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

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 p

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

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

1.2.1 Historical Background of Elastic Wave Theories 4

2.2.2 Mode Shape Coefficients via Dynamic Response 34

2.3.1 Single Damage Location 39

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

3.6 Selective Excitation of Lamb Mode for NDE of Aluminum Plate 85 3.6.1 Theoretical Results for A0 and S0 Dominance 86

3.6.2 Experimental Results for A0 and S0 Dominance 90

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

5.5.2 Linear Semi-through Crack (1.0mm deep) 1585.5.3 Two Continuous Linear Crack at Inclination 159

5.7 Summary 182

6.2 Strength Attenuation of Lamb Wave Across Discontinuities 186

6.3.1 Identifying the Presence of Crack and Location 192

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,

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 (A0 and S0) where the dominating mode (either A0 or S0) 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)

2.1 Geometrical and material properties of aluminum plate 38

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

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

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

6.1 Experimental A0 velocities obtained for aluminum pipe with 206

6.2 Experimental A0 velocities and energy for wave propagation across 215

long aluminum pipe

1.1 Structure of proposed NDE procedure 242.1 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

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

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

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 703.3 Differential Timoshenko beam element under transverse loading 70

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)

3.9 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

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

3.14 Distribution of T33 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

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

X(t) = cos (2 πt), 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, m1 and (c) difference between X(t) and m1, i.e PMF(h1)

4.3 (a) IMF h11, after one more sifting, and (b) IMF h after three more 13 106

siftings (which gives c1) from Figure 4.2(c)

4.4 IMFs obtained for the signal as shown in Figure 4.2(a) 108

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

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 S0 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 A0 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 1st

5.8 Area covered by 4 PZTs in 100 × 100mm square grid arrangement 1325.9 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 × 600mm2

5.11 Positions of intermediate PZTs (A, B, C and D) for locating crack: 135

(a) configuartion 1 and (b) configuration 2

5.13 Quantification of damage extent 138

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

5.20 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 600×600mm2

square plate 5.22 Position of one square grid configuration for detection of 147

5.25 Energy spectra and ellipses obtained for locating through crack 149

using PZTs: (a) 11-21, (b) 21-31, (c) 31-41, (d) 11-41, (e) 11-31

and (f) 21-41

5.26 Identified crack location using square grid configuration at position 1 1515.27 Identified crack location using square grid configuration at position 2 1525.28 Identified crack location using square grid configuration at position 3 1525.29 Energy spectra and ellipses obtained for locating through crack 153

using PZTs: (a) 33-C3 and (b) 43-C3

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) 11-21, (b) 11-41, (c) 21-41

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

at position 1

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

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 L31 165

given in Figure 5.40, and energy spectra obtained by PZT pairs at

(b) 90º, (c) 120º and (d) 150º inclination to L31

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

(f) L4, (g) L4′, (h) L5 and (i) L6

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

and (f) 2I-4I

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

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

5.50 Locating non-linear crack in Type I blind zone: combined ellipse plots 176

for orientation of crack along (a) PZT 3I and 4I, and (b) PZT 1I and 4I

5.51 Locating non-linear crack in Type II blind zone: combined ellipse 177

plots for part of crack along (a) PZT 1II and 3II, and (b) PZT 2II and 4II

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

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

6.11 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) 2016.13 Partition of pipe segment for secondary scan (a, b and c < 1.0) 2026.14 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

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 L0 in 208

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

6.22 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-1B.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[2 πt / 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)

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

c ij = Elastic stiffness coefficient

D i = Electrical displacement in x -direction i

E = Young’s modulus of elasticity

κ = Timoshenko shear coefficient

l = Length of piezoelectric transducer

u = Particle displacement in x direction i

X(t) = Real time series signal

x i = Coordinate in the i-dimension

i

ψ = Angular displacement of beam plane section

〈•〉 = Average, e.g 〈ω〉 = mean frequency

I NTRODUCTION

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

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

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

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

1.2.1 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 19th 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

elastic solids Examples include the rigorous development of (a) frequency equation for waves in plate based on theory of elasticity by Rayleigh (1888) and Lamb (1889), (b) theory of wave propagation in a thin layer overlying a solid medium by Love (1911) who showed that such waves accounted for certain anomalies in seismogram records, and (c)

an approximate theory for wave propagation in plates that provided a general basis for development of higher-order plate and rod theories by Mindlin (1951)

Since then, the interest in elastic waves has continued, stimulated by technological developments related to high-speed equipment, ultrasonics, piezoelectric phenomena, as well as the measurement techniques related to properties in materials The study of wave propagation has now become well-established in the field of applied mechanics

1.2.2 Applications of Elastic Waves in NDE

The development of elastic wave theory has found many applications, especially in the field of non-destructive evaluation (NDE) of components and structures One of the pioneering contributions of NDE using elastic waves is by Worlton (1957, 1961), who recognized the potential of Lamb waves for NDE in plates due to its ability to interrogate through the thickness of the plate over a long propagation range Since then, there has been great interest in using Lamb and other guided waves for NDE applications Viktorov (1967) has published extensively on Rayleigh and Lamb waves for NDE in plates with respect to surface and near-surface defects, defects in shell structures including tubes, and defects in thin-walled structures of complex shapes Doyle and Scala (1978) reviewed the use of bulk waves and surface waves for measuring crack depths via two methods, namely, the time of flight analysis of the wave and the ultrasonic spectroscopic analysis

review, the bulk wave transit time method proved to provide a simpler and reliable quantitative measurement of crack depths Besides the inspection of plates, the use of

cylindrical Lamb modes L(0,1) and L(0,2), which are equivalent to the A0 and S0 Lamb modes in plates (Silk and Bainton, 1979), are also adopted for the health monitoring of pipes (Alleyne and Cawley, 1997) and composite tubes (Beard and Chang, 1997)

The methods adopted in NDE using of elastic propagating waves can be generally classified under two approaches: (a) frequency domain, and (b) time history analysis

Frequency Domain Method

The frequency domain methods make use of modal parameters such as the natural frequency (Cawley and Adams, 1979a,b; Salawu, 1997), modal damping, mode shapes and impedance (Cawley, 1987) of the structure for determining its health In some applications, changes in natural frequencies and modes are related to the changes in structural integrity and proven to be a reliable detector of damages such as debonding between layered materials (Cawley and Adams, 1979a,b; Cawley and Ray, 1988; Koh et al., 2002) However, the frequency domain method has difficulty in providing potentially important information on the type, precise location, orientation, size or geometry for refined damages such as cracks (Kessler et al., 2002) Moreover, to cause a change in the natural frequency will require a significant damage or defect, particularly for large structures (Kim et al., 2003) Hence, it may be unsuitable for small or localized defects such as cracks In addition, the monitoring of localized changes in the stiffness matrix may require measurements of higher modal frequencies to detect a conclusive change, which in turn necessitates the excitation of higher modes The latter is hard to excite and control in practice

Despite the limitations, the frequency domain methods are still used by many for estimating the damage zone or region, for example Pandey et al (1991) adopted the change in the curvature mode shapes, while Pandey and Biswa (1994) monitored the changes in the flexibility Nonetheless, these methods have demanding requirements on the number of sensors for precise measurements of the monitored modal parameters making the procedure expensive for practical implementation In addition, the modal parameters such as damping ratios and mode shapes are estimated via curve fitting, which may vary with the fitting criteria used as well as the curve fitting software

Another frequency domain method for the detection of damage is the use of frequency response function (FRF) An FRF is a measure of how much displacement, velocity, or acceleration response a structure has at an output DOF, per unit of excitation force at an input DOF (Schwarz and Richardson, 1999), giving the receptance, mobility and inertance/accelerance FRFs respectively By curve-fitting the resultant FRF spectrum, structural parameters such as stiffness, damping and mass matrices can be computed (Ewins, 1984) and adopted as signatures for damage detection There also exist methods which adopt the direct monitoring of the FRF spectrum values (Thyagarajan et al., 1998) This method has also received practical applications, for example, Samman and Biswas (1994a, 1994b) adopted the FRF as signatures for the structural integrity of a bridge Despite these demonstrations of FRF as being feasible numerically for the detection and localization of damage (Sampaio et al., 1999; Owolabi et al., 2003), there exist inconsistencies in the practical computation of the FRFs due to variation in practical input loading (Hwang, 1998; Hwang and Kim, 2004)

In a nutshell, albeit the successes of the frequency domain methods, there are

defects, for example, the placing of 20 sensors along the length of a 500mm beam to monitor the mode shape for detection of a defect spanning 25mm (Pandey et al., 1991; Pandey and Biswa, 1994) is more pertinent in numerical simulations Likewise, compromising on the requirement on the sensor quantity gives the only the approximation

of the defect localization Hence, the frequency domain method is generally observed to

be more suitable for global and regional level detection as difficulties and inaccuracies are often observed for localization of the defect

Time-History Method

The time history method that adopts the propagation of elastic wave can be divided into two major categories, namely, monitoring of changes (such as amplitudes and modes) in the propagating wave characteristics over defective areas, and monitoring of the flight times of the propagating wave reflected from boundaries including that of defects

sub-Liu et al (1997) studied the characteristics of the SH wave scattering by the surface-breaking and sub-surface cracks in the energy-time spectrum, whereby a relationship for determining the location, length and depth of the crack was proposed Tseng and Naidu (2002) presented a non-parametric NDE technique for plates using bonded smart piezoelectric ceramic (PZT) transducers In their method, the change in the electrical impedance of the PZT is adopted as the signature for the degree of structural damage This monitoring of the acoustic emission using the PZT is proven to be sensitive

to even small incipient damages Alleyne and Cawley (1992) made use of Lamb wave propagation in plates to investigate the interaction of Lamb wave with defects They found that mode conversion of a single Lamb mode to another proves to be viable for quantifying the depth of defect Tan et al (1995) and Bourasseau et al (2000) also

namely, delamination in unidirectional fibre composites Results showed that the amplitude of the Lamb wave decreases significantly over the delaminated region and provides a means of identifying delaminated areas in composite plates Recently, Long et

al (2003) used the attenuation characteristic of the fundamental modes propagating in buried iron pipes to detect anomalies (joints, fittings, leakage) in the pipes

In fact, many NDE techniques which utilize Lamb wave propagation revolve around the fundamental concept that a propagating wave will be reflected and/or partly transmitted when it encounters a defect or boundary For example, Lowe et al (1998) observed a perfect reflection of the wave for circumferential notches and perfect transmission elsewhere for the NDE in pipes using guided waves By noting the flight times and velocities at selected locations, the presence of a defect and its location can be deduced (Quek et al., 2001; Giurgiutiu et al., 2001; Kehlenbach and Das, 2002; Tua, 2002; Tua et al., 2004, 2005) Many studies have also been carried out to achieve better understanding of the interaction between the propagating wave and the defects for more efficient use of the wave signals for NDE purposes Lowe and Diligent (2002) studied the reflection characteristics of the fundamental symmetric Lamb mode (S0) from surface-breaking rectangular notches in isotropic plates at low propagation frequencies using flight times Lowe et al (2002) further extended the same analysis to the fundamental anti-symmetric Lamb mode (A0)

However, one common problem of using Lamb waves for NDE is the existence of multi-modes caused by its dispersive nature, leading to complexity in interpreting the wave signals To alleviate the complications due to dispersion, selective generation and detection of a single mode within a frequency range to minimize dispersion effect can be

transducer wedge in conjunction with the Hanning window to limit the bandwidth of their input electrical signal Monkhouse et al (2000), Jin et al (2003) and Jin (2003) on the other hand used inter-digital transducer to excite a particular Lamb mode for monitoring plate structures Selective generation of Lamb wave modes is also necessary for detecting vertical and horizontal damage positions (Ghosh et al., 1988) Clézio et al (2002) used the S0 Lamb wave mode by adopting frequency below that corresponding to the S1 mode cut-off, to quantify vertical cracks in an aluminum plate In the NDE for pipes, Park et al (1996) selectively adopted the A0 Lamb mode excited via a lucite wedge transducer for detecting defects in long steel pipes In their study, the time of flight of the reflected wave from artificial flaws (with the smallest having a diameter of 6.35mm) is read of from a real time A-scope display and it is shown that the inspection technique is feasible up to an axial distance of 304.8cm Beard and Chang (1997) likewise selected an operating frequency experimentally for the PZT actuator to achieve a maximum amplitude response

at the sensor for damage detection in a filament wound composite tube Cheong et al

(2004) also selected the L(0,1) wave mode at 500kHz, which is comparable to the A0

Lamb mode, for the detection of both circumferential and axial notches in the feeder pipes

of PHWR nuclear power plants, similarly by monitoring the reflected wave Hence, the choice of the excitation frequency is vital in terms of detecting the type of damage and simplifying the analysis and interpretation

From the successes in the time history methods for assessment of the defects in terms of localization and quantification, it is logical that the next stage will be a detailed procedure for interrogation of the real structural components This prompts the question for the strategic and systematic placement of actuators and sensor to perform the scan for

such as feasibility for the interrogation of large structures such as the hull of ships, or aircraft panels This is because there are possible problems such as of multiple reflections and the retaining of substantial wave strength for provision of reflected signatures from defects after long propagation distances

In general, the NDE processes for structures have progressed considerably over the past years for both the frequency domain method and the time history method This is due

to the advancement in the actuation/sensing and data processing technology which has led

to the reduction in the cost and the increase in the effectiveness and accuracy of the inspection technique In fact, many practical and robust NDE techniques developed for assessment of structural performance involve two key components, namely: (1) data acquisition, and (2) signal processing and interpretation In the following two sections, a brief review in the actuation/sensing and signal processing techniques will be presented

1.2.3 Piezoelectric Actuators and Sensors

The controlled actuation of elastic wave is vital in many NDE processes involving the use of propagating wave to reduce uncertainty and complexity in signal analysis and interpretation Excitation and sensing of ultrasonic waves for NDE can be done using numerous methods that induce time-dependent elastic deformation or pressure Devices for the generation and reception of Lamb waves 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;

et al., 2001; Kehlenbach and Das, 2002; Tua et al., 2002; Quek et al., 2003a, 2004a, 2004c, 2004d; Tua et al., 2004, 2005) Nonetheless, there are pros and cons to these excitation methods For example, for the adoption of the laser vibrometry, despite its effectiveness in generating the particular Lamb mode desired, there are concerns about the safety and health issues of the operator Next, for the inter-digital transducers and comb transducers, the intricate design of the fingers is only suitable for a particular material with

a specific thickness As for the solid and liquid wedge transducers, it will require a trained operator for the adjustment of the transducer incidence angle for effective generation of the desired Lamb mode(s) As such, there is a prompt for the need of a simpler, effective and hazard-free method for controlled actuation of the desired Lamb wave for NDE purpose

The actuation method via piezoelectric crystals provides good control In fact, piezoelectric materials have been utilized in many areas such as actuators and sensors for ultrasonic waves, ultrasonic motors, transducers for vibration control, noise suppression and active structural repair Generally, piezoelectric devices make use of the piezoelectric effect to perform an electronic or mechanical function, whereby electrical energy may be converted into mechanical energy and vice-versa

Piezoelectric materials have triggered great interest over the past century since the discovery of the piezoelectric effect by Pierre and Jacques Curie in 1880 because of its unique electro-mechanical property This resulted in the many applications of PZT, including the field of NDE The highly responsive piezoelectric effect has made the PZT capable of exciting high frequency acoustic waves in the ultrasonic range, and conversely enables the PZT to sense small mechanical movements at high frequencies Being small

and strain gauges as a sensor device for high frequency detection The attractive mechanical coupling properties of the PZT have allowed it to remain for years as the leading form of ultrasonic transducer to excite wave on the bonded substrate as well as a sensor to detect the mechanical wave propagating in the substrate Recently, with the emerging technology on wireless and self-powered PZT sensors and actuators, PZT is displaying great potential in continuing its lead in the actuator / sensing field for NDE

electro-Beard and Chang (1997) proposed a method for damage detection in composite tubes where the stress waves were excited using embedded PZT These embedded piezoelectric patches also doubled as sensors for monitoring the propagating wave by measuring the arrival times of actuated packet waves to locate the damage Kessler et al (2002) employed piezoceramic patches bonded on the surface of plates as actuator and sensor for the detection of delamination, transverse crack and through-defects making use

of the propagation of Lamb waves Jin et al (2005) similarly adopted the plain PZT as sensor and the piezoceramic-based inter-digital transducer for the actuation of the Lamb wave to detect cracks in plates

Analytical models that capture the dynamic response of piezoceramic patches surface-bonded on elastic substrates and embedded in laminate composites have been presented for simple boundary conditions (Crawley and de Luis, 1987; Jin et al 2003) Closed form solutions which account for the electro-mechanical coupling effect were presented but the solution becomes complex when complicated boundary conditions are involved Hence, numerical solutions were subsequently resorted Yi et al (2000) presented the finite element (FE) formulation on the nonlinear dynamic responses of structures integrated with piezoelectric materials based on the updated Lagrangian

electrical degrees of freedom to account the piezoelectric effect are adopted Tua et al (2004) also adopted a similar FE formulation for modeling the repair of cracked beam using PZT patches to estimate the optimal geometry and voltages for effective repair Moulin et al (2000) provided the FE solution using normal modes expansion method for the study of amplitude variation with different Lamb modes excited by both PZT which were surface-bonded and bulk-embedded in the plate The simulated results showed good agreement when compared to the experimental results

Despite the efficiency of the PZT in providing controlled excitation of the required elastic wave for NDE purposes, it must be noted that the use of plain PZT produces non-directional waves in contrast to other specially designed actuators (e.g inter-digital transducers or comb transducers) (Quek et al., 2004a) The other trade-off for using the PZT as the actuator is that it will excite all the existing modes within the excitation range This hence implies the need on proper selection of the excitation range and the need of a reliable signal processing technique for the monitoring of the desired Lamb mode

1.2.4 Signal Processing Techniques in NDE

Although the use of vibration measurement is a simpler and less costly method with respect to instrumentation system compared with infrared thermography, ground-penetrating radar, acoustic emission monitoring and eddy current detection, the key factor for identifying damage lies in having an appropriate data analysis method to accurately estimate the structural parameters and provide meaningful interpretation of the structural condition at its measured state Visual estimation (Lowe et al., 1998; Giurgiutiu et al., 2001; Lowe and Diligent, 2002; Jin, 2003) and enveloping signal packets (Beard and

in the NDE technique involving the time of flight analysis A reliable and efficient signal processing is hence necessary to increase the robustness of the NDE method

Fourier Spectral Analysis

The most fundamental, longest and popular signal processing technique is the Fourier transform (FT) FT based modal analysis has been commonly adopted for obtaining modal parameters such as the natural frequency, damping loss factor and mode shape from dynamic responses of structures for NDE purposes The Fourier spectral analysis has provided a general method for examining the global energy-frequency distributions of a given signal Crema et al (1985) investigated the use of modal analysis

by a FFT analyzer to detect damage in composite structures A broad band impulse input was used The damage was induced by loads well above the working load, causing a small decrease in the eigen-frequencies for several modes Koh et al (2002) on the other hand adopted the FFT to obtain a two-dimensional Fourier spectrum on the time history of the excited Lamb wave for detecting delamination in plate Results showed that the Fourier spectra of the time history taken at the delaminated region exhibit obvious wave dispersion which allowed the degree of damage to be determined Gao et al (2003) likewise adopted the two-dimensional Fourier for imaging of dispersion curves of the multi-mode Lamb waves, whereby the elastic constants of the structure may be obtained via curve-fitting of these images

However, FT is valid under specific conditions, namely, the system must be linear and the data must be periodic or stationary (Huang et al., 1998) These restrictions limit the use of Fourier spectral analysis since many practical records obtained are finite in duration, non-stationary and nonlinear This method uses linear superposition of

only the average characteristics over the window of the data being analyzed Using Fourier spectral analysis on non-stationary data smears the energy over a much wider frequency range, whereas additional harmonics are required to simulate deformed wave-profiles Implicitly, whenever the data deviates from a pure sine or cosine function, the Fourier spectrum will contain harmonics These harmonics induced by nonlinear and non-stationary data cause energy spreading, resulting in misleading energy-frequency distribution for nonlinear and non-stationary data

Spectrogram

On the other hand, many of the NDE techniques for locating damage require meaningful interpretation of the different events registered in the transient response measured by the sensors This often requires the interpretation of the events over the time domain, which is non-stationary and often nonlinear and hence, signal processing techniques more complex than direct FT become necessary A simple technique for this purpose is the short-time Fourier transform (STFT) / spectrogram The STFT is an

simple method which treats the data as piecewise stationary such that Fourier spectral analysis is valid within each segment of stationary data Cawley and Adams (1979b) employed STFT to improve the resolution of the natural frequencies of the structural response obtained from FT, which was performed on one-tenth of the reciprocal spacing between the frequency points given by the FT This reduced the problem of information being diluted over the entire time domain Hurlebaus et al (2001) used the time-frequency spectrum obtained by STFT on Lamb wave signals generated by laser to obtain the group velocity-frequency plot The notches are located from the autocorrelation plot

(2001) used electrical impedance spectroscopy obtained from STFT to detect damage by monitoring changes in the impedance resonance peaks caused by low-speed impact experimentally Cheong et al (2004) also used STFT to obtain the time of flight of reflected Lamb waves from artificially induced notches in pipes

Although it appears that STFT facilitates the extraction of more information from the structural signals for NDE purposes, various drawbacks have been recognized The major drawback of STFT is the problem of leakage due to the reconstruction of the signal based on only limited sinusoidal functions (Yen and Lin, 2000), prompting for a more efficient technique In addition, the choice of the window-width is related to the physical process being studied and the relationship is often unknown Moreover, there is conflict between time and frequency resolutions To localize an event in time, the window width adopted must be narrow whereas the frequency resolution requires longer time series

to overcome the problem of time-frequency resolution The closest to STFT is the Gabor

or Morlet wavelet analysis, where improved results are obtained by using a Gaussian enveloped sinusoidal function

Kishimoto et al (1995) made used of Gabor wavelet analysis to obtain the

time-established the dispersive relation of the group velocity over a wide range of frequencies Liew and Wang (1998) adopted wavelet analysis for identifying transverse crack in a simply supported beam and compared the results with that based on eigenvalue analysis The crack location was identified by the peaks in the imaginary parts of the wavelet coefficients It was found that wavelet analysis is more versatile than eigenvalue analysis for crack detection by virtue of the basis functions Wang and Deng (1999) demonstrated the capability of WT to detect damage by identifying the sudden change in the spatial variation of the transformed deflection or displacement response Two examples were considered, one based on numerically simulated deflection responses of a uniform beam containing a short transverse crack under both static and dynamic load conditions, and the other based on smooth analytical crack-tip displacement fields It was shown that a spatially distributed response signal can be analyzed with WT and may be used for structural damage detection, provided that the signal captured perturbations induced by the presence of damage Jeong and Jang (2000) likewise employed WT to obtain the time-frequency domain data of acoustic waves emitted from fracture source location in plates Lee and Liew (2001) applied the WT to the instantaneous displacement of beam in their proposed NDE method, and showed that the real part of the WT was able to give more precise location of the damage in the beam as compared to its imaginary part Quek et al (2001) on the other hand used wavelet coefficients over the time domain to locate cracks

in beams via the time-of-flight analysis of the wave propagation along the beam Mallet et

al (2004) adopted WT to monitor the changes in the amplitude of propagating Lamb wave, generated and sensed by non-contact laser vibrometry, to detect damage in plates

Yen and Lin (2000), and Sun and Chang (2002) chose the wavelet packet

response for health monitoring of structures It is shown that the time-frequency resolution is significantly improved with WPT especially when the signals are corrupted with synthesized noises Quek et al (2004b) likewise adopted the WPT for decomposing the dynamic responses of structures as inputs into neural network for identifying damaged structural elements

However, signal processing via wavelets does not fully eliminate the limitations faced in Fourier analysis Firstly, there is leakage generated by the limited length of the basic wavelet function which distorts the energy-frequency-time distribution of the signal Secondly, the entire data length is analyzed with the same basic wavelet, which not only restricts the adaptability of the method but may lead to error in data interpretation Attempts to overcome these limitations result in the introduction of new basis functions or wavelets Experience also shows that if the scale is incorrectly chosen, it can produce many spurious harmonics under different scales which makes the analysis difficult or sometimes meaningless (Ong, 2000; Quek et al., 2003b) Despite its limitations, wavelet analysis is amongst the best existing method for analyzing and providing the time-frequency distribution of signals

HHT Spectral Analysis

Subsequent to the use of WT, another powerful signal processing technique known

as the Hilbert-Huang transform (HHT) has recently been proposed and used in NDE The HHT method was first developed by Huang et al (1998) with the aim of representing and interpreting non-stationary and nonlinear data accurately The method consists of the empirical mode decomposition (EMD) procedure to decompose the signal into intrinsic mode functions (IMFs) so as to facilitate the use of Hilbert transform to perform a Hilbert