy crush mode. (b) Progressive strategy crush mode.

Figure 9.2.3. Crush modes of the Design A optimized designs. At t = t2, the conventional strategy’s
optimized design begins to non-progressively crush.

 

 

 

 

 

 

 

 

 

 

(a) Conventional strategy crush mode. (1)) Progressive strategy crush mode.

Figure 9.2.4. Crush modes of the Design B optimized designs. At t # t2, the conventional strategy’s
Optimized design begins to non-progressively crush.

128

 

 

 

 

 

 

 

(a) Conventional strategy crush mode. (b) Progressive strategy crush mode.

Figure 9.2.5. Crush modes of the Design C optimized designs. At t = t2, the conventional strategy’s
optimized design begins to non-progressively crush.

 

 

 

 

 

IE: m I E:
i t=t0

Lit:t3 i t=t4

(a) Conventional strategy crush mode. (b) Progressive strategy crush mode.

Figure 9.2.6. Crush modes of the Design D optimized designs. Both the conventional strategy and
progressive strategy yielded optimized designs that progressively crushed.

EA (kJ) PEA(kJ) EA (k1) PEA (kJ)

 

129

9.3 Progressive Crush Optimization- accoun tin g for mass

Many times in industry, it is desirable to have a design that absorbs as much
energy as possible while not being too heavy. Design statements such as this create high
performing designs that are cheaply made, thus maximizing performance and profits.
This concept can be extended to use with the progressive crush strategy implemented in
the previous section so that it is desired to have a design that absorbs as much progressive
energy as possible while not being too heavy.

Two Optimization studies were performed — one with a conventional strategy
which maximized total energy absorbed per unit mass (specific energy absorption: SBA),
and one with the new strategy which maximized progressive energy absorbed per unit
mass (specific progressive energy absorption: SPEA). The results of both studies are
presented here to assess the ability of each to produce designs that absorb energy
progressively, while accounting for mass.

For each of the two studies, four optimization runs were performed. In each of
these four nms, a different set of starting conditions was used to account for the effects of
stochasticity and starting conditions on the search. The same four starting conditions
were used for the two studies. In each run, 2,000 crash evaluations were performed using
the LS-DYNA explicit finite element code. The hybrid and adaptive algorithm SHERPA
within the HEEDS optimization software was again used for the optimization runs. At
2,000 evaluations, the optimization runs were not fully converged, but they had made
significant progress toward identifying high performing designs, and their rate of
improvement had begun to decrease significantly. Since in most industrial applications of

optimization it is not feasible to achieve complete convergence due to time constraints, it

130

y..: $.14.“ a. 1“"J
‘. _

_ ‘ . _

was once more deemed more valuable here to compare the results of four nearly

converged designs than one fully converged design.

9.3.] Conventional Crush Optimization to Maximize Total Energy Absorbed per Unit
Mass

The following conventional crush optimization problem definition was used:

Maximize: SEA = EA/m
Subject to: F2 5 150 kN

EA _>_ 20 kJ
By Varying: Control Points

Rail Thickness

Where SEA is the total energy absorbed per unit mass by the rail during crush (specific

energy absorbed), F 2 is the maximum reaction force after initial crush initiation, EA is the

total energy absorbed, Control Points are the independent control points varied in Figure
8.1.3, and Rail Thickness is the rail gage thickness, which varies between 1 mm and
3mm. It should be noted that in addition to the force constraint imposed, there is also an
energy constraint. This constraint ensures that low energy absorbing designs with very
low masses are deemed inferior designs. This is necessary to ensure high energy
absorbing designs are still sought over very low mass designs.

Figure 9.3.] (a) shows the shapes of the optimized designs found using this design
statement, while Figure 9.3.2 (a) shows their force-displacement curves. The performance

of these designs is summarized in Table 9.3.1.

131

9.3.2 Progressive Crush Optimization to Maximize Progressive Energy Absorbed per
Unit Mass

The progressive crush optimization problem statement used was:

Maximize: SPEA = PEA/m

Subject to: F2 5 150 kN

PEA Z 14 kJ
By Varying: C ontrol Points

Rail Thickness

Where SPEA is the progressive energy absorbed per unit mass (specific progressive

energy absorbed), F 2 is the maximum reaction force after initial crush initiation, PEA is

the progressive energy absorbed as defined in Equations (7.1,7.2), Control Points are the
independent control points varied, and Rail Thickness is the rail gage thickness, which
varies between 1-3 mm. The constraint on PEA is necessary to ensure that high energy
absorbing designs is sought over low energy absorbing designs with a very low mass.
Figure 9.3.1 (b) shows the shapes of the optimized designs found using this
design statement, while Figure 9.3.2 (b) shows their force-displacement curves. The

performance of these designs is summarized in Table 9.3. 1.

132

 

9. 3.3 Optimization Results

Based on the optimization results, the following conclusions can be reached. Two
out of four runs using the conventional crush design optimization statement yielded
optimized solutions that did not exhibit progressive crush behavior, while one of the
designs (design D) exhibited very good progressive crush and one of the designs (design
A) exhibited moderate progressive crush. All of the optimized designs resulting from the
progressive crush optimization statement performed very well in terms of progressive
crush. Figures 9.3.3-9.3.6 depict the crushing modes of these designs and support these
conclusions.

On average, the progressive crush strategy yielded designs with over 27% more
specific progressive energy absorbed (SPEA) and 12.6% less total specific energy
absorbed (SEA) than did the conventional crush strategy. Perhaps more importantly, the
standard deviation of SPEA for designs based on the progressive crush strategy was
significantly lower than that for designs based on the conventional strategy. This
indicates that the progressive crush strategy was once more, much more robust in terms

of producing designs that behaved as intended.

133

 

 

 

I

Design C-top view. Design C-side view.

h {99. ‘4

Design D-top view. Design D-side view.

     

 

   

 

 

 

 

. a
Design D-top view. Design D-side view.

 

 

 

(a) Optimized design shapes from the conventional
progressive crush strategy (maximizing SEA = EA/m).

PEA/m).

(b) Optimized design shapes from the
crush strategy (maximizing SPEA =

Figure 9.3.1. Comparison of the optimized design shapes from the conventional crush strategy
(maximizing SEA=EA/m) and the progressive crush strategy (maximizing SPEA=PEA/m). After

2000 evaluations the optimization runs were not fully converged but had made significant progress.

134

 

 

   

 

 

 

 

 

Design A Design A

 

 

   

 

 

 

 

 

Design B Design B

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Design C Design C

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

Design D Design D

(a) Force-displacement curves of the optimized designs (b) Force—displacement curves of the
from the conventional crush strategy (maximizing EA/m). optimized designs from the progressive
crush strategy (maximizing PEA/m).

Figure 9.3.2. Comparison of the force-displacement curves for the optimized shapes from the

conventional crush optimization (maximize SEA=EA/m) and the progressive crush optimization
(maximize SPEA=PEA/m).

135

 

 

 

m i I
t=t3 t=t4 t=tf

(a) Conventional strategy crush mode. (b) Progressive strategy crush mode.

 

 

 

 

 

 

 

Figure 9.3.3. Crush modes of the Design A optimized designs. Both the conventional strategy and
progressive strategy yielded optimized designs that progressively crushed.

 

 

   

 

 

 

 

 

 

F12
(a) Conventional strategy crush mode. (b) Progressive strategy crush mode.

Figure 9.3.4. Crush modes of the Design B optimized designs. At t = t1, the conventional strategy’s
optimized design begins to non-progressively crush.

136

 

 

 

t=t0

     

 

 

 

 

 

 

(a) Conventional strategy crush mode. (b) Progressive strategy crush mode.

Figure 9.3.5. Crush modes of the Design C optimized designs. At t = t1, the conventional strategy’s
optimized design begins to non-progressively crush

 

 

 

 

 

 

 

 

 

(a) Conventional strategy crush mode. (b) Progressive strategy crush mode.

Figure 9.3.6. Crush modes of the Design D optimized designs. Both the conventional strategy and
progressive strategy yielded optimized designs that progressively crushed.

Table 9.3.1. Comparison of progressive crush ,and conventional crush optimized results when
accounting for mass.

 

Progressive Crush Strategy Conventional Crush Strate
Opt. EA PEA Mass SPEA SEA EA PEA Mass SPEA SEA
DCSign (U) (U) (kg) (kl/kg) (kl/kg) (U) (U) (kg) (Id/kg) (Id/kg)

A 22.37 18.52 2.85 6.50 7.85 27.35 14.23 2.68 5.34 10.22
B 28.51 17.03 3.06 5.58 9.33 27.31 6.59 2.65 2.49 10.31
C 27.23 14.80 2.86 5.17 9.52 25.82 9.09 2.49 3.65 10.36
D 28.10 16.07 3.06 5.25 9.18 29.30 17.54 2.87 6.11 10.20
Average 26.55 16.60 2.96 5.62 8.97 27.45 1 1.86 2.67 4.40 10.27
Std Dev 2.84 1.57 0.12 0.61 0.76 1.43 4.94 0.16 1.63 0.07

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

137

9.4 Zone 3 Definition Study
9.4.1 Introduction

It was assumed that the displacement measure U3 had to be offset from being
aligned with the end of Zone 3 to account for stackup (recall Figure 8.1.4). This was an
assumption justified by the fact that the material crushed during an optimization does not

vanish, but rather stacks or “builds up” such that there is a distance 8 of stackup (see

Figure 9.4.1). Since it is desired that there be no crush occurring in Zone 4, it was
assumed that there needed to be a lag in U3 of distance 5 from the end of Zone 3 (the start

of Zone 4). This was done with no proof throughout Section 2 of this thesis, with the

justification of this concept intuitively making sense.

 

     

i Desired Crush i i 6

(a) Uncrushed rail with zones labeled. (b) Fully crushed rail.
The desired crush zones are Zones 1-3.

 

 

 

 

Figure 9.4.1. Stackup of a typical rail that progressively crushes. Stackup occurs with a material
buildup of thickness 6.

Alternatively, the stackup 6 is the sum of the stackup occurring in the first three

zones (there is a stackup 61 in Zone 1, a stackup 62 in Zone 2, as well as the stackup

138

occurring in Zone 3 (63)). For an arbitrary rail of N zones, the stackup can be expressed

(9.1)

It has been assumed that accounting for the total stackup (6) at the end of Zone 3 is a
better practice for encouraging progressive crush than not accounting for stackup at all.
The value of 6 however, has been chosen arbitrarily up until now as 83.4 mm (see Figure
9.4.2). The benefit of accounting for 6, as well as the best value for 6 in encouraging

progressive crush will be explored in this section. Also, the effect of using 6 at the end of

Zone 3 as opposed to 61 at the end of Zone 1, 62 at the end of Zone 2, and 63 at the end of

Zone 3 (see Figure 9.4.3) will be explored. The decision to use the former in the previous
work in this thesis instead of the latter was based upon a quick separate study performed.

The validity of this decision will be proved here.

139

U3=250mm

 

U2 = 166.7mm
a.

 

--------_JE----.

 

 

 

 

 

 

U1=100mm i 6:83.4mm
____'. | .
E p—v. \
: : i \
E \
3 3 4 \
....... E
\
\
’< a\

 

100 mm 66.7 mm 166.7 mm 166.7 mm

Figure 9.4.2. Zone definitions and impactor displacement specifications used within this study. The
material stackup has arbitrarily been set at 83.4 mm.

 

 

 

 

 

 

 

 

//////////

Figure 9.4.3. Alternative definition of accounting for stackup: 61 + 62 + 63 = 6.

140

u

9. 4.2 Evaluation of the E fleet of 6
9. 4. 2. 1 Problem Definition

The size and necessity of the stackup distance 6, along with its effect on the
progressive crush optimization strategy, was studied through four optimizations. Each
optimization had the same Optimization problem statement, and began in the same
starting location in the design space with the same random seed for the search. Each

optimization however had a different value for 6 (see Table 9.4.1). A different value for 6

meant that each optimization had a different value of U3 used in the progressive crush

statement. Figure 9.4.4 shows the values of U: used for each optimization. Aside from
this alteration, the analysis model and optimization problem statement remained the same
as used throughout this thesis, with the progressive energy optimization statement here
being:

Maximize: PEA

Subject to: F2 5 150 kN

By Varying: Control Points

Rail Thickness

Where PEA is the progressive energy absorbed (as defined previously), F 2 is the

maximum reaction force after initial crush initiation, Control Points are the independent
control points varied, and Rail Thickness is the rail gage thickness, which varies between

1-3 mm.

141

...--il_ a.
.l

 

Table 9.4.1. Stackup distance 6 allotted for each optimization in the study.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

//////////

 

100mm 66.7mm 166.7mm 166.7mm

(a) Zone definition for Optim. A (6 = 133.4 mm). (b) Zone definition for Optim. B (6 = 83.4 mm).

 

 

 

U3=29l.73mm 5
U2=166.7mm E
HUME 15=41.6mm
: : z»; (
-—.'—~-'r ' -' t
1 ‘2 E 3 4 E
t
\
\

 

 

100mm 66.7mm 166.7mm 166.7mm

(c) Zone definition for Optim. C (6 = 41.6 mm).

 

 

 

Optimization A Optimization B Optimization C Optimization D
6 (mm) 133.4 83.4 41.6 0
1
U3 = 250 mm _1
U2=166.7mm E
l
_ ' I
‘ £2? mm 5 5 8: 83 4 mm
s H
1

100mm 66.7mm 166.7mm 166.7mrn

U3 = 333.33 mm

 

U2= 166.7mm
. ——v

 

V

6=0.0mm

//////////

 

 

 

////7/////

 

 

A
1
7

100mm 66.7mm166.7mm 166.7mm

((1) Zone definition for Optim. D (6 = 0.0 mm).

Figure 9.4.4. Zone definitions used for the different optimizations performed in the study to

determine the effect of 6.

142

 

 

9.4.2.2 Results

The resulting optimized designs from the four optimizations performed with

different values of U3 are shown in Table 9.4.2. From this table it is clear to see that the

second optimization (Optimization B with U3 = 250 mm) yielded the design that

absorbed the most total energy. Comparing the progressive energy for the optimized

designs from the four optimizations is not direct however, since the progressive energy

problem statement used in each optimization was different (due to U3 being different).

Therefore for comparison, the four optimized designs had PEA calculated for four
different values of 6. Table 9.4.3 and Figure 9.4.5 show these results.

The design from the second optimization (Design B) had the highest PEA

regardless of the value of U3 used in the definition of PEA. The designs from the first

(Design A) and fourth (Design D) optimizations had the lowest PEA regardless of the

value of U3 used. Recall that the optimization statement for which Design A was found

used a value of U3 equal to 200 mm (6 = 133.4 mm), while the optimization for which

Design D was found used a value of U3 equal to 333.33 mm (6 = 0.0 mm). Therefore,

optimizing for too large of stackup (as shown for 6 = 133.4 mm) and no stackup at all (6
= 0.0 mm) is not as efficient of an optimization statement as having values of 6 close to

the actual stackup that can be expected. Optimizations seeking progressive crush

therefore should use a definition of U3 that accounts for a realistic stackup 6.

143

 

In addition, the fact that in Figure 9.4.5 the PEA doesn’t change for any of the
four designs when calculating PEA with a statement of 6 = 41.6 mm and a statement of 6
= 0.0 mm, shows that stackup indeed does occur. If this were not the case, from U =
291.73 mm to U = 333.33 mm there would be an increase in energy absorbed in the rail in
Zone 3. This however is not the case demonstrating that the material has stacked up as
much as possible for the design in the first 3 zones and any additional energy absorbed
likely comes from the fourth zone (which is undesired). Figure 9.4.6 shows the crush
modes of the four optimized designs found with the different optimization statements via

the definition of U3.

Table 9.4.2. Results for each optimization.

 

 

 

 

 

 

 

 

Optimization A OJtimization B Optimization C Omimization D
PEA (kl) 12.187 18.429 19.480 17.606
EA (Q) 26.105 29.195 26.600 25.018

 

 

Table 9.4.3. Optimized design from each optimization reevaluated in terms of PEA for four different

values of 6.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Desi n A Desigi B DesigLC Deggn D
6 (mm) PEA EA PEA EA PEA EA PEA EA
(kl) (k1) (kl) (U) (U) (U) (Id) (10)
133.4 12.187 26.105 12.320 29.195 11.043 26.600 10.718 25.018
83.4 14.945 26.105 18.429 29.195 16.666 26.600 15.208 25.018
41.6 16.736 26.105 20.651 29.195 19.480 26.600 17.606 25.018
0.0 16.736 26.105 20.651 29.195 19.480 26.600 17 .606 25.018

 

144

 

 

Effect of U3 on PEA ' 09“"‘3' ”95‘9" A

I Optimal Design B
[1 Optimal Design C
E1 Optimal Design D

 

 

 

 

 

 

PEA (kJ)

 

 

 

 

 

 

 

 

Delta (mm)

 

 

 

Figure 9.4.5. Optimized designs from the four optimizations with PEA calculated for different values
of 6. The optimized design from optimization B had the highest PEA regardless of the statement
used. This shows that realistic values for the stackup 6 occurring in crush should be used in the
optimization problem statement to encourage the best progressive crush.

 

 

‘11 t =12
(a=) Optimized Design from Optimization A (6= 133. 4 mm in optimization problem statement)t=t

_HH

1 = 10 1 =11 ' 1 =12 1 =14 1 =15
(b) Optimized Design from Optimization B (6 = 83.4 mm in optimization problem statement)

 

 

t = t0 ' t =tl t =t2
(d) Optimized Design from Optimization D (6 = 0.0 mm in optimization problem statement)

 

 

 

 

Figure 9.4.6. Crush modes of the optimized designs from the optimization study of the impact of the
value of U3 on the optimization.

145

9.4.3 Total Stackup Represented by the Sum of Individual Zone Stackups
9. 4. 3. 1 Problem Statement

Recall that Equation (9.1) defined the total stackup distance (6) as the sum of the
material stackup of all desirable crush zones in the rail. However, in the optimizations
performed in this report the stackup of the individual layers was ignored and only the

total stackup was accounted for; the optimization problem statements considered 6 at the

end of Zone 3, as opposed to 61 at the end of Zone 1, 62 at the end of Zone 2, and 63 at the

end of Zone 3. The validity of considering only 6 at the end of Zone 3 will be explored
through a series of three optimizations.

Using the observed best value for 6 from the optimization study just performed (6

= 83.4 mm; U3 = 250 mm), two additional optimizations were performed to study the

impact the values of 61, 62, 63 have on the optimization for a fixed 6. The optimizations

used the same problem statement as before, started in the same location in the design
space, and had the same random seed.

Table 9.4.4 displays the differing characteristics among the optimizations and

compares them to that of OptimizationB from before (where 6 = 83.4 mm; U3 = 250

mm). Optimization B recall, had a value of 6 = 83.4- mm applied as 63 only. Therefore, U3

was the only U. offset from the end of the respective zone. Optimizations B-i and B-ii

however, have values of 61 and 62 in addition to 63, meaning U1 and U2 are offset from

the end of their zones as well. Optimization B-i had 61 = 62 = 63 = 27.8 rmn (6 = 83.4

146

_l

.‘.

‘jy.—"_r—_— ..

mm). This optimization statement assumed equal stackup between zones. This likely isn’t

the case however, since the zones are in different locations and have different lengths.

Optimization B-ii therefore, scaled the lengths of 6i according to the length of the zone.
Since Zone 3 was larger than Zone 2, and Zone 1 larger than Zone 2: 63 > 61 > 62 (6 =

83.4 mm).

Table 9.4.4. Stackup definitions used to study the relationship between total stackup (6) and the
individual zone stackups (6i).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

”mm” 5"“) 81mm) 621mm) 63(mm) U1 (mm) U2(mm) U3(mm)
B 83.4 0 0 83.4 100 166.7 250
B-i 83.4 27.8 27.8 27.8 72.2 133.9 305.6
B-ii 83.4 25 16.7 41.7 75 150 291.7
9. 4.3.2 Results

The optimized design from all optimizations had very similar total energy

absorbed (29-30 kJ). Again, due to the definitions of their objective function being

different (PEA defined differently due to different U1, U2, and U3 for all three

optimizations being compared), a direct comparison of progressive energy absorbed
cannot be done without calculating PEA for all definitions of 6 used. Table 9.4.5 and
Figures 9.4.7 and 9.4.8 display these results.

Design B outperforms the other two designs in terms of PEA regardless of the
definition used. At the same time, the designs are very similar in performance (as is
evident by the small standard deviations seen in Figure 9.4.8). This leads to the

conclusion that accounting for total stackup (6) is the same or better than trying to

account for the stackup of each individual zone. This is more practical anyhow since

147

estimating total stackup after the entire crush is performed is likely easier than predicting

stackup at various stages of the crush.

Table 9.4.5. Optimized design from each optimization with energy absorbed calculated for three

U1(mm) U2 (mm) U3 (mm)

 

 

 

 

 

    

 

 

PEA for Optimal Designs with Different Opt. I Des'gn B
' - I Design B-i
Definitions . ..
25,000 I Des:gn B-n
20.000 -
§ 15.000 -
51
a 10.000 -
5.000 -
0.000 4 .
Def. B Def. B-i Def. 341
Definition of PEA

 

 

 

Figure 9.4.7. Progressive energy absorbed by the different optimized designs with the different
optimization definitions.

148

 

Standard Deviation of PEA Among Opt.
Definitions

 

 

 

 

 

 

 

Def. B Def. B-I Def. B-ii
Definition of PEA

 

 

 

Figure 9.4.8. Standard deviation of the progressive energy absorbed among the three designs for the
different optimization definitions.

9. 4.4 Conclusions

It has been shown that accounting for stackup in your definition of PEA (through-
the definition of U1, U2, U3) produces better progressively crushing designs than not

accounting for stackup. In addition, it has been shown that giving reasonable stackup
definitions gives better performing designs than over-predictions or under-predictions of

stackup. Also, it has been demonstrated that approximating the total stackup (6) and

using that to define U3 (or UN-1 for N zones), produces as good or better designs than
accounting for the stackup in individual zones (in defining U1, U2, and U3). This section

therefore justifies and explains the use of U3 = 83.4 mm for all work performed in

Section II of this thesis.

149

CHAPTER 10: SUMMARY AND CONCLUSIONS

There are common optimization problem statements used for optimizing the
performance of hybrid electric vehicles as well as the crashworthiness of front rails in an
automobile vehicle. These optimization statements have been shown to be suitable for
achieving certain desired performance characteristics, but not others. In the current study,
alternative optimization problem statements have been shown to be as effective as
traditional statements for the problems posed, with additional benefits.

Hybrid electric vehicle (HEV) optimizations have primarily been done utilizing a
state of charge (SOC) correction to account for the effects of the initial SOC on
performance. In this study, this common approach (referred to herein as Strategy 2) was
compared with two alternative approaches in optimizing a series hybrid bus. The first
alternative strategy (Strategy 1) utilized multiple drive cycles and multiple initial SOC
load cases as a means to account for initial SOC, instead of an SOC correction. This
optimization strategy considered only the fuel consumption from the engine while
neglecting energy usage by the other components. Like Strategy 2, another alternative
strategy (Strategy 3) accounted for total energy usage as opposed to engine energy only.
This was achieved using the conversion for the electrical energy that can be converted to
gasoline through the efficiency of an average power plant in the United States. Strategy 3
like Strategy 1, did not utilize an SOC correction but rather multiple drive cycles and

multiple initial SOC load cases.

150

Strategy 1 was shown to be effective only if energy usage from the engine is the
primary concern, and a fixed driving route can be guaranteed frequently. Strategies 2 and
3 however, were shown to be effective if total energy usage is the primary interest.
Strategy 3 was shown to have a similar performance as Strategy 2 while being more run-
time efficient for the problem posed.

As with HEV optimizations, there is a typical optimization strategy used for
optimizing the crashworthiness of front rails in automotive vehicles. This common
approach focuses on maximizing total energy absorption by the rail during impact. It does
not however, guarantee the rail will crush progressively, as is desired for safety and repair
cost reasons. An alternative strategy for optimizing front rails therefore was proposed that
accounts for a quantity defined herein as progressive energy absorption (PEA). PEA
considers the time in which the energy absorption occurs in a given region of the rail.
High values of PEA correspond with designs that crush in the front of the rail and
propagate rearward with time.

The alternative approach for optimizing front rails was shown to yield optimized
designs with similar total energy absorption as conventional strategies, but with
significantly improved progressive crush modes. Through multi-objective optimizations,
the relationship between PEA and total energy absorption was explored; it was found that

as PEA increases, so does total energy absorption.

151

REFERENCES

[l] L. Guzzella, A. Sciarretta, Vehicle Propulsion Systems: Introduction to Modeling and
Optimization, Springer, 1 Edition, September 13, 2005.

[2] J. Miller, Propulsion Systems for Hybrid Vehicles, IET, 2004.

[3] M. Ehsani, Y. Gao, J. Miller, Hybrid Electric Vehicles: Architecture and Motor
Drives, Proceedings of the IEEE, Volume 95, Number 4, April 2007, pp. 719-728.

[4] C. Chan, The State of the Art of Electric Hybrid, and Fuel Cell Vehicles, Proceedings
of the IEEE, Volume 95, Number 4, April 2007, pp. 704-718.

[5] W. Gao, C. Mi, A. Emadi, Modeling and Simulation of Electric and Hybrid Vehicles,
Proceedings of the IEEE, Volume 95, Number 4, April 2007, pp. 729-745.

[6] W. Gao, S. Musunuri, Hybrid Electric Vehicle Modeling and Analysis in Generic
Modeling Environment, Proceedings of the IEEE Vehicle Power and Propulsion
Conference, 2006.

[7] W. Gao, S. Neema, et a1, Hybrid Powertrain Design Using a Domain-Specific
Modeling Environment, Proceedings of the IEEE Vehicle Power and Propulsion
Conference, 2005, pp. 530-535.

[8] K. Wipke, M. Cuddy, S. Burch, AD VISOR 2.1: A User-Friendly Advanced
Powertrain Simulation Using a Combined Backward/Forward Approach, National
Renewable Energy Laboratory, August 1999.

[9] ADVISOR User’s Manual, AVL.

[10] PSAT Documentation. [Online]. Available:
http://wwwtransportationanl.gov/software/PSAT

[1 l] PSIM Website. [Online]. Available:
http://www.pwersimtech.com/

[12] VTB Website. [Online]. Available:
http://www.vtb.ee.sc.edu/

152

[13] L. Guzzella, A. Amstutz, CAE Tools for Quasi-Static Modeling and Optimization of
Hybrid Powertrains, IEEE Transactions on Vehicular Technology, Volume 48, Number
6, November 1999, pp. 1762-1769.

[14] K. Oh, J. Kim, et a1, Optimal Power Distribution Control for Parallel Hybrid
Electric Vehicles, IEEE International Conference on Vehicular Electronics and Safety,
2005, pp. 79-85.

[15] M. Montazeri-Gh, A. Poursamad, B. Ghalichi, Application of genetic algorithm for
optimization of control strategy in parallel hybrid electric verhicles, Journal of the
Franklin Institute, 2006, pp. 420-435.

[16] A. Piccolo, L. Ippolito, et al, Optimisation of energy Flow Management in Hybrid
Electric Vehicles via Genetic Algorithms, lEEE/ASME International Conference on
Advanced Intelligent Mechatronics Proceedings, 2001 , pp. 434-439.

[17] W. Gao, S. Porandla, Design Optimization of a Parallel Hybrid Electric Powertrain,
Proceedings of the IEEE Vehicle Power and Propulsion Conference, 2005, Chicago.

[18] T. Markel, K. Wipke, Optimization Tools for Hybrid Vehicle Systems Analysis, FY
Annual Progress Report on Vehicle Propulsion and Ancillary Subsystems Program, 2001,

pp. 5-8.

[19] T. Markel, K. Wipke, AD VISOR Improvement, Validation, and Application, FY
Annual Progress Report on Vehicle Propulsion and Ancillary Subsystems Program, 2001,
pp. 8-12.

[20] D. Assanis, G. Delagrammatikas, et al, An Optimization Approach to Hybrid
Electric Propulsion System Design, Mechanics of Structures and Machines, Volume 27,
No. 4, 1999., pp. 393 - 421.

[21] R. Fellini, et. a1, Optimal Design of Automotive Hybrid Powertrain Systems, IEEE
Proceedings, EcoDesign ’99, First lntemational Symposium On Environmentally
Conscious Design and Inverse Manufacturing, 1999, pp. 400-405.

[22] T. Moore, HE V Control Strategy: Implications of Performance Criteria, System
Configuration and Design, and Component Selection, Proceedings of the American
Control Conference, June 1997, pp. 679-683.

[23] W. Wayne, et. al, A Comparison of Emissions and Fuel Economy from Hybrid-
Electric and Conventional-Drive Transit Buses, Energy and Fuels, 2004, 18, pp. 257-270.

[24] SAE J 271 1, Recommended Practice for Measuring Fuel Economy and Emissions of

Hybrid-Electric and Conventional Heavy-Duty Vehicle, SAE International Surface
Vehicle Recommended Practice, 2002.

153

 

[25] Pagerit, S., Rousseau, A., Sharer, P., Global Optimization to Real Time Control of
HE V Power Flow: Example of 0 Fuel Cell Hybrid Vehicle, International Electric Vehicle
Symposium (EVSZO), Monaco, (April 2005).

[26] M. Duoba, The 1996 F utureCar Challenge Final Rules and Regulations, 1995,
Section E-l 1.3.3, pp. 55.

[27] R. Senger, Validation of AD VISOR as a Simulation T 001 for a Series Hybrid Electric
Vehicle Using the Virginia Tech F utureCar Lumina, MS. Thesis, Virginia Polytechnic
Institute and State University, 1998.

[28] N. Chase, M.Rademacher, E.Goodman, R.Averill, R.Sidhu, A Benchmark Study of
Optimization Search Algorithms, Red Cedar Technology, BMK-3022, 2008.

[29] HEEDS Professional User’s Manual, Version 5.2, Red Cedar Technology, 2008.

[30] TransTeq. [Online]. Available:
http://wwwtrgnsteqcom/

[31] DiPaolo, B.P., Monteiro, P.J.M., and Gronsky, R. , Quasi-static axial crush response
of a thin-wall, stainless steel box component, International Journal of Solids and
Structures, 41:3707-3733, 2004.

[32] Jones, N., Structural Impact, Cambridge University Press, Cambridge,l989.

[33] Karagizova, D., and Jones, N., Counterintuitive Response of Long Circular Tubes to
Axial Impact, XXI International Congress of Theoretical and Applied Mechanics,
Warsaw Poland, August 2004.

[34] Guillow, S.R., Lu, 0., and Grzebieta R.H., Quasi-static axial compression of thin-
walled circular aluminum tubes, International Journal of Mechanical Sciences, 43:2103-
2123, 2001.

[35] Zarei, H.R., and Kroger, M., Multiobjective crashworthiness optimization of circular
aluminum tubes, Thin-Walled Structures, 44:301-308, 2006.

[36] Ku, J.H., Seo, K.S., Park, S.W., and Kim, Y.J, Axial crushing behavior of the
intermittent tack welded cylindrical tubes, International Journal of Mechanical Sciences,
43:521-542, 2001.

[37] Gumruk, R., and Karadeniz, S., A numerical study of the influence of bump type

triggers on the axial crushing of top hat thin-walled sections, Thin-Walled Structures,
46: 1094-1 106, 2008.

154

f ._e-- u'aiz'h.‘_- 'LJ
5
A l,
f
A

[38] Hon, 8., Li, Q., Long, S., Yang, X., and Li, W., Design optimization of regular
hexagonal thin-walled columns with crashworthiness criteria, Finite Elements in
Analysis and Design, 43:555-565, 2007.

[39] Kim, H.-S., New extruded multi-cell aluminum profile for maximum crash energy
absorption and weight efliciency, Thin-Walled Structures, 40:311-327, 2002.

[40] Abramowicz, W., and Jones, N., Transition fiom initial global bending to
progressive buckling of tubes loaded statically and dynamically, International Journal of
Impact Engineering, l9(5-6):415-437, 1997.

[41] Yamazake, K., and Han, J ., Maximization of the cnrshing energy absorption of
tubes, Structural Optimization, Springer-Verlag,16:37-46, 1998.

[42] Sidhu, R., Burgueno, J ., Averill, R., and Goodman, E., Improved Vehicle
Crashworthiness via Shape Optimization, Proceedings of the ASME International
Mechanical Engineering Congress & Exposition, Washington DC, 2003.

[43] Sidhu, R., Burgueno, J., Averill, R., and Goodman, E., Shape Optimization for
Improved Vehicle Safety and Reliability, 2003 ABAQUS User's Conference, 2003.

[44] Cho, Y., Bae, C ., Suh, M., and Sin, H., A vehicle front frame crash design
optimization using hole-type and dent-type crush initiator, Thin-Walled Structures,
44:415-428, 2006.

[45] Kim, H.-S., Chen, W., and Wierzbicki, T., Weight and crash optimization of foam-
filled three-dimensional “S ” frame, Computational Mechanics, 28:417-424, 2002.

[46] Kurtaran, H., Eskandarian, A., Marzougui, D., and Bedewi, N.E., Crashworthiness
design optimization using successive response surface approximations, Computational
Mechanics, 29:409-421, 2002.

[47] Avalle, M., Chiandussi, G., and Belingardi, G, Design optimization by response
surface methodology: application to crashworthiness design of vehicle structures,

Structural Multidisciplinary Optimization, Springer-Verlag, 24:325-332, 2002.

[48] Karbhari, V.M., and Haller, J.E., Rate and architecture eflects on progressive crush
of braided tubes, Composite Structures, 43293-108, 1998.

[49] Hanssen, A.G., Langseth, M., and Hopperstad, O.S., Optimum design for energy
absorption of square aluminum columns with aluminum foam filler, International Journal

of Mechanical Sciences, 43:153-176, 2001.

[50] LS—DYNA Users Manual, 2008.

155

151111111“

"'111111111111111111