EDDY CURRENT NONDESTRUCTIVE EVALUATION USING
MAGNETORESISTIVE SENSING

By
Guang Yang

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Electrical Engineering––Doctor of Philosophy

2013

ABSTRACT
EDDY CURRENT NONDESTRUCTIVE EVALUATION USING
MAGNETORESISTIVE SENSING

By
Guang Yang

Reliable inspection of hidden cracks in multilayer objects, such as the airframe structures still
poses a major challenge in NDE. Conventional electromagnetic methods are limited in their
abilities to detect second and third layer cracks in riveted structures. Cracks are normally found
at fastener sites and the presence of steel fastener (high permeability) produces a strong signal
that masks any indications from a crack. An eddy current (EC) system with sheet current source
for uniform field generation and magnetoresistive (MR) sensing is studied in this dissertation.
The contributions of this research are: 1) A study of three-component measurements using MR
sensors and the use of information in these components to enhance crack detection at steel
fasteners. 2) Experimentally validated model-based study of Pulsed EC excitation and low
frequency EC excitation systems for the inspection of buried cracks at fastener sites. 3) Rotating
current excitation designed to enhance the system capability to detect cracks of all orientations at
fastener sites. 4) A statistical signal processing scheme developed for automated analysis of
measured data. 5) Development of a numerical model for simulating the phenomenon in time
and frequency domains. Model based study is used to assist the overall system and algorithm
design. Results of implementing the techniques on simulation and measurement fully validate the
proposed methods.

To my family, particularly to my mother
For their love and support

iii

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my major advisor and mentor, Dr. Lalita Udpa,
for her extraordinary support, guidance and encouragement during my Ph.D. study. Special
thanks to her invaluable guidance and help in my writing. Dr. Lalita Udpa has advised me not
only on my research, but also on my career and life. I feel fortunate to work with her and proud
of being a member of NDEL research group.
I would like to express my sincere thanks to my co-advisor Dr. Satish S. Udpa for his continuous
support and guidance. I would like to thank my PhD studies committee: Dr. Wei and Dr.
Rothwell for their time, guidance and suggestions. I would like to express appreciation to Dr.
Tamburrino for his invaluable guidance and help for my experimental research and continuous
support during my PhD study.
I would like to thank my previous colleagues Dr. Zeng, Dr. Deng and Dr. Liu for their support
and help. I would like to thank my present colleagues of NDEL. Special thanks goes to Gerges
Dib for all his invaluable helps. Many thanks goes to Naiguang Lei. Many thanks also goes to
Dr. Kim for his guidance and help in signal processing research.
I would like to express my heartfelt gratitude to my family, friends, especially my mother, for
their constant support and encouragement. I would like to thank my beloved parents for their
faith in me. I acknowledge their patience and understanding through various situations in my life,
allowing me to reach this achievement.

iv

TABLE OF CONTENTS

LIST OF TABLES…………………………………………………………….…viii
LIST OF FIGURES………………………………………………………………..ix
CHAPTER 1. INTRODUCTION………………………………………………….1
1.1

1.2
1.3

1.4

Introduction to Nondestructive Testing…………………………………………………...1
1.1.1 Radiographic Testing……………………………………………………………...2
1.1.2 Ultrasonic Testing…………………………………………………………………2
1.1.3 Electromagnetic Testing…………………………………………………………..3
Inspection of Multilayer Structures……………………………………………………….5
Challenges and Goals…………………...………………………………………………...6
1.3.1 Problem Statement………………………………………………………………...6
1.3.2 Research Objectives and Methodologies……………………………………….....8
Organization of the Dissertation………..…………………………………………………9

CHAPTER 2. REVIEW OF ELETROMAGNETIC NDE……………………….11
2.1
2.2
2.3

2.4
2.5

2.6

Introduction………………………………………………………………………………11
Skin Depth and Development of EC Techniques………………………………………..14
Configurations of EC Coil Probes……………………………………………………….16
2.3.1 Conventional Coil Probes………………………………………………………..16
2.3.2 Planar Coil Probes………………………………………………………………..18
2.3.3 Limitations of Coil Sensors….………………………………………………......22
Magnetic Field Sensors for Hybrid EC Testing………………………………………….23
Magnetoresistive (MR) Sensors………………………………………………………….25
2.5.1 Magnetoresistance………………………………………………………………..25
2.5.2 Anisotropic Magnetoresistive (AMR) Sensor.…….……………………………..26
2.5.3 Giant Magnetoresistive (GMR) Sensor..…………………………………………28
2.5.4 NDE Applications of MR Sensors…………………….…………………………31
EC Techniques for Inspection of Riveted Structures…………………………………….32
2.6.1 EC Magneto-Optic Imaging……………………………………………………...33
2.6.2 Other EC Techniques……….……………………………………………………35

CHAPTER 3. EC-MR SENSOR SYSTEM – PULSE EXCITATION...………...38
3.1
3.2

Introduction………………………………………………………………………………38
Background……………………..………………………………………………………..38
3.2.1 Skin Depth in Transient Fields…………………………………………………..38
3.2.2 Transient Signal Characteristics…………………………………………………40
3.2.3 Review of Transient EC NDE for Layered Structure..………………………......43
v

3.3

3.4

3.5

3.6

3.7

3.2.4 Time Domain versus Frequency Domain………………………………………..46
3.2.5 Review of Transient Field Numerical Modeling………………………………...49
PEC Testing System with MR Sensor…………………………………………………...50
3.3.1 Excitation Coil Configuration……………………………………………………52
3.3.2 PEC-GMR Probe Operation………...…...………………………………………55
3.3.3 Giant Magnetoresistive Sensor…………………………………………………..56
3.3.4 Experimental Set-up……………………………………………………………...57
Inspection of Riveted Structures...……………………………………………………….58
3.4.1 A-scan Measurement of Transient Field…………………………………………58
3.4.2 C-scan Image Measurement of Transient Field………………………………….61
Time-domain Modeling of PEC-GMR Testing…..……………………………………...62
3.5.1 FE Modeling………..……………………………………………………………62
3.5.2 Time-domain Modeling Schemes……..…………………………………………68
3.5.3 Modeling in Frequency-domain vs. Time-domain.……………………………...76
3.5.4 Time-domain Model Validation…………………………….…………………...79
MR Measurements of 3-component Transient Fields…..………………………………..81
3.6.1 Ferrous Fastener Inspection……………………………………………………...82
3.6.2 Simulation Study of 3-component Measurements.………………………………83
3.6.3 Experimental Study of 3-component Measurements………………………….....86
Summary………………………………………………………………………………….88

CHAPTER 4. ANALYSIS OF PEC-GMR INSPECTION DATA.……………...89
4.1
4.2
4.3
4.4

4.5

Introduction………………………………………………………………………………89
Review of Signal Enhancement for PEC Inspection…………………………………….89
Multilayer Riveted Specimen……………………………………………………………90
Automatic Analysis of PEC-GMR C-scan Images………………………………………93
4.4.1 Principal Component Analysis…..………………………………………………93
4.4.2 Flaw Detection…………………………………………………………………...95
Results of PEC-GMR Inspection…………………….…………………………………..98
nd
rd
4.5.1 Detection of 2 and 3 Layer Cracks in Sample 1..……………...………...…..98
nd

4.6

4.7

4.5.2 Detection of 2 Layer Cracks in Sample 2……..……………………...………101
4.5.3 Flaw Detection using Tangential-component Measurements…………………..104
Automatic Crack Detection using 3-component GMR Images………………………...110
4.6.1 Feature Extraction………………………………………………………………110
4.6.2 Crack Detection Scheme………………………………………………………..112
Summary………………………………………………………………………………...124

CHAPTER 5. EC-MR SENSOR SYSTEM – LOW FREQUENCY EXCITATION
…………………………………………………………………………………...125
5.1
5.2

Introduction……………………………………………………………………………..125
Low Frequency EC-MR Sensing……………………..………………………………...125
5.2.1 Experimental Set-up…………………………………………………………….125
5.2.2 Inspection of Cracks around Steel Fasteners-Normal Component…………......127
vi

5.3

5.4

5.2.3 Inspection of Cracks around Steel Fasteners-Tangential Component…….........129
Model-based Study of Low Frequency 3D EC-GMR Measurements.…………………131
5.3.1 FE Model of EC-GMR Imaging………………………………………………..132
5.3.2 Experimental Validation...……………………………………………………...135
5.3.3 Image Fusion Method…………………………………………………………..137
5.3.4 Model-based Study-Inspection of Non-ideal Fasteners………………………...137
Summary………………………………………………………………………………..140

CHAPTER 6. EC-MR SENSOR SYSTEM – ROTATING FIELD EXCITATION
…………………………………………………………………………...………142
6.1
6.2

6.3

6.4

6.5

Introduction……………………………………………………………………………..142
Orthogonal Current Excitation………………………………………………………….142
6.2.1 Rotating Field…………………………………………………………………...142
6.2.2 Experimental Set-up…………………………………………………………….143
Detection of Crack Orientation at Rivet Site…………………………………………...144
6.3.1 Parameters in a Practical Design………………………………………………..144
6.3.2 Model-based Investigation of Crack Orientation Detection……………………147
Experimental Validation………………………………………………………………..148
6.4.1 Experimental Detection of Crack Orientations…………………………………148
6.4.2 Design of Array Receiver to Crack Orientations………………………...……..151
Summary………………………………………………………………………………..153

CHAPTER 7. PARAMETRIC STUDY OF EC-GMR DETECTION SYSTEM…...
…………………………………………………………………………………...154
7.1
7.2

7.3

7.4

Introduction……………………………………………………………………………..154
Sensor-tilt Study………………………………………………………………………..154
7.2.1 Sensor-tilt of GMR Sensing…………………………………………………….154
7.2.2 Model-based Investigation of Sensor-tilt……………………………………….155
Invariant Analysis………………………………………………………………………158
7.3.1 Transformation for Invariance to Sensor-tilt…………………………...………158
7.3.2 Invariance Transformations of GMR signals…………………………………...160
7.3.3 Invariance Features and Crack Detection………………………………………165
7.3.4 Implementation to Experimental Data………………………………………….167
Summary………………………………………………………………………………..170

CHAPTER 8. CONCLUSIONS AND FUTURE WORK………………………171
8.1
8.2

Accomplishments and Conclusions…………………………………………………….171
Future Work…………………………………………………………………………….173

BIBLIOGRAPHY……………………………………………………………….174
vii

LIST OF TABLES

Table 3-1 PEC system summary…………………………………………………………………45
Table 3-2 Summary of transient field modeling and simulation……….………………………..51
Table 3-3 Simulation error analysis of the interpolation modeling in time-domain……………..71
Table 3-4 Simulation error analysis of the impulse response based modeling…………………..76
Table 3-5 Simulation signal accuracy enhancement..……………………………………………76
Table 3-6 Computation time comparison…..……………………………………………………78
Table 4-1 Sample 1 – aluminum fastener………………………………………………………..99
Table 4-2 Sample 2 – steel fastener with 2

nd

layer cracks…………………………...………...101

Table 5-1 Feature Fr quantifying the defective steel fastener…………………………………..140

viii

LIST OF FIGURES

Figure 1.1 NDT and NDE technology……………………………………………….....................1
Figure 1.2 Inspection of riveted multilayer structure: (a) Problem of ultrasonic testing and (b)
Desired EC testing
(For interpretation of the references to color in this and all other figures, the reader is referred to
the electronic version of this dissertation.) ……………………………………………………….6
Figure 1.3 Layered structure: (a) Aircraft riveted skin structure geometry and (b) Initiation of
hidden corrosion and cracks at rivet sites……………………………..…………………………..7
Figure 2.1 Principle of the EC inspection: (a) A typical EC probe above a conducting specimen
under test and (b) The measurement of coil impedance………………...……………………….13
Figure 2.2 Eddy current testing system…………………………………………...……………..14
Figure 2.3 Demonstration of skip depth in EC testing (Comsol 3.5 simulation): (a) 100 Hz EC
and (b) 1 KHz EC………….............................................................…………………………….15
Figure 2.4 Typical EC probes: (a) Pancake type coil [50] (b) Bobbin type (inner diameter) coil [2]
(c) Encircling type (outer diameter) coil………………………………………………………....17
Figure 2.5 Coil probes-mode of operation [49, 51]: (a) Double-function probe in absolute mode
(b) Double-function probe in differential mode (c) Separate-function probe in absolute mode (d)
Separate-function probe in differential mode…............................................................................18
Figure 2.6 Planar coil configurations………………………………………..…………………...19
Figure 2.7 Two designs of planar coil probes: (a) a basic MWM probe [56] and (b) a
meander/mesh coupled probe……………………………………………………...…………….21
Figure 2.8 Hybrid probe [49, 74]: EC coil with magnetic field sensor………………………….24
Figure 2.9 Magnetoresistive effect in a thin current strip………………………..………………26
Figure 2.10 AMR device: (a) Barber-pole structure for an optimum alignment and (b) Resistance
change R/R vs. angle  , and resistance R vs. applied field H……......................................27

ix

Figure 2.11 Illustration of the GMR effect [14]: (a) Lots of scatterings due to the alternating
magnetization of the layers (b) Reduced scatterings when the magnetization of the layers is
aligned by an applied field (c) Resistance variation as a function of an applied magnetic
field……………………………………………..………………………………………………..29
Figure 2.12 Microscope picture of a GMR sensor fabricated by NVE Inc……………………...30
Figure 2.13 EC-MO imaging technique: (a) Faraday rotation effect in a MO sensor (b) Schematic
of the MO imaging system [85] (c) MO images of riveted structures (d) Images of riveted
structures using LMOI system in Europe………………...……………………………………...34
Figure 2.14 Self-nulling EC probe: (a) Probe schematic and (b) Inspection of ferromagnetic
protruding head fasteners……………………………………..………………………………….35
Figure 2.15 EC-GMR probes for riveted structure inspection: (a) Schematic of a rotational
D-shaped coil and GMR based probe [93] and (b) A sheet current and AMR sensing
probe……………………………………………………………………..………………………36
Figure 3.1 Skin depths of conventional EC and transient EC fields (Comsol 3.5 simulation): (a)
Conventional 100Hz EC result: induced eddy current and skin depth and (b) 100Hz square-wave
PEC result: induced eddy current and skin depth…...…………………………………………..40
Figure 3.2 PEC signals: (a) A typical reference-subtracted transient response and typical features
in the time domain and (b) Transient response associated with defective information at different
depths (Comsol 3.5 simulation)……………….…………………………………………………42
Figure 3.3 Time domain vs. frequency domain: Transient excitations in different pulse widths
and their DFT spectrum results………………………………………….………………………47
Figure 3.4 Square waveform as a source of pulse excitation (left) and the reconstruction of the
waveform by adding Fourier series harmonics (right)……..……………………………………49
Figure 3.5 Schematic of the multi-line planar probe design……………………...……………..52
Figure 3.6 Simulation results of pancake coil: (a) Tangential component (Bx) of magnetic field
(T) and (b) Induced currents (A/m2)……………………………….............................................52
Figure 3.7 Simulation results of multi-line coil: (a) Normal component (By) of magnetic field (T)
(b) Induced currents (A/m2) (c) Comparison of induced currents due to two coil
configurations……………………………………………………..……………………………..54

x

Figure 3.8 Schematic of the operation of multi-line planar probe……………….………………55
Figure 3.9 Characteristic curve for the calibration of the GMR sensor…………….....................56
Figure 3.10 Schematic of the PEC-GMR inspection system……………………….....................58
Figure 3.11 GMR measurements of the transient field Bz component along a line scan above a
fastener with a subsurface crack: (a) Inspection Geometry (b) Sequence of A-scan signals within
the fastener head region (c) Comparison of transient signals at the fastener head edge areas for
crack indication…………………………………………………………………………………..60
Figure 3.12 Three modes of PEC-GMR signals in the inspection of a riveted
structure……………………………………………………………………………………..……61
Figure 3.13 A typical EC problem with regions, boundary sections and interface.……………...64
Figure 3.14 A geometry used in the time-domain modeling: (a) Simulation geometry and three
scan positions and (b) Geometry FE mesh……………………………..………………………..69
Figure 3.15 The excitation source signal (upper left), and the simulation results of Bz in
time-domain modeling at positions P1, P2, and P3……………………………………………...69
Figure 3.16 The first peak of Bz in the simulation results at positions P1, P2, and
P3………………………………………………………………………………………………...70
Figure 3.17 Simulation results of Bz using the time-domain interpolation modeling: (a)
PEC-GMR signals at P1 (b) PEC-GMR signals at P2 (c) PEC-GMR signals at P3.....................72
Figure 3.18 The strategy for impulse response based time-domain simulation……....................73

Figure 3.19 Impulse response based simulation results vs. the reference signal for the positions
P1, P2, and P3…………………………………………………………...……………………….75
Figure 3.20 Simulations of PEC signals using FE solver in frequency-domain: Predicted transient
signal
of
250
frequency steps
vs.
the
reference
signal
simulated
in
time-domain……………………………………………………………………………………...77
Figure 3.21 Simulations of PEC signals: predicted transient signal of 250 frequency steps vs.
predicted transient
signals with interpolation of 100 and 50 frequency
steps………………………………………………………………………………………………78
xi

Figure 3.22 Model validation: Simulation signals of 250 time steps and signals of the impulse
response based modeling (30 time steps) vs. experimental signals……………………………...79
Figure 3.23 Modeling geometry of a three layer riveted plate with a 3rd layer crack at aluminum
fastener site………………………………………………………………………………………80
Figure 3.24 PEC-GMR signals at three scan positions: (a) Simulation signals and (b)
Experimental signals……………………………………………………………………………..81
Figure 3.25 Numerical results illustrating the challenge of ferrous fastener inspection when
measuring the normal magnetic field component (Bz): (a) Induced field at an aluminum fastener
without crack (left image) and with crack (right image) (b) Induced field at a steel fastener
without crack (left image) and with crack (right image) (c) C-scan image in the presence of a
subsurface 8mm notch a at aluminum fastener site (left image), and at steel fastener site (right
image)……………………………………………………………………………………………82
Figure 3.26 Simulation for steel fastener structures-Test sample: no crack vs. with 2.87mm
notch………………………………………………………………………...................................84
Figure 3.27 Simulation of 3-component measurements for steel fastener structures: (a)-(c)
Simulation signals of Bz, By, Bx components respectively (d) Subtraction of the no flaw
measurements
from
the
2.87
mm
flaw
measurements
for
each
component………………………………………………………………………………………..85
Figure 3.28 GMR sensing 3-component of the magnetic field…………………………………..87

Figure 3.29 PEC-GMR measurement of a steel fastener with a 2.87 mm notch using three
components: (a) Test geometry (b) C-scan images of Bz, By, Bx (c) Transient A-scan signals of
Bz, By, Bx ……………………………………………………...………………………………...87
Figure 4.1 Schematic of Sample 1: three layers aluminum plate with aluminum fasteners and
cracks in second and third layers (a) Side view of cracks in the second layer (b) Side view of
cracks in the third layer (c) Top view of Sample 1………………………………………………90
Figure 4.2 Schematic of Sample 2: top view of a three layers aluminum plate with four rows of
steel fasteners, and cracks dimensions in the second layer at each fastener site in every
row…………………………………………………………..…………………………………...91
Figure 4.3 Schematic of sample 3: two layers aluminum sample with aluminum fasteners and
cracks in the bottom layer………………………………………………………………………..92
xii

Figure 4.4 Flaw detection using the image analysis……………………………….…………….96
Figure 4.5 Principle of applied PCA analysis……………………………………………………97
Figure 4.6 C-scan images of aluminum fasteners in Sample 1 using PEC-GMR
measurements……………………………………………………………………...……………..98
Figure 4.7 Detection of cracks in the 2nd layer of Sample 1 using the PCA method (a) Detection
results by PC1 vs. PC3 representations (b) Detection results by PC3 vs. PC2
representations………………………………………………………………………………….100
Figure 4.8 Detection of cracks in the 3rd layer of Sample 1 using the PCA method (a) Detection
results by PC1 vs. PC3 representations (b) Detection results by PC3 vs. PC2
representations………………………………………………………………………………….100
Figure 4.9 C-scan images of steel fasteners in Sample 2 using PEC-GMR
measurements………………………………………………………………………...................101
Figure 4.10 Detection of cracks around steel fasteners in Row 1 to Row 4 of Sample 2 using the
3D plots of PC1 to PC3: Bz component………………………………………………………...103
Figure 4.11 Detection of cracks in the 2nd layer of Sample 2 using the PCA method (steel
fasteners in Row 1 to Row 4): Bz component…………………………………………………..104
Figure 4.12 PEC-GMR tangential-component measurements of steel fasteners (a) C-scan images
of By measurements (b) C-scan images of Bx measurements…………………………………..105
Figure 4.13 Detection of cracks around steel fasteners in Row 1 to Row 4 of Sample 2 using the
3D plots of PC1 to PC3: By component………………………………………………………...106
Figure 4.14 Detection of cracks in the 2nd layer of Sample 2 using the PCA method (steel
fasteners in Row 1 to Row 4): By component………………………………..............................107
Figure 4.15 Detection of cracks around steel fasteners in Row 1 to Row 4 of Sample 2 using the
3D plots of PC1 to PC3: Bx component………………………………………………………...108
Figure 4.16 Detection of cracks in the 2nd layer of Sample 2 using the PCA method (steel
fasteners in Row 1 to Row 4): Bx component………………………………..............................109
Figure 4.17 Orientation based feature extraction………………………………...……………..111

xiii

Figure 4.18 Asymmetry quantification using moment based features (3rd & 4th
orders)…………………………………………………………………………………………..112
Figure 4.19 Overall approach for automated crack detection…………………….....................113
Figure 4.20 Classification results of steel fasteners in Row 1 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of Bz
component………………………………………………………………………………………114
Figure 4.21 Classification results of steel fasteners in Row 2 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of Bz
component………………………………………………………………………………………115
Figure 4.22 Classification results of steel fasteners in Row 3 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of Bz
component…………………………………………………………………................................116
Figure 4.23 Classification results of steel fasteners in Row 4 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of Bz
component………………………………………………………………...…………………….117
Figure 4.24 Classification results of steel fasteners in Row 1 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of By
component…………………………………………………………………................................118
Figure 4.25 Classification results of steel fasteners in Row 2 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of By
component………………………………………………………………….…………………...119
Figure 4.26 Classification results of steel fasteners in Row 3 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of By
component…………………………………………………………………................................120
Figure 4.27 Classification results of steel fasteners in Row 4 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of By
component…………………………………………………………………................................121
Figure 4.28 Classification results of steel fasteners in (a) Row 1 (b) Row 2 (c) Row 3 (d) Row 4
using feature s and k calculated from PC1: PEC-GMR measurements of Bx
component………………………………………………………………………………………122

xiv

Figure 5.1 Schematic of low frequency EC-GMR system: (a) Experimental Set-up and (b) Signal
demodulation………………………………………………………….………………………...126
Figure 5.2 C-scan images of steel fasteners in Sample 2 using low frequency EC-GMR
measurements: Bz component………………………………………..…………………………127
Figure 5.3 Inspection of steel fasteners in Sample 2 using EC-GMR detection: Bz measurements
(a) Plots of conventional complex trajectories (b) Detection of hidden cracks around steel
fastener sites using the PCA method (c) Polar plots with data rotation for automatic
detection………………………………………………….……………………………………..128
Figure 5.4 C-scan images of steel fasteners in Sample 2 using low frequency EC-GMR
measurements: By component…………………………………………………………………..130
Figure 5.5 Inspection of steel fasteners in Sample 2 using EC-GMR detection: By measurements
(a) Detection of hidden cracks around steel fastener sites using the PCA method (b) Polar plots
with data rotation for automatic detection…………...................................................................131
Figure 5.6 Modeling study of a three layers riveted aircraft structure: (a) Test geometry and (b)
Distributions of 3D induced currents…………………………………………………………...132
Figure 5.7 Simulation of 3-component C-scan images of three cases: (a) Quadrature part of Bz (b)
Quadrature part of By (c) Quadrature part of Bx………………………………………………..134
Figure 5.8 Qualitative comparison of experimental and simulation C-scan images of Bz
component for a steel fastener with 2.8 mm notch: (a)-(b) Experimental in-phase and quadrature
parts (c)-(d) Simulation in-phase and quadrature parts…………………………………………135
Figure 5.9 Qualitative comparison of experimental and simulation C-scan images of By
component for a steel fastener with 2.8 mm notch: (a)-(b) Experimental in-phase and quadrature
parts (c)-(d) Simulation in-phase and quadrature parts…………………………………………136
Figure 5.10 Qualitative comparison of experimental and simulation C-scan images of Bx
component for a steel fastener with 2.8 mm notch: (a)-(b) Experimental in-phase and quadrature
parts (c)-(d) Simulation in-phase and quadrature parts…………………………………………136
Figure 5.11 Fusion of quadrature parts of the 3-component GMR measurements……………..137
Figure 5.12 Geometries of steel fastener structures: ideal and non-ideal
fasteners………………………………………………………………………………………...137
xv

Figure 5.13 Simulation geometries and results: (a) Geometries of three cases: steel fastener
without defect (left), with a 2.8 mm notch (middle) and off-centered fastener without defect
(right) (b)-(d) Bz, By and Bx components (quadrature parts) for the corresponding
cases……………………………………………………………….............................................138
Figure 5.14 Fused images: (a) Defect-free steel fastener (b) Steel fastener with a 2.8 mm notch (c)
Off-centered steel fastener…………………………………………...........................................139
Figure 6.1 Planar multi-line current field: (a)-(b) linear current excitation: linear current field (c)
rotating current excitation: rotating current field………………………………………………143
Figure 6.2 Experimental set-up of the rotating current field…………………………………...144
Figure 6.3 Demonstration of crack detection using the rotating field: (a) No crack case and (b)
Crack at orientation 90° (parallel to Y direction current)………………………………………145
Figure 6.4 Probe lift-off study: (a) Model-based study of rotating field variations for the crack
case (b) Model-based study of rotating field variations for the no crack case (c) Calibrated vs.
ideal rotating current field for the crack case (d) Calibrated vs. ideal rotating current field for the
no crack case………………………………………....................................................................146
Figure 6.5 Detection of crack orientations: (a) Cracks geometry in all directions (b) Rotating
field from cracks around aluminum fasteners (c) Rotating field from cracks around steel
fasteners (steel fastener effect removed)…………………………….........................................147
Figure 6.6 Experimental study of rotating field: (a) Field measurement due to the top source coil
(b) Field measurement due to the bottom source coil (c) Total rotating field sensitive to a crack
around steel fastener site: absolute value of Bz………..……………………………………….149
Figure 6.7 Experimental data from cracks with different orientations: (a) Geometry of crack in
different orientations and (b) Rotating field measurement……………………………………..151
Figure 6.8 GMR image measurement without probe motion: (a) Bz measurement of aluminum
plate and (b) Bz measurement of a defective steel fastener…………………………………….152
Figure 6.9 Application of GMR array receiver: Bz fast image measurement of fastener using
rotating field (a) Without crack and (b) With crack at 90° orientation…….…………………...153
Figure 7.1 Sensor-tilt variations: (a) Probe lift-off and tilt sensor and (b) GMR sensor
measurements of magnetic field components…………………………………...……………...155

xvi

Figure 7.2 Sensor-tilt measurement: (a) Geometry and FE mesh of tested sample: three-layer
riveted structure and (b) Definition of tilt degrees in two directions….......................................156
Figure 7.3 Magnetic field measured under tilt GMR sensor for a crack-free fastener: (a) Real part
of signals and (b) Imaginary part of signals…………………………………………………….157
Figure 7.4 Diagram of ICA based transformation invariant to sensor-tilt……………………...159
Figure 7.5 Transformed signals invariant to sensor-tilt in the inspection of a crack-free aluminum
fastener: (a) Real part of signals and (b) Imaginary part of signals…………………………….160
Figure 7.6 Studied riveted geometries…………………………………………….....................161
Figure 7.7 Measured GMR complex signals of defect-free and defective fasteners: (a) Real parts
of signals and (b) Imaginary parts of signals………………………….......................................161
Figure 7.8 Transformed GMR complex signals of defect-free and defective fasteners: (a) Real
parts of signals and (b) Imaginary parts of signals………………………..................................163
Figure 7.9 Invariance feature analysis: (a) Skewness curves of transformed GMR signals
regarding different fastener states: single cracks vs. no crack (b) Two cracks on both
sides………………………………………………………………………..................................164
Figure 7.10 Crack detection: classification of GMR signals (the real part) using invariance
features………………………………………………………………..………………………...166
Figure 7.11 Classification of GMR signals in Figure 7.10 using higher order invariance
features………………………………………………………………..………………………...167
Figure 7.12 GMR signals collected under two sensor-tilt states………………….....................168
Figure 7.13 Results of invariance analysis: (a) Transformations of measured GMR signals and (b)
Classification result using invariance features…………………….............................................169
Figure 8.1 Detection of the subsurface cracks (less than 1mm) around aluminum fasteners in
Sample 3: (a) Schematic of probe in a reduced size (b-c) C-scan images of normal component (d)
Automatic detection using the PCA processing………………………………………………...173

xvii

CHAPTER 1

INTRODUCTION

1.1 Introduction to Nondestructive Testing
Nondestructive testing and evaluation (NDT/NDE) is the assessment of the structural integrity of
a material or component without causing any physical damage to the test object [1]. NDE
techniques are well developed and widely used by industry to monitor and detect flaws or
crack-like discontinuities. NDT/NDE techniques play a major role in quality control, safety
maintenance, and failure prevention. The application of NDE technology has improved the
reliability of operating aircraft, pipelines, bridges, nuclear power plants, etc. In order to inspect a
variety of materials, a number of NDT techniques, employing different physical principles, have
emerged. As show in Figure 1.1, a typical NDT method consists of an energy source that
interacts with the specimen under test, and a receiving transducer that picks up the response of
energy-material interaction. A measured NDT signal contains the indication of possible defect in
the test object.
Excitation source
Input
transducer

Sample with
flaw

·
·

Defect parameter
Flaw, geometry
Mechanical properties

Receiving
transducer

Signal/image
processing

Figure 1.1 NDT and NDE technology
1

Defect location,
Size, shape

Signal
inversion

Each NDT/NDE method has certain advantages and limitations. Radiographic, ultrasonic, and
electromagnetic methods are some of the commonly used approaches in NDE [1-4].
1.1.1 Radiographic Testing
Radiographic testing involves the use of a penetrating radiation source such as gamma rays or
X-rays that travels through the object under test. The intensity of the beam energy is reduced
after passing through the test specimen. The attenuation depends on material thickness and
absorption coefficient. The energy distribution of the transmitted beam is imaged on a film or
other imaging media. The density in a defect/crack region is generally lower than the rest of the
sample, which produces intensity differences in the radiographic image [3-4].
Radiographic NDT is extensively applied to find internal defects in coating and weld inspection
[4]. However, radiographic imaging is a projection of a cross-section of the test object, and it
requires a two-sided access to the component under examination. The test is highly directional
and a simple radiograph cannot provide depth information of the discontinuity [1, 3-4].
Moreover, radiographic NDT has limitations due to the radiation hazard involved in its use and
also, the equipment is relatively expensive.
1.1.2 Ultrasonic Testing
Ultrasonic testing uses the transmission of high frequency elastic waves (0.1 and 25 MHz) into a
material to detect imperfections or locate changes in material properties. Acoustic energy is
transmitted, reflected and scattered within the object under test or redirected by internal
interfaces or anomalies. The reflected beam is captured by the transducer that is located in
contact or in close proximity to the test object, and analyzed to determine the presence and
2

location of flaws or discontinuities [1, 3-4]. The most common ultrasonic examination,
pulse-echo testing, employs a piezoelectric transducer that is energized in a pulsed mode to direct
and propagate sound energy into the specimen. The features in the received signals (echoes) are
evaluated to identify discontinuities [3-4].
Ultrasonic NDT is widely used to measure material thickness and qualify the internal structure of
metallic and non-metallic materials. However, ultrasonic testing needs couplant to inject energy
efficiently into material and in general, cannot be used effectively in a layered structure with air
gaps. Furthermore, small and thin objects and coarse-grained materials are difficult to be
inspected, due to high scattering of the elastic waves in those materials. Interpretation of
acquired signals demand advanced signal interpretation algorithms [3-4].
1.1.3 Electromagnetic Testing
Electromagnetic NDT techniques covering a broad range of the electromagnetic spectrum are
non-contact and offer a low-cost means for high speed, large scale testing of metallic materials.
Electromagnetic NDT includes magnetic flux leakage technique (static fields), eddy current (EC)
method and remote field EC testing (quasi-static fields), microwave testing (high frequency
fields), etc. [5]. In these techniques, the material under examination is excited
electromagnetically and changes associated with electromagnetic fields are monitored and
measured. Received signals contain information about material anomalies that affect electrical
conductivity, magnetic permeability or dielectric permittivity. Electromagnetic methods have
been used extensively in nuclear, aerospace, marine, high pressure and high temperature
environments. They have been applied for flaw detection, microstructure characterization, and
3

evaluation of mechanical properties and residual stresses [5-8].
Electromagnetic NDT techniques differ in their detection sensitivity and capability, and signal
analysis techniques for crack characterization [5]. Magnetic flux leakage testing, active or
residual, is established by magnetizing a ferromagnetic material. The presence of a flaw in a
material causes a discontinuity in its magnetic permeability. This distorts the distribution of the
magnetic flux lines, and a part of the flux ‘leaks’ into the air in the vicinity of the flaw. During
testing, the leakage field is captured by scanning the specimen’s surface with a flux-sensitive
transducer. However, this method is limited to detect defects on the surface or near the surface of
a ferromagnetic object. At the other end of the spectrum, microwave and Terahertz NDE
methods are employed for defect detection by measuring differences in dielectric properties of
non-conducting materials [6, 8-9].
Conventional EC technique is the most common electromagnetic method used for the inspection
of conductive components in several industries, such as nuclear and aerospace. It is widely
employed to inspect surface defects, subsurface corrosion and coating characterization of
conductive materials. In particular, this NDT method offers advantages in testing layered
structures [2, 6-9]. An EC testing system consists of a probe coil excited by an alternating current.
The discontinuities in component properties cause changes in induced current or magnetic field.
Resultant fields provide complex signals representing probe coil impedance changes, which
carries information about material properties [2, 5-7]. Recently, EC testing systems using
advanced magnetic sensors have been investigated [8]. A detailed review of EC techniques is
presented in Chapter 2 of this dissertation.
4

1.2 Inspection of Multilayer Structures
The examination of multilayer structures poses a major challenge in the maintenance of aging
aircraft and the aerospace industry [10-11]. Aeronautical components such as aircraft wings and
riveted fuselage lap joints, undergo fatigue damage that occur around fasteners due to
mechanical stresses. Undetected cracks hidden at fastener sites in layered structures can lead to
catastrophic failures. Therefore, reliable NDT methods are required to detect these embedded
cracks. EC methods are popularly used for detecting corrosion and subsurface fatigue cracks in
riveted multilayer structures [11-12]. The penetration of low frequency electromagnetic fields
through multiple layers provides the ability to detect hidden cracks in subsurface layers or small
cracks under fastener heads without safety hazards. Figure 1.2 compares the penetration of
electromagnetic and ultrasonic fields through the thickness of a multilayered structure.

Sound
wave

EC testing:
Electromagnetic field penetration

Ultrasonic testing:
No penetration through
air gap

Air gap

Air gap

Air gap

Air gap
Fastener
Flaw
Multilayer wing splice
(a)

Fastener
Flaw
Multilayer wing splice
(b)

Figure 1.2 Inspection of riveted multilayer structure: (a) Problem of ultrasonic testing and (b)
Desired EC testing
(For interpretation of the references to color in this and all other figures, the reader is referred to
the electronic version of this dissertation.)
However, due to skin depth effect, conventional EC method suffers attenuation of EC intensity
along the depth of structure under test. In addition, the fastener behaves as a strong discontinuity
5

through the full depth of the layered structure, masking the response or indication due to small
fatigue cracks. Hence, techniques for enhancing the signal-to-noise ratio in EC measurements are
required. This dissertation focuses on the development of EC NDE techniques to reliably detect
small cracks at fastener sites in layered structures.
1.3 Challenges and Goals
EC techniques that offer deep penetration of induced currents have been studied for the detection
of subsurface discontinuities in layered structures. These techniques include low frequency EC
testing and pulsed eddy current (PEC) methods. Particularly in the aerospace industry, EC testing
is currently used for detecting fastener holes in aircraft components [12-17]. Low frequency EC
method offers the potential to detect cracks that are not detectable by X-ray radiography [18].
However, present EC techniques require the removal of fasteners or perform inspections limited
to corrosion detection, large size subsurface slots, and near-surface cracks within a few
millimeters from the surface. Additionally, these methods do not quantify the reliability of defect
detection under variable factors during inspection [18]. This dissertation attempts to address
these problems.
1.3.1 Problem Statement
A typical aircraft skin structure including fuselage skin or wing splice that is joined together by
fasteners is shown schematically in Figure 1.3 (a). Fasteners are typically made of aluminum,
titanium or steel and typical diameters are about 20 mm. This type of structure tends to produce
high stress concentration around fastener holes [10-11]. Hence, fatigue flaws, stress corrosion
and cracks usually initiate at rivet sites in subsurface layers, as demonstrated in Figure 1.3 (b).
6

Fastener or Rivet

Third layer (a)

Hidden corrosion

Fastener/Rivet
Embedded crack
Multiple
layers

(b)
Figure 1.3 Layered structure: (a) Aircraft riveted skin structure geometry and (b) Initiation of
hidden corrosion and cracks at rivet sites
EC techniques have been widely used to inspect aluminum or titanium fastener structures
(non-magnetic materials). However, the examination of a ferromagnetic fastener remains a
challenge [2, 7, 19-22]. Ferromagnetic materials are characterized by a large change in magnetic
permeability that strongly influences the measured signals associated with the induced magnetic
field. Therefore, the dominant signal from a ferrous rivet in the lap joint masks the relatively low
amplitude signal from a hidden defect propagating around the fastener hole. Consequently, the
presence of a ferrous fastener confounds crack detection. Currently, fastener removal is required
by EC techniques during the inspection of aircraft wing structures [22]. Some of the research
solutions using EC techniques for ferromagnetic fastener examination and their limitations are

7

reviewed in Chapter 2.
Incorporation of advances in magnetic sensors, signal and image processing, image fusion and
numerical model based investigations has significantly enhanced the scope and applicability of
EC techniques [23]. In particular, magnetoresistive (MR) imaging has improved EC inspection
of complex structures such as riveted components. In contrast to impedance analysis of a single
scan (conventional EC data analysis), flaw detection is evaluated based on asymmetry features in
EC C-scan image data [24]. However, there are several potential sources of coherent noise that
yield responses similar to a defect scenario. These include the asymmetric gaps between
fasteners and holes, probe tilt, lift-off variation and irregular geometric factors. Such factors can
interfere with defect detection [18]. Studies presented in [25-26] showed the enhanced detection
of cracks beneath installed fastener heads using phase-based signal processing methods. A
discussion of the benefits using phase shift or rotation to minimize the response of fastener is
given in [27]. However, finding an optimum phase shift can be difficult in a noisy image.
Additionally, a phase shift based flaw is affected by fastener type and lift-off variations.
Model-based approaches for flaw detection and characterization, and model-assisted probability
of detection (POD) have also been studied for riveted structure inspection [28-29]. However, the
procedure for implementing the model-based approach is computationally intensive since these
are iterative procedures involving 3D numerical models.
1.3.2 Research Objectives and Methodologies
The objective of this dissertation is to develop a reliable EC sensor system and automatic signal
interpretation for detecting cracks buried around steel fastener sites in layered structures.
8

Additionally, the proposed system should be sensitive to cracks of all orientations emanating
radially from fastener holes.
The feasibility of proposed sensor systems is investigated using modeling and experiments. The
use of uniform excitation currents with 3D MR sensing is explored using laboratory specimens.
Low frequency excitation current methods as well as pulsed excitation with transient response
are investigated. Simulation models using efficient finite element (FE) analysis in time and
frequency domains are used for conducting parametric study that could assist in system design.
1.4 Organization of the Dissertation
This chapter introduced the research problem and summarized the research objectives. This
dissertation addresses several topics in EC inspection: system design and modeling, experimental
validation and algorithms for data analysis. Chapter 2 presents a review of EC techniques and its
application to multilayer structures. A discussion of EC testing systems developed for riveted
structures is presented. Chapter 3 proposes the design of a Pulsed Eddy Current-Giant
Magnetoresistor

(PEC-GMR)

system.

A

numerical

model

for

simulating

transient

electromagnetic field and GMR sensing in time domain is described. The feasibility of
measuring the 3-components of the magnetic field using 3D GMR sensors is investigated and
proposed as a solution to find defective ferromagnetic fasteners in a layered aircraft structure.
Chapter 4 introduces a signal analysis scheme for automatic detection using statistical analysis of
time-domain PEC-GMR signals. Chapter 5 presents the design of low frequency EC-GMR
inspection and associated data analysis in the frequency domain. Chapter 6 proposes an
EC-GMR rotating current excitation design that is sensitive to orientations of radial crack around
9

the fastener site. Numerical modeling studies and experimental measurements using rotating
field are presented. Chapter 7 describes a parametric study of the proposed EC-GMR system. An
invariance analysis scheme is introduced to render the measurements insensitive to sensor tilt
that could cause unwanted response received by GMR sensor. Conclusions and
recommendations for future research are summarized in Chapter 8.

10

CHAPTER 2

REVIEW OF ELETROMAGNETIC NDE

2.1 Introduction
The operation of EC testing is based on the principles of electromagnetic induction. A harmonic
field at a specific frequency (typically Hz-MHz) is produced by a time-harmonic current through
a source coil, which induces eddy currents in the object under examination. The presence of a
defect or discontinuity behaves as a high resistance barrier which disturbs induced current flows.
The resulting perturbations of the associated magnetic field are measured [2, 5-7].
These phenomena can be described by Maxwell’s equations:

D
(Ampere’s Law)
t
B
 E  
(Faraday’s Law)
t
  B  0 (Gauss’ Law)
J  E

 H  J 

(2.1)
(2.2)
(2.3)
(2.4)

where the variables are:

E : electric field intensity (volt/meter)
H : magnetic field intensity (ampere/meter)
2

D : electric flux density (coulomb/meter )
B : magnetic flux density (tesla)
2

J : electric current density (ampere/ meter )

 : electric conductivity (mhos/meter)
According to Ampere’s law in Eq. (2.1), a time-varying current source generates a time-varying
magnetic field, as a primary field H shown in Figure 2.1 (a) [5]. As dictated by Faraday’s law in
Eq. (2.2), a time-varying magnetic field induces an electromotive force that is proportional to the
11

time-rate of change of the magnetic induction flux density:

 

d B
dt

(2.5)

This electromotive force interacts with the test material and results in currents induced inside the
specimen. The induced currents are called eddy currents. Based on Lenz’s law, these eddy
currents produce a secondary magnetic field that opposes the source field due to the excitation
coil, as shown in Figure 2.1 (a) [5]. By sensing the changes in the total electromagnetic field,
discontinuities in the conductivity or permeability of a conductive structure are detected. The net
change in the magnetic flux is linked to changes of the coil impendence (z), a complex parameter
with magnitude |z| and phase angle  as:

z  V / I  R  jX  z 

(2.6)

Since the inductance of a coil is associated with the flux linkage per ampere, the presence of
eddy currents generate a resistive power loss. This results in a small increase in the effective
resistance of the coil, which changes the coil impendence when it approaches a conducting
specimen. Thereby, the net effect caused by the reduction and redistribution of eddy currents due
to a defect is reflected in the variations of the probe coil’s resistance and inductance. As shown
in Figure 2.1 (b), the EC inspection monitors the impedance changes when the probe coil scans
along the object surface. The effective inductance and resistance of the coil changes relative to
the value in air [2, 5-7].

12

Primary magnetic field

Primary H direction
Coil

X

Direction of
primary current
Secondary
magnetic field
Conducting specimen
(a)

A: Coil in air
B: Coil over a defective
nonferromagnetic specimen
C: Coil over a defect-free
nonferromagnetic specimen

A
B

Direction of
induced current
Induced H direction

C
(b)

R

Figure 2.1 Principle of the EC inspection: (a) A typical EC probe above a conducting specimen
under test and (b) The measurement of coil impedance [6]
A typical EC testing system is shown in Figure 2.2. Such a system involves excitation, signal
preparation, demodulation, and analysis [2, 5-7]. A probe consisting of a coil or a set of coils is
excited, and the interaction of induced electromagnetic field with the sample is measured.
Traditional EC technique monitors the induced voltage of a pick-up coil (same or different from
the excitation coil) or collects the variations in inductance and resistance of the same source coil.
A demodulator is a phase-magnitude receiver. As the probe scans above the specimen, response
signals are represented in the impedance plane after noise filtering, amplification or other signal
conditioning circuitry. Discrimination, summation or comparison, and signal processing may be
included at the signal interpretation stage.

13

Crack

Eddy current
Receiver/
Measurement

Primary magnetic field
Input
current
source

Induced
currents
Secondary magnetic field
Signal/Image
display

Demodulator

Phase

Imaginary

Coil probe

Real
Defection
analysis

Figure 2.2 Eddy current testing system
The ability to detect a flaw depends on the orientation of the defect’s largest dimension relative
to the flow path of induced currents. Discontinuities are most detectable when their longest
dimensions are perpendicular to induced currents [7, 30]. However, edges or boundaries in the
test specimen also distorts current flow paths and generate a signal similar to a flaw response,
and hence must be eliminated by signal processing.
2.2 Skin Depth and Development of EC Techniques
Conventional EC techniques have a limited field penetration through the material depth as
dictated by the skin effect [7]. Skin depth  is characterized as:



1
f

(2.7)

where  is the conductivity of conductor under test,  is the permeability of conductor, and

f is the excitation frequency. The magnitude of induced eddy currents decreases exponentially
in the conductive material. Hence, the amplitude of fields in the conductor at depths along X-axis
is expressed as [7, 9, 31]:

14

J ( x)  J 0  e  x / 

(2.8)

The standard skin depth of penetration is defined as the depth where the eddy current density is
about 37% (1/e) of its surface value. Since greater penetration depth of eddy currents is needed
to inspect embedded flaws, the selection of excitation frequency is critical [5-7, 9, 31]. Detecting
a deeper flaw requires lower excitation frequency. Figure 2.3 presents how the skin depth affects
the distribution of eddy current densities inside a copper plate at high and low frequencies.

Copper wire
100Hz EC
Skin depth:   6.5mm
37% of surface induced
current density
Copper plate:
20mm thickness

(a)
Copper wire
1kHz EC
Skin depth:  2.06mm
37% of surface induced
current density
(b)

Figure 2.3 Demonstration of skip depth in EC testing (Comsol 3.5 simulation):
(a) 100 Hz EC and (b) 1 KHz EC
The capabilities of conventional EC methods that employ single frequency excitation are limited
to detecting defects at one or two skin depths. Multi-frequency EC techniques are introduced to
provide additional information related to induced fields at different depths [7, 9, 32-34]. The
design of a multi-frequency instrument needs to employ multiplexing strategy in the time or
frequency domain [6-7]. When excitation signals at a swept-frequency mode are employed
simultaneously, a frequency-division de-multiplexing method is applied to isolate individual

15

response signals. In references [35-37], an EC probe operated at the sinusoidal swept-frequency
from a 100Hz to several MHz is used to inspect different layers. Multi-frequency EC testing is
particularly useful in removing undesired signals using advanced signal processing or
information mixing. Different algorithms have been utilized to selectively suppress unwanted
indications due to geometry and retain defect indication [38-41].
The inclusion of a broad range of frequencies led to pulsed excitation in EC testing that applies a
square, triangular, or a saw tooth waveform as a source current [7, 31, 42]. PEC techniques
measure transient signals that contain a broad spectrum of frequencies and provides capabilities
to detect and characterize deep corrosion and hidden defects. This technique also offers
advantages in correlating depth information with time-dependent characteristics in the response
signals [2, 43].
Owing to deeper field penetration, the application of PEC techniques has been extensively found
in the detection of cracks hidden inside multilayered aircraft components [2, 44-48]. Studies and
details of PEC technique in detecting deeply buried cracks around fastener sites are investigated
in Chapters 3 and 4 of this dissertation.
2.3 Configurations of EC Coil Probes
The distribution of eddy currents primarily depends on the source coil design. The pattern of
induced currents is decided by the size, orientation and shape of the source coil. Controlling the
eddy currents distribution is critical for detecting discontinuities at all possible orientations [30].
2.3.1 Conventional Coil Probes
Common EC probes are designed as a flat coil, pancake coil, or encircling coil [7]. As shown in
16

Figure 2.4, coil configurations depend on different applications: 1) surface probes (Figure 2.4 (a))
that can be pancake shaped to scan along the surface and yield magnetic flux perpendicular to the
surface; 2) Bobbin (inner diameter) probes (Figure 2.4 (b)) are wound on a bobbin to move along
the inside of the tubes and produce axial magnetic flux, 3) outside diameter probes (Figure 2.4
(c)) that can be wound to encircle the specimen [2, 49-50].
Primary magnetic field H
Coil

Coil

(a)

Eddy current
flow
Crack

Coil
(b)

(c)

Figure 2.4 Typical EC probes: (a) Pancake type coil [50] (b) Bobbin type (inner diameter) coil [2]
(c) Encircling type (outer diameter) coil [2]
Coil probes can operate in double-function mode, separate-function mode and hybrid mode, as
displayed in Figure 2.5. The double-function operation includes two approaches: 1) An absolute
probe which generally contains a single coil that is used as the source excitation as well as sense
changes relative to induced magnetic field; 2) A differential probe which has two active coils
usually wound in opposition for eddy currents generation and as well as pickup. The two coils
give no signal in a flaw-free area while they produce a differential signal when the probe scans
over a defect in the sample under test. The impedance change of double-function coil indicates
defect existence.
Absolute probes can be overly sensitive to material variations, temperature changes, lift-off and
other variations during inspection. Differential probes are relatively insensitive to slow or

17

gradual discontinuity or composition changes of a test structure. Additionally, a differential probe
detects large flaws only when they are over the beginning and end locations of the flaw, since the
output signal is canceled when it is placed over uniform parts of the defective region [2, 49-51].

Double-function probe:
single coil/coils for
source and sensing

(a)

Separate-function probe:
two separate coilsone for source and one for sensing

(b)

(c)

(d)

Figure 2.5 Coil probes-mode of operation [49, 51]: (a) Double-function probe in absolute mode
(b) Double-function probe in differential mode (c) Separate-function probe in absolute mode (d)
Separate-function probe in differential mode
Separate-function probes employ a primary coil to provide source currents and a secondary coil
(pick-up coil) to sense the secondary field due to eddy currents. Separate-functions probes can
also be used in an absolute or differential mode. This probe type is also called Transmit/Receive
(T/R) probe. The configuration of transmit coil is specially designed for optimizing the eddy
current flow pattern, and the receiving coil configuration is designed to achieve a maximum
sensitivity to defect [2].
2.3.2 Planar Coil Probes
It is fundamental to EC testing that defects that distort the continuity of induced currents are
detectable. Therefore, the configuration of excitation coil is critical since it decides the pattern
and distribution of induced currents [7, 52]. Additionally, coil probes provide high sensitivity to
defects if a flaw dimension is comparable to the size of coil transducer. Therefore, the shape,
18

cross-section, and size of the source coil vary for different applications [2, 52]. In the case of
conventional coil probes, small diameter coil probes are preferred for higher sensitivity to small
cracks. However, coil size is also crucial to obtain a signal with high signal-to-noise (SNR). With
the development of microelectronics and integrated circuits, planar coil probes are being
investigated in NDT areas and pursued particularly in EC probe applications [2, 52-53]. Planar
coils are made of flexible windings with a certain number of turns that are fabricated on a printed
circuit board (PCB).

Figure 2.6 Planar coil configurations [52-53]
As shown in Figure 2.6, the patterns of the planar windings can take different forms depending
on the required induced eddy current directions [52-53]. Four research groups independently
studied planar coil probes designed for electromagnetic NDE.
The first study of planar coils as NDT sensors was introduced by General Electric (GE) [52-55].
In order to inspect complex engine parts, they deposited the separated driving and sensing coil

19

elements in a layered flexible structure as an array of EC planar probes. Their follow-on work
conducted FE modeling and experimental studies for probe designs optimized for the inspection
of rotating aircraft engine parts. They were able to detect Electrical Discharge Machining (EDM)
notches 0.01’’ long and 0.005’’ deep.
A second group that has investigated the design of planar coils is JENTEK® Sensors Inc. They
introduced the planar coil probe with Meandering Winding Magnetometer (MWM) and a signal
processing algorithm using grid measurements (a model-based technique) [52, 56-58]. MWM
coils consist of thin and conformable coils. Multiple MWMs can be integrated to form a sensor
array. The coil probe has a single-drive winding (primary windings) and one or more sensing
elements on a thin and conformable substrate (secondary windings). Figure 2.7 (a) shows the H
field distribution introduced in a MWM probe, which is generated by the linear current ID in the
primary windings. The voltages of the secondary windings in VS1 and VS2 measure the field
changes. The distance  between windings of the planar meander coil can be optimized. In
aging aircraft applications, the permanently mounted MWM array sensors were able to detect
cracks of 40µm length and 20µm depth during the fatigue test of aluminum specimens [59-60].

20

z

ID

y

Primary
winding

x
Material under
test

H

VS 2

VS1

Secondary
winding

ID

(a)

Mesh coil
Meander coil
Induced voltage

B

Excitation current
Crack

Testing material
(b)

Figure 2.7 Two designs of planar coil probes: (a) a basic MWM probe [56] and (b) a
meander/mesh coupled probe [61-62]
A similar design using a pair of planar coils – a planar meander as the source coil but a planar
mesh as the pick-up sensor was developed by collaborative effort between Kanazwa University
in Japan and the University of Toronto [52, 61-63]. Figure 2.7 (b) shows a schematic of the
planar meander/mesh probe. The application of this probe was mainly for PCB inspection.
The fourth study of planar coil probes was carried out in structural health monitoring of aircraft
structures [52, 64-65]. A conformable sensor film that uses planar rectangular or meandering coil
configuration around the fastener shank is integrated with EC system for in situ monitoring of
fatigue cracks at fastener holes in layered metallic joints. Other efforts to study planar coil probes

21

include the IOnic EC probe [66] that was specifically produced to detect a unique
structure-friction stir welding, and a planar rectangular coil that was designed and optimized in
[67].
Planar technology allows large scale production of precise and reproducible coil probes [68].
Additionally, planar coil technology enables the possibility of integrating identical array
elements into an EC probe for fast inspection [8, 68-69]. Construction and characterization of EC
probes with planar coils can be conducted using numerical investigations. Numerical studies are
used in the design process of planar source coils for generating eddy currents in different path
patterns [70-72]. PEC techniques using planar coil probes have shown considerable promise in
detecting and monitoring fatigue cracks in layered structures [52].
2.3.3 Limitations of Coil Sensors
Traditional EC methods use coils as sensors (pick-up coils) to measure changes in the magnetic
field. Based on the Faraday’s law of induction, the voltage response of a pick-up coil is
proportional to the rate of change of the induced magnetic field not the magnetic field itself.
Therefore, it results in poor SNR ratio particularly at low frequencies [2, 14, 69, 73]:

Vcoil signal  Nr 2

dB
 Nr 2 f
dt

where N is the number turns of coil wire, r 2 is the area of the loops and dB
change of magnetic field that is proportional to the operating frequency f .

22

(2.9)

dt

is the rate of

Magnetic
field sensor
I
I

Coil current flow

Hall element sensor

Magneto resistor

Figure 2.8 Hybrid probe [49, 74]: EC coil with magnetic field sensor
Consequently, coil sensors are fundamentally limited by the poor sensitivity at low frequencies.
Unfortunately, the sensitivity at low frequency is needed in the inspection of thick components
and subsurface flaws. Similar to traditional coils, planar coils also present limited sensitivity
when they are used as pick-up or inductive coils for sensing low frequency magnetic field.
Alternately, EC probes that are operated in hybrid mode have been developed to overcome those
limitations. As shown in Figure 2.8, hybrid EC techniques employ conventional or planar coils to
generate eddy currents, and utilize magnetic field sensors to directly measure field variations
associated with discontinuities [2, 6, 49].
2.4 Magnetic Field Sensors for Hybrid EC Testing
The magnetic field associated with induced currents can be measured using magnetic field
sensors such as magnetometers, superconducting quantum interference devices (SQUID), Hall
sensors, magnetoresistive (MR) sensors, or magneto-optic sensors [51]. In contrast to pick-up
coils, electromagnetic field sensors are sensitive to weak magnetic fields, obtain linear
characteristics for a broadband of frequencies and produce a voltage output proportional to the
magnetic field [2, 14, 69, 73]. With the help of electromagnetic sensors, hybrid EC techniques
have enhanced the sensitivity and spatial resolution of detecting subsurface defects [68].
23

Therefore, field sensors are finding increasing applications at low frequency EC testing and
electromagnetic field imaging [2, 14-15].
Hall element sensors utilize the Lorentz force that affects the trajectory of electrons in a
magnetic field, and produce a proportional Hall voltage across a conductor or semiconductor that
carries currents. Hall sensors are used mainly in the mT range and can be easily integrated on
microelectronic circuits. However, Hall devices typically suffer limited sensitivity (much lower
than MR devices), high level of noise, a relatively large offset and a limited dynamic range [2, 14,
73]. Other magnetic sensors such as fluxgates in EC testing consist of an advanced
magnetometry technique. A Fluxgate sensor is a solid state device that measures the intensity
and direction of a magnetic field with a sensitivity range of 10

-10

to 10

-4

T. However, these core

saturation magnetometers require a large size for sufficient sensitivity, so lateral resolution is
relatively low [75].
SQUID devices are the most sensitive magnetometers that have been applied in NDE areas. They
are based on the interactions of electrical currents and magnetic fields. When the
superconducting wires are cooled, SQUID sensors become superconductors below a certain
temperature. Although SQUID sensors have exceptional low-frequency sensitivity and stability,
testing systems using SQUID devices are of very high complexity. They require cryogenic
cooling to reach the superconducting transition temperature. Therefore, the expensive cost and
maintenance associated with the closed cycle refrigeration or cryogenic system significantly
restrict their applications.
MR sensors based on anisotropic magnetoresistance (AMR) or giant magnetoresistance (GMR)
24

effects offer high sensitivity over a wide range of frequencies. The hybrid EC technique that
utilizes MR sensors has been successfully introduced for higher sensitivity, particularly in low
frequency electromagnetic NDE applications [14, 73-76]. Low frequency and multi-frequency
EC methods using MR sensors are particularly useful in detecting hidden corrosion that typically
produces a gradual thinning of structures. It is difficult to image corrosion using conventional
techniques [14].
With the development of sensor fabrication and commercial packaging technology, MR sensors
can be integrated with EC probes [14]. Research of planar coils used for EC probes reported the
sensitivity can be improved by introducing MR sensors [57].
2.5. Magnetoresistive (MR) Sensors
2.5.1 Magnetoresistance
Magnetoresistance is a galvanomagnetic phenomenon caused by the effect when a magnetic field
applied to magnetic material. With the force exerted on the material electrons, they are redirected
or scattered when they try to travel along microscopic domains that form a consistent magnetic
orientation, as demonstrated in Figure 2.9 (a). The amount of redirection and scattering is a
function of magnetization M that is decided by the direction of external magnetic field H A
shown in Figure 2.9 (b) [51, 77]. Therefore, the resistance variation R/R of magnetic material
called magnetoresistive effect is a function of the external magnetic field B [78]:
R=f(B)

(2.10)

Ferromagnetic thin film material is commonly used in MR sensing, and as seen in Figure 2.9, the
rotation direction of magnetization M is determined by the film shape and the easy axis direction
25

that is designed during the film deposition. Hence, the application of an external magnetic field
results in resistance changes associated with the rotation variation of magnetization direction
[78].

No external field

Electron
drift path

Current flow
Electron
Strong external field
drift path

Magnetic domains

(a)

(b)
Figure 2.9 Magnetoresistive effect in a thin current strip [51, 77]
2.5.2 Anisotropic Magnetoresistive (AMR) Sensor
MR phenomenon was first studied in anisotropic magnetoresistive (AMR) materials such as iron
and Permalloy (NiFe), and it was practically developed in magnetic sensing later when thin film
technology was introduced [77]. Anisotropic resistance R depends on the angle  between
applied current I and magnetization M as shown in Figure 2.9 (b). This distorts electron orbits
and results in different scattering. This is expressed as a function [14, 73, 78]:

R  R0  R c o 2s ( )

26

(2.11)

Bias current Permalloy

Out - Shorting bars

Vb

Gnd

Easy axis

Out +
(a)

Sensitive axis

R / R
Magnetoresistance
Linear operating
region

 900

00

450

900 Angle (ɵ) of

Magnetization field to current flow
(b)
Figure 2.10 AMR device: (a) Barber-pole structure for an optimum alignment and (b) Resistance
change R/R vs. angle  , and resistance R vs. applied field H [73]
The anisotropic resistance is minimum when the magnetization direction is perpendicular to the
external current direction, since electrons in the film travel freely in microscopic domains. On
the other hand, the maximum resistance R is produced when the two directions are perpendicular
to each other, and electron orbits are blocked due to the magnetization force. According to Eq.
(2.11), the maximum sensitivity and linearity is found at an angle   45º. This 45º optimum
alignment is usually designed by patterning a barber-pole configuration. As illustrated in Figure
2.10, the configuration consists of diagonal strips of highly conductive metal where the current
flows in the 45º direction.
Two configurations have been used in MR material sensors: R/R and dR / dH . R/R or

27

(Rmax-Rmin)/Rmin measures the absolute resistance change in percentage for a MR device.

dR / dH or (Rmax-Rmin)/(Hsat-0) measures the resistance change as the magnetic field increases
from zero till the field Hsat that achieves maximum resistance change,. The dR/dH configuration
is preferred when the sensitivity to small magnetic field is needed [77]. In general, a ratio MR is
traditionally used and it is defined as:

R
-R
MR  m a x m i n
Rm i n

(2.12)

Most AMR sensors commonly use Permalloy deposited onto silicon substrates in a Wheatstone
bridge configuration. With an external magnetic field applied perpendicularly to the deposited
film, the magnetization vector rotate and change the angle  . Therefore, the corresponding
resistance variation produces a measurable change of voltage output in the Wheatstone bridge.
AMR thin film can have a resistance change MR level of 2% to 3% [73]. Available commercial
AMR sensors are described in references [69, 78].
2.5.3 Giant Magnetoresistive (GMR) Sensor
Recent developments in thin-film technology have found a large resistance change in films when
a magnetic field is applied to multiple thin-film layers. This giant MR effect was discovered in
1988 [73, 78-79]. GMR films have two or more ferromagnetic metal layers separated by a
non-magnetic metallic spacer layer. The spacer layers need to be thin relative to the average free
path of electrons and this causes free motion of electrons from one layer into the other layers
instead of electron scattering [14].
As displayed in Figure 2.11, the spin due to material electrons generates small magnetic fields

28

when structures of magnetic and non-magnetic materials are formed in thin layers. These layers
are automatically coupled in ferromagnetical mode, Figure 2.11 (a) (where the magnetic layers
are aligned in the same direction) or antiferromagnetical mode, Figure 2.11 (b) (where the
magnetizations are opposite).

No external field

With external field

Magnetic
layers
Spacer
layers
(a)

(b)

Resistance (kΩ)

Layer orientation
4.2
4.0
3.8
3.6
-400

0
400
Applied field (oe)
(c)

Figure 2.11 Illustration of the GMR effect [14]: (a) Lots of scatterings due to the alternating
magnetization of the layers (b) Reduced scatterings when the magnetization of the layers is
aligned by an applied field (c) Resistance variation as a function of an applied magnetic field
Without magnetic force, electrons are not able to move across magnetic layers without
experiencing adverse interaction with the formed magnetic domains. With an external magnetic
field applied to the structure, the anti-ferromagnetic coupling is overcome, and scattering of
electrons is reduced at layer interfaces. Therefore, the resistance variation is produced in Figure
29

2.11 (c). The MR level is maximum when the magnetic layers are antiparallel and minimum
when they are parallel. Typical MR levels are about 10% to 20% [14, 77, 79].
The commonly used structures in GMR sensor elements are unpinned sandwiches,
antiferromagnet pinned spin valves, antiferromagnetic multilayers and magnetic tunnel junction
[77-79]. GMR effects can be obtained by different arrangements of changes in the relative
orientation of the magnetization in adjacent layers, and antiparallel configurations of magnetic
alignment in thin ferromagnetconductor multilayers when an external magnetic field is applied.

Flux concentrators

Shielded devices

Active devices

Figure 2.12 Microscope picture of a GMR sensor fabricated by NVE Inc. [14]
The challenging work in GMR research is finding materials and structures that exhibit large MR
ratio at low magnetic fields. Developed structures include NiFeCo-CoFe-Cu multilayers
(currently manufactured by NVE Inc. as shown in Figure 2.12), and granular films of Co–Cu and
Co–Ag. They are heterogeneous alloys and exhibit GMR effects due to spin-dependent scattering
in which metal particles are aligned or re-oriented and result in resistance variations with an
30

applied magnetic field [68, 77-79].
GMR sensors are commercially available [69, 73]. Thin-film GMR materials are deposited on
silicon substrates and can be fabricated into configurations with voltage output such as resistors,
resistor pairs or half bridges, and Wheatstone bridges. GMR multilayers present the sensitivity in
the form of R/R or dR/dH. They are similar to AMR sensors but with higher linearity in their
MR response [68]. Additionally, GMR sensors have better directional characteristics than AMR
sensors. MR sensors detect the vector component of a magnetic field along their sensitive axis.
GMR sensors are insensitive to fields applied perpendicularly to the sensitive axis. In contrast,
the sensitivity of AMR sensors is reduced by a field perpendicular to the sensitive axis due to a
cross axis sensitivity. It might reverse the sensor response at high field values [75, 80-81].
Based on MR effect and magnetoresistive materials, the use of these solid-state magnetic sensors
represents a significant advance in sensing low fields over traditional inductive probes. In
addition, the small size and low power consumption of these sensors enable the fabrication of
compact array sensors on PCB boards and on-chip sensor arrays. Thin-film sensors can be
fabricated on a planar board to locally sense the magnetic field in a region as small as tens of
micrometers. They could also be arranged in arrays for high resolution imaging.
2.5.4 NDE Applications of MR Sensors
The use of MR sensors in EC systems and electromagnetic imaging has grown considerably in
the past few years. Their linear response makes them suitable for detecting low amplitude
electromagnetic field when a low-frequency or pulsed excitation is applied [2, 8], and they have
been used successfully for detected subsurface cracks under riveted structures [14, 16-17, 76]. In
31

particular, GMR devices have higher directionality, sensitivity, and wider bandwidth compared
to other MR sensors [2, 14, 51, 75], Therefore, GMR based EC testing exhibits significant
advantages in detecting complex geometry such as layered component inspection [44, 81]. The
directional property of GMR sensor had been used to locate edge cracks in aluminum specimen
[34, 81]. A needle type GMR imaging technique named the SV–GMR system was designed for
the inspection of a bare PCB structure, and for the measurement of magnetic fluid density
injected in a living body [74-75].
High resolution GMR elements fabricated in a small package of sensors arrays have been
developed. An interesting application of this array probe was found in the evaluation of metal
medical implants for invisible cracks [8]. A linear array of 20 GMR elements was packaged to
image a hole defect in a steel plate using 1 Hz excitation. Designs of GMR array probes in
identical elements were studied to detect subsurface cracks [14, 68]. High density GMR arrays
are especially promising for rapid scanning of large area as well as high resolution imaging
[34-35]. Another type of GMR array sensors that use two-directional elements was investigated
in EC testing to detect surface cracks of unknown orientation. They measure both X-component
and Y-component of the magnetic field at a same point under examination [81].
2.6 EC Techniques for Inspection of Riveted Structures
Commercial EC probes such as sliding probe fabricated with multiple coils in drive/pick-up
operation, and remote field EC coil probe have been investigated for detecting aircraft skin
structures employing coil sensors at low frequency excitations [82]. However, sliding probes can
only detect defects in one direction and lead to false call or undetected flaws in the case of rivets
32

that are not aligned in a row [10].
As an improvement, imaging based EC techniques enable efficient flaw detection using richer
and more comprehensive data than traditional Lissajous patterns obtained from a single EC scan
[18, 83-84].
2.6.1 EC Magneto-Optic Imaging
A Magneto-optic (MO) sensor is based on Faraday rotation effect, in which the polarization
plane of a linearly polarized light rotates in the presence of an applied magnetic field. When
polarized light is transmitted through the specimen, the direction of polarization is rotated by the
magnetic field associated with the induced currents in the specimen. A MO sensor consists of a
thin film of bismuth-doped iron garnet grown on a substrate of gadolinium gallium garnet and
directly produces an image. The variations due to the presence of structure like a rivet or defect
generate a non-zero normal component of magnetic field. The response is imaged and viewed as
the black and white images in Figure 2.13 (c) [85-86].
Shih and Fitzpatrick in the early 1990s presented a MO imaging system for detecting surface and
subsurface cracks, and corrosion in aircraft skins [85-86]. As illustrated in Figure 2.13 (a-b), this
technology employs an induction foil that carries an alternating current and induces eddy
currents in the conductive sample under inspection. The generated magnetic flux is tangential to
the specimen surface under normal conditions. Discontinuities in the specimen divert uniformly
induced currents and produce a normal component of the magnetic flux density that is detected
and imaged by MO sensor.

33

Sensor (garnet film)
Linearly polarized light
after rotation

Linearly polarized light
before rotation

Path length

(a)

(b)

a crack
rivet with
crack

rivet without
crack
rivet

(d)

(c)

Figure 2.13 EC-MO imaging technique: (a) Faraday rotation effect in a MO sensor (b) Schematic
of the MO imaging system [85] (c) MO images of riveted structures (d) Images of riveted
structures using LMOI system in Europe [87]
A similar system, named the linear MO imager (LMOI) was patented in Europe [87]. It acquires
an image based on the stroboscopic approach. A riveted structure results in an image with two
semicircular shapes as shown in Figure 2.13 (d). Instead of using polarized light, Cheng et al [88]
combined a laser into the MO imaging system. Multiple tests have shown that the MO imaging
technique is fast, reliable and capable of detecting fatigue cracks and corrosions in large areas
such as aircraft skins. However, current MO images of rivet holes, cracks, and corrosion lack a
34

quantitative measurement of fields. MO imaging systems are also costly [89-90].
2.6.2 Other EC Techniques
Wincheski et al. [91] proposed a self-nulling EC probe to detect cracks under ferromagnetic
protruding head fasteners. A flux concentrator is introduced to focus the magnetic flux field and
minimize the flux linkage through the pick-up coil. In this way, only a minimal magnetic field is
able to reach the interior area of the probe unless any discontinuity is present in the specimen
under detection. Later, he developed a rotating self-nulling probe incorporating a commercial
GMR sensor to enhance low frequency capabilities [8, 92], as shown in Figure 2.14. With image
processing techniques, their system improved the SNR and enhanced the detection of deeply
buried flaws in conductive materials. The use of this self-nulling probe that prevents the
th

saturation of MR sensor has imaged flaws in the 10 layer of 13 layers of 1 mm thick aluminum
plates using a 185 Hz excitation frequency [14].

RMS
voltmeter
Drive coil

Current
source

Pick-up coil
or GMR sensor

Flux concentrator
(a)

Rivet
Self-nulling
probe
Scan location
(b)

Figure 2.14 Self-nulling EC probe: (a) Probe schematic and (b) Inspection of ferromagnetic
protruding head fasteners [91-92]
Similar to the GMR based self-nulling probe, a design using D-shaped excitation coils and a
GMR sensor was introduced for detecting buried cracks and flaws emanating from fastener holes
[93]. As displayed in Figure 2.15 (a), the D-shaped coil that is placed with its straight edge above
35

the fastener, rotates around the center of the fastener. The GMR sensor is attached to the
excitation coil and positioned above the fastener edge with sensitivity axis tangential to the edge.
Using a rotational scan, corner cracks of 2.5 mm in length were detected around a bolt hole in the
nd

2

layer of a 13 mm thick two-layer structure. Linear scan inspection had been also investigated

using this probe. Transverse notches of 2 mm length, 1 mm height were detected around a row of
holes in a two-layer specimen using linear scan probes.

Axis of sensitivity

D-coil

Buried crack
Rotation about
the center of the hole
GMR sensor

Stainless steel fastener

(a)

Fastener hole

Slot in third layer AMR sensor

Excitation coil
in PCB board (b)

Figure 2.15 EC-GMR probes for riveted structure inspection: (a) Schematic of a rotational
D-shaped coil and GMR based probe [93] and (b) A sheet current and AMR sensing probe [17]
A sheet current in a double rectangular spiral probe has been used to detect slots in the presence
of stainless steel fasteners by Avrin [17]. An AMR sensor placed at the center of the coil is
sensitive to the magnetic field perpendicular to the specimen surface. When the probe size is
much larger than the fastener hole geometry (Figure 2.15 (b) shows the probe size of 19x19cm),
it is insensitive to small lift-off variations. Subsurface slots (9.5 mm long, 6.3 mm height and

36

rd

0.25 mm wide in the 3 layer, 19 mm from the top of a three-layer 25 mm thick aluminum plate)
were detected.
It has been indicated that the inspection of structures containing ferromagnetic components
within thick multilayer is a challenging task. For the detection of defective ferrous fastener
structure, a design proposed by Ko and Steffes [21] magnetized fasteners during inspection, to
reduce the noise caused by the permeability. The use of a GMR sensor coupled with a lock-in
amplifier increased the sensitivity. The EC data obtained at low frequencies was processed to
nd

detect 2

layer defects occurring 10 mm below the surface of an aluminum sample with steel

fasteners. However, the detected cracks were large (about 10 mm).
In this dissertation, the EC systems using the planar coil probe with 3-component MR sensors are
studied to detect cracks hidden in non-ferromagnetic and ferromagnetic riveted structures. The
configuration of source coil is designed to generate a uniform magnetic source field. Transient
and low frequency EC excitations are investigated for improved sensitivity to subsurface cracks
with the help of MR sensors.

37

CHAPTER 3

EC-MR SENSOR SYSTEM – PULSE EXCITATION

3.1 Introduction
Pulsed excitation produces transient signals with a wide range of frequency components and
hence it contains more information compared to single frequency excitation. This chapter
presents a study of PEC-GMR system. The detection of cracks at steel fastener sites and small
cracks embedded in multilayer aircraft skin are investigated numerically and experimentally. A
novel implementation of FE numerical model is developed to study the feasibility of defect
detection in fasteners using transient EC techniques.
3.2 Background
Transient electromagnetic testing employs a voltage pulse or current pulse to diffuse into a
conductive material. Induced transient currents are attenuated as they diffuse through the
structure as the electromagnetic pulse energy is dissipated by Joule heating [94].
3.2.1 Skin Depth in Transient Fields
The analytical derivation of skin depth assumes a planar electromagnetic field propagating into a
semi-infinite conductor [7]. Induced eddy currents decay exponentially with depth along the
conductor in accordance with skin effect. The skin depth in conventional EC testing was
presented in Chapter 2, Section 2.2. This section derives the skin depth expression due to a
transient excitation.
The governing equation in terms of time-dependent magnetic field B within a material is given
by:

38

 2 B   

2B
B
 
2
t
t

(3.1)

where  is the electrical conductivity,  is the material permeability and  the permittivity.
For a good conductor with  <<  , the first term in the right hand side of Eq. (3.1) can be
neglected in the frequency range of Hz-MHz [95], reducing Eq. (3.1) to:

 2 B  

B
t

(3.2)

Similar to the diffusion of heat in solids, the solution of B can be estimated from:
B
B

and  2 B  B /  2
t
τD

(3.3)

where τ D is the characteristic diffusion time and  is a characteristic length for the system,
which is dependent on the conductor geometry.
Since the magnetic field vector can be separated in space and time domain, the general solution
to diffusion equation in Eq. (3.4) is obtained by the separation of variables method in Eq. (3.5) as
[95]:

B (t )  f (e  t /  D )

(3.4)

2
B (t )  F ( z )e  k t / 

(3.5)

Hence, the characteristic diffusion time τ D that is in the form of  D   2 can be
expressed as:

1

D



k2



(3.6)

As opposed to the standard skin depth of EC testing in Eq. (3.7):



1
T

f


39

(3.7)

the skin depth for the transient response is obtained as:

1





D
1

k


(3.8)

Comparing Eq. (3.8) and Eq. (3.7) gives the relation:


1

 1.77

1/ 

(3.9)

Therefore, it is found that the penetration of transient electromagnetic field within a conductor is
about 1.8 times greater than the standard depth for the steady-state case. This scenario is tested
by numerical simulations. Figure 3.1 compares the skin depth calculated for conventional EC
field to that of transient field. It is observed that a pulsed excitation offers deeper penetration into
the conductive plate.

Copper wire
Skin depth:   6.5mm
37% of surface induced
current density
Copper plate:
20mm thickness

(a)
Copper wire

Skin depth:  11.5mm
37% of surface induced
current density

(b)

Figure 3.1 Skin depths of conventional EC and transient EC fields (Comsol 3.5 simulation): (a)
Conventional 100Hz EC result: induced eddy current and skin depth and (b) 100Hz square-wave
PEC result: induced eddy current and skin depth
3.2.2 Transient Signal Characteristics
Transient field can be generated by two modes, namely current driven or voltage driven [96]. In
40

the current driven mode, a constant current is provided regardless of the coil inductance (within a
specified range). In the voltage driven mode, the driver applies a given voltage drop across the
excitation coil. The voltage driven mode is generally less complicated in design and allows the
adjustment of the current. However, the magnetic field generated by the excitation coil is
proportional to the coil current not the voltage. Therefore, this dissertation uses the current
driven mode to employ a transient source.
Similar to ultrasonic testing where the measured time of flight in the received signal can
determine a defect’s depth, transient eddy current propagation through the material and the
transient shape of the response signal are related to discontinuities at different depths [52, 94-97].
Transient parameters and features allow flaw discrimination and characterization in the time
domain [7, 52]. Interpreted in the time domain, the defects that are closer to a conductor surface
activate PEC response earlier than those located further below the surface. The information about
sub-surface flaws is mostly contained in the tail part of the transient signal.
The most common features in transient characteristics of PEC signals are the peak amplitude,
time to peak amplitude and time to zero crossing [52, 94, 96-98]. The peak amplitude is used to
determine the defect size. The time to zero crossing is popularly used to find the depth of a flaw,
and the time to peak amplitude can be used to identify the defect depth or material thickness.
However, a balancing procedure is required to make those features indicative of flaw presence
[52, 94, 96-97]. A common balancing procedure used is to subtract a reference signal that is
collected over a region without flaws. A typical reference-subtracted PEC signal and its features
are demonstrated in Figure 3.2 (a).
41

GMR output (V) Source current
(A)

1
0
-1
0

0.002

0.2

0.004

0.006

0.008

0.01

Peak height

0

Zero-crossover point
Peak time

-0.2
0

0.002

0.004

0.006

0.008

0.01

Time (s)
(a)
3-layer conducting specimen
Defect at first layer
Defect at second layer
Defect at third layer

1 x 10

-5

defect at 1st layer
defect at 2nd layer
defect at 3rd layer

Bz(T)

0.5
0

-0.5
-1
0

Travelling time

0.005

0.01

0.015 0.02
Time(s)
(b)

0.025

0.03

Figure 3.2 PEC signals: (a) A typical reference-subtracted transient response and typical features
in the time domain and (b) Transient response associated with defective information at different
depths (Comsol 3.5 simulation)
Since hidden discontinuities in a layered structure take longer time to interact with the attenuated
transient signal, the depths or layers where flaws are present can be inferred from transient
42

rd

signals. As shown in Figure 3.2 (b), the corrosion in the 3 layer interacts with the transient field
after deeper penetration and hence is indicated at a later time in the response signal. Furthermore,
this deep defect also reduces the peak magnitude of transient signal.
As a result, the pulsed EC is able to detect discontinuities at different layers with a single
transient excitation. It superimposes a range of frequencies in one spatial location, while the
conventional EC needs to multiplex different frequencies to provide the information at various
depths [5, 99].
3.2.3 Review of Transient EC NDE for Layered Structure
The earliest application of transient eddy current can be traced to the publication by Waidelich
[100], where PEC was used to measure cladding thickness of reactor fuel elements. Furthermore
investigation by Waidelich showed that transient signals presented characteristics that were
independent of the distance between the probe and the specimen under test. This result was
studied as a transient feature insensitive to lift-off [96] that has been investigated in the detection
and characterization of corrosion by Lepine, Lefebvre and Giguere [46, 97, 101].
The earliest study of PEC for crack detection in layered structures with installed fasteners was
conducted by Harrison [102-103]. Giguere also studied the detection of cracks beneath rivet
heads using transient EC techniques [104].
Transient excitation of coil probes with two MR sensors or two Hall sensors in differential mode
have been studied by Lebrun at al. [105-106], and used for characterizing crack parameters. Tai
et al. [107] studied similar transient features for an inversion scheme to qualify the conductivity
and thickness of samples. Moulder et al. [108] and Bieber et al. [109] developed quantitative
43

methods for crack and corrosion detection using C-scan images by the time gating of transient
signals.
Papers by Smith et al. [110-111] presented a PEC technique named TRECSCAN system
(QinetiQ product) for the inspection of aircraft structures. Other PEC techniques were reported
for the examination of layered or riveted structures [112-118]. Table 3-1 summarizes different
PEC systems developed by several research groups and their applications.
Pulsed EC imaging can be generated based on characteristics of the transient response [96].
Since an A-scan measurement refers the transient response at a single position, the mapping of a
feature of each A-scan onto the probe position allows the construction of a C-scan image. Any
time-dependent feature representing the dissipation of transient field associated different depths
can be employed to produce the C-scan image. Therefore, the image produced contains
information about the surface, near surface and subsurface [96, 119]. Data in the form of images
is helpful if defects with complex shapes are encountered [23].
The C-scan measurement can be also generated by means of linear combinations of the
parameters such as peak height, peak arrival time and zero crossing time [96]. The time gating
method forms C-scan images by plotting those peak heights that have a zero crossing within a
given time window. This technique was used for image information at various depths and
discriminate signals from fastener structure against other interfering factors [108].

44

Table 3-1 PEC system summary.

PEC system

Excitation Coil

Sensing

QinetiQ (UK)

Conventional coil

Hall sensor

Corrosions at layered structures
Cracks at riveted structures

Research Institute (France)

Conventional coil

Hall/GMR
sensor

Cracks at riveted structures

Royal Military College & National Research
Council (Canada)

Conventional Coil/
Pick-up coil
Planar coil

Corrosions at layered structures
Cracks at riveted structures
Material characterization
Corrosions at layered structures
Cracks at riveted structures
Corrosions & defects at single layer structures
Cracks at riveted structures

Iowa State University (USA)

Conventional coil

Hall sensor/
Pick-up coil

University of Newcastle & Huddersfield (UK)

Conventional coil

Hall/GMR
sensor

National University of Defense Technology
(China)

Conventional coil

Pick-up coil

General Electric (USA)

Conventional coil

Hall sensor/
Pick-up coil

45

Applications

Corrosions at layered structures

Corrosions at layered structures

3.2.4 Time Domain versus Frequency Domain
Considering  

2
2


 , the transient skin depth in Eq. (3.8) is given by:
T
2Tt Tt

 PW 

2Tt



(3.10)

where  PW is called the pulse width based skin depth. Therefore, increasing the pulse width
(duty cycle) enables deeper transient penetration [95]. The relationship between the width of a
pulse source and the penetration depth of electromagnetic transient wave has been investigated
by Sather [96]. Results indicate that the penetration depth is increased by lengthening the pulse
duration.
In addition, the time interval between successive transient waveforms must be sufficient to allow
each transient response to decay to zero. Since the diffusion velocity of the EC signal is heavily
dependent upon the material, the transient response duration due to one pulse is also material
dependent. Also, the transient response duration increases with the thickness of a specimen under
test. According to Eq. (3.10), a higher value of Tt is required for a higher skin depth, i.e. a lower
rate of pulse repetition is necessary for defect detection along deeper depth [97].
Studies of characteristics of the excitation pulse can be performed in the frequency domain. Two
pulse sources in different forms using Discrete Fourier Transform (DFT) are presented in Figure
3.3. Time-dependent signals are decomposed into their harmonic components in the frequency
domain, and this helps to design transient excitation waveform.

46

1

Current (A)

0.5
0

-0.5
Pulse-1
Pulse-2
-1
0

0.005

0.01

Time (s)

400

Pulse-1

200
0
0

2000

4000

6000

8000 10000 12000 14000 16000

400

Pulse-2

200
0
0

2000

4000

6000

8000 10000 12000 14000 16000

f (Hz)
Figure 3.3 Time domain vs. frequency domain: Transient excitations in different pulse widths
and their DFT spectrum results
Let the transient pulse source is a square waveform:

A 0
source(t )  
0

kT  t  kT  Tt
kT  Tt  t  (k  1)T

(3.11)

where k is an integer, T is the pulse period, and Tt is the excitation pulse width shown in Figure
3.4. The Fourier series of this pulse source are expressed as:

47

source(t )  a0 



 [an cos

m 1

2n
2n
t  bn sin
]
T
T

(3.12)

and the Fourier coefficients are evaluated as:

a0 

T
1
1
source(t )dt  A0Tt

T
T
0

T
A T
n2T
2
2n
a n   source(t ) cos
dt  0 ( s i n t )
T
T
n2
T
0
T
A T
n2Tt
2
2n
bn   source(t ) sin
dt  0 ( cos
 1)
T
T
n2
T
0

(3.13)

If the cycle Tt =1/2T (50% duty cycle), the source is represented in harmonics:

A
AT
1
1
1
source(t )  0  0 [sint  sin3t  sin5t  ...  sinnt ]
2

3
5
n
where n is odd and  

(3.14)

2
. Therefore, the square wave is approximated by a summation of odd
T

harmonics of the fundamental frequency with decreasing amplitude proportional to the harmonic
number. As shown in Figure 3.4, a better approximation is achieved when more sinusoidal
components are included in the summation. The transient field can be numerically studied in the
frequency domain or in the time domain [120-121].

48

Source (t)

2

A0

1

Tt
T

0

Time -1
-2
0

0.01

0.02

0.03

0.04

Time (s)
Figure 3.4 Square waveform as a source of pulse excitation (left) and the reconstruction of the
waveform by adding Fourier series harmonics (right)
3.2.5 Review of Transient Field Numerical Modeling
Theoretical models play an important role to help understand the underlying physics and
application of inspection strategy [122-123]. The landmark work for analytical solution of a
single frequency EC testing and coil impedance calculation was studied in [124-125]. Analytical
methods for solving transient EC testing were implemented in [126-127]. However, analytical
approaches are, in general, conducted for relatively simple geometries such as a conducting
half-space and hence have limited abilities to simulate complex structures. Numerical methods
have therefore been the method of choice [5, 123, 128].
The popular numerical methods are FE analysis, finite difference analysis, integral analysis,
boundary element method, and meshless method. Main contributions in numerical modeling of
transient electromagnetic NDE are summarized in Table 3-2 [128, 129-144]. The approaches
using transfer function or transient circuit method for modeling PEC system have been
introduced in [132, 145-147]. The primary advantage of FE methods is the ability to study
irregular or complex features of geometries in discretized elements [18].

49

Numerically, the transient field can be calculated by two methods: summation of harmonic
components in the frequency domain and step marching in the time domain [120-121]. A strategy
of interpolation in the frequency domain was proposed to reduce the required number of
simulations by reducing the total number of harmonics [137]. However, FE techniques based on
frequency selection or interpolation might suffer from low accuracy and need varying mesh size
for low or high frequency components [126-127]. Therefore transient field modeling in the time
domain is preferred [144, 148]. This dissertation investigates a scheme in the time domain for
efficiently modeling the pulsed EC excitation and GMR sensor signals.
3.3 PEC Testing System with MR Sensor
Planar coils were also designed for the inspection of ferrous riveted airframes [22]. However, in
these applications, conventional planar coils have limited SNR, and the sizes of detectable cracks
are larger than 1 mm and the detected depths are limited to few millimeters below the surface. A
design of a rectangular planar coil in differential symmetry with a GMR sensor array along the
centric axis has been patented by Boeing company in 2008 [149]. The patented device was
designed for scanning layered structures such as aircraft fuselage and wing components. As
shown in Figure 3.5, it incorporates an excitation coil with multi-line conductors on a flexible
membrane. In collaboration with the NDE laboratory at Michigan State University, this probe
was studied for developing an effective EC-GMR imaging system [150]. This dissertation
extends the multi-line probe for the use of a pulsed excitation to enhance the inspection
capabilities.

50

Table 3-2 Summary of transient field modeling and simulation.

Modeling research

Modeling method

Solution domain

Applications

J. R. Bowler (USA)

Transfer function
Integral method
Analytical method

Frequency domain

Material characterization
Conductor at half-space
Crack profile inverse

T. Theodoulidis (Greece)

Integral method
Analytical method

Frequency domain

Conductor at half-space

C. Mandache & T. W. Krause (Canada)

Transient circuit Method
Comsol package (FE method)

Time domain

Layered structure
Riveted structure

F. Thollon (France)

FE method
Transfer function

Frequency domain

Riveted structure

G. Y. Tian (UK)

Comsol package (FE method)
Analytical method

Frequency domain
Time domain

Layered structure

T. Takagi & Z. Chen (Japan, China)

FE method
Hybrid method

Frequency domain
Time domain

Single layer structure
Crack profile inverse

51

Sheet current

GMR sensor array
Sensor axis orientation
Sensor PCB board

Figure 3.5 Schematic of the multi-line planar probe design [149]
3.3.1 Excitation Coil Configuration
To demonstrate the advantages of using planar coil as an excitation source, the induced fields
due to a multi-line planar coil are compared to those due to a pancake coil. A riveted structure
nd

with two cracks in the 2

and 3

rd

layers is studied. The distributions of the magnetic field and

induced currents are investigated by numerical studies. Two coils are excited by a same 1A
current source at 100Hz frequency. Figures 3.6-3.7 present the magnetic fields and eddy currents
generated by the two coil configurations.

1´10

4

10000

0.2
0

0

-1´10
3rd layer crack

4

-0.2

5000

-0.5

nd
(a) 2 layer crack

0
(b)

0.5

Figure 3.6 Simulation results of pancake coil: (a) Tangential component (Bx) of magnetic field
2

(T) and (b) Induced currents (A/m )

52

In Figure 3.6 (a), the pancake coil has 5mm inner radius and 10mm outer radius, and the eddy
currents flow in circular paths and are parallel to the turns of the coil. As shown in Figure 3.6 (b),
the case without crack is used for studying the skin depth associated with a coil configuration.
The maximum density of eddy currents occurs close to coil windings that is also the edge of the
fastener. In the central region of the structure under test, eddy currents are self-canceling.
Meanwhile, eddy currents exponentially decay as the depth increases. The amplitude of currents
induced at the sample surface is reduced by 34.71% at the bottom layer, and the skin depth (37%
of the induced current density at the surface) is about 10mm.
In Figure 3.7 (a), the multi-line planar coil has a dimension of 98mm by 104mm with 2mm
spacing between the wires, and the planar wire is 0.05mm thickness and 0.5mm height. The
multi-line coil is driven by the current flowing in a same direction, and acts like a current sheet.
The multi-line planar coil produces uniform and linear eddy currents. As shown in Figure 3.7 (b),
the induced currents still keep 56.37 % of its energy after penetrating through all three layers.
Therefore, a skin depth of more than 14mm is generated and this provides enhanced sensitivity to
detect buried cracks. Additionally, the disturbances of eddy currents caused by the two defects
around the fastener site generate a measurable magnetic field in the 2
captured by a magnetic field sensor.

53

nd

rd

and 3 layers that can be

I
1.75´10

6

0.2

´104

0

10
5

0
-1.81´10

Normalized EC amplitude

3rd layer crack

6

-0.2
-0.5

nd
(a) 2 layer crack

0
(b)

0.5

0

1

Surface layer
0.5 of riveted
geometry

Bottom layer
of riveted
geometry

Pancake coil
Multi-line planar coil
0
-0.5
-4.5
-6.5 -9.2
(c)

-11.4

Z (mm)

-22.58

Figure 3.7 Simulation results of multi-line coil: (a) Normal component (By) of magnetic field (T)
2

(b) Induced currents (A/m ) (c) Comparison of induced currents due to two coil configurations

Furthermore, the induced currents along the depth due to these two coil configurations, as two
dash lines shown in Figure 3.6 (b) and Figure 3.7 (b) are plotted in Figure 3.7 (c) using the
normalized amplitude. It is seen that the multi-line coil generates stronger induced currents and
provides deeper penetration of the induced field. In conclusion, the multi-line planar coil
produces higher sensitivity to detect subsurface cracks hidden in riveted structures. Moreover,
this coil configuration is relatively insensitivity to lift-off [52, 97, 149].

54

3.3.2 PEC-GMR Probe Operation
Numerical studies have validated the detection capability of the multi-line planar coil. This
planar coil used for pulsed current excitation is studied in this chapter.
As described schematically in Figure 3.8, in the absence of any discontinuity, due to the
symmetry of the coil geometry, the normal component of the magnetic field is zero on the line of
symmetry at the center of the source coil. When the uniform distribution of induced currents is
distorted by a fastener and/or a crack, the zero induced field on the line of symmetry is destroyed.
A GMR sensor placed at this location is utilized to acquire the induced magnetic field. In the
case of pulsed excitation, the induced transient currents diffuse into the test sample. A nonzero
transient signal of the normal component is produced and captured by the GMR sensor. This
measured signal represents information about cracks around fastener sites.

Line of
Multi-line GMR sensor symmetry
coil

Crack

Line of
Line of
symmetry symmetry
Measurement
region

Defect
Discontinuities Defect free Defective
free region
fastener
fastener

Figure 3.8 Schematic of the operation of multi-line planar probe
In this probe design, the induced field and eddy currents due to the return loop current at the
edge sides of the probe are minor. Consequently, similar to MO imaging, but at much lower cost
and simple design, single directional eddy currents in parallel pattern are induced around a
fastener site. Subsurface discontinuities that distort these linear eddy currents are detected by the
55

GMR sensor that measures specific components of the magnetic field.
3.3.3 Giant Magnetoresistive Sensor
As described earlier, GMR sensors show large resistance changes when they are subjected to a
magnetic field [51, 151]. The variation in resistance is about 2% for ferromagnetic materials and
up to 300% for special materials [97]. GMR sensors have been used in low frequency EC testing
[14-17, 21, 24, 76-77, 79-80, 92-93]. In this dissertation, the use of GMR sensors in conjunction
with pulsed EC sensing is investigated. The advantages of this system are its high sensitivity,
small dimension of field receiver, low cost, low power supply requirement, and linear sensitivity
over a broad frequency range (from DC up to 1 MHz). Moreover, the front-end electronics are
simple and relatively inexpensive [14, 152].

55
GMR output (V)

4.5

44
3.5

33
Bias point

2.5

22
1.5

11
0.5
0
0-0.4

-0.3
-0.3

-0.1
0.1
0.2
0.3
00 0.1
-0.1
0.3
Applied magnetic field (Oe)

-0.2

0.4

Figure 3.9 Characteristic curve for the calibration of the GMR sensor
Typical characteristic of the commercial AAH002 GMR sensor by NVE Corporation is obtained

56

experimentally and is shown in Figure 3.9. Due to its unipolar output, the GMR sensor needs to
be biased appropriately to permit bipolar operation before it can be used for field measurements.
Usually, the DC bias field is realized using a coil or a permanent magnet. Once the sensor is
biased, the characteristic curve can be used for calibrating the output of the GMR sensor to
achieve a reliable and quantitative estimate of the magnetic field.
3.3.4 Experimental Set-up
Experimental measurements are performed using a high resolution scanning system. A
two-dimensional raster scan around each fastener is generated. At each scan position, the planar
coil is excited by a pulse. The GMR sensor measures the normal component of the changing
magnetic field due to induced eddy currents in the specimen. It should be noted that a single
GMR sensor at the center of the symmetry line of the coil probe or an array of GMR sensors
along the line symmetry could be used.
A schematic of the overall PEC-GMR inspection system is shown in Figure 3.10. The X-Y
scanner is controlled by a PC, which produces a trigger signal to control the data acquisition at
each scan position. The function generator supplies a square wave current excitation of
frequency 100 Hz and 50% duty cycle as shown. The square waveform amplitude is adjustable
by a power amplifier and it is fed into the multi-line excitation coil. A permanent magnet is used
as a bias field for the GMR sensor. The DC bias is filtered out to get the pure response of the
GMR sensor. A two-stage amplifier is used to amplify the output signal of the GMR sensor. The
amplified output is connected to the data acquisition card in a differential mode to reduce the
noise due to long connecting cables and interference from the environment. At each position, the
57

transient response of the GMR sensor is acquired at a sampling frequency of 50,000 samples per
second for the duration of 2.56 seconds. The measurements are averaged over 256 cycles of the
excitation waveform for further noise reduction.

PC

Function
Generator
Scan area
0.5 mm
resolution

Square wave
excitation

Excitation current (A)

X-Y scanner

Time (S)
Power
Amplifier
Trigger pulse

Biasing field
(Permanent magnet)
Probe

Excitation coil
Channel 1
Differential mode
PC

DAQ
Channel 0
Differential mode

Excitation
current

GMR
Sensor
GMR
output
Amplifier
DC Filter

Figure 3.10 Schematic of the PEC-GMR inspection system
3.4 Inspection of Riveted Structures
The performance of the system was evaluated using multilayer riveted specimens with machined
subsurface cracks.
3.4.1 A-scan Measurement of Transient Field
GMR measurements due to a crack located at a fastener site through the second layer of the

58

sample are illustrated in Figure 3.11. As in ultrasonic measurements, the A-scan signal is the
time-dependent response collected at each scan point. A total of 19 scan positions above the
fastener head are used to collect the GMR A-scan signals. These A-scan signals are the
measurements of the normal transient field (Bz) at 2mm lift-off. Scan position 5 is located at the
left edge of the fastener, scan position 11 is located at the fastener center, and scan position 17 is
located at the right edge of the fastener. Scan positions 17-19 are located at the crack region.
As shown in Figure 3.11, the A-scan signals present a characteristic trend when the probe scans
the fastener region. In the plots in Figure 3.11 (c), the peak magnitude of the GMR response
presents an ascending trend when the probe moves towards the left edge of fastener (Scans 1-5).
The response achieves the highest magnitude at the left edge location (Scan 5). The transient
response magnitude decreases and reaches almost a null point at the center of the fastener (Scan
11). When the probe continues to move to away from the fastener center, the peak magnitude of
transient response increases again and presents a maximum value at the right edge location (Scan
17). The plots in Figure 3.11 (d) show that the peak magnitude of the signal decreases as the
probe moves away from the fastener’s right edge.
The different characteristics of the signals are representative of the sample and defect geometry,
and any discontinuity encountered at the corresponding scan position. Thus, the discriminations
between transient signals at the two edges can be considered as a feature for the detection of
embedded crack.

59

GMR output (V)

Scan 17

A line scan positions: 1-19
Scan 11: Fastener center area
Scan 17: Right edge
Scan 5:
Left edge
6.5 mm
2.87 mm
(a)

0.06
0.6
0.04
0.4

0.2
0.02

Scan 11

00

-0.02

-0.2
-0.04
-0.4
-0.06
-0.6
0

14 mm
6.5 mm

Scan 5
3
1
2
Time (ms)

4

5
x (b)
10

-3

0

GMR output (V)

-0.01
-0.02

Scan1

-0.03
-0.04

Scan2
Scan3

-0.05
-0.06

Scan4

Scan5
-0.07
0

1

2

3

4

5
-3

0.08

Time (ms)

x 10

(c)

Scan17

GMR output (V)

Scan18
0.06

0.04

Scan19

0.02

0
0

1

2

3

4

5

-3
Time (ms) (d)
x 10
Figure 3.11 GMR measurements of the transient field Bz component along a line scan above a

fastener with a subsurface crack: (a) Inspection Geometry (b) Sequence of A-scan signals within
the fastener head region (c) Comparison of transient signals at the fastener head edge areas for
crack indication
60

3.4.2 C-scan Image Measurement of Transient Field
The magnitude mapping using the peak value of each A-scan is performed to obtain the C-scan
image. The experimental GMR measurements of A-scan signal along a line across a defective
fastener shown in Figure 3.12 (a) and the corresponding C-scan data are presented in Figure 3.12
(b). The asymmetry observed in the C-scan image indicates the feasibility to infer the presence of
a defect at the rivet site. The GMR response from multiple A-scan measurements or C-scan
image data is utilized in this dissertation for data analysis and crack detection.

Defective
Fastener

GMR output (V)

0.06
0.04

2.87 mm

Transient signals
A-scan

0.02
0
-0.02
-0.04

GMR output (V)

0.1

Time (s)
0.002

0.004

0.006

Magnitude Projection
Multiple line
scans along
the cross-section

0.05
0
-0.05
-0.1
0

0.008

0.01

(a)

C-scan image
-0.05

Y (mm)

-0.06
0

0

0.05

30
20
10

20

A line scan

40

10

(b)

20
30
X (mm)

Figure 3.12 Three modes of PEC-GMR signals in the inspection of a riveted structure

61

3.5 Time-domain Modeling of PEC-GMR Testing
A time domain based FE model is studied for simulating the PEC-GMR inspection of multilayer
aircraft frame. The proposed strategy provides a faster solution compared to the approach
implemented in the frequency domain [137].
3.5.1 FE Modeling
FE methods based on magnetic vector potentials have been successful in modeling EC NDE
problems [153-155]. In general, Maxwell’s equations introduced in Chapter 2, Eq. (2.1) to Eq.
(2.4) are formulated using vector potentials, along with the following continuity equation and the
constitutive relationships:

 D  
J 


0
t

(3.15)
(3.16)

B  H

(3.17)

J  E

(3.18)

where the variables are:
3

D: electric flux density (coulum/meter )
3

 :electric charge density (coulomb/ meter )

 :magnetic permeability, 4 ´ 10  7 ( henries/meter) for nonmagnetic materials

 : electric conductivity (mhos/meter)
Various formulations have been used for modeling electromagnetic field, including the A-V-A
potential formulation, and the Ar  V  Ar reduced vector potential formulation.

62

I. FE Model: A-V-A Potential Formulation
In a typical EC testing problem, a solution region ( Ω ) is depicted in Figure 3.13 which consists
of a nonzero conductivity region with eddy currents ( Ω1 ), the region free of eddy currents but
with source currents ( Ω 2 ), interface and boundary sections. The magnetic vector potential (A) in
the entire region is related to the magnetic flux density as:

B  ´ A

(3.19)

And the magnetic field intensity is also expressed by A :

H

1



´ A

(3.20)

The electric scalar potential ( V ) in eddy currents region ( Ω1 ) is defined by the identity:

 ´ V  0

(3.21)

Substituting equation (3.19) into Maxwell’s equation of Eq. (2.1), we get:

 ´ (E 

A
)0
t

(3.22)

Combing Eq. (3.22) and Eq. (3.21):

E

A
 V
t

(3.23)

Considering the source currents, and using Ohm’s law:

J  E  J s

(3.24)

Maxwell’s equations are formed by the A V  A formulation as:

1
A
 ´ (  ´ A)   (  V )  J s

t
  (

A
 V )  0
t

in the whole solution domain by neglecting the displacement current term
where J s presents the source current density.
63

(3.25)

D
, and
t

Source
currents

Ω2

Eddy
currents

No eddy currents

12 : Interface

Ω1

 BC :Boundary conditions
Figure 3.13 A typical EC problem with regions, boundary sections and interface
In the solution of Eq. (3.25), a gauge condition is necessary to ensure the uniqueness of A . Two
gauge conditions, Lorentz gauge and Coulomb gauge are generally used. The Lorentz gauge is
expressed as:

 A

1 V
0
c 2 t

(3.26)

where c is the speed of light in free space. Lorentz gauge leads the potentials suitable for a set
of wave equations in high frequency problems. The Coulomb gauge, defined as:

 A  0

(3.27)

is usually utilized in low frequency problems due to the absence of the displacement current and
the resulting equations are simplified.
II. FE Model: Ar  V  Ar Reduced Vector Potential Formulation
Although the

A V  A formulation has been widely studied for FE modeling of

time-harmonic and transient electromagnetic NDE [126, 143, 150, 153-156], the meshing of the
source coil probe becomes very cumbersome, particularly if the probe motion is to be taken into
account [137, 153-154, 157-158]. Moreover, accurately meshing the complex coil structure at
64

each scan position associated with the test sample poses difficulties in mesh discretization. A
scheme

that

helps

to

alleviate

this

problem

using

reduced

vector

potential

formulation Ar  V  Ar is introduced [153-154, 157-158].
The magnetic vector potential is decomposed into potentials due to excitation source and
induced currents. Correspondingly the magnetic flux density B is similarly split into two parts:

B  Bs  Br  0 H s  Br

(3.28)

where B s and H s are the flux density and field density due to the source current in free
space, and Br is the flux density due to induced current or magnetization and 0 is the
free-space permeability. Considering equation (3.19), the magnetic vector potential A is defined
as:

A  As  Ar ,  ´ As  Bs and  ´ Ar  Br

(3.29)

The vector potential As in air is due to the excitation current and Ar is due to the induced
and/or magnetization currents. Furthermore, As can be evaluated by Biot-Savart’s law:

´ Hs  Js


J r 
As  0   s
dΩ
4 Ω r  r 

(3.30)

Where  ' is the volume of source currents, and r and r' denote the coordinates of
observation and source points, respectively.
Correspondingly, the governing equations (3.25) can be expressed as:
 ´(

1



 ´ Ar )  

As
Ar
1
  V   ´ H s   ´ (  ´ As )  
t

t

65

 (

A
Ar
 V)     s
t
t

(3.31)

The advantages of the reduced vector potential formulation are as follows [157-158]:
1) Mesh generation with complex coil shape becomes much easier because the excitation coil is
discretized independently for computing the source potential.
2) Convergence of the iterative solver is faster because the current source can be modeled
accurately.
3) Scanning of the coil over a sample involved in a typical EC testing process can be simulated
without re-meshing. Computational errors due to remeshing are removed.
4) Incomplete factorization of the system matrix, which is the most time-consuming process in
the solution phase, is performed only once.
5) Only the secondary field due to magnetization and/or induced currents is solved. Hence the
solution time can be reduced because the secondary field is much smaller than the source field.
6) It is efficient for conducting parametric studies without changing the mesh, such as lift-off
variation and tilt in angle.
III. FE Method Implementation
The numerical approximation of the potentials as unknowns is based on a discretized FE mesh.
The potentials can be expanded in terms of shape functions associated with the nodes of mesh:

A   Axi Ni ˆx A yi Ni ˆy  Azi Ni ˆz   N k Ak

i

(3.32)

k
V   NiVi

i
66

(3.33)

Ar   Arxi N i ˆx Aryi N i ˆy  Arzi N i ˆz   N k Ak
i
k

(3.34)

Where Axi , A yi , Azi and Vi are the three Cartesian components of the potentials at node i ,
and N i is the shape function associated with node i that assumes the value of one at this node
and the value of zero at any other node. The vectors ˆx, ˆy, ˆz are the Cartesian unit vectors.
The Galerkin formulation of weighted residual method [153-155] is implemented to solve Eq.
(3.25) and Eq. (3.31) in two presented formulations:

Ω  ´ Ni   ´ A  Ni  A / t  Ni  V dΩ  Γ Ni   ( A / t  V   nˆ dΓ
  Ni  J s dΩ
Ω

(3.35)

Ω  ´ Ni   ´ ( Ar  As )  Ni  ( Ar  As ) / t  Ni  V d


Γ

Ni   ( ( Ar  As ) / t  V   nˆ d  Ω Ni  J s d

(3.36)

where N i ( i  1,2, N with N the number of nodes) are shape functions,  the solution
domain, and   1 /  is reluctivity.  is the conductor surface and nˆ is the unit outward
normal vector of . By neglecting the surface integral in Eq. (3.35) or Eq. (3.36), we implicitly
set the normal component of induced currents on the conductor surface to zero.
The FE procedure results in a linear algebraic system of equations that must be solved to
determine the unknown coefficients of the shape functions. The global stiffness matrix is
obtained by assembling each element matrix together. The value at each entry is the sum of
values contributed by all the connected elements:

GA  S

(3.37)

where G is a complex, symmetric sparse matrix, A is the vector of unknowns consisting of the
electric scalar potential and the three components of the magnetic vector potential or the

67

magnetic reduced vector potential at each node, and S is the load vector incorporating the
current source.
The equations can be solved using either direct or iterative methods. Either Dirichlet boundary
conditions or Neumann boundary conditions need to be specified. Since Neumann boundary
conditions are usually included implicitly in the FE formulation, one only needs to impose
Dirichlet boundary conditions. Current continuity conditions will be explicitly imposed at the
interface boundaries to avoid spurious solutions.
3.5.2 Time-domain Modeling Schemes
The Ar  V  Ar formulation is used as the basis for the time domain modeling scheme. The
backward difference method is used to treat time and the transient values are evaluated by
iterations t n 1  t n  t . The time derivative term

A An 1  An
is implemented by

t
t

considering As and Ar separately:

As As n 1  As n Ar Ar n 1  Ar n
,


t
t
t
t

(3.38)

The governing equations of this formulation can be written as:

 2 Ar n 1t  Ar n 1  V n 1t  1  vr  ´ H s n 1t   ( As n 1  As n )
 Ar n

  Ar n 1  V n 1t      ( As n 1  As n )    Ar n



(3.39)

I. Interpolation based Time-domain Modeling
The simulation of PEC signals using an interpolation scheme in the time domain is proposed to
increase the simulation efficiency. As shown in Figure 3.14, the geometry for this simulation

68

study is a 3 mm thick aluminum plate with a fastener hole of 10 mm diameter. A 1 mm crack is
included at the right edge of the fastener hole. Transient signals of the normal component at three
positions are simulated with the multi-line current excitation: position 1 (P1) is at hole center,
position 2 (P2) is at the left edge, and position 3 (P3) is directly above a crack near the right
edge.

P2 P1 P3

1 mm long
crack
10 mm
(a)

(b)

Source
current

1
0
0
1

0.005

-1
0

0.01
P1

0
0.005

Bz (T)´10-3

2

0.01

Time (s)

2

P2

0

-2
0
2

Bz (T)´10-3

Bz (T)´10-4 Current (A)

Figure 3.14 A geometry used in the time-domain modeling:
(a) Simulation geometry and three scan positions and (b) Geometry FE mesh

0.005

P3

0

-2
0

0.01

0.005

Time (s)

0.01

Figure 3.15 The excitation source signal (upper left), and the simulation results of Bz in
time-domain modeling at positions P1, P2, and P3
A 100 Hz 50% duty cycle square waveform, with a total duration of 10 ms, is applied as source,
shown in Figure 3.15. Solutions to Eq. (3.39) at the three positions in Figure 3.14 are calculated

69

over 500 time steps ( t  2e  5 s). Transient signals simulated at three positions P1, P2 and P3
are shown in Figure 3.15. A zoomed representation of the three signals is shown in Figure 3.16.
These signals are used as a reference for comparison with other implementation of the time
domain model.
-4

x 10

P1
-P2
P3

Bz (T)´10-4

10

5

0
0

1

2
Time (ms)

3

4

5
-3

x 10
Figure 3.16 The first peak of Bz in the simulation results at positions P1, P2, and P3

The use of a larger sampling time step t with linear interpolation is investigated. Two cases,
namely, 125 time steps ( t1  2t = 4e  5 s), and 50 time steps ( t 2  5t = 1e  4 s) are
simulated. These simulation results are interpolated such that t = 2e  5 s. Figure 3.17 shows
the results at positions P1, P2, and P3, before and after interpolation. Compared to the reference
signals in Figure 3.16, the error in interpolated signals is listed in Table 3-3.

error 

Breference ( f )  Binterpolation ( f )
Breference ( f )

´ 100%

The results in Table 3-3 show that a larger time step produces higher simulation error.

70

(3.40)

Table 3-3 Simulation error analysis of the interpolation modeling in time-domain.
Number of
time steps

Position

125

P1
P2
P3
P1
P2
P3

50

Relative error to
reference signal
1.64%
1.38%
1.39%
7.58%
6.68%
6.59%

Bz (T)

10-5

10-5

Simulation time step

Time (ms)
(a)

Bz (T)

10-3

10-3

Simulation time step

Time (ms)
(b)

Figure 3.17 Simulation results of Bz using the time-domain interpolation modeling: (a)
PEC-GMR signals at P1 (b) PEC-GMR signals at P2 (c) PEC-GMR signals at P3
71

Figure 3.17 (cont’d).

Bz (T)

10-3

10-3

Simulation time step

Time (ms)
(c)

II. Impulse Response based Time-domain Modeling
A linear and time-invariant (LTI) system can be described by its impulse response [146-147]. In
an LTI system, the response due to an arbitrary excitation is a convolution of an impulse
response with the arbitrary excitation function [159-160]. Using this approach, results from
different excitation signals could be calculated from a single simulation of the impulse response.
Additionally, since less number of time steps is required for impulse response based time domain
modeling, this strategy uses less computation time compared to conventional methods in time or
frequency domain.
The impulse response approach is depicted in Figure 3.18. An impulse  (t  2) excitation
source is applied to the FE time domain solver:

0 t  1, 3, ,t1
1 t  2

(t  2 )  

(3.41)

where t is the discrete time. The output f(t) is the impulse response obtained due to the excitation

72

 (t ) , and t1 is the number of time steps used in the simulation.

Impulse source ( t )

Current (A)

1

0.5

50

100

Time domain solver
Impulse response
6
signal f (t )

4
2
0
-2
0

50

Current (A)

Bz (T)´10-3

0
0

100

Simulation time step

Convolution

Transient current
source s(t)
2
1
0
0

500

Simulation time step

-4-4

1

x 10

Bz (T)

0.5
0

-0.5
-1
0

100

200

300

Time step

400

500

Figure 3.18 The strategy for impulse response based time-domain simulation
A square waveform is given as a current source s(t), which is sampled at t 2 time intervals,
and with a total of t 2  500 time steps, the system response p(t) can be computed by
convolving f(t) with s(t):

73

p( t )  f ( t )* s( t ) 



 f ( t   )s(  )d 


  f ( j )s( i  j )
j

f ( 1t1 )* s( 1t 2 )
(3.42)

where the transient signal p(t ) is response due to the pulsed current source s(t ) . The indices
i , j are time steps and the length of p(t ) is t1  t 2  1 .

This approach is applied for the simulation of pulsed EC-GMR testing. The transient signals at
the three positions P1, P2 and P3 are shown in Figure 3.19, and they are compared to the
reference signal (250 time steps) in Figure 3.16. The simulation errors relative to different
number of time steps are presented in Table 3-4. It is observed that the error in simulated signal
depends on the number of time steps used in convolution.
In order to increase the simulation accuracy using less number of simulation time steps, the result
obtained with 30 time steps is extended by padding the signal with the last time-step value

f (30) as:
f ' (t )  [ f (1), f (2), f (30) f (30) f (30) f (30)  f (30)]



extra 20 time steps

p' (t )  f ' (t ) * s(t )  [ f ' (1), f ' (2), f ' (50)] *[s(1), s(2),s(500)]

(3.43)

The simulation error relative to the reference signal in Figure 3.16 is shown in Table 3-5. Using
this padding procedure has effectively reduced the simulation error shown in Table 3-4, when
only 30 time steps are used.

74

-5
-5

10

x 10

Reference simulation signal P1:500 simulation time steps
Impulse response based simulation P1:90 simulation time steps

8

Bz (T)

6
4
2
0
-2
0

Time (ms)

-3

1

2

3

4

0

5
-3

-3

x 10

x 10

-0.2

Bz (T)

-0.4
Reference simulation signal P2:500 simulation time steps
Impulse response based simulation P2:90 simulation time steps

-0.6
-0.8
-1
-1.2
0

1.2

Time (ms)
1

3

4

5
-3

x 10

Reference simulation signal P3:500 simulation time steps
Impulse response based simulation P3:90 simulation time steps

1
0.8

Bz (T)

2

-3
-3
x 10

0.6
0.4
0.2
0
0

1

2 Time (ms) 3
4
5
-3
10 for the positions
Figure 3.19 Impulse response based simulation results vs. the referencex signal
P1, P2, and P3

75

Table 3-4 Simulation error analysis of the impulse response based modeling.
Impulse response based
modeling
Number of
GMR sensor
time steps
location
90
P1
P2
P3
70
P1
P2
P3
50
P1
P2
P3
30
P1
P2
P3
25
P1
P2
P3

Relative error to
reference signal
0.04%
0.58%
1.01%
0.13%
1.69%
2.26%
0.75%
5.16%
6.07%
5.22%
17.80%
19.73%
8.69%
25.09%
27.55%

Table 3-5 Simulation signal accuracy enhancement.
GMR sensor
location
P1
P2
P3

Relative error to
reference signal
1.79%
2.81%
2.61%

3.5.3 Modeling in Frequency-domain vs. Time-domain
The simulation of PEC testing is also evaluated using a frequency domain model presented in
[137]. For position P1 in the geometry of Figure 3.14, the predicted transient response is shown
in Figure 3.20 using 250 harmonic components ranging from 100 Hz to 25,000 Hz in 100 Hz
step. Simulation accuracy is decided by the total number of frequency components representing
76

the spectrum of excitation pulse in Figure 3.15. The simulation results have an error of 2.37%
relative to the reference signal in Figure 3.16.
-4
-4

1

x 10

Predicted simulation of 250 frequency steps - P1
Reference simulation - P1

Bz (T)

0.5
0

-0.5
-1
0

0.002

0.004

0.006

0.008

0.01

Time (s)

Figure 3.20 Simulations of PEC signals using FE solver in frequency-domain: Predicted transient
signal of 250 frequency steps vs. the reference signal simulated in time-domain
In order to reduce computation time, results were predicted with less number of harmonics and
interpolation was used to compensate for the missing harmonics. Simulation results of the
transient response using interpolation with only 100 and 50 uniformly spaced harmonic
components from 100Hz to 25000Hz are predicted in Figure 3.21. The accuracy deteriorates
when less harmonics are used in the modeling. The error is 0.44% for 100 harmonic components
and 5.93% for 50 harmonic components. In contrast, the proposed approach provides a more
accurate solution using 30 simulations in time domain.

77

-4
-4

1

x 10

Predicted simulation of 250 frequency steps-P1
Predicted simulation of 100 frequency steps-P1

Bz (T)

0.5
0

-0.5
-1
0 -4
-4-4
x x10
1 1 10

0.002

0.006

0.008

0.01

Predicted
Predictedsimulation
simulationofof250
250frequency
frequencysteps-P1
steps-P1
Predicted
simulation
of
50
frequency
steps-P1
Predicted simulation of 50 frequency steps-P1

0.5
0.5

Bz (T)

0.004

00

-0.5
-0.5
-1-1
00

0.002
0.002

0.004
0.004

0.006
0.006

0.008
0.008

0.01
0.01

Time (s)
Figure 3.21 Simulations of PEC signals: predicted transient signal of 250 frequency steps vs.
predicted transient signals with interpolation of 100 and 50 frequency steps
Additionally, the simulation in time domain uses a fixed computation time at each time step,
while the computation time increases with higher harmonic components used in frequency
domain simulation method as seen in Table 3-6. Therefore, the presented FE model based on the
convolution with the impulse response is superior in speed and accuracy relative to the frequency
domain model in [137].
Table 3-6 Computation time comparison.
FE model

Solve domain

Proposed
method
Reference
method

Time domain
Frequency
domain

Simulation
steps
30
50

Computation
time (each step)
4 mins
4 mins:20 mins

78

Relative
error
1.79%
5%

Node

12996
0

3.5.4 Time-domain Model Validation
The time-domain modeling strategy described in this section is validated using experimental
PEC-GMR measurements of the specimen shown in Figure 3.14. The validation of the signals at
three probe positions corresponding to P1, P2, and P3 is presented in Figure 3.22.

Normalized Bz

1
0.5

Experimental signal - P1
Impulse response based simulation - P1
Reference simulation signal - P1

0

-0.5
-1
0

Time (s)
0.001 0.002 0.003 0.004 0.005

Normalized Bz

0.5
0
-0.5
-1
0

Experimental signal - P2
Impulse response based simulation - P2
Reference simulation signal - P2
0.001 0.002 0.003 0.004 0.005

Time (s)

Normalized Bz

1
0.5

Experimental signal - P3
Impulse response based simulation - P3
Reference simulation signal - P3

0

Time (s)

-0.5
0
0.001 0.002 0.003 0.004 0.005
Figure 3.22 Model validation: Simulation signals of 250 time steps and signals of the impulse
response based modeling (30 time steps) vs. experimental signals

79

The proposed FE model is then applied to multilayer riveted structure inspection. A three-layer
aluminum plates with a 5 mm crack in the 3

rd

layer around the aluminum fastener is modeled.

The three dimensional geometry is meshed using hexahedral elements with 8 nodes. A narrow
air gap is introduced around the fastener structure and also in between plate layers. The
cross-sectional geometry of the model is shown in Figure 3.23. The simulation of PEC-GMR
measurements at three positions displayed in Figure 3.24 is performed. The Bz component
signals are studied using the impulse response based time-domain modeling. The experimental
PEC-GMR measurements of the Bz component are presented for comparison.

Scan position:P2

Scan position: P1
Scan position: P3

6mm
4mm
4mm
3mm crack
rd

Figure 3.23 Modeling geometry of a three layer riveted plate with a 3 layer crack at aluminum
fastener site

80

x 10 -4
-4

2

Simulation signal at P1
Simulation signal at P2
Simulation signal at P3

Bz (t)

1
0

-1

GMR measurement of Bz(V)

-2

0 -3
-3

1

2 Time (ms) 3

4

(a)

x 10
6

5
x 10

-3

Experimental signal at P1
Experimental signal at P2
Experimental signal at P3

4
2
0
-2
-4
0

1

2 Time (ms) 3

4

5
-3

(b)
x 10
Figure 3.24 PEC-GMR signals at three scan positions: (a) Simulation signals and (b)
Experimental signals
3.6 MR Measurements of 3-component Transient Fields
In order to resolve the challenges of detecting cracks under steel fasteners, measurement of all
3-components of the magnetic field (normal component- B z , tangential components- B x , B y )
using MR sensors is proposed. The model-based study in [161] reports the enhanced detection of
defective steel fastener using the additional information in the tangential components in low
frequency EC-GMR inspection.

81

3.6.1 Ferrous Fastener Inspection
Due to ferromagnetism, ferrous fasteners become the areas of flux concentration, even for a
relatively low applied field intensity [7, 21]. Consequently, the response due to ferrous fastener
can mask small defect indications as seen in the distributions of the magnetic flux density for
aluminum and steel fasteners in Figure 3.25 (a-b).

With a 3rd layer crack

No crack

(a)

No crack

With a 3rd layer crack

(b)
Figure 3.25 Numerical results illustrating the challenge of ferrous fastener inspection when
measuring the normal magnetic field component (Bz): (a) Induced field at an aluminum fastener
without crack (left image) and with crack (right image)
(b) Induced field at a steel fastener without crack (left image) and with crack (right image) (c)
C-scan image in the presence of a subsurface 8mm notch a at aluminum fastener site (left
image), and at steel fastener site (right image)

82

Figure 3.25 (cont’d).

Al fastener

Steel fastener

(c)

The C-scan images of normal component data also demonstrate the difficulty in detecting a
subsurface crack around steel fastener hole (Figure 3.25 (c)). That the C-scan image of a
defective aluminum fastener demonstrates an observable asymmetry in the left and right lobes,
however, this asymmetry is not easily detected in a defective steal fastener.
Little study is done for ferrous fastener examination using transient EC methods. The study in
[21] is limited to relatively large crack sizes (8mm, under surface up to 6mm), and
one-dimensional transient signal analysis. The reliable detection of cracks under steel fasteners
in layered structures is studied in this dissertation using GMR measurements of the three
components of magnetic field.
3.6.2 Simulation Study of 3-component Measurements
The FE model developed in the time domain is employed to study the 3-component
measurements in a layered geometry with a steel fastener. Using the impulse response based
scheme, the formulation in Eq. (3.39) is solved in the time domain. The three components of the
magnetic flux density are calculated from the solution vector as:

83

B z  dA y / dx  dAx / dy

(3.44)

B x  dAz / dy  dA y / dz

(3.45)

B y  dAx / dz  dAz / dx

(3.46)

The mesh for the FE model, and the geometrical dimensions of sample and crack are shown in
Figure 3.26. The sensing position is shown to be at the right edge of the fastener head. The
measured Bz, By, and Bx components for the defect and no defect cases are shown in Figure 3.27
(a), (b), and (c) respectively. Figure 3.27 (d) shows the 3-components after baseline subtraction.
It can be seen that the Bx components give a large difference compared with Bz. In this study, the
FE model is used as a tool to generate signals for a variety of defective rivet geometries.

Scan position: P3

Scan position: P3

6.5mm
14mm
6.5mm
No flaw case

2.87mm flaw case

Figure 3.26 Simulation for steel fastener structures-Test sample: no crack vs. with 2.87mm notch

84

x 10-4
-4

8

Simulation signal at P3: no crack
Simulation signal at P3: with crack

Bz(T)

6
4
2
0
-2
0

1
-5
-5

4

4

5
x 10

-3

x 10

Simulation signal around P3: no crack
Simulation signal around P3: with crack

3

By(T)

2 Time (ms) 3
(a)

2
1
0
-1
0

1

2 Time (ms) 3
(b)

4

5
x 10

-3

Figure 3.27 Simulation of 3-component measurements for steel fastener structures: (a)-(c)
Simulation signals of Bz, By, Bx components respectively (d) Subtraction of the no flaw
measurements from the 2.87 mm flaw measurements for each component

85

Figure 3.27 (cont’d).

x 10-4
-4

15

Simulation signal at P3: no crack
Simulation signal at P3: with crack

Bx(T)

10
5
0
-5
0

1

2 Time (ms) 3
(c)

4

5
x 10

-3

-6
-6

1 x 10

B(T)

0
-1
Simulation signal:Bz difference
Simulation signal:By difference
Simulation signal:Bx difference
-3
0
0.5 Time (ms) 1
(d)

-2

1.5
-3
x 10

3.6.3 Experimental Study of 3-component Measurements
The GMR sensor, as presented in Figure 3.28, placed at the center can be oriented to be sensitive
to a selected component of the magnetic field. The experimental measurement of the three
components in the case of a steel fastener with a subsurface 2.87 mm notch through the 2

nd

layer

is conducted. Two types of NVE GMR sensors (AAH002 for the normal component and AA002
for the tangential components) are used with different linear response ranges.

86

Sensitive axis-By

Sensitive axis-Bz

GMR sensor
Sensitive
axis-Bx

GMR
sensor

GMR
sensor

Multi-line coil

Multi-line coil

Multi-line coil

Figure 3.28 GMR sensing 3-component of the magnetic field

The C-scan images of these inspection data are shown in Figure 3.29. The application of PEC
inspection of laboratory samples with 3D GMR measurements, and features from the C-scan
images of 3-component data and signal processing algorithms for automatic crack detection will
be implemented in Chapter 4.

Scan area

(a)

Bz

By

Bx

25

20

30

20

Y(mm)

15

15

20

10

10

10

5

(b)

10

20

X(mm)

30

5

10

20

X(mm)

30

10

20

30

40

X(mm)

Figure 3.29 PEC-GMR measurement of a steel fastener with a 2.87 mm notch using three
components: (a) Test geometry (b) C-scan images of Bz, By, Bx (c) Transient A-scan signals of Bz,
By, Bx

87

Figure 3.29 (cont’d).
0.3

0.6

Experimental signal: By

GMR signal (V)

Experimental signal: Bz
0.4

0.2

0.2

0.1

0

0

-0.2
0

Time (ms)
2

4

GMR signal (V)

0.15

(c)

Time (ms)

-0.1

0
2
6
-3
x 10
Experimental signal: Bx

4

6
x 10

-3

0.1
0.05
0

-0.05
0

Time (ms)
2

4

6
x 10

-3

3.7 Summary
This chapter presents the development of an EC-GMR inspection system, which uses a pulsed
excitation applied to a planar multi-line coil to generate a transient field that is detected using
GMR sensor. The transient skin depth of electromagnetic field associated with the diffusing
fields is shown to be greater than that associated with steady state case. A novel simulation
strategy is developed to model the PEC system in the time domain and validated by experimental
results. The scheme that measures 3-component of transient fields is numerically and
experimentally demonstrated as a feasible approach for the inspection of ferromagnetic fasteners.

88

CHAPTER 4

ANALYSIS OF PEC-GMR INSPECTION DATA

4.1 Introduction
This chapter describes methods for the analysis of PEC-GMR data obtained from the inspection
of multilayer riveted structures. C-scan image data of GMR response is collected experimentally.
A strategy using principal component analysis (PCA) method is adopted to process the C-scan
image for crack detection near fastener sites. Initial results show feasibility for detecting the
embedded cracks at steel fastener sites using 3D GMR measurements.
4.2 Review of Signal Enhancement for PEC Inspection
Signal transformation methods have been studied to represent transient signals in different
domains, such as frequency domain, time-frequency domain, and wavelet transform [162-167].
Another study found in [168] used a Fisher discriminative model for defect classification in PEC
testing.
Although Safizadeh [165] studied the time-frequency distribution of PEC signals for the removal
of interlayer gap and lift-off noise, the analysis of A-scan signals is not reliable to detect
embedded cracks in riveted or layered structures [18, 23].
Signal processing using PCA and independent component analysis (ICA) techniques were
introduced as strategies for new feature extraction in [98, 163, 169-171]. The time series
constituting transient signals were reduced to single points in principal component space for
defect detection [171]. The detection schemes need training data and a training model to classify
the data.

89

4.3 Multilayer Riveted Specimen
Three laboratory specimens consisting of multilayer aluminum plates with aluminum or steel
fasteners are used in this work. Sample 1 is a three-layer aluminum plate (aluminum alloy 3003
and 1145) with mushroom-head aluminum fasteners drilled through the plates. The layer
thicknesses are: 6 mm (top layer), 4 mm (middle layer) and 4 mm (bottom layer). The fasteners
are of diameter 6 mm at the top and tapering to 3 mm diameter at the bottom layer. Cracks of
nd

various radial dimensions located at fastener sites in the 2

rd

layer (Row 1) and the 3

layer

(Row 2) of the sample are machined. A schematic of Sample 1 is shown in Figure 4.1.

6mm
4mm
4mm
1mm

2mm
(a)

6mm
4mm
4mm
1mm

3mm

5mm
(b)

Fastener Fastener Fastener Fastener
1-2
1-3
1-4
1-1
1 mm
1 mm

3 mm

2 mm
5 mm

Fastener Fastener Fastener Fastener
2-1
2-2 (c) 2-3
2-4

Figure 4.1 Schematic of Sample 1: three layers aluminum plate with aluminum fasteners and
cracks in second and third layers (a) Side view of cracks in the second layer (b) Side view of
cracks in the third layer (c) Top view of Sample 1
90

Sample 2 is a layered aluminum (aluminum 7075-T6) plate containing steel fasteners. This
sample consists of a three layer aircraft skin structure. The thicknesses of the three layers are: 6.5
mm (top layer), 14 mm (middle layer) and 6.5 mm (bottom layer). The steel fasteners are of 14.5
nd

mm top diameter and 7.9 mm bottom diameter. Through-wall notches in the 2

layer with

different radial lengths are machined at Rows 2 and 4. Corner notches of four sizes are installed
in Rows 1 and 3. Sample 2 is illustrated in Figure 4.2.

Bottom corner notches

Fastener 1
Row 1
Row 2

Fastener 8

Row 3
Row 4
Top corner notches
1.524mm 3.048mm 4.572mm 6.096mm
5
6
Row 1: Fastener # 4
7
0.6604mm 0.9652mm 1.3716mm 1.9812mm 2.8702mm
Row 2:
Fastener #

4

3

6.096mm
Row 3:
Fastener #
Row 4:
Fastener #

1

2

5

4.572mm

6

8

8

7

3.048mm 1.524mm

4
5
2
3
2.8702mm 1.9812mm 1.3716mm 0.9652mm 0.6604mm
3

4

5

6

7

Figure 4.2 Schematic of Sample 2: top view of a three layers aluminum plate with four rows of
steel fasteners, and cracks dimensions in the second layer at each fastener site in every row

91

Sample 3 is a two-layer aluminum sample (aluminum alloy 3003 and 1145) with small cracks in
the bottom layer around the fasteners. The layer thicknesses are 4 mm (top layer) and 2 mm
(bottom layer) with drilled aluminum fastener of 6mm top diameter, 5mm bottom diameter in the
first row, and 3mm bottom diameter in the second row. The machined cracks are less than 1mm
long, as shown in Figure 4.3. Fastener 1-2 contains a radial crack of length 0.2 mm, and fastener
2-3 has a 0.5mm crack. Fastener 1-3 has two radial cracks of lengths 0.8 mm and 0.7 mm
extending at diametrically opposite sides.

Fastener 1-1

Fastener 1-2

Fastener 1-3

0.7 mm

0.8 mm

0.2 mm

0.5 mm
Fastener 2-3

0.2 mm 0.7 mm 0.8 mm

0.5 mm

4 mm
2 mm
4 mm
2 mm

Figure 4.3 Schematic of sample 3: two layers aluminum sample with aluminum fasteners and
cracks in the bottom layer
The three samples are inspected using the PEC-GMR system, and the measured A-scan signals
are used to generate C-scan images using the maximum value of transient signals. The three
components of magnetic fields associated with induced eddy currents are measured for the
inspection of steel riveted structures.
92

4.4 Automatic Analysis of PEC-GMR C-scan Images
Image based data analysis is more reliable than the treatment of individual A-scan and line scan
measurements. In this chapter, a strategy exploiting underlying statistical characteristics of
C-scan image data is developed for automatic crack detection in the presence of fastener signals.
Automatic damage detection using PEC-GMR measurements is performed using unsupervised
classification.
4.4.1 Principal Component Analysis
Principal component analysis is an eigenvector-based multivariate analysis tool for analyzing and
structuring data sets. It is applied to the image data of PEC-GMR measurements for reducing the
dimensionality of measured data. This allows easier interpretation of the data in a lower
dimensional space [172-173]. The PCA analysis is also known as the Karhunen Loeve (KL)
transform or the Hotelling transform. The PCA technique is known for its ability to generate
independent features. This data transformation is particularly useful for classification and
compression [162, 174]. In the case of multi-frequency EC signal analysis, the PCA method has
been used as a source separation algorithm [175-176].
In PCA processing, the procedure seeks to retain the maximum variance in the processed data.
PCA method decorrelates the data sets to find the orthogonal principal components (PCs), and
maps the original data onto the PCs subspace using a linear transformation. This is done by
finding the eigenvectors of the covariance matrix of input data [172-173].

93

Let measured signals be represented by X  [ x1 , x2 , , xn ] T , the mean of the signals is:

  E[X ]

(4.1)

where n is the number of sampled signals, E[.] is the expected value. The covariance of the
data X is calculated as matrix C:
C  E( X   )( X   )T

The

algorithm

performs

a

singular

value

decomposition

(4.2)
of

matrix

C,

and

computes eigenvectors as the rows of matrix V that diagonalizes the covariance matrix:
V 1CV  D

(4.3)

where D is the diagonal matrix.
The matrix decomposition defines the k th principal component (PC) of X as the normalized
eigenvector v k corresponding to the eigenvalue  k of matrix C x , which is obtained by
solving:

C x v k  k v k

(4.4)

where k  1, 2,, n . This is equivalent to finding the solutions of the characteristic equation:

| C x  I | 0, vk  k vk

(4.5)

where I is the unity matrix.
PCA method finds the directions that decorrelate the input data. Principal components are formed
by projecting the data on the eigenvectors which are arranged according to descending
eigenvalues. The first eigenvector has the direction of the largest variance of X and it determines
the direction with the most significant amount of energy.

94

4.4.2 Flaw Detection
The PCA method is applied for the automatic flaw analysis of PEC-GMR measurements. A

n m C-scan image is obtained at each fastener site, and the image data of all fasteners
machined in a row of a sample are used in PCA. As demonstrated in Figure 4.4, the C-scan
images of the 7 fasteners from row 1 of sample 2 are formed. The image data D are formed by
287 points (pixels) in each row, and with a total of 40 line scan, resulting in 40 pixels in each
column. The zero-mean data of D is represented by a matrix M with a size of 40  287. Each
40  41 data set in matrix M represents the measurements from a single fastener.
The eigenvector decomposition is performed on the covariance matrix C of M and the
eigenvectors are calculated as the vectors Vi in matrix V  { V1 ,V2 ,,V40 } . A new
representation of data M is implemented by the linear projection into a lower dimensional space:
T

S=V M

(4.6)

where the vector S is in PCs coordinates. Each row of S is the component

PC k  Vk T M , k  1,,40 .

95

Column
in a 
fastener-row

 size
 of
all
C-scan
 
 
1         285

1 
Number of
 
line scans
40

C-scan images of fasteners in each row
Linear transformation using
PCA
Signal projection/transformation for crack
detection
Figure 4.4 Flaw detection using the image analysis
From a geometrical standpoint, the PCA procedure rotates the coordinate system so that the axes
follow the directions of the largest variances of the analyzed data in the new space. These axes
are referred to as principal axes [174]. In general, the dimensionality of the PCs subspace is
selected to retain at least 90% of the energy in original data. The energy in 3 PCs is calculated as:



 i /  i

i 1:3

(4.7)

i 1: k

The first three PCs: PC1 to PC3 are found to carry   95% energy of input data presented in
Figure 4.4. Therefore, the first three PCs with k  3 are used in this chapter for the image data
processing and analysis.
The C-scan data of two fasteners without cracks and one defective fastener are processed
following the procedure demonstrated in Figure 4.4. As shown in Figure 4.5 (a), the first two
PCs (PC1 and PC2) are plotted for each pixel row in the C-scan image (this corresponds to
column size of the image). Since the fastener information is the dominant energy in the input
data, the plot of PC1 that is relative to the largest eigenvalue represents the fastener signals.
96

The plot of PC2 that is calculated by the smaller eigenvalue represents the residual energy, and
indicates the signal variation relative to defect response. In Figure 4.5 (b), the components PC1
vs. PC2 are represented by a phase-magnitude polar plot. It is observed that the data due to
fasteners and cracks correspond to different regions in the plot.

No crack

30

No crack

With 6mm crack

20
10
20

40

60

80

Column size of
each C-scan image

Column size of
each C-scan image

120

Column size of
each C-scan image

0.02
No crack
0
No crack
6mm crack

0

-0.2
0

20

40

-0.02
0

60

Column size of each C-scan image

(a)

PC2

0.2

PC1

100

10

20

30

Column size of each C-scan image

90 8
120

6

60

4

150

30

2

Fastener corresponding signals

180

0

210

330
240

300
270

Abnormal signals

(b)

Figure 4.5 Principle of applied PCA analysis
97

40

Therefore, crack detection is implemented by exploiting the uncorrelated PCs to represent the
fastener data and crack signals in different directions in PC subspace. In This scheme does not
need training data. Automatic crack detection is performed by plotting the data in the PCs
subspace.
4.5 Results of PEC-GMR Inspection
nd

4.5.1 Detection of 2

and 3

rd

Layer Cracks in Sample 1

Experimental measurements of Sample 1 are presented as the C-scan images in Figure 4.6. For
each row, 40 line scans are measured with 215 points at 1mm interval in each line scan. The
excitation current source is a 100Hz and 1.4A square waveform. The normal component B z of
the transient field is measured. The peak value of each A-scan signal is utilized to generate the
C-scan image. Defects machined in Sample 1 are summarized in Table 4-1.
x 10
120

3rd layer
3rd layer
3rd layer
100
No crack
1 mm crack 3 mm crack 5 mm crack

Fasteners
in Row 1

80

Y (mm)

Fasteners
in Row 2

4
3 10

-3

2

60

1

40

0

20
0

-3

-1

No crack

-20

2nd layer
2nd layer No crack
1 mm crack 2 mm crack

-2
-3

-40
50

100

150

200

X (mm)
Figure 4.6 C-scan images of aluminum fasteners in Sample 1 using PEC-GMR measurements

98

Although the asymmetry observed in the C-scan images of aluminum fasteners with cracks, it is
not a reliable indication in the case of 2

nd

or 3

rd

layer crack. In addition, it is also possible to get

an asymmetric image in the case of improper fastener installation or sensor tilt.
Table 4-1 Sample 1 – aluminum fastener.
Sample1
Fastener1-1

Defect size Location
0
nd
2 layer

Fastener1-2

1 mm

Fastener1-3

2 mm

Fastener1-4

0

Fastener2-1

0

Fastener2-2

1mm

Fastener2-3

3mm

Fastener2-4

5mm

nd

2

nd

2

nd

2

rd

3

rd

3

rd

3

rd

3

layer
layer
layer
layer
layer
layer
layer

PCA method for crack detection is performed on the C-scan images of aluminum fasteners
nd

(Figure 4.6) in Row 1 (2

layer cracks) and Row 2 (3

rd

layer cracks) of Sample 1. The C-scan

images of Sample 1 are first processed for mean removal and are represented by a matrix M of
size (40  215). A denoising linear spatial filter represented by a ‘gaussican’ 10 by 10 mask is
used for de-noising.

99

2 x 10

PC3

Fastener 1-1:
no crack
1
Fastener 1-4:
no crack
0 1-2:
Fastener
1mm crack
Fastener
-1 1-3:
2mm crack

5
0

-5
0

-3

PC2

-4

10 x 10

0.005

-2
-1

0.01

0

(a) PC1

(b)
nd

Figure 4.7 Detection of cracks in the 2

PC3

1

-3 -3
10

x 10

layer of Sample 1 using the PCA method (a) Detection

results by PC1 vs. PC3 representations (b) Detection results by PC3 vs. PC2 representations
-3

PC2

4 x 10

Fastener 2-1:
no crack
2
Fastener 2-2:
1mm crack
0
Fastener 2-3:
3mm crack
-2 2-4:
Fastener
5mm crack

PC3

2
0

-2
-4
-5

-3

4 x 10

0

5

10 15
PC1
-3 -3
(a)
10
x 10
rd

Figure 4.8 Detection of cracks in the 3

-4
-4

-2

0PC3 2
(b)
10-3-3
x 10

layer of Sample 1 using the PCA method (a) Detection

results by PC1 vs. PC3 representations (b) Detection results by PC3 vs. PC2 representations
Projection of input data into PC1 vs. PC3, and PC3 vs. PC2 subspace domains is shown in

100

Figure 4.7 and 4.8. It is seen that discriminatory information about cracks are successfully found
in PC3 vs. PC1 or PC3 vs. PC2 plots. As shown in Figures 4.7-4.8, the uncorrelated PCs have
significantly suppressed fastener signals and enhanced the crack information contained in the
collected image data.
nd

4.5.2 Detection of 2

Layer Cracks in Sample 2

The PEC-GMR experimental C-scan images of sample 2 are shown in Figure 4.9. Table 4-2
describes the cracks machined in sample 2.
0.06

Fasteners in
Row 4 100

0.04

Y (mm)

150

0.02

Row 3
Row 2 50

0

Row 1

-0.02
0

2

3

4

5

6

7

8

-0.06

X (mm)

-50
50

100

150

-0.04

200

250

Figure 4.9 C-scan images of steel fasteners in Sample 2 using PEC-GMR measurements
Table 4-2 Sample 2 – steel fastener with 2
Row1
Fastener
1-2
1-3
1-4
1-5
1-6
1-7
1-8

Crack
size
(mm)
0
0
0
1.524
3.048
4.572
6.096

Row2
Fastener
2-2
2-3
2-4
2-5
2-6
2-7
2-8

Crack
size
(mm)
0
0.6604
0.9652
1.3716
1.9812
2.8702
0
101

Row3
Fastener
3-2
3-3
3-4
3-5
3-6
3-7
3-8

nd

layer cracks.

Crack
size
(mm)
4.572
3.048
1.524
0
0
0
0

Row4
Fastener
4-2
4-3
4-4
4-5
4-6
4-7
4-8

Crack
size
(mm)
0
2.8702
1.9812
1.3716
0.9652
0.6604
0

5
PC3

0
-5
0.02

-3
-3
x 10

no crack
no crack
no crack
1.524mm crack
3.048mm crack
4.572mm crack
6.096mm crack
0.2
0.1

Row 1 steel fasteners
with corner cracks at
right sites

PC2

0
-0.02 -0.2

0 PC1

-0.1

Row 2 steel fasteners
with notch cracks at left sites
PC3
PC3
0.01

0.1
0

0
- 0.01

-0.1
- 0.1

- 0.05

PC2 0

0.05

0.1

0.15

no c r ac k
0.015
0.6604m m c r ac k
0.9652m0.01
m c r ac k
1.3716m m c r ac k
0.005
1.9812m
m c r ac k
2.8702m m c r ac k
0
no c r ac k
- 0.005
PC1
- 0.01

Row 3 steel fasteners

0.2 with corner cracks at left sites
PC3 0
-0.2
0.02
PC2

0
-0.02
-0.2

-0.1

0

4.572mm crack
3.048mm crack
1.524mm crack
no crack
no crack
no crack 0.2
no0.1
crack
PC1

Figure 4.10 Detection of cracks around steel fasteners in Row 1 to Row 4 of Sample 2 using the
3D plots of PC1 to PC3: Bz component

102

Figure 4.10 (cont’d).

0.01

0.01
PC3

0

-0.01
0.01
PC2 0

-0.01 -0.1

0

-0.01
0.01 Row 4 steel fasteners
0 notch cracks at right sites
with
-0.01 -0.1
PC1-0.05
0.05

-0.05

0

no crack
2.8702mm crack
1.9812mm crack
1.3716mm crack
0.9652mm crack
PC1
0.6604mm crack
no crack
0

0.1 0.05

0.1

C-scan images of steel fasteners in Row 1 to 4 (Figure 4.9) are processed using PCA method.
Linear transformations of image data into PC1 to PC3 subspace are shown in Figure 4.10. The
signal representations in PC1 vs. PC2 domain are found to exhibit the trajectories that can
discriminate the steel fasteners without cracks from the fasteners with radial cracks. Therefore,
the signals in PC1 vs. PC2 representations are employed for automatic crack detection and the
results are shown in Figure 4.11.
In this case, few false calls are observed: the image data of steel fastener #8 (no flaw) in Row 2,
and steel fasteners #2 and #3 (2.87mm and 1.98mm) and #8 (no flaw) in Row 4. These false
identifications were attributed to possible variations in lift-off, and a limited sensitivity of a
single component of the magnetic field.

103

PC2

0.015

Row 1 steel fasteners with
corner cracks at right sites

0.015

0.01
no
crack
no crack
0.005
no crack
1.524mm crack
0
3.048mm crack
4.572mm crack
-0.005
6.096mm crack
-0.01

Row 2 steel fasteners
with notch cracks at left sites

no 0.01
crack
0.6604mm crack
0.9652mm
0.005
crack
1.3716mm crack
1.9812mm
crack
0
2.8702mm crack
no
crack
-0.005
Variation

-0.015

-0.2 -0.1

0

-0.01

0.1

-0.2 -0.1

PC3

0.03 Row 3 steel fasteners with
corner cracks at left sites

0.02
4.572mm crack
0.01
3.048mm
crack
1.524mm crack
0
no crack
no
crack
-0.01
no crack
no
crack
-0.02
-0.03

-0.2

-0.1

PC1

0

0

0.1

PC1

PC1
-3
-3

x 10 Row 4 steel fasteners with
5
notch cracks at
no crack
right sites
2.8702mm crack
Variation
1.9812mm crack
0
1.3716mm crack
0.9652mm crack
0.6604mm crack
no crack
-5

-10

0.1
nd

Figure 4.11 Detection of cracks in the 2

-0.1

PC1

0

0.1

layer of Sample 2 using the PCA method (steel

fasteners in Row 1 to Row 4): Bz component

4.5.3 Flaw Detection using Tangential-component Measurements
Data analysis using PEC-GMR measurements of By and Bx components are investigated in this
section. Tangential-component measurements of steel fasteners in Sample 2 are presented in the
C-scan images of Figure 4.12.

104

C-scan By measurement

Y (mm)

Row 4
Row 3
Row 2
Row 1
(a) X (mm)

Y (mm)

Row 4
Row 3
Row 2
Row 1
(b) X (mm)
Figure 4.12 PEC-GMR tangential-component measurements of steel fasteners (a) C-scan images
of By measurements (b) C-scan images of Bx measurements

Image data of By and Bx measurements are processed using PCA technique, and the results are
presented in Figures 4.13-4.14 (By component) and Figures 4.15-4.16 (Bx component). The 3D
plots using the first three PCs are studied, and the signal representations in the PCs subspace are
exploited to detect defective steel fasteners with cracks in the 2

nd

layers.

PCA applied to measurements of By component are seen to be effective in detecting cracks at
steel fastener sites in Rows 2 and 4. The smallest crack (0.66mm length) is missed. The
measurements of Bx component are sensitive to all cracks in four rows. Hence, the tangential
components of the magnetic field are validated as a reliable option for the inspection of steel
fasteners.

105

PC3

no crack
no crack
no crack
1.524mm crack
3.048mm crack
4.572mm crack
0
6.096mm crack

-3
5 10

0
-5
5 -3
PC2
10
0

Row 1 steel fasteners
with corner cracks at right sites

-5 -0.02

0.02

PC1

-3

x 10

0

10-3

-2
PC3
-4

Row 2 steel fasteners
with notch cracks at
left sites

-6
0.02

0.01
PC2

0
-0.01

-0.02

-0.04

no crack
0.6604mm
0.9652mm
1.3716mm
1.9812mm
2.8702mm
0
no crack

crack
crack
crack
crack PC1
crack 0.02

0.04

-3

x 10
10

10-3

4.572mm crack
3.048mm crack
1.524mm crack
no crack
no crack
no crack
no crack

PC3

5

0

-5
-0.02

Row 3 steel fasteners
with corner cracks at
left sites
-0.01

PC2 0

0.01

0.02

0.03

0.01

0

-0.01
PC1

-0.02

-0.03

Figure 4.13 Detection of cracks around steel fasteners in Row 1 to Row 4 of Sample 2 using the
3D plots of PC1 to PC3: By component
106

Figure 4.13 (cont’d).
no crack
2.8702mm crack
1.9812mm crack
1.3716mm crack
0.9652mm crack
0.6604mm crack
no crack
0.05

Row 4 steel fasteners
with notch cracks at right sites

PC3
0.02

0.01
0

0 PC1

-0.01
0.03

0.02

PC2

PC2 0

-0.03

-0.05

0.01
0.6604mm crack
0.9652mm crack
0.005 crack
1.3716mm
1.9812mm crack
0 crack
2.8702mm
no crack
-0.005

PC1

-0.02

0.01
PC3

-0.02

0.015Row 2 steel fasteners with
with corner cracks at
notch cracks at left sites
no
crack
right sites
Variation

no crack
4
no crack
no crack
2 crack
1.524mm
3.048mm crack
0 crack
4.572mm
6.096mm crack
-2
-4

-0.01

x 10-3Row 1 steel fasteners
-3

6

0.01

0

0.02

PC1
-0.01
-0.06 -0.04 -0.02 0

Row 3 steel fasteners with
corner cracks at left sites

0.015

Row 4 steel fasteners with
notch cracks at right sites

no crack
0.01
2.8702mm
crack
1.9812mm crack
0.005
1.3716mm crack
0.9652mm crack
0.6604mm
crack
0
no crack

0.005

4.572mm
crack
0
3.048mm crack
1.524mm crack
-0.005
no crack
no crack
-0.01
no
crack
no crack
-0.015

0.02

-0.005
Variation

-0.04 -0.02

PC1

0

-0.01
-0.06 -0.04 -0.02

0.02

0

PC1

0.02

Figure 4.14 Detection of cracks in the 2nd layer of Sample 2 using the PCA method (steel
fasteners in Row 1 to Row 4): By component
107

0.1
no crack
no crack
no crack
1.524mm crack
3.048mm crack
4.572mm crack
6.096mm crack
0.06
0.04

PC3
0.1
0
-0.1
0.08

0.05
0 PC1
Row 1 steel fasteners
with corner cracks at right sites

0.02 PC2 0

-0.02

-0.05

-0.04

-0.1

0.02

PC3

0

- 0.02 0.01

no c r ac k
0.6604m m
0.9652m m
1.3716m m
1.9812m m
2.8702m m
no c r ac k

0.02

0.1
PC2
0
- 0.02

Row 2 steel fasteners with
notch cracks at left sites
- 0.1

0.02

- 0.05

c r ac k
c r ac k
c r ac k
c r ac k
c r ac k

0.05

0

0.1

PC1

4.572mm crack
3.048mm crack
1.524mm crack
no crack
no crack
no crack
no crack

0.1

0 PC3
-0.02 0.1
0.04

0.1

0.02

Row 3 steel fasteners
with corner cracks at
PC2
left sites
-0.02

0.1

0

0.05
0

PC1

-0.05
-0.1
Figure 4.15 Detection of cracks around steel fasteners in Row 1 to Row 4 of Sample 2 using the

3D plots of PC1 to PC3: Bx component

108

Figure
4.15 (cont’d).
0.15
Row 4 steel fasteners
with notch cracks at right sites

PC3

0.1

no crack
2.8702mm
1.9812mm
1.3716mm
0.9652mm
0.6604mm
no crack

0.05
0

crack
crack
crack
crack
crack
-0.2
-0.1

-0.05
0

0.02

0

0.04 PC2 0.06

0.08

Row 1 steel fasteners
with corner cracks at right sites
no crack
0.02
no crack
no crack
1.524mm crack 0.01
3.048mm crack
4.572mm crack
0
6.096mm crack

0.08
0.06

PC2

0.04
0.02

Row 2 steel fasteners
with notch cracks at left sites
no crack
0.6604mm crack
0.9652mm crack
1.3716mm crack
1.9812mm crack
2.8702mm crack
no crack

-0.01

0

-0.02

-0.02
-0.04

PC1

0.1

PC1
-0.05

0

0.05

0.1

-0.03

Row 3 steel fasteners
with corner cracks at left sites

PC1
-0.1

0

0.1

Row 4 steel fasteners
with notch cracks at right sites
no crack
2.8702mm crack
1.9812mm crack
1.3716mm crack
0.9652mm crack
0.6604mm crack
no crack

0.06

PC2

0.02

0.04

4.572mm crack
0
3.048mm
crack
1.524mm crack
no crack
-0.02
no
crack
no crack
no crack
-0.04
-0.1

0.2

PC3

0.02
0

-0.02

PC1
-0.05
0

-0.04
0.05

PC1
-0.05

0

0.05

0.1

Figure 4.16 Detection of cracks in the 2nd layer of Sample 2 using the PCA method (steel
fasteners in Row 1 to Row 4): Bx component
109

4.6 Automatic Crack Detection using 3-component GMR Images
This section describes the design of quantitative signal analysis and classification developed to
utilize information contained in the three components of the magnetic flux density with respect
to feature based detection.
4.6.1 Feature Extraction
PCA based automated crack detection has proved to be promising in discriminating between
signals from fasteners with and without cracks. A quantitative feature set is derived for reliable
automatic crack detection. Three types of signal features containing discriminatory information
are defined for automated classification.
Orientations of corresponding signals in projected PC subspace are first studied. As shown in
Figure 4.17, the orientations of signals in PCs representation are extracted quantitatively as:
ori  atan [( y 2  y1 ) /( x2  x1 )]

(4.8)

where (x1,y1) and (x2,y2) are coordinates of the signal maximum and minimum in PC1 vs. PC2
or PC1 vs. PC3 subspace.

110

0.015

No crack
0.01

PC2

0.005

ori

0

-0.005
-0.01
-0.1

-0.05

0

0.05

0.1

0.05

0.1

0.01

With crack

PC2

0.005

ori
0

-0.005

-0.01
-0.1

-0.05

0

PC1

Figure 4.17 Orientation based feature extraction
A feature quantifying asymmetry calculated by the 3

rd

order moment, and a feature quantifying

th

sharpness calculated by the 4 order moment are defined next. As shown in Figure 4.18, the two
features s and k quantify the asymmetry associated with the crack in PC subspace. These two
features based on the statistical moments skewness and kurtosis [24, 89, 156, 177] and are
defined as:

111

p

 ( sigi _ PC  sigi _ PC )3

s  i 1

( p  1 )s t d3

p

 ( sigi _ PC  sigi _ PC )4

k  i 1

(4.9)

( p  1 )std 4
nd

where sigi _ PC is the fastener image data associated with the 2

PC component, and

sigi _ PC is the mean and p is number of signal data points. The term std is the standard

deviation of the signal.

0.015

s=0.0994
k=1.9201

No crack
With crack

PC2

0.01
0.005
0

s=0.3591
k=3.8046

-0.005
-0.01
0

10

20

30

40

50

Column size of C-scan image of fastener
rd

th

Figure 4.18 Asymmetry quantification using moment based features (3 & 4

orders)

4.6.2 Crack Detection Scheme
The overall approach for automated fastener classification is depicted in Figure 4.19. Data from
each row of the C-scan images from the 3-component EC-GMR system are applied to the PCA
processor for enhancing the indications due to cracks present at fastener sites. GMR images of

112

three components are analyzed sequentially. Corresponding signals represented in PC1 vs. PC2
or PC1 vs. PC3 domain are used for feature extraction.

C-scan images of fastener in each
row
PCA processor
Corresponding signals in PCs
domain
Feature extraction
Signal orientation based
feature

Skewness and kurtosis based
features

Classification
Automatic crack detection
Figure 4.19 Overall approach for automated crack detection
Classification results of Bz, By, Bx measurements using three features are performed. As
presented in Figures 4.20-4.23 (Bz measurements) and Figures 4.24-4.27 (By measurements), the
automatic classification and crack detection are implemented using the plots of features ori vs. k
and features ori vs. s. Figures 4.28 presents the automatic classification and crack detection for
Bx measurements using feature s vs. k.

113

90

3

120

60
2

Cracks
150

30
1

180

0

No cracks
210

330

240

300
270

(I) ori vs. k

0.8
0.6

Cracks

0.4

s

0.2
0

-0.2

No cracks

-0.4
-0.6
-0.8
0

0.5

ori

1

(II)

1.5

2

Figure 4.20 Classification results of steel fasteners in Row 1 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of Bz component

114

90

3

120

60
2

Cracks
150

30
1

180

0

No cracks
210

330

240

300
270

(I) ori vs. k

0.7
0.6

Cracks

0.5

s

0.4
0.3
0.2

False calls

0.1
0
-0.1
-0.2
-0.3
0

No cracks
0.5

ori

1

(II)

1.5

2

Figure 4.21 Classification results of steel fasteners in Row 2 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of Bz component
115

90

4

120

60
3
2

150 No cracks

30

1
180

0

Cracks
210

330

240

300
270

0.4

(I) ori vs. k

0.3

No cracks

0.2

s

0.1
0

-0.1
-0.2
-0.3
-0.4
-0.5
0

Cracks
0.5

ori

1

(II)

1.5

2

Figure 4.22 Classification results of steel fasteners in Row 3 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of Bz component
116

90

3

120

60
2

Cracks
150

30
1

180

0

No cracks

210

330

240

300
270

(I) ori vs. k

0.6
0.5

Cracks

0.4
0.3

No cracks

False
call

0.2

s

0.1
0

-0.1

False calls

-0.2
-0.3
-0.4
0

0.5

ori

1

1.5

2

(II)

Figure 4.23 Classification results of steel fasteners in Row 4 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of Bz component
117

90

2.5

120

150

60

2
1.5

Cracks

30

1
0.5

180

No cracks

210

0

330

240

300
270

(I) ori vs. k

0.8
0.7

Cracks

0.6

s

0.5
0.4
0.3
0.2
0.1
0

No cracks

-0.1
-0.2
0

0.5

ori

1

(II)

1.5

2

Figure 4.24 Classification results of steel fasteners in Row 1 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of By component
118

90

3

120

60
2

Cracks
150

30
1

180

No cracks

210

0

330

240

300
270

(I)

1.2
1

ori vs. k

Cracks

s

0.8
0.6

False call

0.4
0.2
0

No cracks
-0.2
0

0.5

1

ori

1.5

2

(II)

Figure 4.25 Classification results of steel fasteners in Row 2 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of By component
119

90

2.5

120

60

2
1.5

150

Cracks

30

1
0.5

180

No cracks

210

0

330

240

300
270

(I)

ori vs. k

0.5
0.4
0.3
0.2

s

0.1

Cracks

0
-0.1
-0.2
-0.3
-0.4
-0.5
0

No cracks
0.5

1

ori

1.5

(II)

2

2.5

Figure 4.26 Classification results of steel fasteners in Row 3 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of By component
120

90
120

3

Cracks

60

2
150

30
1

180

No cracks

210

0

330

240

300
270

(I)

ori vs. k

1
0.8

Cracks
s

0.6
0.4
0.2
0

False calls

-0.2

No cracks
-0.4
0

0.5

1

ori

1.5

2

2.5

(II)

Figure 4.27 Classification results of steel fasteners in Row 4 using features ori calculated from
PC1 and PC2, s and k calculated from PC2: PEC-GMR measurements of By component
121

2.5
2
1.5
1

Cracks

s

0.5
0
-0.5

No cracks

-1
-1.5
2

3

4

5

k (a)6

7

8

9

2.3

2.4

2.5

1

0.5

No cracks

s

0

-0.5

-1

Cracks
-1.5
1.8

1.9

2

2.1

k

2.2

(b)

Figure 4.28 Classification results of steel fasteners in (a) Row 1 (b) Row 2 (c) Row 3 (d) Row 4
using feature s and k calculated from PC1: PEC-GMR measurements of
Bx component
122

Figure 4.28 (cont’d).
1.05
1
0.95
0.9

False calls

0.85

s

No cracks

0.8
0.75
0.7

Cracks

0.65
1.8

1.9

2

2.1

k

2.2

(c)

2.3

2.4

2.5

-0.5
-0.6

No cracks
No cracks

-0.7
-0.8

False call

s

-0.9
-1
-1.1

Cracks
Cracks

-1.2
-1.3
1.8

2

2.2

k

2.4

123

(d)

2.6

2.8

3

4.7 Summary
Crack detection using the PCA analysis has been explored for the automatic inspection of
defective fasteners. A feature set has been derived for quantifying asymmetry in GMR images. A
strategy using 3-component GMR measurements has been validated for detecting subsurface
cracks at steel fastener sites in layered structures.

124

CHAPTER 5 EC-MR SENSOR SYSTEM – LOW FREQUENCY EXCITATION
5.1 Introduction
The inspection of multilayer structures with buried cracks is examined using a low frequency EC
testing with 3D GMR sensors. The experimental inspection of subsurface cracks under steel
fastener heads is presented. A FE model that is validated with the experimental EC-GMR images
is used to develop data fusion algorithms using 3-component measurements of the magnetic flux
density.
5.2 Low Frequency EC-MR Sensing
The multi-line coil in presented in Chapter 3 is excited by a low frequency (100Hz) sinusoidal
waveform, which generates a time-harmonic uniform field and linear EC currents. A GMR
sensor placed on the line of symmetry measures the single component of magnetic field.
5.2.1 Experimental Set-up
The EC-GMR system consists of signal excitation, signal modulation, signal preparation and
signal demodulation. In this section, an analog in-phase/quadrature (I/Q) detection scheme is
used. The complex components of a GMR signal can be directly computed. The I/Q detection
scheme exploits synchronous AM demodulation which results in a baseband signal whose
bandwidth is a function of flaw characteristics. The raw GMR signal is processed for SNR
enhancement and then fed into the I/Q detector to calculate in phase (real) and quadrature
(imaginary) parts simultaneously. This system diagram is shown in Figure 5.1 (a).

125

The implementation of I/Q detection is based on the mathematical equations:

S s  A0 sin ( t )
S GMR  An sin ( t   n )

(5.1)

where S s is the input excitation signal (also the reference signal) at frequency  and
amplitude A0 . SGMR is the measured GMR signal at the same frequency but different
amplitude An and phase  n . The complex sinusoidal field is expanded as:

A B
An sin( t   n )B sin( t )  n
[cos( 2t   )  cos( n )]
2
A B
An sin( t   n )B cos( t )  n
[sin( 2t   )  sin( n )]
2

Raw
GMR signal

(5.2)

DC bias
Remover

Low noise
Amplifier

Adjustable high gain
amplifier
Signal Conditioning

I/Q detector

Output
(a)

Reference signal
90 degree
phase delay

Mixer 1
Multiplier 1

GMR
signal

GMR bias signal
remove

LPF1

Q

Mixer 2
Multiplier 2

I/Q demodulation

LPF2

I

(b)
Figure 5.1 Schematic of low frequency EC-GMR system: (a) Experimental Set-up and (b) Signal
demodulation
126

By multiplying the GMR signal with sin(t ) and cos(t ) , in-phase and quadrature
components are obtained along with a high frequency sinusoidal terms at 2  frequency. Low
pass filtering is used to filter out the AC component ( cos( n ), sin( n ) ). The Lock-in amplifier
is employed to “lock” onto the input signal and maintain the reference output at the proper
frequency. The schematic of I/Q demodulation system is displayed in Figure 5.1 (b).
5.2.2 Inspection of Cracks around Steel Fasteners –Normal component
Two rows of steel fasteners in Sample 2 (described in Chapter 4, Figure 4.2) are examined
experimentally. Row 1 has corner cracks at right fastener sites and Row 2 has notch cracks
through the 2

nd

layer at left fastener sites. The C-scan images of the normal component B z are

Y (mm)

measured at 100Hz excitation frequency and shown in Figure 5.2.

Row 2
Row 1

In-phase part

60

0.02

40

0

20
0

-0.02

Y (mm)

50

Row 2
Row 1

100

150

200

250

Quadrature part

60

0.02

40

0

20

-0.02

0
50

100

150

200

250

X (mm)
Figure 5.2 C-scan images of steel fasteners in Sample 2 using low frequency EC-GMR
measurements: Bz component

127

Imaginary part

0.04
0.02
0
-0.02
-0.04

Real part
-0.02 -0.01

-5
-0.1 -0.05

0

0.05

-0.1 -0.05

(a)

PC1

150

90

0.1

0.05

Cracks
30

300

Variation

0.05

30

180

330

270

0.1
60

150

0

210

120

No crack

180

240

0.05

Row 2 steel fasteners
with notch cracks at left sites

60

Cracks

0
PC1

Row 1 steel fasteners
with corner cracks at right sites
120

Variation

0
-4

0

90

0.01 0.02

no crack
Row 2 steel
0.6604mm crack fasteners with
0.9652mm crack notch cracks
1.3716mm crack at left sites
1.9812mm crack
crack
-3 2.8702mm
-3
10 x 10no crack
4

no crack
no crack
no crack
1.524mm crack
3.048mm crack
-3 -34.572mm crack
10 x 10 6.096mm crack
5

Row 1 steel
fasteners with
corner cracks
at right sites

PC2

0

(a)

0

210

(c)

330
240

300
270

Figure 5.3 Inspection of steel fasteners in Sample 2 using EC-GMR detection: Bz measurements
(a) Plots of conventional complex trajectories (b) Detection of hidden cracks around steel
fastener sites using the PCA method (c) Polar plots with data rotation for automatic detection
128

Using the conventional method that interprets EC signals in the impedance plane, the Lissajous
plots of in-phase part vs. quadrature components are presented in Figure 5.3 (a). These Lissajous
plots are from the line scans across the peak value of C-scan images in the complex plane. The
defect indications are not easily detectable from these plots. Consequently, the PCA scheme
described in Chapter 4 is employed.
The crack detection using the PCA method is applied to the C-scan images of quadrature parts,
and the results are shown in Figure 5.3 (b). The data representations in PCs subspace (PC1 and
PC2 components) are rotated so that crack data is at 90 and plotted in Figure 5.3 (c). Two
clusters that represent fasteners without cracks and fasteners with subsurface cracks are achieved
although false calls are also found.
5.2.3 Inspection of Cracks around Steel Fasteners –Tangential component
The results in Figure 5.3 have shown the feasibility of flaw detection in the presence of steel
fasteners, using the PCA processing of B z measurements with a low frequency excitation. In
this section, tangential components of low frequency EC field are examined.
The GMR sensor placed at the center of the source coil can be oriented to be sensitive to a
selected component of the magnetic field, as displayed in Figure 3.28. The C-scan images of
Sample 2 using tangential component By at a 100Hz excitation are presented in Figure 5.4.

129

-3
-3

80

In-phase part

Y (mm)

60

10

Row 140
Row 2

20

5

0

0

-20

50

80

Y (mm)

x 10
0
15

100

150

200

250

Quadrature part

60

15
10
5
0
-5

Row 1 40
Row 2

20
0

-20

X (mm)
50

100

150

200

-3
-3

x 10
0

250

Figure 5.4 C-scan images of steel fasteners in Sample 2 using low frequency EC-GMR
measurements: By component

The same procedure using the PCA method is applied to enhance the data analysis. Automatic
detection is implemented and presented in Figure 5.5. Similarly, the crack information is
recovered in the By images of quadrature parts of GMR signals, and is indicated after data
processing. In summary, it is feasible to use low frequency EC and GMR measurements to detect
defective steel fasteners with embedded cracks.

130

no crack
Row 2 steel
0.6604mm crack fasteners with
0.9652mm crack notch cracks at
1.3716mm crack
left sites
1.9812mm crack
-3 2.8702mm crack
10 x 10-3
no crack

no crack
no crack
no crack
1.524mm crack
3.048mm crack
4.572mm crack
6.096mm crack

Row 1 steel
fasteners with
corner cracks at
right sites

0.01

PC3

2
0
-2
-4

PC2

Variation

0
-0.01
-0.02

0

0.02

PC1

-0.02

90 0.04

Row 2 steel fasteners
with notch cracks at left sites

60

120

0.02

30

150

0

0

210

300
270

30

180

330
240

60

No crack

180

210

90 0.025

Cracks

Variation

150

0.02 0.04

PC1

Row 1 steel fasteners
with corner cracks at right sites
Cracks 120

0

(a)

330
240

(b)

300
270

Figure 5.5 Inspection of steel fasteners in Sample 2 using EC-GMR detection: By measurements
(a) Detection of hidden cracks around steel fastener sites using the PCA method (b) Polar plots
with data rotation for automatic detection
5.3 Model-based Study of Low Frequency 3D EC-GMR Measurements
The FE model based investigations are performed to enhance the analysis of EC-GMR image
data associated with crack identification. C-scan image fusion of three components of
time-harmonic magnetic flux density is developed.
131

5.3.1 FE Model of EC-GMR Imaging
A FE model developed in [26, 156] is used to simulate 3D GMR inspection with low frequency
excitation of the multi-line coil. This model employs an infinite sheet coil in place of the used
finite and planar coil, which eliminates the need for scanning the sample and meshing the source
coil. The A -V - A formulation is used in this FE model.
As shown in Figure 5.6 (a), the excitation current source is a waveform of 100 Hz frequency with
a current density Js along the ˆy direction (Y-axis). The infinite current sheet is located at 1 mm
above the sample. Homogeneous Dirichlet boundary conditions (values of A or V on the
boundary) are imposed to obtain a unique solution. The riveted geometry consisting of a three
layer structure is studied. The top layer and the bottom layer are 6.5 mm thick respectively. The
nd

2

layer is 14 mm thick. The material properties of steel fastener and aluminum plate are

incorporated in the model.

Current (A)

Excitation probe
Steel fastener
1

Top
layer (6.5 mm)

0

2
layer (14 mm)
Bottom
layer (6.5 mm)

-1
0

nd

0.005

Time (s)

0.01

(a)

Through
notch

Multilayer structure and steel fastener

Figure 5.6 Modeling study of a three layers riveted aircraft structure: (a) Test geometry and (b)
Distributions of 3D induced currents

132

Figure 5.6 (cont’d).
Jz

Gauss

Jy

Gauss

Jx

Gauss

(b)
The A -V - A formulation presented in Eq. (3.35) is solved for the unknown nodal quantities.
The induced currents inside the specimen are calculated by Eq. (5.3), and their 3D distributions are
displayed in Figure 5.6 (b)-(d).

133

J ind  E

(5.3)

Gauss
No crack

2.87mm crack

4.6mm crack

(a)
Gauss
No crack

2.87mm crack

4.6mm crack

(b)

Gauss
No crack

2.87mm crack

4.6mm crack

(c)
Figure 5.7 Simulation of 3-component C-scan images of three cases: (a) Quadrature part of Bz (b)
Quadrature part of By (c) Quadrature part of Bx
The C-scan images of 3D magnetic flux density associated with three steel fasteners R1 (no
defect), R2 (2.87 mm radial long defect) and R3 (4.6 mm radial long defect) are plotted in Figure

134

5.7 (a), (b) and (c) respectively. It is observed that the cracks at fastener sites magnify the
asymmetry in C-scan images, particularly in the images of tangential components. Additionally,
the degree of asymmetry is also related to the length of the crack.
5.3.2 Experimental Validation
The model predictions of 3-component fields are compared with experimental measurements on
the defective steel fastener in Figure 5.6. The C-scan images (normalized values of in-phase and
quadrature) of B z , B y , B x components are presented in Figures 5.8-5.10 respectively. These
results provide a qualitative validation of the FE simulation model for EC-GMR inspection,
allowing the use of this model for further investigation of 3-component signals.

30

Y (mm)

30

20

20

10

10
10

20 30
(a)

10
30

20

20

10

10

Y (mm)

30

10
20
X (mm)
(c)

30

10

20
(b)

30

20 30
X (mm)
(d)

Figure 5.8 Qualitative comparison of experimental and simulation C-scan images of Bz
component for a steel fastener with 2.8 mm notch: (a)-(b) Experimental in-phase and quadrature
parts (c)-(d) Simulation in-phase and quadrature parts

135

Y (mm)

40
40
30
30

40
30
30

20
20
10
10

20
20
10
10
10
10

30
30

10
10

20
20
(b)
(b)

10
10

20
20

40
40
30
30

YY(mm)
(mm)

40
40
30
30

20
20
(a)
(a)

20
20
10
10

30
30

20
20
10
10
10
10

20
20

30
30

(c) X (mm)

30
30

X (mm) (d)

Figure 5.9 Qualitative comparison of experimental and simulation C-scan images of By

Y (mm)

component for a steel fastener with 2.8 mm notch: (a)-(b) Experimental in-phase and quadrature
parts (c)-(d) Simulation in-phase and quadrature parts

30

30

20

20

10

10

Y (mm)

20
(a)

40

20
(b)

30

30

20

20

10

10
10
(c)

20 30
X (mm)

10

40

20 30
X (mm)
(d)

Figure 5.10 Qualitative comparison of experimental and simulation C-scan images of Bx
component for a steel fastener with 2.8 mm notch: (a)-(b) Experimental in-phase and quadrature
parts (c)-(d) Simulation in-phase and quadrature parts
136

5.3.3 Image Fusion Method
Based on the prior analysis, a simple image fusion method is investigated to combine the
quadrature parts in C-scan images of 3-component data. A simple approach for this fusion is
shown schematically in Figure 5.11. Two issues are studied using this linear data processing.

Quadrature part
Bz

Abs
(Im(Bz))

Quadrature part
By

Abs
(Im(By))

Quadrature part
Bx

Im(Bx)

Fused image
f ( x, y )  Wx  Im( Bx ) 

Fused image
Sum

W y  Im( B y ) 
Wz  Im( Bz )
Wx  Sgn()
W y  Sgn()
Wz  1

Figure 5.11 Fusion of quadrature parts of the 3-component GMR measurements
5.3.4 Model-based Study – Inspection of Non-ideal Fasteners
A commonly encountered problem in riveted structures is the non-ideal case of a tilted fastener
or off-center fastener as shown in Figure 5.12. These imperfect geometric factors also produce
asymmetric responses during the inspection, which can be erroneously interpreted as a crack
signal [26, 28].

Fastener hole
Non-ideal steel fastener-1Non-ideal steel fastener-2
Air gap
Ideal steel fastener

Non-ideal steel fastener-3 Non-ideal steel fastener-4
Figure 5.12 Geometries of steel fastener structures: ideal and non-ideal fasteners

137

No notch steel fastener 2.8 mm notch at Non-ideal steel fastener
steel fastener bottom
(a)

Gauss

Gauss

Y (mm)

Gauss

X (mm)
(b)

X (mm)

Gauss

X (mm)

Gauss

Y (mm)

Gauss

X (mm)
(c)

X (mm)

Gauss

Gauss

Y (mm)

Gauss

X (mm)

X (mm)

X (mm)
(d)

X (mm)

Figure 5.13 Simulation geometries and results: (a) Geometries of three cases: steel fastener
without defect (left), with a 2.8 mm notch (middle) and off-centered fastener without defect (right)
(b)-(d) Bz, By and Bx components (quadrature parts) for the corresponding cases

138

Simulation results of the three field components for the cases depicted in Figure 5.13 (a) were
computed. The test cases are 1) Ideal fastener with no defect, 2) Ideal fastener with 2.8 mm notch
in the 2

nd

layer and 3) Non-ideal (off-centered) fastener with no defect. The quadrature

components of the corresponding simulation fields are shown in Figure 5.13 (b)-(d).
The fused image of three field components is designed to enhance the asymmetry information
useful for crack detection relative to the conventional single component method. As seen in Figure
5.14, the results of image fusion serve to suppress the contribution from steel fasteners and
enhance the signals due to defect. Figure 5.14 (a) has no features once the fastener contribution is
eliminated. In Figure 5.14 (b), an asymmetric image is produced in the presence of a defect.
Non-ideal steel fastener yields a fused image in Figure 5.14 (c) with substantially different
characteristics from that of a crack.

-8

-5

Y(mm)

-6

X(mm)
(a)

X(mm)
(b)

X(mm)
(c)

Figure 5.14 Fused images: (a) Defect-free steel fastener (b) Steel fastener with a 2.8 mm notch (c)
Off-centered steel fastener
These differences are captured and quantified by means of an algorithm based on PCA method.
Specifically, the components PC1 and PC2 corresponding to two largest eigenvectors of the
139

covariance matrix are computed, which have been utilized for signal representation and crack
detection in Chapter 4 and Sections 5.2. Here, the asymmetry of fused image is quantified using
the function Fr , defined by the ratio as:
Fr  min( abs( PC1 / PC 2 ))

(5.4)

Table 5-1 presents the comparison of feature values for the case of defect-free, defective and
non-ideal steel fasteners. It is seen that the fused image of defect-free case produces a feature
value close to 0, whereas the asymmetric image of fastener with 2.8 mm notch results in larger
values of Fr. In the case of a non-ideal steel fastener, the values of Fr are significantly smaller
than that due to a defect.

Table 5-1 Feature Fr quantifying the defective steel fastener.
Steel fastener

Defect size

Fastener1
Fastener2
Fastener3
Fastener4
Fastener5
Fastener6
Fastener7

0
2.8 mm
4.6 mm
Non-ideal-1
Non-ideal-2
Non-ideal-3
Non-ideal-4

Ratio feature Fr
0.03
1.1
2.62
0.57
0.03
0.55
0.001

5.4 Summary
Eddy current testing at low frequency with 3D GMR sensors is studied for the detection of
embedded cracks under steel fastener heads. Experimental inspection of a layered aircraft structure
has been used to validate the FE model utilizing infinite coil source. Model based studies are then

140

conducted to effectively study the 3-component measurements of induced magnetic fields.
Signal processing and image fusion of B z , B x , B y data are further investigated to enhance SNR
for detecting cracks around steel fastener sites. The inspection of improperly installed fasteners is
performed with promising initial results, but more extensive studies are needed using simulation
and experimental measurements.

141

CHAPTER 6 EC-MR SENSOR SYSTEM – ROTATING FIELD EXCITATION
6.1 Introduction
The EC-GMR sensor system presented so far have one drawback in that it is sensitive largely to
cracks that are perpendicular to induced current direction. The multi-line uniform coil cannot
detect cracks that are parallel to the direction of linear currents [6-7]. Mechanically rotating EC
probes around fastener sites can be used to capture flaws in all directions [91-93]. Alternatively,
a rotating current excitation can be designed to rotate the fields and currents electrically that
generates the uniform sensitivity to cracks at all directions around fastener sites.
6.2 Orthogonal Current Excitation
6.2.1 Rotating Field
The EC-GMR probe is developed in a rotating field mode using two multi-line coils with linear
currents in orthogonal directions carrying currents with 90º phase shift. As presented in Figure
6.1, a simple design of linear current sources that are excited in two orthogonal directions is
introduced. A rotating current field is generated by the 90º phase difference of the current in two
multi-line coils:

J rot  ˆyJ 0  ˆxjJ 0

(6.1)

where yˆ and xˆ are unit vectors along Y- and X-axis, and j   1 represents the 90º phase
shift. These two orthogonal coils are on top and bottom sides of a planar PCB film and share the
same geometrical center. The GMR sensor placed at the center of this probe measures the normal
component of the total rotating field due to J rot currents.

142

Brot  ( B1r  jB1 j )  j( B2r  jB2 j )

(6.2)

where B1r , B1 j are the real and imaginary parts of the field due to ˆyJ 0 and B 2r , B 2 j are
the corresponding fields produced by jˆxJ 0 .

yˆ

linear
current

linear
current

j xˆ

linear current

GMR
sensor

-50mm

0

linear
current

linear current

50mm

yˆ

j xˆ -50mm
linear current

0

50mm

Figure 6.1 Planar multi-line current field: (a)-(b) linear current excitation: linear current field (c)
rotating current excitation: rotating current field
6.2.2 Experimental Set-up
The low frequency EC-GMR system in Chapter 5 is extended to two orthogonal coils excited by
two sinusoidal sources with 90º phase shift, produced by a function generator. The sinusoidal
waveform in 0º phase is locked in as the reference for the I/Q detector. The normal component
of the induced flux of the rotating field is sensed by the GMR sensor. The real and imaginary

143

parts of GMR response are obtained after signal conditioning and demodulation, as show in
Figure 6.2.

Two
sinusoidal sources

º

90

º

0 reference

Raw
GMR signal

DC bias
Remover

Low noise
Amplifier

I/Q detector

Output

Adjustable high gain
amplifier
Signal Conditioning
Figure 6.2 Experimental set-up of the rotating current field
6.3 Detection of Crack Orientation at Rivet Site
6.3.1 Parameters in a Practical Design
The rotating field operation is studied with respect to its sensitivity to cracks parallel in direction
as shown in Figure 6.3. From the image data in Figure 6.3 (a)-(b), it is seen that the rotating
EC-GMR sensor captures the crack orientation successfully. However, the practical design of the
rotating current excitation has challenges in that the two orthogonal multi-line coils are located
at different lift-off from the specimen surface. Therefore, the magnetic fields generated by two
coils need to be normalized or calibrated corresponding to a reference lift-off.
The model-based study of the geometry used in Figure 6.3 addresses this issue and the
corresponding results are shown in Figure 6.4. The FE model developed for simulating the
EC-GMR system in Chapter 5 is employed in this study. Two cases are considered: Case 1) Ideal
rotating current probe - the two coils are at the same lift-off of 1 mm. Case 2) Practical rotating

144

current probe - coil 1 is at 1mm lift-off and coil 2 is at 2 mm lift-off. The sensor is always
considered to be at 2 mm lift-off. Aluminum fastener without a flaw and with a 90º orientation
crack is simulated. Crack-free fastener signals for the two cases are used to calibrate the signal
from the practical probe (Case 2) as shown in Figure 6.4 (a). This calibration is applied to Case 2
signal from an Aluminum fastener with 90º orientation crack. The calibrated signal from a
practical probe is compared to that of an ideal probe signal in Figure 6.4 (b).

No crack

fastener hole
Rotating current field
Field: Y direction current Field: X direction current
(a)

crack

fastener hole
Field: Y direction current Field: X direction current
Crack at orientation 90º

Rotating current field Flux density near crack
(b)
Figure 6.3 Demonstration of crack detection using the rotating field: (a) No crack case and (b)
o
Crack at orientation 90 (parallel to Y direction current)

145

By
jBx

No crack

Probe

By
jBx

Probe

jBx
By

2mm
1mm
2mm
1mm
lift-off
lift-off
lift-off lift-off
(a)
Sample
Sample
Ideal rotating
field
at same lift-off

Gauss

25

40

15

Calibrated
20 rotating field

5

10
(b)

By
jBx

º

90 orientation
crack

Ideal rotating
field
at same lift-off

Probe

By
jBx

Probe

jBx
By

2mm
1mm
1mm
2mm
lift-off
lift-off
lift-off
lift-off
Sample
(c)
Sample
Gauss

30

50

20

30 rotating

Calibrated
field

5

10

(d)
Figure 6.4 Probe lift-off study: (a) Model-based study of rotating field variations for the crack
case (b) Model-based study of rotating field variations for the no crack case (c) Calibrated vs.
ideal rotating current field for the crack case (d) Calibrated vs. ideal rotating current field for the
no crack case

146

6.3.2 Model-based Investigation of Crack Orientation Detection
Model-based investigations for detecting crack orientations in three-layer riveted lap-joint
samples are described in this section. The model uses a low frequency (10Hz) excitation and
studies the detection of 8mm cracks through the 2

nd

layer in all orientations. The simulation

results of rotating fields for aluminum and steel fasteners are studied and displayed in Figure 6.5
respectively.

Crack

Crack

Crack

Crack

Crack

orientation 0º orientation 0º orientation 90º orientation 45º orientation 135º

Crack
Crack
Crack
Crack
Cracks at
both sides orientation 180º orientation 270º orientation 315º orientation 225º
(a)

Crack
No crack

Cracks at
both sides

Crack

Crack

Crack

orientation 0º orientation 90ºorientation 45º orientation 135º

Crack

Crack

orientation 180º orientation 270º
(b)

Crack
Crack
orientation orientation 225º
315º

Figure 6.5 Detection of crack orientations: (a) Cracks geometry in all directions (b) Rotating
field from cracks around aluminum fasteners (c) Rotating field from cracks around steel
fasteners (steel fastener effect removed)
147

Figure 6.5 (cont’d).

No crack

Crack

Cracks at
both sides

Crack

Crack

Crack

Crack

orientation 90º orientation 45º orientation 135º

Crack

Crack

Crack
orientation 0º orientation 180º orientation 270ºorientation 315º
orientation 225º
(c)

Although the cracks are not easily visible with a single current excitation, cracks in different
orientations are captured with rotating current excitation, validating the hypothesis. It should be
noted that the data from steel fasteners are first processed to suppress the fastener response.
6.4 Experimental Validation
6.4.1 Experimental Detection of Crack Orientations
EC-GMR measurements using rotating field excitation is first calibrated. In order to compensate
for the varying liftoff of the two orthogonal coils on top and bottom sides of a film, two
sinusoidal currents with 90º phase shift but different amplitudes are used. In Figure 6.6, a
defective steel fastener is tested. The two source currents are operated individually or
simultaneously and the GMR sensor located at the center measures the normal component of
magnetic field.
C-scan image of single coil operation-top coil is shown in Figure 6.6 (a), and that of the bottom
148

coil is shown in Figure 6.6 (b). The total rotating field using two simultaneous excitations can

2

Y (mm)

detect crack orientation as seen in Figure 6.6 (c).

Top current

40

Real part of Bz

0.02
0
-0.02
-0.04

20

1

-20
Y (mm)

0
-1
-2
0

0.005

40

Imaginary part of Bz

0.01

-20 0

Bottom current

1

Y (mm)

(a)

-20
Y (mm)

-1
0.005

30
20
10

0.01

Time (s)

(b)

20 40 60

0.04
0.02
0
-0.02

X (mm)

30
20
10

0

-2
0

20 40 60

20

Time (s)

2

0

-20

Real part of Bz

0
-0.02
-0.04
0

20

40

60

Imaginary part of Bz

0

20

40

0.04
0.02
0
60

X (mm)

Figure 6.6 Experimental study of rotating field: (a) Field measurement due to the top source coil
(b) Field measurement due to the bottom source coil (c) Total rotating field sensitive to a crack
around steel fastener site: absolute value of Bz

149

Figure 6.6 (cont’d).

Steel fastener

4

Top
layer (6.5 mm)

2

2nd layer
(14 mm)

Through notch

Bottom current
Top current

0
-2

Time (s)

Bottom layer
(6.5 mm)

-4
0

0.005

0.01
0.03
0.02

GMR-Bz
(V)

0.01
40

0.05
0

0
30

-0.05
0

20

Y (mm)

10
20

10

X (mm) 30
40

(c)

0

Experimental validation of the model-based study was carried out using Sample 2 with steel
fasteners. Rotating fields sensitive to different crack orientations are presented in Figure 6.7. The
measurements demonstrate the feasibility of the proposed rotating field sensor to detect cracks of
all orientations, in a qualitative manner.

150

1.524mm

3.048mm

4.572mm

1 Crack orientations

6.096mm

4
5
1
2
1.3716mm 1.9812mm 2.8702mm
5

4

2

3

3

5
(a)

6

5

6
2

1

3

4

X (mm)
5

6

Y (mm)
(b)
Figure 6.7 Experimental data from cracks with different orientations: (a) Geometry of crack in
different orientations and (b) Rotating field measurement
6.4.2 Design of Array Receiver to Crack Orientations
The use of a GMR array receiver is investigated for rapid imaging without moving the probe.
The simulation of GMR array measurement is performed using the infinite coil modeling (FE
model in Chapter 5), which generates the measured C-scan image of array receiver. Using the
single coil excitation on the top side, GMR array measurement of Bz field in the fastener area
40mm  30mm is performed experimentally. The top coil of the rotating current probe is excited
and the corresponding GMR images are obtained without probe scan.

151

Aluminum plate
40mm
by 30mm

Multi-line
planar probe

Experimental data

Simulation data

Y (mm)

15

0.9

0.8

0.7
0

0.4

0.5 0
0.3

-15
-20

0.8
0.2

0.1
0
X (mm)

20

-15
-20
(a)

Aluminum plate

20

Multi-line
planar probe

Experimental data
15

0
X (mm)

Defective fastener

40mm
by 30mm

Y (mm)

1

15

Simulation data
-0.8 15

0.9
0.7

-0.9 0

0

0.5
0.3

-15
-10

0
X (mm)

-1 -15
10
-10
(b)

0.1
0
X (mm)

10

Figure 6.8 GMR image measurement without probe motion: (a) Bz measurement of aluminum
plate and (b) Bz measurement of a defective steel fastener

As presented in Figure 6.8, in the case of an aluminum plate (Figure 6.8 (a)) and defective steel
fastener (Figure 6.8 (b)), the comparisons between the experimental and simulation data have

152

presented the feasibility of introducing the GMR array sensors for measuring the normal
component of the magnetic field. The image response of the rotating current excitation is
sensitive to all crack orientations and can be measured by the GMR array receiver, as
demonstrated in Figure 6.9.

GMR array receiver

crack

(a)

(b)

Figure 6.9 Application of GMR array receiver: Bz fast image measurement of fastener using
rotating field (a) Without crack and (b) With crack at 90ºorientation

6.5 Summary
An EC-GMR system with orthogonal current excitation, that produces rotating currents, is
developed for inspecting thick riveted multilayer structures with cracks in all directions.
Capability of the sensor to detect cracks of all orientations at fastener sites was demonstrated
using simulation and experiments. FE model based studies and experimental measurements
validate the hypothesis. The model based study was used to optimize the design of a practical
probe. More extensive experimental work to detect subsurface flaws in all directions need to be
performed in the future.
153

CHAPTER 7

PARAMETRIC STUDY OF EC-GMR DETECTION SYSTEM

7.1 Introduction
In a practical inspection scenario, signals measured by GMR sensors depend on several
parameters such as lift off, sensor tilt, top and bottom layer conductivity, and edge effect. In
particular, the signals are affected by slight tilts of the sensor which alters the probability of
detection of subsurface defects. A parametric study is conducted to analyze variations in signal
due to sensor tilt. The FE model is applied to investigate changes in defect signals in the
presence of sensor tilt. A procedure for rendering the signals invariant under sensor-tilt is also
proposed.
7.2 Sensor-tilt Study
7.2.1 Sensor-tilt of GMR Sensing
During the inspection of riveted samples, variations in EC-GMR probe lift-off from the sample
and sensor wobble resulting in sensor tilt can occur. As illustrated in Figure 7.1, this affects the
fields measured by the sensor since only the component of B z normal to the sensor is measured
according to Eq. (7.2). Also, induced magnetic fields associated with eddy currents through the
sample are no longer uniform distributions. Consequently, some asymmetry of image data is seen
to occur even when no crack is present.

VG M R BG M R Bz

VG M R BG M R Bz  c o s(  )  Bx  s i n(  )

154

(7.1)
(7.2)

7.2.2 Model-based Investigation of Sensor-tilt
A systematic study of the effect of GMR sensor-tilt is performed using the FE model. In this
study, the application of an infinite coil that is used for modeling the multi-line coil in Chapter 5
obviates the need for simulating the scan operation. Therefore, the FE model using
Ar  V  Ar formulation is implemented to study the finite coil and its sensor-tilt scenario.

z
GMR sensor
Multi-line coil

x

-line
or
Multi
R se n s
M
G
l
Distance z
co i
variation

Probe lift-off
(a)

z

 tilt angle

Probe lift-off and
tilt sensor

s: Sensitive axis:
e a xi
v
i
t
i
s
Sen nd Bx
Bz component
x
Bz a nents
o
e n so r
co m p
GMR s tilt angle

Multi-line coil
GMR sensor
Multi-line coil

(b)

Figure 7.1 Sensor-tilt variations: (a) Probe lift-off and tilt sensor and (b) GMR sensor
measurements of magnetic field components
Model-based study is conducted using a three-layer aluminum sample with aluminum fasteners.
The sample thicknesses are 6.5 mm (top layer), 14mm (middle layer) and 6.5mm (bottom layer).
nd

Excitation frequency is 100 Hz and current density Js is along ˆy direction. The cracks are 2

layer through-wall Electrical Discharge Machined (EDM) notches of different lengths in x

155

0

0

0

direction. GMR sensor measures the normal component under normal (0 ) and tilted (-2.5 : 2.5 )
states, as shown in Figure 7.2. The magnetic field measured by the GMR sensor is calculated by
Eq. (7.2) for normal, positive and negative tilt angles.

Aluminum sample
Top layer (6.5 mm)

2nd layer (14 mm)
Bottom layer (6.5 mm)
(a) 2nd layer through notch

z
x
tilt angle 

GMR sensor
 tilt angle

Multi-line
coil
(b)
Figure 7.2 Sensor-tilt measurement: (a) Geometry and FE mesh of tested sample: three-layer
riveted structure and (b) Definition of tilt degrees in two directions
Figure 7.3 presents the real and imaginary parts of GMR signals under tilt variations for the case
of a crack-free fastener geometry. It is seen that the measurements of both normal and tangential
components introduce asymmetric image data that is normally interpreted as existence of a flaw.
This could potentially results in false calls. It is hence necessary to render GMR signals
insensitive to sensor tilt while preserving sensitivity to defects.

156

x 10-5
-5

6

0
Tilt angle in unit:

GMR measurement (T)

4

2

0

0
0.5
-0.5
1
-1
1.5
-1.5
2
-2
2.5
-2.5

-2

-4

-6

0

5

1D scan position
10
(a)

15

-5
-5

6

x 10

0
Tilt angle in unit:
GMR measurement (T)

4

2

0

0
0.5
-0.5
1
-1
1.5
-1.5
2
-2
2.5
-2.5

-2

-4

-6

0

1D scan position
5
10
(b)

15

Figure 7.3 Magnetic field measured under tilt GMR sensor for a crack-free fastener: (a) Real part
of signals and (b) Imaginary part of signals
157

7.3 Invariant Analysis
Techniques for invariant pattern recognition have been studied to achieve invariance to specified
operational parameters and preserve crack information in NDE applications [180-182].
Invariance schemes have been developed in magnetostatic flux leakage and eddy current NDE,
to eliminate sensitivity to permeability or lift-off variations respectively. A novel invariance
analysis with regard to sensor tilt is explored here.
7.3.1 Transformation for Invariance to Sensor-tilt
Independent component analysis [183-184] is a useful signal-processing tool to separate multiple
unknown sources [171, 177]. In this section, the ICA analysis is applied to transform the GMR
measurements insensitive to sensor-tilt variations. Assuming the GMR measurements under n tilt
states to be composed of multiple signal components, the GMR signal g j at the jth tilt state
is expressed as a linear combination of m independent components (ICs):

g j  a j1s1  a j s 2    a jm s m , j  1,2, n
2

(7.3)

where components s1 , s2 ,sm are zero mean random variables that are mutually independent
and elements a j 1 , a j 2 ,, a jm , j  1,2 n are mixing coefficients. A vector-matrix notation of
Eq. (7.3) is represented as:

G  AS

(7.4)

where A is coefficient matrix and row components of S are estimated ICs.
The scheme for invariant transformation is depicted in Figure 7.4. Simulations of 11 GMR
0

0

0

signals are measured with tilt angles in the range [-2.5 : 0.5 : 2.5 ] and 15 scan positions. Tilt
signals are computed by Eq. (7.2). Linear interpolation is used to generate signals from other
158

sensor-tilt angles to get a dense set of measurements. After the interpolation, the GMR
measurements are re-sampled as an input vector T  [t1 ,t 2 , t p ] , where p is the total number
of signals for ICA analysis. The RobustICA Matlab module is used for ICA decomposition. The
measured GMR signal (with or without sensor-tilt effect) is expressed as a linear weighted sum
of ICs with weight coefficients.

t1 
 s1 
t  a a  a
 
p  s2 
2 1 2
   
  

  
  
t
 p 
 s p 

(7.5)

Invariance transformation is obtained by projecting GMR signals T onto the ICs domain to
generate transformed signals D .

d1  t1 
d  t  a a  a
 1 2
2
2
p
D      

   



   
d p  t p 

Sensor-tilt [-2.50 : 0.50 : 2.50 ]
11 measured states
A fastener
geometry

(7.6)

Interpolation:
Increase sampling points and
signal numbers for analysis

GMR
measurements
X(11,15)
Invariance transformation
D

GMR signals
T(50,140)

ICA processing

Figure 7.4 Diagram of ICA based transformation invariant to sensor-tilt

159

7.3.2 Invariance Transformations of GMR signals
The invariance processing is implemented on the signals in Figure 7.3 and the results are
presented in Figure 7.5. The GMR signal is a linear combination of conventional measurement
and signal caused by sensor tilt. Hence sensor-tilt effects serve as an interference source that
should be suppressed relative to crack indication. The results of suppression of the contributions
of sensor tilt are shown in Figure 7.5 (a) for the real part and Figure 7.5 (b) for the imaginary

GMR measurement (T)

part.

-9
-9

10-9
xx 10
4
4

Real part

22
00
-2
-2
-4
-4 0
0

50
50

(a)

100
100

150
150

GMR measurement (T)

-9

-9
x 10-9
4 x 10
4
2
2
0
0
-2
-2
-4
-4 0
0

Imaginary part

50
50

(b)

100
100

150
150

Figure 7.5 Transformed signals invariant to sensor-tilt in the inspection of a crack-free aluminum
fastener: (a) Real part of signals and (b) Imaginary part of signals

160

The ICA scheme for tilt invariance is applied to data from fastener geometries in Figure 7.6,
which include fasteners with different crack sizes or locations. The invariance transformations of
GMR measurements are presented in Figures 7.7-7.8.

No notch

1mm 1.98mm
notch notch

2.87mm 2.87mm notch
notch on both sides

Figure 7.6 Studied riveted geometries
-5
-5

6

x 10

GMR measurement (T)

4

2

0

-2

-4

-6

1D scan position
0

50

(a)

100

150

Figure 7.7 Measured GMR complex signals of defect-free and defective fasteners:
(a) Real parts of signals and (b) Imaginary parts of signals

161

Figure 7.7 (cont’d).

x 10 -5
-5

6

GMR measurement (T)

4

2

0

-2

-4

1D scan position
-6

0

50

(b)

100

150

As seen in Figures 7.7, the interpretation of signals is rather difficult. However, the transformed
signals in Figure 7.8 have successfully ameliorated this difficulty and enhanced the contributions
from different cracks. The distinguishable characteristics of transformed signals indicate the
potential for crack detection.

162

-8
-8

2.5

x 10

2.87mm notch

GMR measurement (T)

2
1.5
1

1.98mm notch

No notch

0.5
0
-0.5

2.87mm notch
on both sides

-1

1mm notch

-1.5
-2
-2.5

1D scan position
(a)
50
100

0

150

-8
-8

1.5

x 10

1.98mm notch

GMR measurement (T)

1

2.87mm notch

0.5

1mm notch

0
-0.5

2.87mm notch
on both sides

No notch

-1
-1.5
-2

1D scan position
0

50

(b)

100

150

Figure 7.8 Transformed GMR complex signals of defect-free and defective fasteners: (a) Real
parts of signals and (b) Imaginary parts of signals
163

7.3.3 Invariance Features and Crack Detection
Signal features that are insensitive to sensor-tilt variations are extracted from the data after ICA
transformation. Features based on skewness and kurtosis that were described in Chapter 4 are
utilized to detect cracks in the presence of sensor tilt. The skewness values of real parts of
transformed GMR signals in Figure 7.8 (a) are calculated. The skewness curves in Figure 7.9 (a)
are seen to follow a constant curve demonstrating their insensitivity to changes in sensor-tilt
angles during inspection.

-3
-3

x 10
8

Skewness feature

6

2.87mm notch

4
2

1.98mm notch

0
-2

1mm notch

-4
-6

No notch

-8
-10
-3

-2

-1

0

1

2

3

Sensor-tilt degree
(a)
Figure 7.9 Invariance feature analysis: (a) Skewness curves of transformed GMR signals
regarding different fastener states: single cracks vs. no crack (b) Two cracks on both sides

164

Figure 7.9 (cont’d).

1.6

Skewness feature

1.4
1.2

2.87mm notch
on both sides

1
0.8
0.6
0.4
0.2
0

-0.2
-3

-2

-1

0

Sensor-tilt degree
(b)

1

2

3

It is also found that the used feature is able to identify the signals due to cracks at rivet sites from
the case without crack. An interesting phenomenon is observed in Figure 7.9 (b). In the case of
two cracks on both sides of the rivet, the skewness values vary from positive to negative
numbers with respect to sensor-tilt changes, while the signals due to single cracks yield
consistent skewness value. A similar phenomenon is observed in the study of kurtosis values.
Therefore, skewness and kurtosis are employed as invariance features for signal classification, as
shown in Figure 7.10. Considering the performance of skewness feature in Figures 7.9-7.10,
work was on done on effectiveness of higher-order moments. Moments of order

5th ,6th 11th  were investigated with respect to their behavior with sensor tilt and defects.
The classification using 5 th order moments is displayed in Figure 7.11 where insensitivity to
sensor-tilt is achieved, while detection of cracks is retained.

165

x 10 -3
-3

8

2.87mm notch

Skewness feature

6
4
2

1.98mm notch

0

1mm notch

-2
-4
-6

No (0mm) notch

-8
-10

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Kurtosis feature
Figure 7.10 Crack detection: classification of GMR signals (the real part) using invariance
features

166

-3
-3

8

x 10

2.87mm notch

6

Skewness feature

4
2

1.98mm notch

0
-2

1mm notch

-4
-6

No (0mm) notch
-8
-10
-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

5th order moment feature
Figure 7.11 Classification of GMR signals in Figure 7.10 using higher order invariance features
7.3.4 Implementation to Experimental Data
The strategy described above is implemented on the experimental data from Sample 2. As shown
in Figure 7.12, GMR measurements of line scan signals along the center of steel fasteners in
Row 1 are collected under two sensor-tilt conditions. Transformed experimental signals after ICA
processing are presented in Figure 7.13 (a). Invariance analysis and classification of GMR
signals are shown in Figure 7.13 (b), which demonstrates the potential use of the scheme for
EC-GMR signal analysis in the presence of sensor-tilt.

167

Measurements of fasteners in Row 1 of Sample 2 under tilt angle_1
0.05
0.04

GMR output (V)

0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
0

10

20

30

40

50

X scan position: line scan (mm)
Measurements of fasteners in Row 1 of
Sample 2 under tilt angle_2

0.04

GMR output (V)

0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
0

10

20

30

X scan position: line scan (mm)

40

Figure 7.12 GMR signals collected under two sensor-tilt states

168

50

x 10-3
-3

2

Measurements of fasteners
in Row 1 of Sample 2

After signal
1.5 transformation:

GMR output (V)

1

1.524mm crack

0.5
0
-0.5
-1

3.048mm
crack

No crack

4.572mm crack
X scan position: line scan (mm)
10
20
40
(a) 30

-1.5
-2
0

50

th order moment feature

1.5

1

0.5

no crack
no crack
no crack
1.524mm crack
3.048mm crack
4.572mm crack

5

0

-0.5

Kurtosis feature
-1
1.85

1.9

1.95

2

(b) 2.05

2.1

2.15

2.2

Figure 7.13 Results of invariance analysis: (a) Transformations of measured GMR signals and (b)
Classification result using invariance features
169

7.4 Summary
Sensor–tilt is a major source of error in the proposed EC-GMR sensor. A novel invariance
analysis scheme based on independent component analysis is studied and validated in this
chapter. Model-based parametric studies successfully validated the performance of proposed
invariance transformation. Invariance features are extracted from transformed GMR signals and
their ability to detect defective fastener in the presence of sensor-tilt noise is demonstrated. The
results of the experimental data validate the feasibility of proposed strategy.

170

CHAPTER 8

CONCLUSIONS AND FUTURE WORK

8.1 Accomplishments and Conclusions
The research carried out during the course of this dissertation resulted in the following
contributions to the field of electromagnetic NDE:
(1) The applications of electromagnetic field GMR sensors in EC technique have been studied
extensively. Image measurements using three-component MR sensors are proposed and GMR
measurements of three-component magnetic flux density have been experimentally and
numerically validated for improving the detection of subsurface cracks under steel fastener sites.
The overall optimization was done using model-based studies for sensor design and signal
processing algorithms for data analysis and classification.
(2) Inspection systems using pulsed excitation and low frequency excitation are developed and
studied for the inspection of buried cracks at fastener sites. These studies comprise, model-based
simulation results validated by experimental measurements and development of signal
processing techniques for classification of measurements.
(3) Design of rotating field using two orthogonal-current excitations has enhanced the system
capability to detect cracks of all orientations at fastener sites. Crack orientations in all radial
directions around fastener site can be detected using appropriate signal processing algorithms.
(4) A statistical signal processing scheme is developed for automated analysis of measured data.
(5) An invariance analysis strategy is developed and evaluated and experimentally validated for
crack detection under sensor-tilt conditions.
(6) FE models that compute electromagnetic fields associated with the EC-GMR sensor
171

geometry are investigated in time and frequency domains. A fast numerical model for pulsed EC
technique is developed in time domain.
8.2 Future Work
Although a number of signal processing algorithms have been proposed, these algorithms have
not been tested with a lot of experimental data. The proposed probe design and signal analysis
algorithms must be tested more extensively. In addition, the remaining work can be pursued in
the coming years:
(1) More quantitative feature extraction for crack sizing.
(2) 3-component GMR measurement and data fusion for crack profile in riveted structure.
(3) More experimental validation of the rotating field probe and array receiver.
(4) Extension of proposed techniques to inspect other geometries.
(5) Effect of coil size to reduce edge effect. An initial study of this effect is presented. In order to
alleviate edge effects, the coil size is reduced. The system capability to inspect a riveted structure
is studied with decreasing the size of multi-line planar coil. Sample 3 with small subsurface
cracks (less than 1mm size) is examined using an excitation coil with just two turns, as shown in
Figure 8.1.
The C-scan images of the normal component are measured in Figure 8.1 (b)-(c), and the analysis
results are shown in Figure 8.1 (d) after the PCA processing. Initial results indicate feasibility of
the approach. Decreased coil size is beneficial in reducing artifacts due to edges. A more
systematic study is warranted.

172

Y (mm)

80

2mm

Fastener
3-1

-3
Fastener x 10-3
3-3 5

Fastener
3-2

60
40

0

0.8 mm &
0.7 mm
0.2 mm
No crack
cracks -5
crack
50
100
150
X (mm)
(b)
-3
Fastener 3-4
Fastener 3-5 x 10-3
20

6mm
(a)

Y (mm)

80

4

60

2
40

0

20

No crack
20

40

60
X (mm)
(c)

-2
0.5 mm
crack -4
80 100 120

0.02

No crack
No crack
0.2mm crack
0.8&0.7mm crack
0.5mm crack

PC2

0.01
0

-0.01
-0.02
0

0.005

0.01

PC1
(d)

0.015

0.02

0.025

Figure 8.1 Detection of the subsurface cracks (less than 1mm) around aluminum fasteners in
Sample 3: (a) Schematic of probe in a reduced size (b-c) C-scan images of normal component
(d) Automatic detection using the PCA processing

173

BIBLIOGRAPHY

174

BIBLIOGRAPHY

[1] Nondestructive Evaluation and Quality Control, ASM Handbook, vol. 17.
[2] G. M. Javier, G. G. Jaime and V. S. Ernesto, “Non-Destructive Techniques Based on Eddy
Current Testing,” Sensors, pp. 2525-2565, Nov. 2011.
[3] Course 30001 Reader: Non-destructive Testing, online resource.
[4] Non-destructive Testing book, online resource.
[5] S. S. Udpa and O. P. Moore, Nondestructive testing handbook: eletromagnetic testing,
American Society for Nondestructive Testing, 2004.
[6] S. S. Udpa and L. Udpa, “Eddy current nondestructive evaluation,” Encyclopedia of
Electrical and Electronics Engineering, John G Webster, Editor, John Wiley, vol. 6, pp. 149-163,
Dec. 1999.
[7] H. L. Libby, Instruction to Electromagnetic Nondestructive Test Methods, John Wiley and
Sons, New York, 1971.
[8] Y. Deng and X. Liu, “Electromagnetic imaging methods for nondestructive evaluation
applications,” Sensors, pp. 11774-11808, Nov. 2011.
[9] D. J. Hagemaier, Fundamentals of Eddy Current Testing, ASNT, 1990.
[10] D. C. Latia, Nondestructive testing for aircraft, Jeppesen, 1994.
[11] National Research Council Final Report, Aging of U.S. Air Force aircraft, National
Academy Press, Washington, D.C. (United States), 1997.
[12] “Eddy Current Testing of Aerospace Materials,” NASA Report.
[13] P. I. Beda and V. M. Sapunov, “Experience in eddy-current testing of mounting holes in
aircraft components,” Russian Journal of Nondestructive Testing, vol. 36, no. 4, pp. 241-245,
2000.

175

[14] A. Jander, C. Smith, and R. Schneider, “Magnetoresistive sensors for nondestructive
evaluation,” Proceedings of 10th SPIE International Symposium, Nondestructive Evalulation for
Health Monitoring and Diagnostics, vol. 5770, pp. 1-13, 2003.

[15] O. Hesse and S. Pankratyev, “Usage of magnetic field sensors for low frequency eddy
current testing,” Measurement Science Review, vol. 5, no. 3, pp. 86-93, 2005.
[16] T. Dogaru, C. H. Smith, R. W. Schneider, and S. T. Smith, “Deep crack detection around
fastener holes in airplane multi-layered structures using GMR-based eddy current probes,”
Proceedings of AIP Conference, vol. 700, pp. 398–405, 2004.
[17] W. F. Avrin, “Eddy-current measurements with magnetoresistive sensors: third-layer flaw
detection in a wing-splice structure 25 mm thick,” Review of Progress in QNDE, vol. 3994, pp.
29-36, 2000.
[18] J. S. Knopp, J. C. Aldrin, and K. V. Jata, “Computational methods in eddy current crack
detection at fastener sites in multi-layer structures,” Nondestructive Testing and Evaluation, vol.
24, pp. 103-120, 2009.
[19] J. M. Buckley and J. H. Calvert, “Improved eddy current techniques for the aerospace
industry,” Air Transport Association Non-Destructive Testing Forum, 1995.
[20] S. Natht, B. Wincheskii, J.P. Fultont and M. Namkung “Study of the new eddy current
non-destructive testing sensor on ferromagnetic materials,” IEEE Transactions on Magnetics, vol.
30, No. 6, pp. 4644-4646, Nov. 1994.
[21] R. T. Ko and G. J. Steffes, “Deep defect detection within thick multilayer aircraft structures
containing steel fasteners using a giant-magneto resistive (GMR) sensor,” Review of Progress in
QNDE, vol. 27, pp. 865-851, 2008.
[22] P. P. Whalen, “Transient eddy current inspection in the presence of ferrous fasteners in
multi-layered aluminum structures,” M. S. thesis, Royal Military College of Canada, 2010.
[23] B. P. C. Rao and T. Jayakumar, “Recent trends in electromagnetic NDE techniques and
future directions,” Proceedings of 18th World Conference on Nondestructive Testing, Apr. 2012,
South Africa.
[24] Project final report, “Advanced nondestructive evaluation sensor modeling for multi-site
inspection,” 2008.

176

[25] Y. Deng, X. Liu, Z. Zeng, B. Koltenbah, R. Bossi, G. Steffes, and L. Udpa, “Automated
analysis of eddy current giant magneto-resistive data,” Review of Progress in Quantitative
Nondestructive Evaluation, vol. 1096, pp. 588-595, 2009.
[26] Z. Zeng, Y. Deng, X. Liu, L. Udpa, S. S. Udpa, B. Koltenbah, R. Bossi, and G. Steffes,
“EC-GMR data analysis for inspection of multilayer airframe structures,” IEEE Transactions on
Magnetics, vol 47, No. 12, pp. 4745-4752, 2011.
[27] W. F. Avrin, “Magnetoresistive eddy-current sensor for detection deeply buried flaws,”
Review of Progress of Quantitative Nondestructive Evaluation, vol. 15, pp. 1145-1150, 1996.
[28] J. C. Aldrin, G. Steffes and J. S. Knopp, “Simulation and automated data classification for
eddy current inspection of fastener sites using a GMR sensors array with sheet current
excitation,” Review of Progress of Quantitative Nondestructive Evaluation, vol. 28, pp. 342-349,
2009.
[29] J. C. Aldrin, J. S. Knopp, E. A. Lindgren and K. V. Jata, “Model-based Inversion in Eddy
Current Image Processing,” Review of Progress in Quantitative Nondestructive Evaluation, vol.
28, pp. 719-726, 2009.
[30] C. Hellier, Handbook of Nondestructive Evaluation, McGraw-Hill, Mar., 2001.
[31] J. D. Jackson, Classical Electrodynamics, John Wiley & Sons, New York, 1998.
[32] B. Bos, S. Sahlén and J. Andersson, “Automatic scanning with multi-frequency eddy current
on multilayered structures,” Aircraft Engineering and Aerospace Technology, vol. 75, pp.
491-496, 2003.
[33] T. J. Davis and C. B. Perry, “Digitally controlled multi-frequency eddy current test
apparatus and method,” Unite States Patent, 1981.
[34] J. D. Young, K. H. Hedengren and D. C. Hurley, “Method and apparatus for a multi-channel
multi-frequency data acquisition system for nondestructive eddy current inspection testing,”
Unite States Patent, 1983.
[35] B. Sasi, B. P .C. Rao, and T. Jayakumar, “Dual-frequency eddy current non-destructive
detection of fatigue cracks in compressor discs of aero engines,” Defence Science Joumal, vol.
54, no. 4, pp. 563-570, Oct. 2004.
[36] P. Xiang, “Automatic multi-frequency rotating-probe eddy-current data analysis,” Ph.D.
dissertation, Iowa State University, 2005.
177

[37] G. Scheer, L. Frische and T. Meier, “Multi-frequency eddy current inspection of rivet rows
on aircraft structures,” ECNDE, 2006.
[38] Avanindra, “Multifrequency eddy current signal analysis,” M. S. thesis, Iowa State
University, 1997.
[39] Z. Liu, M. S. Safizadeh, D. S. Forsyth, and B. A. Lepine, “Data fusion method for the
optimal mixing of multi-frequency eddy current signals,” Review of Progress in QNDE, vol. 22,
no. pp. 577-584, 2003.
[40] H. J. Jung, Y. B. Kong, S. J. Song, C.H. Kim, Y. H. Choi, S.-C. Kang and M. H. Song,
“Investigation of frequency mixing techniques for eddy current testing of steam generator tubes
in nuclear power plants,” Review of Progress in QNDE, vol. 26, pp. 603-610, 2007.
[41] W. Yin, S. J. Dickinson and A. J. Peyton, “A multi-frequency impedance analyzing
instrument for eddy current testing,” Measurement Science and Technology, vol. 17, pp. 393-402,
2006.
[42] C. V. Dodd, W. E. Deeds, and L. D. Chitwood, “Eddy current inspection of ferromagnetic
materials using pulsed magnetic saturation,” Material Evaluation, vol. 46, pp. 1592-1597, Nov.
1988.
[43] R. E. Beissner, J. H. Rose, and N. Nakagawa, “Pulsed eddy current method: An overview,”
Review of Progress in QNDE, vol. 18A, pp. 469-475, 1998.
[44] J. C. Bowler and M. Johnson, “Advances in transient eddy current nondestructive
evaluation,” Nonlinear Electromagnetic Systems, pp. 623-627, 1996.
[45] Y. Bar-Cohen, “Emerging NDT technologies and challenges at the beginning of the third
millennium, part I,” Materials evaluation, vol. 58, pp. 17-30, 2000.
[46] B. A. Lepine, J. S. R. Giguere, D. S. Forsyth, J. M. S. Dubois, and A. Chahbaz, “Applying
pulsed eddy current NDI to the aircraft hidden corrosion problem,” Proceedings of 5th
NASA/FAA/DoD Conference Aging Aircraft, Sep. 2001.
[47] T. Hocking, F. Spears, and Y. Plotnikov, “Pulsed eddy current technology and aerospace
application,” GE Research, GEIT, Nov. 2005.
[48] T. J. Cadeau, “Increased field depth penetration with pulsed eddy current,” M. S. thesis,
Royal Military College of Canada, 2008.

178

[49] NDT resource center:
http://www.ndt-ed.org/EducationResources/CommunityCollege/EddyCurrents/ProbesCoilDesign
/ProbesConfig.htm.
[50] Institut Dr. Foerster Home Page. Available online: http://www.foerstergroup.com (accessed
on June 2012).

[51] J. E. Lenz, “A Review of Magnetic Sensors,” Proceedings of the IEEE, vol. 78, no. 6, pp.
973-989, June 1990.
[52] C. L. Wendland, “Optimization of flexible coils for embedded detection and monitoring of
cracks in aluminum structures using pulsed eddy current,” M. S. thesis, Royal Military College
of Canada, June 2005.
[53] R. J. Filkins, J. P. Fulton, T. C. Patton and J. D. Young, “Recent advances and
implementation of flexible eddy current probe technology,” Review of Progress in QNDE, vol.
17, pp. 1809-1816, 1998.
[54] D. C. Hurley, K. H. Hedengren, P. J. Howard, W. P. Kornrump, G. E. Sutton and J. D. Young,
“An eddy current array system for aircraft engine inspection,” Review of Progress in QNDE, vol.
13, pp. 1111-1118, 1994.
[55] J. P. Fulton, K. H. Hedengren, J. D. Young, R. J. Filkins and T. C. Patton, “Optimizing the
design of multilayer eddy current probes-a theoretical and experimental study,” Review of
Progress in QNDE, vol. 16, pp. 973-980, 1997.
[56] J. Melcher, “Apparatus and methods for measuring permeability and conductivity in
materials using multiple wave number magnetic interrogations,” Unite States Patent, May 1991.
[57] N. Goldfine, V. Zilberstein, A. Washabaugh, D. Schlicker, I. Shay and D. Grundy, “Eddy
current sensor networks for aircraft fatigue monitoring,” ASNT Materials Evaluation, Aerospace
Health Monitoring, vol. 61, no, 7, pp. 1-13, Jul. 2003.
[58] T. Yentzer, S. Kramer et al, “High-resolution eddy current sensor arrays for detection of
hidden damage including corrosion and fatigue cracks,” NASA/FAA/DoD Conference on Aging
Aircraft, pp. 1-13, Sep. 2001, Florida.
[59] V. Zilberstein, D. Schlicker, K. Walrath, V. Weiss and N. Goldfine, “MWM eddy current
sensors for monitoring of crack initiation and growth during fatigue tests and in service,”
International Journal of Fatigue, vol. 23, pp. 477-485, 2001.
179

[60] V. Zilberstein, K. Walrath, D. Grundy, D. Schlicker and N. Goldfine, “MWM eddy current
sensors for monitoring of crack initiation and growth,” International Journal of Fatigue, vol. 25,
pp. 11477-1155, 2003.
[61] S. Yamada, M. Katou, M. Iwahara and F. P. Dawson, “Eddy current testing probe composed
of planar coils,” IEEE Transactions on Magnetics, vol. 31, no. 6, pp. 3185-3187, Nov. 1995.

[62] S. Yamada, M. Katou, M. Iwahara and F. P. Dawson, “Defect images by planar ECT probe
of meander-mesh coils,” IEEE Transactions on Magnetics, vol. 32, no. 5, pp. 4956-4958, Sep.
1996.
[63] S. C. Mukhopadhyay, “A novel planar mesh-type microelectromagnetic sensor. Part I.
Model formulation,” Sensors Journal, IEEE, vol. 4, no. 3, pp. 301-307, 2004.
[64] A. Rakow, “A structural health monitoring fastener for tracking fatigue crack growth in
bolted metallic joints,” Ph.D. dissertation, Stanford University, 2008.
[65] A. Rakow and F. Chang, “A structural health monitoring fastener for tracking fatigue crack
growth in bolted metallic joints,” Structural Health Monitoring, vol. 11, pp. 253-267, 2012.
[66] L. Rosado, “Non-destructive testing based on eddy currents,” M. S. thesis, Instituto Superior
Técnico, Nov. 2009.
[67] J. Fava, M. Ruch and A. E. Obrutsky, “Design and construction of eddy current sensors with
rectangular planar coils,” Non-Destructive Testing Condition Monitoring, vol. 46, pp. 268-274,
2004.
[68] T. Dogarl, “Giant magnetoresistace based eddy current probes for nondestructive testing,”
Ph.D. dissertation, University of North Carolina, 2002.
[69] T. Dogaru, C. H. Smith, R. W. Schneider and S. T. Smith, “New directions in eddy current
sensing,” Albany Instruments, NVE Corp. and UNC Charlotte.
[70] T. P. Theodoulidisa and E. E. Kriezisb, “Impedance evaluation of rectangular coils for eddy
current testing of planar media,” NDT & E International, vol. 35, no. 6, pp. 407-414, Sep. 2002.
[71] R. J. Ditchburn, S. K. Burke and M. Posada, “Eddy-Current Nondestructive Inspection with
Thin Spiral Coils: Long Cracks in Steel,” Journal of Nondestructive Evaluation, vol. 22, no. 2,
pp. 63-77, June 2003.

180

[72] R. J. Ditchburn and S. K. Burke, “Planar rectangular spiral coils in eddy-current
non-destructive inspection,” NDT & E International, vol. 38, no. 8, pp. 690-700, Dec. 2005.
[73] M. J. Caruso, T. Bratland, C. H. Smith and R. Schneider, “A new perspective on magnetic
field sensing,” Honeywell and NVE Corp.
[74] M. Spies, “Course on Electromagnetic NDT Methods,” Online resource.
[75] S. Cherepov, O. Hesse, G. Mook, S. Pankratyev and V. Uchanin, “Optimisation of low
frequency eddy current sensors using improved inductive coils and highly sensitive AMR and
GMR sensor modules,” Online resource.
[76] J. K. Na, M. A. Franklin and J. R. Linn, “Detection of hidden cracks on aircraft lap joints
with GMR based eddy current technology,” Review of Progress in QNDE, vol. 25, pp. 345-352,
2005.
[77] E. S. Boltz, D. W. Cutler and T. C. Tiernan, “Low-frequency magnetoresistive eddy-current
sensor for NDE of aging aircraft,” Proceedings of SPIE, vol. 3397, pp. 39-49, 1998.
[78] C. Reig, M. D. Cubells-Beltrán and D. R. Muñoz, “Magnetic field sensors based on giant
magnetoresistance (GMR) technology: applications in electrical current sensing,” Sensor, vol. 9,
no. 10, pp. 7919-7942, 2009.
[79] Carl H. Smith and Robert W. Schneider, “Low-field magnetic sensing with GMR sensors,”
NVE Corp.
[80] T. Dogaru and S. T. Smith, “Giant magnetoresistance-based eddy-current sensor,” IEEE
Transactions on Magnetics, vol. 37, no. 5, pp. 3831-3838, Sep. 2001.
[81] F. Di Iorio, “Low field magnetic sensing with giant magneto resistive sensors,” Ph.D.
dissertation, University of Naples “Federico II”, 2007.
[82] Y. Sun, T. Ouyang and S. Udpa, “Multi-layer aircraft structure inspection using
super-sensitive Remote-Field Eddy-Current system,” Review of Progress in QNDE, vol. 20, pp.
1906-1913, 2001.
[83] R. A. Smith and D. Edgar, “Advances in transient eddy-current imaging for aerospace
applicarions,” Proceedings of World Conference on NDT, 2004.
[84] M. Gibbs and J. Campbell, “Pulsed eddy current inspection of cracks under installed
fasteners,” Materials Evaluation, vol. 49, no.1, pp. 51-59, Jan. 1991.
181

[85] G. L. Fitzpatrick, D. K. Thome, R. L. Skaugset, E. Y. C. Shih and W. C. L. Shih,
“Magneto-optic/eddy current imaging of aging aircraft: A new NDI technique,” Material
Evaluation, vol. 51, pp. 1402-1407, 1993.
[86] I. Elshafiey and L. Udpa, “Sensitivity analysis of magneto-optic imaging in nondestructive
evaluation of pipelines,” Proceedings of 3rd Middle East Nondestructive Testing Conference &
Exhibition, Nov. 2005, Manama.

[87] P. Y. Joubert, J. Pinassaud, “Linear magneto-optic imager for non-destructive evaluation,”
Sensors Actuator A, vol. 129, pp. 126-130, 2006.
[88] Y. H. Cheng, Z. F. Zhou, G. Y. Tian, “Enhanced magneto-optic imaging system for
nondestructive evaluation,” NDT&E Intentional, vol. 40, pp. 374-377, 2007.
[89] Y. Deng, X. Liu, Y. Fan, Z. Zeng, L. Udpa, and W. Shih, “Characterization of
magneto-optic imaging data for aircraft inspection”, IEEE Transactions on Magnetics, vol. 42,
pp. 3228-3230, Oct. 2006.
[90] G. Rubinacci, A. Tamburrino, S. Ventre, P. Joubert and J. Pinassaud, “Numerical modeling
of a continuous level Eddy Current Imager,” Electromagnetic Non-destructive Evaluation (X), pp.
33-40, 2007.
[91] B. Wincheski and M.Namkung, “Electromagnetic detection of fatigue cracks under
protruding head ferromagnetic fasteners,” Technical Report, NASA Langley Research Center,
USA, 1999.
[92] B. Wincheski, J. Simpson, M. Namkung, D. Perey, Ed Scales and R. Louie, “Development
of giant magnetoresistive inspection system for detection of deep fatigue cracks under airframe
fasteners,” Review of Progress in QNDE, vol. 21, pp. 1007-1014, 2002.
[93] T. Dogaru, C. H. Smith, R. W. Schneider, and S. T. Smith, “Deep crack detection around
fastener holes in airplane multi-layered structures using GMR-based eddy current probes,”
Proceedings of AIP Conference, vol. 700, pp. 398–405, 2004.
[94] D. J. Harrison, “The detection of corrosion in layered structures using transient eddy
currents,” Nondestructive Testing of Materials, pp. 115-124, 1995.
[95] T. W. Krause, C. Mandache, and J. H. V. Lefebvre, “Diffusion of pulsed eddy currents in
thin conducting plates,” Proceedings of AIP Conference, vol. 975, pp. 368-375, 2008.

182

[96] S. Giguere, “Pulsed eddy current for corrosion detection”, M. S. thesis, Royal Military
College of Canada, 1999.
[97] J. H. Vivier Lefebvre, “Simultaneous conductivity and thickness measurements using pulsed
eddy current,” M. S. thesis, Royal Military College of Canada, 2003.
[98] A. Sophian, “Characterisation of surface and sub-surface discontinuities in metals using
pulsed eddy current sensors,” Ph.D. dissertation, Huddersfiled University, 2003.

[99] C. Murner and J. P. Hansen, “Buried corrosion detection in multi-layer airframe structures
using pulsed eddy current,” Proceedings of 17th World Conference on Nondestructive Testing,
2008.
[100] D. L. Waidelich, J. A. DeShong and W. J. McGonnagle, “A pulsed eddy current technique
for measuring clad thickness,” Argonne National Laboratory Report, 1955.
[101] S. Giguere, B. A. Lepine and J. M. S. Dubois, “Pulsed eddy-current characterization of
material loss in multi-layer structures,” Canadian Aeronautics and Space Journal, vol. 46, pp.
204-208, 2000.
[102] D. J. Harrison, “Progress in the detection of cracks under installed fasteners using eddy
currents,” Proceedings of AGARD Conference, vol. 462, 1989.
[103] D. J. Harrison, “Eddy current inspection using Hall sensor and transient excitation,”
Defense Research Agency DRA/SMC/TR941008, 1995.
[104] J. S. R. Giguere, B. A. Lepine and J. M. S. Dubois, “Detection of cracks beneath rivet
heads via pulsed eddy current technique,” Review of Progress of Quantitative Nondestructive
Evaluation, vol.21, pp. 1968-1975, 2002.
[105] B. Lebrun, Y. Jayet and J. C. Babous, “Pulsed eddy current applications to the detection of
deep cracks,” Materials Evaluation, vol. 53, pp. 1296-1300, 1995.
[106] B. Lebrun and J. C. Babous, “Pulsed eddy current signal analysis: application to the
experimental detection and characterization of deep flaws in highly conductive materials,”
NDT&E International, vol.30, pp. 163-170, 1997.
[107] C. C. Tai, J. H. Rose and J. C. Moulder, “Thickness and conductivity of metallic layers
from pulsed eddy current measurements,” Review of Scientific Instruments, vol.67, pp.
3965-3972, Nov. 1996.
183

[108] J. C. Moulder, J. A. Bieber, W. W. Ward III and J. H. Rose, “Scanned pulsed-eddy-current
instrument for non-destructive inspection of aging aircraft,” Nondestructive Evaluation of Aging
Aircraft, Airports and Aerospace Hardware, Proceedings of SPIE, vol. 2945, pp. 2-13, 1996.
[109] J. A. Bieber, S. K. Shaligram and J. H. Rose, “Time-gating of pulsed eddy current signals
for defect characterization and discrimination in aircraft lap-joints,” Review of Progress in
QNDE, vol. 16, pp. 1915-1922, 1997.
[110] R. A. Smith and G. R. Hugo, “Deep corrosion and crack detection in aging aircraft using
transient eddy current NDE,” Proceedings of 5th Joint NASA/FAA/DoD Conference on Aging
Aircraft, Orlando, 2001.
[111] R. A. Smith, G. R. Hugo and D. J. Harrison, “Essential factors in improving the
characterization of cracks and corrosion using transient eddy currents,” Proceedings of 6th Joint
FAA/NASA/DoD Conference on Aging Aircraft, Scan Francisco, Sep. 2002.
[112] A. Sophian, G. Y. Tian, D. Taylor and J. Rudlin, “Design of a pulsed eddy current sensor
for detection of defects in aircraft lap-joints,” Sensors & Actuators: A. Physical, vol. 101, pp.
92-98, 2002.
[113] M. J. Johoson, J. R. Bowler and F. Azzem, “Pulsed eddy-current at Iowa State
University-recent progress and results,” Review of Quantitative Novdestructive Evaluation, vol.
22, pp. 390-396, 2003.
[114] T. Hocking, F. Spears and Y. Plotnikov, “Pulsed eddy current technology and aerospace
application,” GE Research, 2005.
[115] G. Y. Tian, A. Sophian, “Defect classification using a new feature for pulsed eddy current
sensors,” NDT&E International, vol.38, no. pp.77-82, Jan. 2005.
[116] B. F. Yang, F. L. Luo and D. Han, “Scanned pulsed eddy current technique used for
nondestructive inspection of aging aircraft,” Insight, pp.6129-6132, 2006.
[117] Y. He, F. Luo, M. Pan, F. Weng, X. Hu, J. Gao and B. Liu, “Pulsed eddy current technique
for defect detection in aircraft riveted structures,” NDT & E International, vol. 43, pp. 176-181,
2010.
[118] Y. He, F. Luo, M. Pan, X. Hu, B. Liu and J. Gao, “Defect edge
identification with rectangular pulsed eddy current sensor based on transient response signals ,”
NDT & E International, vol. 43, pp. 409-415, 2010.

184

[119] B. A. Lepine, B. P. Wallace, D. S. Forsyth and A. Wyglinski, “Pulsed eddy current method
developments for hidden corrosion detection in aircraft structures,” NDT.net, vol.4, no. 1, Jan.
1999.
[120] B. A. James, “Time-domain solutions of two and three-dimensional transient
electromagnetic fields,” Ph.D. dissertation, Carnegie-Mellon University, 1990.
[121] C. C. Tai and S. S. Lee, “Time-domain and frequency-domain eddy current simulations by
the finite element method,” Key Engineering Materials, vols. 270-273, pp. 585-592, Aug. 2004.
[122] E. E. Kriezis, T. D. Tsiboukis, S. M. Panas and J. A. Tegopoulos, “Eddy currents: theory
and applications,” Proceedings of the IEEE, vol. 80, no. 10, Oct. 1992.
[123] J. Mackerle, “Finite-element modelling of non-destructive material evaluation, an
addendum: a bibliography,” Modeling and Simulation in Materials Science and Engineering, vol.
12, pp. 799-834, 2004.
[124] David H. S. Cheng, “The reflected impedance of a circular coil in the proximity of a
semi-infinite medium,” IEEE Transactions on Instrumentation and Measurement, vol. 14, no. 3,
pp. 107-116, Sep. 1965.
[125] C.V. Dodd and W. E. Deeds, “Analytical solutions to eddy-current probe-coil problems,”
Journal of Applied Physics, vol. 39, no. 6, pp. 2829-2838, May. 1968.
[126] R. Ludwig and X. W. Dai, “Numerical and analytical modeling of pulsed eddy-currents in
a conducting half-space,” IEEE Transactions on Magnetics, vol. 26, no. 1, pp. 299–307, Jan.
1990.
[127] J. Bowler and M. Johnson, “Pulsed eddy-current response to a conducting half-space,”
IEEE Transactions on Magnetcis, vol. 33, no. 3, pp. 2258-2264, May. 1997.
[128] N. Ida, Numerical Modeling for Electromagnetic Non-Destructive Evaluation, Chapman &
Hall, London, 1995.
[129] J. R. Bowler, “Pulsed eddy current inversion for the determination of crack shape,”
Electromagnetic Nondestructive Evaluation (III), pp. 263-269, 1997.
[130] F. Fu, “Transient eddy current response due to a subsurface crack in a conductive plate,”
Ph.D. dissertation, Iowa State University, 2006.
[131] T. Theodoulidis, “Developments, in calculating the transient eddy current response from a
conductive plate,” IEEE Transactions on Magnetics, vol. 28, no. 2, pp. 97-102, April, 1995.
185

[132] T. J. Cadeau and T. W. Krause, “Pulsed eddy current probe design based on transient
circuit analysis,” Review of Progress in Quantitative Nondestructive Evaluation, vol. 28, pp.
327-334, 2009.
[133] V. Babbar, P. Whalen and T. Krause, “Finite element modelling of transient eddy currents
from defects in the presence of ferrous fasteners in multi-layered aluminum structures,”
Conference of 3rd International CANDU In-Service-Inspection and NDT, Canada, 2010.
[134] F. Thollon, B. Lebrun, N. Burais and Y. Jayet, “Numerical and experimental study of eddy
current probes in NDT of structures with deep flaws,” NDT & E International, vol. 41, pp.
477-483, 2008.
[135] Y. Li, G. Y. Tian and A. Simm, “Fast analytical modeling for pulsed eddy current
evaluation,” NDT & E International, vol. 41, pp. 477-483, 2008.
[136] G. Preda, B. Cranganu-Cretu, F. I. Hantila, O. Mihalache, Z. Chen, and K. Miya,
“Nonlinear FEM–BEM formulation and model-free inversion procedure for reconstruction of
cracks using pulse eddy currents,” IEEE Transactions on Magnetics, vol. 38, no. 2, pp.
1241-1244, Mar. 2002.
[137] S. Xie, Z. Chen, T. Takagi, and T. Uchimoto, “Efficient numerical solver for simulation of
pulsed eddy-current testing signals,” IEEE Transactions on Magnetics, vol. 47, pp. 4582 - 4591,
2011.
[138] C. H. Ahn, B. S. Jeong, and S. Y. Lee, “Efficient hybrid finite element-boundary element
method for 3-dimensional open-boundary field problems,” IEEE Transactions on Magnetics, vol.
27, no. 5, pp. 4069-4072, Sep. 1991.
[139] J. R. Bowler and D. J. Harrison, “Measurement and calculation of transient eddy-currents
in layered structures,” Review of Progress in Quantitative Nondestructive Evaluation, vol.11, pp.
241-248, 1992.
[140] I. A. Tsukerman, A. Konrad, G. Bedrosian and M. V. K. Chari, “A Survey of Numerical
Methods for Transient Eddy Current Problems,” IEEE Transactions on Magnetics, vol. 29, no. 2,
pp. 1711-1716, 1993.
[141] U. Patel and D. Rodger, “Finite element modeling of pulsed eddy currents for
nondestructive testing,” IEEE Transactions on Magnetics, vol. 32, pp. 1593-1596, 1996.
[142] O. Biro, P. Bohm, K. Preis and G. Wachutka, “Edge finite element analysis of transient skin
effect problem,” IEEE Transactions on Magnetics, vol. 36, no. 4, pp. 835-839, Jul. 2000.

186

[143] L. Xuan, Z. Zeng, B. Shanker and L. Udpa, “Meshless method for numerical modeling of
pulsed eddy currents,” IEEE Transactions on Magnetics, vol. 40, no. 6, pp. 3457-3462, Nov.
2004.
[144] I. Elshafiey, „Comparison of computational modeling techniques of pulsed eddy current
inspection‟, Review of Progress in Quantitative Nondestructive Evaluation, vol. 28, pp. 319-326,
2009.
[145] C. Lee, M. J. Johnson and N. Nakagawa, “Development of a pulsed eddy current system
and its characterization,” Review of Progress in Quantitative Nondestructive Evaluation, vol.26,
pp. 354-361, 2007.
[146] M. Dadic, “A system identification approach to the modeling of pulsed eddy-current
system,” NDT&E international, vol. 38, pp. 107-111, 2005.
[147] M. Dadic, “Enhanced time-stepping FEM simulation using digital signal processing,”
Simulation, vol. 84, no. 4, pp. 169–178, April 2008.
[148] Y. K. Shin, D. M. Choi, H. S. Jung and T. G. Um, “Performance evaluation of several types
of pulsed eddy current probes for detecting wall thickness reduction,” Review of Progress in
Quantitative Nondestructive Evaluation, vol. 29, pp. 393-400, 2010.
[149] R. D. Rempt and G. A. Perry, “Flexible hand held MR scanning array for cracks/flaws,”
Unite States Patent, May 2008.
[150] N. Nair., V. Melapudi., J. Hector, X. Liu, Y. Deng, Z. Zeng, L. Udpa, J. M. Thomas and S.
Udpa, “A GMR-based eddy current system for NDE of aircraft structures,” IEEE Transactions on
Magnetics, vol. 42, pp. 3312-3314, 2006.
[151] S. Yamada, K. Chomsuwan and M. Iwahara, “Application of giant magnetoresistive sensor
for nondestructive evaluation,” Proceedings of the IEEE Sensors, pp. 927-930, Oct. 2006.
[152] A. Tamburrino, S. Ventre, L. Ferrigno, and S. Udpa, “Characterization and implementation
of a GMR based probe for eddy current testing,” International Journal of Applied
Electromagnetics and Mechanics, vol. 28, pp. 329-336, 2008.
[153] O. Biro and K. Preis, “On the use of the magnetic vector potential in the finite-element
analysis of three-dimensional eddy currents,” IEEE Transactions on Magnetics, vol. 25, no. 4, pp.
3145-3159, Jul. 1989.

187

[154] O. Biro and K. Preis, “Finite element analysis of 3-D eddy currents,” IEEE Transactions
on Magnetics, vol. 26, no. 2, pp. 418-423, Mar. 1990.
[155] J. Jin, The Finite Element Method in Electromagnetics, IEEE press: Wiley, May. 2002.
[156] Z. Zeng, X. Liu, Y. Deng, L. Udpa, L. Xuan, W. C. L. Shih and G. L. Fitzpatrick, “A
parametric study of magneto-optic imaging using finite-element analysis applied to aircraft rivet
site inspection,” IEEE Transactions on Magnetics, vol. 42, pp. 3737-3744, 2006.
[157] Z. Zeng, X. Liu, Y. Deng and L. Udpa, “Reduced magnetic vector potential and electric
scalar potential formulation for eddy current modeling,” Przeglad Elektrotechniczny, vol. 83, no.
6, pp. 35-37, Mar. 2007.
[158] Z. Zeng, L. Udpa, S. S. Udpa, and M. S. C. Chan, “Reduced magnetic vector potential
formulation in the finite element analysis of eddy current nondestructive testing,” IEEE
Transactions on Magnetics, vol. 45, no. 3, pp. 964-967, Mar. 2009.
[159] L. Ljung, System Identification: Theory for the user, Englewood Cliffs: Prentice-Hall,
1999.
[160] T. Clauzon, F. Thollon and A. Nicolas, “Flaws characterisation with pulsed eddy current
NDT,” IEEE Transactions on Magnetics, vol.35, no. 3, pp.1873-1876, 1999.
[161] G. Yang Z. Zeng, Y. Deng, X. Liu, L. Udpa, A. Tamburrino, S. S. Udpa, “ 3D EC-GMR
sensor system for detection of subsurface defects at steel fastener sites,” NDT and E
International, vol. 50, pp. 20-28, Sep. 2012.
[162] H. S. Mohammad Saleh “Detection of hidden corrosion by pulsed eddy current using time
frequency analysis,” Ph.D. dissertation, University of Montreal, 2012.
[163] G. Y. Tian, A. Sophian, D. Taylor and J. Rudlin, “Wavelet-based PCA defect classification
and quantification for pulsed eddy current NDT,” IEE Proceedings: Science Measurement and
Technology, vol. 152, no.4, pp. 141-148, Jul. 2005.
[164] T. L. Chen, G. Y. Tian, A. Sophian, P. W. Que, “Feature extraction and selection for defect
classification of pulsed eddy current NDT,” NDT & E international, vol.41, no.6, pp. 467-476,
Apr. 2008.
[165] M. S. Safizadeh, B. A. Lepine, D. S. Forsyth and and A. Fahr, “Time-frequency analysis of
pulsed eddy current signals,” Journal of Nondestructive Evaluation, vol. 20, pp. 73-86, 2001.

188

[166] M. S. Safizadeh, Z. Liu, D. S. Forsyth and A. Fahr, “Automatic classification and
characterization of hidden corrosion using pulsed eddy current data,” Proceedings of 5th
International Workshop, Advances in Signal Processing for Non Destructive Evaluation of
Materials, vol.27, pp. 25-30, 2006.
[167] D. G Park and C. S. Angani, “Evaluation of pulsed eddy current response and detection of
the thickness variation in the stainless steel,” IEEE Transactions on Magnetics, vol. 45, pp.
3893-3896, 2009.
[168] Z. Q. Lang, A. Agurto, G. Y. Tian and A. Sophian, “A system identification based approach
for pulsed eddy current non-destructive evaluation,” Measurement Science and Technology, vol.
18, pp. 2083-2091, 2007.

[169] B. F. Yang, F. L. Luo and D. Han, “Research on edge identification of a defect using pulsed
eddy current based on principal component analysis,” NDT & E International, vol. 40, pp.
294-299, 2007.
[170] G. Yang, G. Y. Tian, P. W. Que and T. L. Chen, “Independent Component Analysis-Based
Feature Extraction Technique for Defect Classification Applied for Pulsed Eddy Current NDE,”
Research in Nondestructive Evaluation, vol. 20, no. 4, pp. 230-245, Oct. 2009.
[171] P. Horan, P. R. Underhill and T. W. Krause, “Pulsed eddy current detection of cracks in
F/A-18 inner wing spar without wing skin removal using modified principal component
analysis,” NDT & E International, vol. 55, pp. 21-27, 2013.
[172] J. M. Lattin, J. D. Carroll and P. E. Green, Analyzing Multivariate Data, CA : Thomso n
Brooks/Cole, 2003.
[173] H. Wolfgang, and S. Léopold, Applied multivariate statistical analysis, New York:
Springer, 2007.
[174] F. Lingvall, T. Stepinski, “Automatic detecting and classifying defects during eddy current
inspection of riveted lap-joints,” NDT and E International, vol.33, pp. 47-55, 2000.
[175] Y. L. Diraison, P. Y. Joubert and D. Placko, “Characterization of subsurface defects in
aeronautical riveted lap-joints using multi-frequency eddy current imaging,” NDT and E
International, vol. 42, no. 2, pp. 133-140, Mar. 2009.

189

[176] P. Y. Joubert, E. Vourch, A. Tassin and Y. L. Diraison, “Source separation techniques
applied to the detection of subsurface defects in the eddy current NDT of aeronautical
lap-joints,” NDT and E International, vol. 43, no. 7, pp. 606-614, Oct. 2010.
[177] K. V. Mardia, “Measures of multivariate skewness and kurtosis with applications,”
Biometrika, vol. 57, no. 3, pp. 519-530, 1970.
[178] J. P. Egan, Signal detection theory and ROC analysis, series in cognition and perception,
New York: Academic Press, 1975.
[179] Receiver operating characteristic:
http://en.wikipedia.org/wiki/Receiver_operating_characteristic
[180] S. Mandayam, L. Udpa, S. S. Udpa and W. Lord, “Invariance transformation for magnetic
flux leakage signals,” IEEE Transactions on Magnetics, vol. 32. no. 3, pp. 1577-1580, 1996.
[181] D. Kim, L. Udpa and S. S. Udpa, “Lift-off invariance transformations for eddy current
nondestructive evaluation signals,” Review of Progress in QNDE, vol. 21, pp. 615-622, 2002.
[182] J. C. Aldrin and J. S. Knopp, “Method for crack characterization with noise invariance for
eddy current inspection of fastener sites,” Review of Progress in QNDE, vol. 25, pp. 315-322,
2006.
[186] C. Pierre, “Independent component analysis: a new concept?” Signal Processing, vol. 36,
no. 3, pp. 287–314, 1994.
[187] A, Oja E. Hyvärinen, “Independent component analysis: algorithms and applications,”
Neural Networks, vol. 13, no. 4-5, pp. 411–430, 2000.
[188] B. H. Shin, P. Ramuhalli, L. Udpa, and S. Udpa, “Independent component analysis for
enhanced feature extraction from NDE,” Review of Progress in QNDE, vol. 23, pp. 597-604,
2004.

190

PUBLICATIONS
∗ Journals
[1] G. Yang, Z. Zeng, Y. Deng, et al, „Sensor-tilt Invariance Analysis for Eddy Current Signals‟,
NDT & E International, Vol. 52, 2012.
[2] G. Yang, Z. Zeng, Y. Deng, et al, „3D EC-GMR Sensor System for Detection of Subsurface
Defects at Steel Fastener Sites‟, NDT & E International, Vol. 50, 2012.
[3] G. Yang, T. Khan, L. Zhang, L. Udpa, et al, „Pre-processing Methods for Eddy Current Data
Analysis using Hilbert-Huang Transform‟, International Journal of Applied Electromagnetics and
Mechanics, Vol. 39, 2012.
[4] G. Yang, A. Tamburrino, L. Udpa, et al, „Pulsed Eddy Current based GMR System for the
Inspection of Aircraft Structures‟, IEEE Transactions on Magnetics, Vol. 46(3), 2010.
[5] Q. Zhang, T. Chen, G. Yang, et al, „Time and Frequency Domain Feature Fusion for Defect
Classification Based on Pulsed Eddy Current NDT‟, Research in Nondestructive Evaluation, Vol.
23(3), 2012.
[6] J. Kim, G. Yang, L. Udpa, et al, „Classification of Pulsed Eddy Current GMR Data on Aircraft
Structures‟, NDT & E International, Vol. 43(2), 2010.
[7] G. Dib, R. Lattral, L. Udpa, G. Yang, „A wireless sensor node for structural health monitoring
using guided wave inspection‟, Material Evaluation, Vol. 71, 2013.
∗ Conference Proceedings
[8] G. Yang, Y. Huang, L. Udpa, S. Udpa, „Enhanced EC-GMR Inspection of Buried Cracks at
Ferromagnetic Fastener Sites‟, Proceedings of 18th International Workshop on Electromagnetic
NonDestructive Evaluation, Bratislava, Slovak Republic, 2013, In Press.
[9] G. Yang, A. Tamburrino, Z. Zeng, et al, „Low frequency EC-GMR detection of cracks at
ferromagnetic fastener sites in thick layered structure‟, Review of Progress in QNDE, Vol. 32,
2013.
[10] G. Yang, G. Dib, J. Kim, et al, „Nonlinear, Non-stationary Image Processing Technique for
Eddy Current NDE‟, Review of Progress in QNDE, Vol. 31, 2012.
[11] G. Yang, Z. Zeng, L. Udpa, et al, „Modeling and Signal Processing Sensor Tilt in Eddy
current-GMR Inspection‟, Electromagnetic Nondestructive Evaluation (XIV), Vol. 35, 2011.
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[12] G. Yang, Q. Zhang, Y. Yang, „Novel Statistical Technique of Defective Information
Extraction in Pulsed Eddy Current NDE‟, Information and Automation, IEEE Conference
Publications, 2011.
[13] G. Yang, J. Kim, S. Udpa, et al, „Classification of Pulsed Eddy Current-GMR Data using
Principle Component Analysis‟, Electromagnetic Nondestructive Evaluation (XIII), Vol. 33, 2010.
[14] G. Yang, Z. Zeng, Y. Deng, et al, „Pulsed Eddy Current-GMR Inspection and Image Analysis
of Multilayer Airframe Structures‟, Proceedings of Global Chinese Forum on NDT Technologies,
2011.
[15] Y. Deng, X. Liu, G. Yang, „Model Based POD Techniques for Enhancing Reliability of
Steam Generator Tube Inspection‟, Prognostics & Health Management, IEEE Conference
Publications, 2011.
[16] M. Cacciola, G. Ripepi, G. Yang, et al, „ICA based Algorithms for Flaw Classification in
Pulsed Eddy Current Data: A Study‟, Proceedings of the conference on Neural Nets WIRN, 2011.
∗ Peer-Reviewed Conference Papers and Presentations
[17] G. Yang, A. Tamburrino, Z. Zeng, et al, „Sensitivity of EC-GMR Sensors to Orientation of
Radial Cracks at Fastener Sites‟, 39th Review of Progress in QNDE, Denver, Colorado, July, 2012.
[18] G. Yang, Y. Deng, L. Udpa, et al, „Development of Novel EC-GMR Sensor Systems for
Inspection of Multilayer Structures with Steel Fasteners‟, 18th World Conference on NDT, Durban,
South Africa, April, 2012.
[19] G. Yang, Y. Deng, Z. Zeng, et al, „Invariant Analysis of Sensor-tilt Effect in Eddy Current
NDE‟, 30th Progress In Electromagnetics Research Symposium Conference, Suzhou, China,
September, 2011.
[20] G. Yang, Z. Zeng, Y. Deng, et al, „EC-GMR Detection of Subsurface Defects at Steel
Fastener Sites in Multilayer Structures‟, 38th Review of Progress in QNDE, Burlington, Vermont,
July, 2011.
[21] G. Yang, Z. Zeng, Y. Deng, et al, „Detection of Subsurface Defects in Multilayer Structures
with Steel Fasteners‟, 29th Progress In PIERS, Marrakesh, Morocco, March , 2011.
[22] G. Yang, L. Udpa, S. Udpa, et al, „Modelling of Sensor Tilt in Eddy Current–GMR
Inspection and its Use in POD Estimation‟, 36th Review of Progress in QNDE, Kingston, Rhode
Island, July 2009.

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[23] G. Yang, L. Udpa, S. Udpa, „A GMR Based System for Pulsed Eddy Current NDE of Aircraft
Structures‟, IEEE International Magnetics Conference, Madrid, Spain, May, 2008.

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