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 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. i 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. 2. Introduction 1.1 Background 1.2 Literature Review 1.2.1 Historical Background of Elastic Wave Theories 1.2.2 Application of Elastic Waves in NDE 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 Locating Damage Zones in Large Components 29 2.1 Introduction 29 2.2 Zoning Damage via Changes in Mode Shape 31 2.2.1 31 Structural Integrity and Mode Shape 2.2.2 Mode Shape Coefficients via Dynamic Response ii 34 2.3 3. 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 53 Limitations of Proposed Method 2.4 Experimental Verification 56 2.5 Summary 63 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 A0 and S0 Dominance 86 3.6.2 Experimental Results for A0 and S0 Dominance 90 3.7 4. Finite Element Simulation Summary 94 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 iii 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 5. Summary 116 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 5.5 5.4.4 Blind Zones 141 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 iv 6. 5.6 Detection of Micro-width / Impurities In-filled / Repaired Cracks 177 5.7 Summary 182 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 7. 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 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 v 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 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, vi (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 (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) vii 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 undamaged plate 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 plate with half-through notch 60 2.5 Summary of experimental FRF values corresponding to first mode for plate with through notch 63 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 conditions 179 6.1 Experimental A0 velocities obtained for aluminum pipe with actuator at A1 206 6.2 Experimental A0 velocities and energy for wave propagation across long aluminum pipe 215 viii LIST OF FIGURES 1.1 Structure of proposed NDE procedure 24 2.1 Simply-supported beam with equally spaced sensors at a apart 34 2.2 Comparison of (a) power spectrum values and (b) square-rooted power spectrum values with theoretical mode shape for modes 1-3 35 2.3 (a) Impact load and corresponding (b) power spectrum 36 2.4 (a) Dynamic response and corresponding (b) power spectrum for S3 in Figure 2.1 36 2.5 Frequency response function for S3 in Figure 2.1 37 2.6 Division of plate into (a) (Q1-Q4) and (b) 16 (S01-S16) monitoring regions 40 2.7 Normalized shape for mode of square plate using (a) points and (b)16 points 41 2.8 Simulated accelerance FRF values of undamaged plate for (a) points and (b) 16 points 42 2.9 Relative change in mode for 50% reduction in E at D10 using (a) points and (b) 16 points 42 2.10 (a) Further partitioning of region S09, S10, S13 and S14 in Figure 2.6 into 16 regions, and the (b) relative change in mode for 50% reduction in E at D10 43 2.11 Maximum relative change in mode for varying severity of damage at D10 44 2.12 Relative change in mode for 50% reduction in E at D13 using (a) points and (b) 16 points 45 2.13 Relative change in mode for 50% reduction in E at D14 using (a) points and (b) 16 points 45 ix APPENDIX A ANALYTICAL SOLUTION OF PZT ACTUATED WAVE where a m ( x3 ) are the modal amplitudes. Substituting equations (A.33) and (A.34) into vector ( v1 ,T1 ) and Lamb wave mode -n in vector ( v ,T2 ) of the reciprocity relation given in equation (3.36) yields ⎤ iξ ( − n ) x ⎫ ∂ ⎧⎡ ⎨⎢∑ am ( x2 )v′m ( x3 ) ⋅ T− n − v − n ⋅ ∑ am ( x2 )Tm′ ( x3 )⎥ e ⎬ ⋅ xˆ2 = ∂x2 ⎩⎣ m m ⎦ ⎭ − ∂ i (ξ + ξ ( − n ) ) x (v′ ⋅ T− n − v− n ⋅ T ′) ⋅ xˆ3e ∂x3 (A.35) Integrating (A.35) with respect to x3 through the cross-section of the host plate gives ∂ ∂x ∑a m ( x )W( m )( − n ) e iξ ( − n ) x i (ξ +ξ )x = −(v ′ ⋅ T− n − v − n ⋅ T ′) ⋅ xˆ e ( − n ) x3 =b x3 = − b . m (A.36) From the mode-orthogonality condition presented in equation (A.32), only W( n )( − n ) remains in the left side of equation (A.36), and hence W( n )( − n ) ∂ iξ i (ξ +ξ )x x [a n ( x )e ( − n ) ] = −(v ′ ⋅ T− n − v − n ⋅ T ′) ⋅ xˆ e ( − n ) ∂x x3 =b x3 = − b . (A.37) Taking the origin of the x -axis for the free field to be at the center of the PZT, for wave propagating in the positive x -direction (n >0), a n (0) = . Integrating with respect to x from to l/2, the amplitude of mode n is obtained as ⎛ l ⎞ − (v ′ ⋅ T− n − v −n ⋅ T ′) ⋅ xˆ an ⎜ ⎟ = W( n )( − n ) ⎝ 2⎠ x3 =b x3 = − b −i (ξ +ξ (−n) 1− e i(ξ + ξ ( − n ) ) )l / (A.38) Equation (A.38) thus gives the amplitudes of Lamb waves propagating in the free field for an arbitrary wavenumber ξ, based on the acoustic solution for the confined field A-12 APPENDIX A ANALYTICAL SOLUTION OF PZT ACTUATED WAVE excited by the PZT. This coefficient implicitly contains the Fourier transformed potential distribution φ (ξ ) x3 = − h − b at wavenumber ξ introduced in equation (A.20c). Consequently, the entire acoustic field distribution can be obtained by integration through the wavenumber domain, u ( x2 ) = 2π ∫ ∞ u (ξ )eiξ x dξ (A.39) where u (ξ ) is the acoustic field corresponding to the arbitrary wavenumber, ξ. A-13 APPENDIX B – IMPLEMENTATION OF HHT USING MATLAB This appendix contains the implementation of the HHT on MATLAB 6.1 platform. MATLAB is selected because of its vast collection of highly optimized, applicationspecific functions built in for signal processing in the Toolbox as well as Simulink. A number of subroutines in signal analysis are readily available for utilization in the implementation of HHT, such as Hilbert transform, differentiation, contour plot and spline fitting, are all written in m-file format which facilitates the implementation of the HHT with ease. In addition, the toolbox functions built in MATLAB provide straightforward access to data from external devices and other software packages. This allows scope for further development with the implementation of the HHT to be used as a structural assessment tool since direct processing of dynamic data is possible by linking the program to data acquisition devices. This is further supported by the fact that over 300 third-party hardware and software products are compatible with the MathWorks tools. Data acquired through digital oscilloscope can be converted into Microsoft Excel format which allows the MATLAB to have easy access to the data. Lastly, MATLAB allows the creation of a graphical user interface (GUI) that enables implementation of the HHT in a more presentable and user-friendly manner. B-1 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB B.1 Flow Chart and Program Listing The flow chart for implementing the entire HHT method is shown in Figure B.1. A brief description of the implementation assuming a given input signal, X(t), is presented as follows: 1. Given a signal, X(t), where the values from to T are given at regular time steps of Δt, the data is first saved in the Microsoft Excel spreadsheet with the first and second column comprising the discrete data values and corresponding timings, respectively. 2. The EMD is carried out by executing the EMD.m file. The required inputs are the data filename and the SD value, denoted as ‘Cr’, for terminating the sifting process. EMD.m reads the data, X(t) using the function xlsread(‘filename’); The data is then passed to a subroutine, IMF.m for extracting the IMF components. 3. In the IMF.m, the data is first input into the ENVLP.m subroutine, whose function is to find the upper and lower envelopes of the input data. To find the upper and lower envelopes of the data, the maximum and minimum points are identified using a ‘for’ loop to track changes in the trend of the data through the entire data length. A change in sign between two successive increments from positive to negative implies a maxima and a vice versa. After identifying the extrema, all the maxima are joined using a cubic spline fit to form the upper envelope, and similarly for the lower envelope using the following code Upper = interp1(MaxTime,MaxPt,Step,'cspline'); Lower = interp1(MinTime,MinPt,Step,'cspline'); B-2 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB where ‘MaxPt’ and ‘MinPt’ are the maxima and minima recorded, ‘MaxTime’ and ‘MinTime’ are the corresponding timings, respectively, ‘Step’ is the time step Δt between discrete data points and ‘cspline’ refers to cubic spline function to join the maxima or minima. Returning the output back to the IMF.m, the mean, m1 of X(t) can be found by taking the mean of the upper and lower envelopes. Taking the difference between X(t) and the mean, m1 , produces h1 . 4. The result h1 is then subjected to another subroutine h_IMF.m, which performs the sifting process. In h_IMF.m, the ENVLP.m is again called to find the upper and lower envelope for h1 . The process is similar to that described in step (3). 5. Returning the upper and lower envelope back to h_IMF.m, the mean for h1 is then computed and the difference, h11 , is obtained by subtracting m1 from h1 . The SD between the two consecutive siftings, i.e. h1 and h11 is then computed based on equation (3.12). 6. If the computed SD is greater then ‘Cr’, then steps (4) and (5) are repeated k times until SD < ‘Cr’. When SD < ‘Cr’, the program exits from the subroutine h_IMF.m back to IMF.m, and the corresponding h( k −1) is designated the first IMF, c1 . The data value for c1 is then saved as a “c1.dat” file using the code save(‘c1.dat’,'c1','-ascii','-tabs'); where ‘c1’ is the discrete data values. 7. The data c1 is then subtracted from X(t) to obtain the residual, r1 , which is then subjected to steps (3) to (6) until the second IMF is obtained. B-3 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB 8. Step (7) is repeated n times until the final residual, rn becomes a monotonic function and no more IMFs can be extracted. The program then exits from IMF.m. 9. The individual IMFs are then subjected to HT using zi = hilbert(ci); where ‘ci’ is the data and ‘zi’ the result after HT of the ith IMF. 10. The result of the HT on individual IMFs is then saved as the real and imaginary parts in a zi.dat file. 11. Steps (9) and (10) are repeated n times for n number of IMFs. The program then exits from EMD.m and the EMD process is completed. 12. After performing the HT, the results are then processed by the routine HS.m. 13. In HS.m, the instantaneous energy of the signal IMFs are computed based equation (3.3a), and the instantaneous frequency computed based equation (3.3b) and (3.4) using the following codes phase = wrap(angle(zi)); inst_freq = gradient(phase); 14. Lastly, the results are plotted either as separate time-frequency and time-energy distribution using the command plot(time, frequency); or as a contour 3-dimensional energy-frequency-time distribution using the command contour(time,frequency,energy); B-4 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB Data acquisition Data, X(t) collected is saved as Microsoft Excel format X(t) EMD.m Read X(t) Specify SD criteria, Cr X(t) IMF.m n =i Yes ri Save ci as c(i).dat file Find residual, ri ri = [X(t) or r(i-1)] – ci i=i+1 Is rn monotonic? Call ENVLP.m X(t) / ri No ENVLP.m Find upper & lower envelopes of input. Find mean, mi hi = [X(t) or r(i-1)] – mi hi h_IMF.m Call ENVLP.m hi(1-k) h(k-1)i Find mean, mik hi(k-1) = hi – mik No k=k+1 ci = hik ci = an IMF Yes Find SD using equation (2.4.5) SD < Cr ? Read c(i).dat and plot data Perform HT on IMF using hilbert.m Save result as Z(i).dat Repeat for n number of IMFs HS.m Read complex data Z(i).dat Compute instantaneous energy using equation (2.2.3(a)) Compute instantaneous phase using equation (2.2.3(b)) Compute instantaneous frequency using equation (2.2.4) using gradient.m Plot hilbert spectrum using plot.m / contour.m Repeat for n number of IMFs End of Program Figure B.1. Flow chart of implemented HHT program using MATLAB B-5 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB B.2 Validation of HHT Program To validate the program, the following simple harmonic waveforms, and some Stokian waves presented by Huang et al. (1998) are analyzed. First, consider the simple harmonic waves, X (t ) = sin (20π t ) (B.1) X (t ) = sin (10π t ) + sin (40π t ) (B.2) Equation (B.1) consists of a harmonic signal with a singular frequency of 10Hz (Figure B.2(a)). Subjecting the signal to EMD, the IMF components are obtained as shown in Figure B.2(b), which consist of one IMF that is equivalent to the original signal and a residual trend that is equal to zero. This corresponds to the expected result since the signal is a pure sine wave with mean about zero. By performing the HT on the single IMF component, the HS can be obtained as shown in Figure B.2(c). By plotting the timefrequency and time-energy separately in Figure B.2(d) respectively, it can be observed (a) (b) FREQUENCY (Hz) 11 10.5 10 9.5 0.2 0.4 0.6 TIME (s) (c) 0.8 (d) Figure B.2. (a) Original data; (b) IMFs; (c) HHT spectrum and (d) timefrequency and time-energy plots for X(t) = sin (20πt) B-6 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB that the constant frequency of 10Hz is clearly displayed and the intensity of the spectrum is also a constant, which is expected as the amplitude of the waveform is a constant. Equation (B.2) is a summation of simple harmonics (Figure B.3(a)) with frequencies of 5Hz and 20Hz and amplitudes of and respectively. The IMFs after performing the EMD on the signal are shown in Figure B.3(b), depicting the two basic waveforms. Performing HT on the IMFs yield the HS shown in Figure B.3(c) where two frequencies over the length of the signal are obtained corresponding to the two harmonics of the original signal. Due to the imperfection of the spline fit and the end effects during the sifting process, small fluctuations in frequencies can be observed. However, the mean correspond to 5Hz and 20Hz. Observing the separate time- frequency and time-energy (Figure B.3(d)), it can be seen that the mean amplitude equals 1.0 for the higher frequency of 20Hz, and 2.0 for the lower frequency of 5Hz. C(1) -1 C(2) -2 0.2 0.4 0.6 TIME (s) 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.6 0.8 0.6 0.8 -2 0.1 -1 -3 RES AMPLITUDE -0.1 TIME (s) (b) FREQUENCY (Hz) (a) 30 20 20 10 15 0 0.2 0.4 0.2 0.4 AMPLITUDE FREQUENCY (Hz) 25 30 10 0 0.2 0.4 0.6 TIME (s) (c) 0.8 0 TIME (s) (d) Figure B.3. (a) Original data; (b) IMFs; (c) HHT spectrum and (d) time-frequency and time-energy plots for X(t) = 2sin (10πt) + sin (40πt) B-7 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB For the third validation, HHT analysis of a simple cosine wave (Figure B.4(a)) with one frequency suddenly switched to another frequency is performed. This signal is itself an IMF. Hence performing the EMD results in only one IMF component and a zero residual trend as shown in Figure B.4(b). From the HS shown in Figure B.4(c), the sudden change in the frequency from 0.033Hz to 0.0166Hz at approximately 500s can be detected accurately. Comparing with Morlet wavelet spectrum for the same cosine wave (Figure B.5(a)), the wavelet spectrum shows poorer frequency and time localization for the frequency shift event. Figure B.5(b) gives the Fourier spectrum for the same cosine wave. The Fourier spectrum is able to identify the frequencies fairly accurately but unable to identify the time localization of the frequency shift. It should also be noted that Fourier spectral analysis produce superior results only for strictly linear and stationary data. (a) (b) 0.1 0.09 Frequency, (Hz) 0.08 0.07 Figure B.4. (a) Original data; (b) IMFs and (c) HHT spectrum of simple cosine wave with one frequency suddenly switching to another frequency 0.06 0.05 0.04 0.03 0.02 0.01 0 100 200 300 400 500 600 700 800 900 1000 Time, t(s) (c) B-8 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB AMPLITUDE 0 0.02 0.04 0.06 FREQUENCY (Hz) 0.08 0.1 (a) (b) Figure B.5. (a) Morlet (Huang et al., 1998) and (b) Fourier spectra of cosine wave shown in Figure B.4(a) The fourth validation involves two Stokian waves which were presented by Huang et al. (1998). The frequency modulated waveform ⎡ 2π t ⎛ 4π t ⎞⎤ + 0.3 sin ⎜ X (t ) = cos ⎢ ⎟⎥ ⎝ 64 ⎠⎦ ⎣ 64 (B.3) considered is shown in Figure B.6(a). From the HS shown in Figure B.6(b), there is a clear frequency modulation between 0.01 and 0.02. This corresponds to that presented by Huang et al. (1998). According to the classical wave theory, the frequency of the Stokes wave can be computed and is given by, ω (t ) = [1 + 0.6 cos (2π t )] 64 (B.4) The frequency plot in Figure B.6(c) derived by the classical wave theory shows a frequency modulation with the range very close to that of the HS. The difference between HHT and classical wave theory is due to leakage of energy into the negative frequency range for the HS (Huang et al., 1998), nonetheless the general agreement is still clear. However, details of the intrinsic frequency variation are lost in the Morlet spectrum shown B-9 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB in Figure B.6(d) for the same waveform. This example illustrates that HHT is able to show physically meaningful intrawave frequency modulation. 0.1 0.8 0.08 0.6 Frequency (Hz) AMPLITUDE 0.4 0.2 -0.2 -0.4 -0.6 0.06 0.04 0.02 -0.8 100 200 300 TIME (s) 400 500 0 100 200 300 400 500 Time t(s) (a) (b) 0.1 0.09 0.08 AMPLITUDE 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 100 200 300 TIME (s) 400 500 (c) (d) Figure B.6. (a) Original data (b) HHT spectrum; (c) frequency modulation based on classic wave theory; and (d) Morlet spectrum for X(t) = cos[2πt / 64 + 0. 3sin(2πt / 64)] The other Stokes wave analyzed is amplitude modulated given by ⎛ 2π t ⎞ X (t ) = e − 0.01 t cos ⎜ ⎟ ⎝ 32 ⎠ (B.5) As observed from the plot of the waveform in Figure B.7(a), the waveform is also an IMF and hence there is no need to invoke the EMD. Figure B.7(b) shows the HS of the amplitude modulated wave. Because of the amplitude variation, there is an introduction of approximately 1.5% instantaneous frequency modulation about the mean of the carrier frequency of 0.03125Hz. The uneven range of frequency modulation is caused by amplitude fluctuation in the signal (Cohen, 1995). However, this frequency modulation B-10 APPENDIX B IMPLEMENTATION OF HHT USING MATLAB has not caused a change to the mean frequency. Comparing to that produced by the Morlet wavelet analysis on the same scale as given in Figure B.7(c), this fluctuation range is negligible. This example hence demonstrates that while amplitude variation can cause intrawave modulation, the effects are negligible compared to nonlinear distortion. 0.1 0.8 0.08 0.6 Frequency, (Hz) Amplitude 0.4 0.2 -0.2 -0.4 0.06 0.04 0.02 -0.6 -0.8 -1 100 200 300 Time, t(s) (a) 400 500 0 100 200 300 400 500 Time, t(s) 0.032 0.0318 0.0316 0.0314 0.0312 0.031 0.0308 0.0306 0.0304 100 200 300 400 500 (b) (c) Figure B.7. (a) Original data; (b) HHT spectrum and (c) Morlet spectrum (Huang et al., 1998) of X(t) = exp(-0. 01t) cos(2πt/32) B-11 APPENDIX C – PUBLICATIONS IN THIS RESEARCH Book Chapter [1] Quek S T, Tua P S and Wang Q 2005 Comparison of Hilbert-Huang, Wavelet and Fourier transforms for selected applications. Chaper 10 of Hilbert Huang Transform in Engineering, edited by Norden E. Huang & Nii O Attoh-Okine, CRC Press. [Invited presentation at the Mini-Symposium on Hilbert-Huang Transform in Engineering Applications October 31 – November 01, 2003, Newark, Delaware] Journal Papers [1] Quek S T, Tua P S and Wang Q 2003 Detecting anomaly in beams and plate based on Hilbert-Huang transform of real signals Smart Mater. Struct. 12(3) pp 447-460 [2] Tua P S, Quek S T and Wang Q 2004 Detection of cracks in plates using piezoactuated Lamb waves Smart Mater. Struct. 13(4) pp 643-660 [3] Tua P S, Quek S T and Wang Q 2005 Detection of crack in cylindrical pipes and plates using piezo-actuated Lamb waves Smart Mater. Struct. 14(6) pp 1325-1342 [4] Quek S T, Tua P S and Jin J 2004 Comparison of plain piezoceramics and interdigital transducer for crack detection in plates J Intel. Mat. Sys. Str. (Under review) [5] Quek S T and Tua P S 2005 Using frequency response function and wave propagation for locating damage in plates Smart Struct. Sys. (Under review) C-1 APPENDIX C PUBLICATIONS IN THIS RESEARCH Conference Papers [1] Quek S T, Tua P S and Wang Q 2003 Comparison of Hilbert-Huang, Wavelet and Fourier transforms for selected applications Mini-Symposium on Hilbert-Huang Transform in Engineering Applications October 31 – November 01, 2003, Newark, Delaware [2] Quek S T, Jin J and Tua P S 2004 Comparison of plain piezoceramics and interdigital transducer for crack detection in plates Smart Structures and Materials / NDE for Health Monitoring and Diagnostics 14-18 March, 2004, Town and Country Resort & Convention Center, San Diego, California USA [3] Quek S T, Loh K W and Tua P S 2004 Damage assessment of structures using wavelet transform and neural network The US-Korea Joint Seminar/Workshop on Smart Structures Technologies 01-03 September 2004, Seoul, Korea [4] Quek S T, Tua P S and Wang Q 2005 Detection of crack in thin cylindrical pipes using piezo-actuated Lamb waves Smart Structures and Materials / NDE for Health Monitoring and Diagnostics 6-10 Mar 2005, Town and Country Resort & Convention Center, San Diego, California USA [5] Quek S T and Tua P S 2005 Using frequency response function and wave propagation for locating damage in plates, The Second International Workshop on Advanced Smart Materials and Smart Structures Technology, July 21-24, 2005, Gyeong-ju, Korea C-2 APPENDIX C PUBLICATIONS IN THIS RESEARCH [6] Tua P S, Jin J, Wang Q and Quek S T 2002 Analysis of Lamb modes dominance in plates via Hilbert-Huang transform for health monitoring The Fifteenth KKCNN Symposium on Civil Engineering, December 19-20, 2002, Singapore pp S157S162 [7] Tua P S, Quek S T and Duan W H 2004 Finite element analysis on repair of cracked beam with piezoelectric patch The Seventeenth KKCNN Symposium on Civil Engineering, December 13-15, 2004, Thailand pp 211-216 C-3 [...]... change in mode 1 for 20% increase in E at D10 using (a) 4 points and (b) 16 points 46 2.15 Relative change in mode 1 for 50% reduction in E at D08 and D10 using (a) 4 points and (b) 16 points 47 2.16 Relative change in mode 1 for 50% and 20% reduction in E at D12 and D13 respectively using (a) 4 points and (b) 16 points 48 2.17 Relative change in mode 1 for 50% and 20% reduction in E at D10 and D13... 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... crack in Type II blind zone 174 5.49 Energy spectra and ellipses obtained for locating nonlinear crack in Type I blind zone using PZTs: (a) 1I-2I and (b) 1I-4I 175 5.50 Locating non-linear crack in Type I blind zone: combined ellipse plots for orientation of crack along (a) PZT 3I and 4I, and (b) PZT 1I and 4I 176 5.51 Locating non-linear crack in Type II blind zone: combined ellipse plots for part of. .. respectively using (a) 4 points and (b) 16 points 48 2.18 Relative change in mode 1 for 50% reduction in E at D1, D8, D10 and D15 using (a) 4 points and (b) 16 points 49 2.19 (a) Impact load with longer contact and corresponding (b) power spectrum 51 2.20 Relative change in mode 1 accelerance values for using impact load with longer contact time for (a) 4 points and (b) 16 points 52 2.21 Power spectrum of response... 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... configuration of PZTs to simulate (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 171 5.46 Energy spectra and ellipses obtained for locating crack in Type I blind zone using PZTs: (a) 1I-2I, (b) 2I-3I, (c) 3I-4I, (d) 1I-4I, (e) 1I-3I and (f) 2I-4I 172 5.47 Locating linear crack in Type I blind zone 173 5.48 Locating linear... 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, groundpenetrating radar, acoustic emission monitoring and eddy current detection, ... 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,... spectra and ellipses obtained for locating nonlinear crack using PZTs: (a) 1-A and (b) 2-A 160 5.38 Identified crack location using square grid configuration given in Figure 5.22 161 5.39 (a) Ellipses obtained by PZT pairs lined at different angular 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... 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 . 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. DETECTION OF CRACKS IN PLATES AND PIPES USING PIEZOELECTRIC MATERIALS AND ADVANCED SIGNAL PROCESSING TECHNIQUE TUA PUAT SIONG (B.Eng.(Hons.),. 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