Detection of cracks in plates and pipes using piezoelectric materials and advanced signal processing technique

DETECTION OF CRACKS IN PLATES AND PIPES USING
PIEZOELECTRIC MATERIALS AND
ADVANCED SIGNAL PROCESSING TECHNIQUE




TUA PUAT SIONG
(B.Eng.(Hons.), NUS)




A THESIS SUBMITTED
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CIVIL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2005
i
ACKNOWLEDGEMENTS

The author would like to express his deepest gratitude to his supervisors, Professor
Quek Ser Tong and Assoc. Prof. Wang Quan for offering this project, which had given
him an opportunity to learn many new things. Prof. Quek’s patient guidance, supervision
and encouragement throughout this research project are greatly appreciated. His
innovative suggestions in this research had not made this study possible but also a very
fruitful learning experience for the author. Prof. Quek had not only been a supervisor but
also a close guardian giving valuable advises throughout the course of this research.
The author also wishes to express his greatest appreciation to Dr. Jin Jing for

offering his kind advices and experience in this field of research. Dr. Jin has provided his
very valuable guidance to the author throughout this study and offered many help in
making this study possible.
The author is also grateful to all staff and officers in the structural laboratory,
especially, Ms Tan Annie, Mr. Ow Weng Moon, Mr. Ang Beng Onn and Mr. Choo Peng
Kin, for their time and assistance in making this project possible.
The author would also like to extend his thanks to his fellow research colleagues,
Mr. Zhou Enhua and Mr. Duan Wenhui for sharing their experiences in the field of finite
element analysis and the use of ABAQUS.
The author would like to express his deepest gratitude to his family members for
their support and encouragement throughout his course of study. Last, but not least, the
author would like to give his special thanks to his girlfriend, Ms Yap Fung Ling, for her
continuous encouragement, support, understanding, and love during the past few years.
ii
TABLE OF CONTENTS

Acknowledgements i

Table of Contents ii

Summary vi

List of Tables viii

List of Figures ix

List of Symbols xviii


CHAPTER

1. Introduction 1

1.1 Background 1

1.2 Literature Review 4

1.2.1 Historical Background of Elastic Wave Theories 4

1.2.2 Application of Elastic Waves in NDE 5

1.2.3 Piezoelectric Actuators and Sensors 11

1.2.4 Signal Processing Techniques in NDE 14

1.3 Objectives and Scope of Study 22

1.4 Organization of Thesis 26

2. Locating Damage Zones in Large Components 29

2.1 Introduction 29

2.2 Zoning Damage via Changes in Mode Shape 31

2.2.1 Structural Integrity and Mode Shape 31

2.2.2 Mode Shape Coefficients via Dynamic Response 34

iii

2.3 Finite Element Simulation 38

2.3.1 Single Damage Location 39

2.3.2 Multiple Damage Locations 46

2.3.3 Consistency of FRF under Varying Impacts 50

2.3.4 Limitations of Proposed Method 53

2.4 Experimental Verification 56

2.5 Summary 63

3. Locating Damage in Structures via Elastic Wave Propagation 66

3.1 Introduction 66

3.2 Wave Propagation in Beams 67

3.2.1 Longitudinal Wave 68

3.2.2 Flexural Wave 70

3.3 Lamb Wave Propagation in Plates 75

3.4 Locus of Crack Position in Plate via Flight Time of Waves 79

3.5 Actuation of Lamb Wave in Plates Using PZT 80

3.6 Selective Excitation of Lamb Mode for NDE of Aluminum Plate 85

3.6.1 Theoretical Results for A
0
and S
0
Dominance 86

3.6.2 Experimental Results for A
0
and S
0
Dominance 90

3.7 Summary 94

4. Advanced Signal Processing Technique - HHT 96

4.1 Introduction 96

4.2 Instantaneous Frequency 98

4.3 Intrinsic Mode Function (IMF) 102

4.4 Empirical Mode Decomposition (EMD) 103
iv
4.5 Hilbert Spectrum 109

4.6 Special Considerations During Implementation 111

4.6.1 Enveloping the Signal through Spline Fitting 112

4.6.2 Criteria for Termination of Sifting Process 113

4.6.3 End Effects of Hilbert Transform 116

4.7 Summary 116

5. Detection of Crack in Aluminum Plate 118

5.1 Introduction 118

5.2 Choice of Actuation Wave, Frequency and Duration 119

5.2.1 Actuation Frequency 119

5.2.2 Duration of Signal for Analysis 121

5.2.3 Example Involving an Aluminum Plate 122

5.3 Shielding of Reflected Lamb Wave 122

5.4 Procedure for Damage Identification 130

5.4.1 Signal Processing via HHT 130

5.4.2 Locating Crack 132

5.4.3 Quantifying the Extent of Crack 136

5.4.4 Blind Zones 141

5.5 Experimental Verification 146

5.5.1 Linear Through Crack 148

5.5.2 Linear Semi-through Crack (1.0mm deep) 158

5.5.3 Two Continuous Linear Crack at Inclination 159

5.5.4 Tracing Arc-Shape Crack 166

5.5.5 Blind Zones 170
v
5.6 Detection of Micro-width / Impurities In-filled / Repaired Cracks 177

5.7 Summary 182

6. Detection of Crack in Aluminum Pipe 185

6.1 Introduction 185

6.2 Strength Attenuation of Lamb Wave Across Discontinuities 186

6.3 Procedure for Damage Identification 191

6.3.1 Identifying the Presence of Crack and Location 192

6.3.2 Tracing Crack Geometry 197

6.3.3 Complications of Multiple Cracks 199

6.4 Experimental Verification 202

6.4.1 Fully Exposed Pipe 204

6.4.2 Buried Pipe 208

6.5 Practical Detectable Range for Aluminum Pipe 212

6.6 Summary 215

7. Conclusions 216

7.1 Conclusion 217

7.2 Recommendations for Future Study 220

References 222

Appendix A – Analytical Solution of PZT Actuated Wave A-1

Appendix B – Implementation of HHT Using MATLAB B-1

Appendix C – Publications in This Research C-1

vi
SUMMARY

The main objective of this research is to devise a methodology for the non-destructive

evaluation (NDE) of plate and cylindrical structures using time-of-flight (TOF) analysis of
Lamb wave propagation in the structures with the aid of an advanced signal processing
technique. The major problem in the NDE of structures using the Lamb wave for ultrasonic
inspection is dispersion, which results in the generation of multi-modes. This complicates the
analysis of the wave signals, and adds difficulty to the localization of defects. The main scope
of this study include: (a) the investigation on inducing suitable Lamb wave mode(s) for
efficient NDE of homogeneous thin plates and pipes using piezoelectric material (namely,
PZT), and (b) the design of a comprehensive procedure for the detection and localization of
cracks in plates and pipes based on the TOF analysis of Lamb wave using appropriate signal
processing techniques that are available. For large plates and long pipes (extending say more
than 100 times the wavelength of the wave adopted for NDE); it is more efficient to identify
zones of damage first so as to reduce the number of scans in the wave propagation NDE
technique. As such, the proposed overall NDE procedure is divided into 3 stages; namely, (i)
global level – where the question is simply is there a damage present, (ii) regional level –
where isolation and approximation of the damage zone is sort, and lastly (iii) localized level –
which seeks the answer to the precise location and the quantification of the defect.
The first and second stage (i.e. global and regional level) is realized by monitoring the
relative changes in the frequency response functions (FRF) values corresponding to the first
modal frequency. Numerical examples showed the feasibility of the FRF technique for
damages of varying severity, locations and number of damages. The method viability is also
confirmed experimentally using an aluminum plate with two different degrees of damage,
namely a half-through notch and a through notch. This method works especially well for
localized damages (e.g. cracks), where change in the overall structural frequency is minimal.
Prior to the presentation of the NDE using wave interrogation, a review of NDE using
ultrasonic guided Lamb wave is carried out which indicates three vital components, namely,
vii
(a) choice of wave to be excited to minimize dispersion, (b) method of excitation and sensing,
and (c) an efficient and reliable signal processing technique. Based on the dispersion relation,
the generation of Lamb wave is limited to fundamental anti-symmetric and symmetric modes
(A

0
and S
0
) where the dominating mode (either A
0
or S
0
) can be selectively monitored to
further reduce the complications. This can be done via excitation at a controlled frequency
and amplitude which can be realized using PZT actuators. For efficient and reliable
processing of nonlinear and non-stationary signals to accurately locate defects in plates and
pipes based on the TOF of propagating wave, the Hilbert-Huang transform (HHT) technique
is adopted.
For the localized level detection, comprehensive methodologies for the detection of
cracks in plates and pipes are devised. For plates, a square array of PZTs is adopted as a
primary network of actuator/sensors at suitable distance apart for initial estimation of the
crack based on the elliptical loci constructed from the TOF analysis of the actuated wave.
Blind zones are addressed with a set of secondary PZT actuator/sensors placed at selected
intermediate positions within the network. Exact geometry of the crack and its extent is traced
using a pair of PZTs as actuator and sensor, lined collinearly to the initial estimate of the crack
position. A novel wave shield device is also developed, which aims to minimize
complications due to “unwanted” reflections during the geometry trace. Experimental results
on an aluminum plate for both linear and nonlinear notches, and sub-millimeter width notches
filled with impurities and concealed under finishes confirmed the feasibility of the proposed
NDE methodology. In NDE of pipes, initial isolation of the crack is based on monitoring the
degrees of attenuation of the wave propagating along different paths. The method is shown to
be feasible experimentally for an aluminum pipe with a through notch under both exposed and
buried conditions.

Keywords : non-destructive evaluation (NDE), time-of-flight (TOF) analysis, Lamb wave,

frequency response function (FRF), piezoelectric transducer (PZT), cracks, plates, pipes,
Hilbert-Huang transform (HHT)
viii
LIST OF TABLES

2.1 Geometrical and material properties of aluminum plate 38

2.2 Summary of experimental FRF values corresponding to first mode for 58
undamaged plate

2.3 Comparison of FRF values obtained for simulation and experiment 58

2.4 Summary of experimental FRF values corresponding to first mode for 60
plate with half-through notch

2.5 Summary of experimental FRF values corresponding to first mode for 63
plate with through notch

3.1 Geometrical and material properties of aluminum beam 74

3.2 Frequency constants of PZT 83

3.3 Properties of piezoceramic material (C6) used 86

5.1 Experimental results for on aluminum plate with different crack 179
conditions

6.1 Experimental A
0
velocities obtained for aluminum pipe with 206

actuator at A1

6.2 Experimental A
0
velocities and energy for wave propagation across 215
long aluminum pipe










ix
LIST OF FIGURES

1.1
Structure of proposed NDE procedure
24


2.1 Simply-supported beam with 7 equally spaced sensors at a apart 34

2.2 Comparison of (a) power spectrum values and (b) square-rooted 35
power spectrum values with theoretical mode shape for modes 1-3

2.3 (a) Impact load and corresponding (b) power spectrum 36

2.4 (a) Dynamic response and corresponding (b) power spectrum for 36
S3 in Figure 2.1

2.5 Frequency response function for S3 in Figure 2.1 37

2.6 Division of plate into (a) 4 (Q1-Q4) and (b) 16 (S01-S16) 40
monitoring regions

2.7 Normalized shape for mode 1 of square plate using (a) 4 points 41
and (b)16 points

2.8 Simulated accelerance FRF values of undamaged plate for (a) 4 points 42
and (b) 16 points

2.9 Relative change in mode 1 for 50% reduction in E at D10 using 42
(a) 4 points and (b) 16 points

2.10 (a) Further partitioning of region S09, S10, S13 and S14 in 43
Figure 2.6 into 16 regions, and the (b) relative change in mode 1 for
50% reduction in E at D10

2.11 Maximum relative change in mode 1 for varying severity of 44
damage at D10

2.12 Relative change in mode 1 for 50% reduction in E at D13 using 45
(a) 4 points and (b) 16 points

2.13 Relative change in mode 1 for 50% reduction in E at D14 using 45
(a) 4 points and (b) 16 points

x
2.14 Relative change in mode 1 for 20% increase in E at D10 using 46
(a) 4 points and (b) 16 points

2.15 Relative change in mode 1 for 50% reduction in E at D08 and D10 47
using (a) 4 points and (b) 16 points

2.16 Relative change in mode 1 for 50% and 20% reduction in E at D12 48
and D13 respectively using (a) 4 points and (b) 16 points

2.17 Relative change in mode 1 for 50% and 20% reduction in E at D10 48
and D13 respectively using (a) 4 points and (b) 16 points

2.18 Relative change in mode 1 for 50% reduction in E at D1, D8, D10 49
and D15 using (a) 4 points and (b) 16 points

2.19 (a) Impact load with longer contact and corresponding 51
(b) power spectrum

2.20 Relative change in mode 1 accelerance values for using impact load 52
with longer contact time for (a) 4 points and (b) 16 points

2.21 Power spectrum of response at monitored point Q1 in Figure 2.6 52
under impact load described by (a) Figure 2.3 and (b) Figure 2.19

2.22 Relative change in mode 1 for 50% reduction in E at extended D10 55
region using (a) 4 points and (b) 16 points

2.23 Accelerance FRF values of undamaged plate for (a) 4 points 57
and (b) 16 points

2.24 Relative change in mode 1 for plate with half-through notch using 61
(a) 4 points and (b) 16 points

2.25 Relative change in mode 1 for plate with through notch using 62
(a) 4 points and (b) 16 points


3.1
A beam (a) with coordinate x and displacement u of a section and
68

(b) stresses acting on a differential element of the beam


3.2
Particle displacement of under longitudinal wave motion
70


3.3
Differential Timoshenko beam element under transverse loading
70


3.4
Particle displacement under flexural wave motion
72

xi
3.5
Dispersion relation for flexural wave based on Timoshenko beam
74

model


3.6
(a) Longitudinal and (b) transverse displacement components for
76

first three symmetric and antisymmetric Lamb wave modes


3.7
Group dispersion curve for aluminum plate (Adopted from
78

Monkhouse et al., 2000)


3.8
Elliptical loci of possible crack positions
80


3.9

PZT with applied potential,
φ
across the thickness
82


3.10
(a) Pictorial view of mobile PZT actuator/sensor device, and
84

(b) closed up view of the PZT transducer part


3.11
Fabrication of mobile PZT actuator/sensor
84


3.12
Two-dimensional model of PZT actuator on plate surface
87


3.13
Amplitude ratio of A
0
to S
0

88

3.14
Distribution of
33
T at far field along the thickness of plate at 600kHz
89


3.15
Experimental setup for generation of Lamb waves propagation in
90

aluminum plate


3.16
Actuation pulse using equation (3.18) at frequency = 600 kHz
91


3.17
(a) Response collected at PZT 3 at 200kHz and (b) corresponding
92

energy-time plots via HHT


3.18
Experimental and theoretical group velocities

93


4.1
(a) Signal X(t); (b) phase and (c) frequency plots based for
101

X
(t) = cos (2πt), X(t) =0.5 + cos (2πt) and X(t) =1.5 + cos (2πt)


4.2
(a) Original data, X(t); (b) upper, lower envelopes (dotted lines) and
105

mean,
1
m and (c) difference between X(t) and
1
m , i.e. PMF(
1
h )


4.3
(a) IMF
11
h , after one more sifting, and (b) IMF
13
h after three more

106

siftings (which gives
1
c ) from Figure 4.2(c)


4.4
IMFs obtained for the signal as shown in Figure 4.2(a)
108
xii
4.5
HHT spectrum obtained for the signal as shown in Figure 4.2(a)
110


4.6
(a) Time-frequency and (b) time-energy plot obtained for the first
111

IMF of signal as shown in Figure 4.2(a)


4.7
Leakage due to imperfection in cubic spline fitting for envelopes in
112

sifting process.

4.8
(a) Plot of X(t) = 10 + sin (2
π
t); (b) IMFs obtained at SD = 0.01 and
115

(c) IMFs obtained at SD = 0.001.


4.9
Figure 3.9. IMFs obtained at N = 3 for signal given in Figure 4.8(a)
116


5.1 Schematic view of ‘shielding’ device for reflected Lamb wave 124

5.2 Finite element meshing of the shielding devices with: (a) one, 125
(b) two, (c) three and (d) four aluminum strips mounted on host plate

5.3 Energy spectra for the response collected at Node 1 and 2 for S
0
127
mode propagation across shielding with (a) no shielding, (b) one,
(c) two, (d) three and (e) four shielding strips

5.4 Energy spectra for the response collected at Node 1 and 2 for A
0
128
mode propagation across shielding with (a) no shielding, (b) one,
(c) two, (d) three and (e) four shielding strips

5.5 Experimental setup for testing of shielding effect 129

5.6 Energy spectra obtained by PZT sensor given in Figure 5.5: 129
(a) without shielding and (b) with shielding

5.7 (a) Response signal collected by a PZT sensor, (b) IMF components 131
of signal after EMD; (c) frequency and (d) energy spectra for the 1
st

IMF component

5.8
Area covered by 4 PZTs in 100 × 100mm square grid arrangement
132

5.9 Area coverage provided by: (a) PZT 1 & 2; (b) PZT 2 & 3; 133
(c) PZT 3 & 4; (d) PZT 1 & 4; (e) PZT 1 & 3 and (f) PZT 2 & 4

5.10
Procedure for scanning a 600 × 600mm
2
aluminum plate
134

5.11 Positions of intermediate PZTs (A, B, C and D) for locating crack: 135
(a) configuartion 1 and (b) configuration 2

xiii
5.12 Determination of crack orientation 137

5.13 Quantification of damage extent 138

5.14 Determination of nonlinear crack orientation 138

5.15 Quantification of damage extent 139

5.16 Blind zones (a) Type I and (b) Type II 141

5.17 Locating crack on Type I blind zone 142

5.18 Locating nonlinear crack on Type I blind zone; (a) results obtained 143
by six primary actuator/sensor pairs, additional ellipses by PZTs:
(b) 2-A and 2-D and (c) 4-D and 4-A

5.19 Locating crack on Type II blind zone 144

5.20 Locating nonlinear crack on Type II blind zone; (a) results obtained 145
by six primary actuator/sensor pairs, additional ellipses by PZTs:
(b) 1-A, 3-B and 3-C and (c) 2-A, 4-C and 4-D

5.21 Square grid configuration at positions: (a) 1, (b) 2 and (c) 3 147

for 600×600mm
2
square plate

5.22 Position of one square grid configuration for detection of 147
nonlinear crack

5.23 Position of arc-shaped crack on aluminum plate 147

5.24 Pictorial view of the experimental setup 148

5.25 Energy spectra and ellipses obtained for locating through crack 149
using PZTs: (a) 1
1
-2
1
, (b) 2
1
-3
1
, (c) 3
1
-4
1
, (d) 1
1
-4
1
, (e) 1
1
-3
1

and (f) 2
1
-4
1

5.26 Identified crack location using square grid configuration at position 1 151

5.27 Identified crack location using square grid configuration at position 2 152

5.28 Identified crack location using square grid configuration at position 3 152

5.29 Energy spectra and ellipses obtained for locating through crack 153
using PZTs: (a) 3
3
-C
3
and (b) 4
3
-C
3


xiv
5.30 (a) Ellipses obtained by PZT pairs lined at different angular 154
inclinations to through crack orientation, and energy spectra
obtained by PZT pairs at (b) 0º, (c) 15º and (d) 30º inclination to
normal of crack

5.31 Positions of actuator and sensor along different lines normal to 155
through crack, and outline of crack extent (
* denotes higher intensity

and

× denotes lower intensity)

5.32 Energy spectra obtained to determine extent of though crack by PZT 156
pairs along lines (a) L1, (b) L2, (c) L3, (d) R1, (e) R2 and (f) R3

5.33 Energy spectra and ellipses obtained for locating semi-through crack 157
using PZTs: (a) 1
1
-2
1
, (b) 1
1
-4
1
, (c) 2
1
-4
1


5.34 Identified semi-through crack location using square grid configuration 158
at position 1

5.35 Outline of semi-through crack extent 159

5.36 Energy spectrum and ellipse obtained for locating nonlinear crack 160
using PZT pair 1-2

5.37 Energy spectra and ellipses obtained for locating nonlinear crack 160
using PZTs: (a) 1-A and (b) 2-A

5.38 Identified crack location using square grid configuration given in 161
Figure 5.22

5.39 (a) Ellipses obtained by PZT pairs lined at different angular 162
inclinations to one linear part of the geometric crack orientation, and
energy spectra obtained by PZT pairs at (b) 0º, (c) 15º and (d) 30º
inclination to normal of crack

5.40 Positions of PZT pairs along different lines normal to first and 164
second linear portion of the crack, and outline of crack extent

5.41 (a) Positions of PZT pairs along lines at different inclinations to L
31
165
given in Figure 5.40, and energy spectra obtained by PZT pairs at
(b) 90º, (c) 120º and (d) 150º inclination to L
31


5.42 Energy spectra obtained with PZT pairs on the convex side 166

of arc-shaped crack at inclinations of (a) 0°, (b) 15° and 30° from the
normal to the tangent at point ‘
X’ in Figure 5.23

xv
5.43 (a) Outline of arc-shaped crack with PZT pairs on convex side, and 168

corresponding energy spectra along lines (b) L

1
, (c) L
2
, (d) L
2
′, (e) L
3
,

(f) L
4
, (g) L
4
′
,
(h) L
5
and (i) L
6


5.44 Outline of arc-shaped crack with PZT pairs on concave side 170

5.45 Orientation of square grid configuration of PZTs to simulate 171
(a) Type I and (b) Type II blind zone on plate with linear crack, and
(c) Type I and (d) Type II blind zone on plate with nonlinear crack

5.46 Energy spectra and ellipses obtained for locating crack in Type I 172
blind zone using PZTs: (a) 1
I

-2
I
, (b) 2
I
-3
I
, (c) 3
I
-4
I
, (d) 1
I
-4
I
, (e) 1
I
-3
I

and (f) 2
I
-4
I


5.47 Locating linear crack in Type I blind zone 173

5.48 Locating linear crack in Type II blind zone 174

5.49 Energy spectra and ellipses obtained for locating nonlinear crack in 175

Type I blind zone using PZTs: (a) 1
I
-2
I
and (b) 1
I
-4
I


5.50 Locating non-linear crack in Type I blind zone: combined ellipse plots 176
for orientation of crack along (a) PZT 3
I
and 4
I
, and (b) PZT 1
I
and 4
I


5.51 Locating non-linear crack in Type II blind zone: combined ellipse 177
plots for part of crack along (a) PZT 1
II
and 3
II
, and (b) PZT 2
II
and 4
II

5.52 Schematic view of experimental set-up on portion of aluminum plate 178
with micro-width crack and actuator/sensor pair

5.53 Energy-time spectrum collected by sensor in Figure 5.52 for aluminum 179
plate with micro-width crack induced by (a) wire-cut and (b) EDM

5.54 Energy-time spectrum collected by sensor in for aluminum plate with 180
micro-width crack filled with (a) grease, (b) araldite epoxy,
(c) metallic epoxy, and (d) spray paint

5.55 Schematic view of experimental setup on the portion of aluminum 181
plate containing the weld repaired crack

5.56 Energy-time spectrum collected by sensor in Figure 5.55 along lines 182
(a) B-B’ and (b) A-A’

6.1 Ambiguity in use of time-of-flight analysis for NDE of pipe 187

xvi
6.2 Experimental set-up for investigating wave strength attenuation 188
across crack

6.3 Energy-time spectrum of (a) actuation signal; and sensor response on 189

(b) Line A; (c) Line B (90°); (d) Line C (60°); (e) Line D (30°) and

(f) Line E (0°)

6.4 Illustration of alternative shortest wave propagation path in plate due 190

to presence of crack

6.5 Schematic to illustrate scanning a pipe segment for identifying crack 193
location with actuator at A

6.6 Coverage of pipe segment described in Figure 6.5 with actuator at 194
positions (a) A; (b) C; (c) A’ and (d) C’

6.7 Possible crack positions after scanning of pipe segment 195

6.8 (a) Example of inability for crack isolation in a pipe segment scan; and 196
(b) isolation of the crack position by performing of half segment scan

6.9 Geometry tracing of crack in pipe 198

6.10 Schematic view of modified shields for pipe 198

6.11 Pipe segment having two cracks with range of direct wave paths 200
experiencing attenuation for actuator at (a) A and (b) A’; and
(c) deduced crack position based on intersection of the two sets of
results

6.12 Partition of pipe segment for secondary scan (a < 1.0) 201

6.13 Partition of pipe segment for secondary scan (a, b and c < 1.0) 202

6.14 Schematic view of aluminum pipe with through crack for experiment 203

6.15 Energy-time spectrum of signal collected by sensor at position: (a) S1, 205
(b) S2, (c) S3, (d) S4, (e) S12, (f) S14, (g) S34 and (h) S23 given in

Figure 6.14

6.16 (a) Isolation of possible crack positions for the segment of aluminum 207
pipe investigated; and (b) geometry trace of crack (marked by ‘
’)

6.17 Energy spectrum of signal collected by sensor along the Line L
0
in 208
Figure 6.16
xvii
6.18 Schematic view of buried aluminum pipe 209

6.19 Energy spectrum of signal collected by (a) Sensor 1 and (b) Sensor 2 210
in Figure 6.18 for healthy aluminum pipe

6.20 Energy spectrum of signal collected by (a) Sensor 2 and (b) Sensor 3 211
in Figure 6.18 for aluminum pipe with crack

6.21 Schematic view of 5.0m long aluminum pipe 212

6.22 Energy spectrum of signal collected by sensor at position: (a) S1, 213
(b) S2, (c) S3, and (d) S4 given in Figure 6.21

6.23 Illustration of incident wave paths with actuator/sensor pair along 214
longitudinal axis of pipe

A.1
Two-dimensional model of PZT actuator on plate surface
A-1

B.1
Flow chart of implemented HHT program using MATLAB.
B-5


B.2
(a) Original data; (b) IMFs; (c) HHT spectrum and (d) time-frequency
B-6

and time-energy plots for X(t) = sin (20πt)


B.3
(a) Original data; (b) IMFs; (c) HHT spectrum and (d) time-frequency
B-7

and time-energy plots for X(t) = 2sin (10πt) + sin (40πt)


B.4
(a) Original data; (b) IMFs and (c) HHT spectrum of simple cosine
B-8

wave with one frequency suddenly switching to another frequency


B.5
(a) Morlet (Huang et al., 1998) and (b) Fourier spectra of cosine

B-9

wave shown in Figure B.4(a)


B.6
(a) Original data; (b) HHT spectrum; (c) frequency modulation
B-10

based on classic wave theory; and (d) Morlet spectrum for

X
(t) = cos[2πt / 64 + 0. 3sin(2πt / 64)]


B.7
(a) Original data; (b) HHT spectrum and (c) Morlet spectrum
B-11

(Huang et al., 1998) of X(t) = exp(-0. 01t) cos(2πt/32)







xviii
LIST OF SYMBOLS

The following symbols are used in this study:

A, B, C = Amplitude of wave solutions in piezoelectric layer
A
′
,
B
′
, C
′
,D
′
= Amplitude of wave solutions in metallic substrate
α
(
ω
) = Frequency response function
b = Half plate thickness
c
ij
= Elastic stiffness coefficient
c
g
= Group velocity
P
c
= Phase velocity of wave
10
/ cc
= Longitudinal wave velocity without/with Poisson effect

2
c
= Transverse wave velocity

D
i
= Electrical displacement in
i
x -direction
E = Young’s modulus of elasticity
e
ij
= Piezoelectric constant
ε
i
= Dielectric constant
Φ
= Scalar potential function
f = Frequency
f
R
= Basic resonance frequency for PZT
φ
= Electric potential
F = Body force vector
G = Shear modulus
xix
H = Vector potential function
H[•] = Hilbert transform
),( tH

ω
= Hilbert spectrum
h = Piezoelectric transducer thickness
h(
ω
) = Marginal spectrum
I = Moment of inertia
IE(t) = Instantaneous energy density level
K
= Stiffness matrix
κ
= Timoshenko shear coefficient
l = Length of piezoelectric transducer
λ
= Wavelength
M = Mass matrix
v = Particle velocity vector
P = Force vector
Q = Surface charge
θ
= Phase angle
r(t) = Residue component
ρ
= Density
S
ij
= Strain tensor
σ
= Stress
T

ij
= Stress tensor
T
c
= Curie temperature of piezoelectric transducer
t = Time
xx
τ
= Cauchy stress
i
u = Particle displacement in
i
x direction
ν = Poisson’s ratio
ω
= Angular frequency
X(t) = Real time series signal
x
i
= Coordinate in the i-dimension
i
Ξ
= Electric field
ξ
= Wavenumber
ψ
= Angular displacement of beam plane section
〈•〉 = Average, e.g. 〈
ω
〉 = mean frequency

1
CHAPTER 1
INTRODUCTION

1.1 BACKGROUND
The assessment of the performance of structures in terms of serviceability,
durability and prevention of catastrophic failure has always been an important issue.
Early detection of anomaly such as defects or damages in a structure is necessary for
optimal decisions with regard to its rehabilitation, strengthening, and/or reconstruction.
This has led to the development of many practical and robust non-destructive evaluation
(NDE) techniques for assessment of structural health especially over recent years. These
ranges from the basic visual inspection, to liquid or fluid penetration (e.g. pressure test for
pipes), monitoring of changes in modal parameters (e.g. natural frequencies, modal
damping, mode shapes), ultrasonic scanning using propagating waves in structures (e.g.
impulse-echo technique), and more recent imaging techniques using advanced equipments
such as infra-red (thermo-graphic inspection) or laser (radiographic inspection) scanning.
Nonetheless, detection at either the structural level or the element level still poses a
considerable challenge (Salawu, 1997). Ultrasonic inspection technique using
propagating wave signals can be considered one of the most commonly used techniques
and its application has been increasing rapidly over the past two decades due to the
corresponding advancement in electronic equipment, which makes the technique practical,
cheaper and readily available.
Wave propagation in solids may be generally categorized into three categories.
The first makes use of elastic waves, where the stresses in the material obey Hooke’s Law.
CHAPTER 1: INTRODUCTION

2
This is commonly used in NDE utilizing ultrasonic guided waves because the deformation
of the material due to the propagating wave is often small and within the elastic range.
The other two categories make use of (a) visco-elastic waves, where viscous as well as
elastic stresses govern, and (b) plastic waves, in which the yield stress of the material is
exceeded. The latter two categories are not suitable for NDE because structures stressed
well beyond the linear range may need different considerations, and also may need to be
demolished that damage detection is no longer necessary.
NDE using the elastic wave propagation can generally be performed in the
frequency or time domain. In the frequency domain, the modal parameters such as the
natural frequency (Cawley and Adams, 1979a; Cawley and Ray, 1988; Salawu, 1997) or
impedance (Cawley, 1987) of the structure are analyzed. The structural health may be
related to changes in these modal parameters. Albeit the success in detection and
quantification of the damage, the localization of the damage using frequency domain
methods still pose a challenge as the excitation and measurement of high order modes are
necessary. In addition, most of these techniques require prior data, simulated results or a
database for comparison in order to assess the health state of the structure. The changes in
the natural frequencies are also small and significant damage is required for any
conclusive observable changes, which render it unsuitable for the detection of refined
damages such as cracks. As such, a more appropriate method for detection of such
damages is the time domain analysis.
In time domain analysis, there are likewise many methods developed for the
purpose of NDE, such as the monitoring of time-impedance using eddy current, time-
frequency under controlled excitations using sweeping frequency, and ultrasonic scanning
using wave propagation. The wave propagation technique is one of the most common and
CHAPTER 1: INTRODUCTION

3
well adopted among these. The concept hinges on the fact that an induced propagating
wave will be reflected and/or partly transmitted when it encounters a defect or boundary.

By noting the flight times and velocities at selected locations, the presence of a defect and
its location can be deduced.
Wave propagations in solids are often excited easily by inducing an impact on the
structure. However, uncontrolled excitation leads to problems arising from waves that are
broad-band with unpredictable amplitudes. As such, devices which produce a controlled
input for the generation of guided waves are adopted to increase the efficiency of
detection. Examples include ultrasonic laser vibrometry (Gao et al., 2003; Staszewski et
al., 2004; Mallet et al., 2004), solid and liquid wedge transducers (Bourasseau et al., 2000;
Wilcox et al., 2001; Lowe et al., 2002), electromagnetic acoustic transducers (EMATs),
air-coupled transducers, comb transducers (Rose et al., 1998), inter-digital transducers
(Wilcox et al., 1998; Monkhouse et al, 2000; Jin, 2003; Jin et al., 2005) and the surface-
mounted piezoelectric transducers (Giurgiutiu et al., 2001; Kehlenbach and Das, 2002;
Tua et al., 2002; Quek et al., 2003a, 2004a, 2004c, 2004d; Tua et al., 2004, 2005).
The excitation of elastic waves with the aid of piezoelectricity allows narrow band
actuation with the desired amplitude by controlling the electrical input signal.
Piezoelectricity is a phenomenon in which mechanical energy is converted into electrical
energy and vice-versa. By definition, a material possessing piezoelectric property will
generate an electrical charge when a mechanical pressure is applied to it. Likewise, the
material will experience a geometric change when an electrical charge is applied to it.
Due to this efficient electromechanical property of the piezoelectric crystals, the actuation
of guided waves via piezoelectric materials has gain popularity over the years. There are a
few natural materials that exhibit piezoelectricity, of which piezoelectric ceramics (Lead
CHAPTER 1: INTRODUCTION

4
Zirocondate Titanate, or in short, PZT) and piezoelectric polymers (Polyvinylidene
Fluoride, denoted as PVDF) are the two commercially available and frequently used
piezoelectric actuators for excitation of elastic waves.
As the NDE of structures based on elastic wave propagation involves
interpretation of signals, the adoption of a signal processing technique is inevitable. There

are several signal processing techniques available, each having its own advantages and
strengths for extracting different information from the signals. These techniques ranges
from the classical Fourier transform (FT) (which is highly capable of extracting modal
parameters from the dynamic response of structures), to wavelet transform (WT) (which is
competent of performing analysis in the time domain), and to the recently developed
Hilbert-Huang transform (HHT) which has shown its capability in interpreting
meaningfully nonlinear and non-stationary data.
Some published works on NDE techniques using elastic wave propagation,
including the necessary constituent components are reviewed in the following section.

1.2 LITERATURE REVIEW
1.2.1 Historical Background of Elastic Wave Theories
The study of wave propagation in elastic solids has a long history. Most of the
early studies involve quantitative observations of musical tones or water waves, which are
the two most common types of wave motions. Since the early 19
th
century, the description
of wave motion as a propagation of disturbance had motivated great mathematicians such
as Cauchy and Poisson to contribute to the development of the theory of elasticity. The
next hundred years saw the significant discovery of specific wave propagation effects in