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(1)Akademia Gorniczo - Hutnicza im. Stanisßlawa Staszica Wydziaßl In zynierii Mechanicznej i Robotyki Katedra Robotyki i Mechatroniki. Praca doktorska. Wykrywanie uszkodze« w metalicznych oraz kompozytowych konstrukcjach pßlytowych w z zastosowaniem przetworniko piezoelektrycznych Lß ukasz Ambrozi«ski. Promotor prof. dr hab. in z. Tadeusz Uhl Ko-promotor dr hab. in z. Tadeusz Stepinski Krakow 2014.

(2) AGH Univeristy of Science and Technology Faculty of Mechanical Engineering and Robotics Department of Robotics and Mechatronics. PhD Dissertation. Damage detection in plate-like metallic and composite structures using multiple piezoelectric transducers Lß ukasz Ambrozi«ski. Supervisor Professor Tadeusz Uhl Co-supervisor Professor Tadeusz Stepinski Krakow 2014.

(3) Acknowledgements. Skßladam serdeczne podzi

(4) ekowania moim promotorom: prof. dr hab. in z. Tadeuszowi Uhlowi za rozbudzenie we mnie pasji naukowej, za stawianie przede mn

(5) a interesuj

(6) acych problemow, ktorych rozwi

(7) azywanie przyczynißlo si

(8) e do mojego rozwoju oraz prof. dr hab. in z. Tadeuszowi Stepinskiemu za wyrozumiaßlosc, pomoc i cenne wskazowki w trakcie prowadzenia bada« i w czasie pisania pracy. W sposob szczegolny chciaßlbym wyrazic wdzi

(9) ecznosc prof. dr hab. in z. Bogdanowi Piwakowskiemu, ktory goszcz

(10) ac mnie w swoim laboratorium w École centrale de Lille, wprowadzißl mnie w problematyk

(11) e bada« ultradzwi

(12) ekowych wykorzystuj

(13) acych powietrze jako osrodek sprz

(14) egaj

(15) acy. Wsp oßlpraca z prof. Piwakowskim zaowocowaßla powstaniem rozdziaßlu 4 oraz 8 tej pracy. Osobne podzi

(16) ekowania nale za

(17) si

(18) e moim rodzicom, a tak ze mojej z onie Ligii za cierpliwosc i wsparcie.. L ß ukasz Ambrozi«ski, maj 2014.

(19) Streszczenie Badania nieniszcz

(20) ace (ang. nodestructive testing NDT) s

(21) a szeroko stosowane by zapewnic bezpieczn

(22) a eksploatacj

(23) e konstrukcji. Monitorowanie stanu konstrukcji (ang. structural health monitoring SHM) jest interdyscyplinarnym podejsciem, ktore dzi

(24) eki integracji NDT z badanymi obiektami pozwala na utworzenie inteligentnych, samodiagnozuj

(25) acych si

(26) e struktur. Niniejsza rozprawa dotyczy metod bada« nieniszcz

(27) acych i monitorowania stanu konstrukcji wykonanych z cienkich pßlyt z zastosowaniem ultradzwi

(28) ekowych fal Lamba. W pierwszej cz

(29) esci pracy poruszono problem dyspersyjnej i wielo-modowej natury tych fal, przedstawiaj

(30) ac podejscia pozwalaj

(31) ace na eksperymentalne wyznaczanie charakterystyki dyspersyjnej. Nast

(32) epnie, przedstawiono obrazowanie struktur pßlytowych z zastosowaniem wieloelementowych przetwornikow. W pracy por ownano r oz ne podejscia do ogniskowania fal aktywn

(33) a metod

(34) e phased array oraz podejscie wykorzystuj

(35) ace syntetyczne ogniskowanie. Ponadto, zaprezentowano technik

(36) e coarray, pozwalaj

(37) ac

(38) a na efektywne projektowanie rzadkich matryc wielo-przetwornikowych. W kolejnym rozdziale przedstawiono algorytmy zdolne do samo-ogniskowania fal w miejscu defektow, szczegolßowo przedstawiono jedn

(39) a z technik samo-ogniskowania oraz zaproponowano jej modykacj

(40) e pozwalaj

(41) ac

(42) a na polepszenie rozdzielczosci metody. Analizy te zostaßly przedstawione z u zyciem danych symulacyjnych oraz eksperymentalnych. W kolejnej cz

(43) esci poruszono jeden z najwa zniejszych problemow w aplikacjach SHM, czyli wpßlyw temperatury na propagacj

(44) e fal. Jako rozwi

(45) azanie tego problemu zaproponowano now

(46) a metod

(47) e kompensacji tego zjawiska, opart

(48) a o faz

(49) e chwilow

(50) a sygnaßlow. Dziaßlanie tej metody porownano z innymi podejsciami, pokazuj

(51) ac jej wy zsz

(52) a skutecznosc. Ostatni temat zaprezentowany w pracy dotyczy nieniszcz

(53) acych bada« paneli kompozytowych z zastosowaniem przetwornikow wykorzystuj

(54) acych powietrze jako medium sprz

(55) egaj

(56) ace. W rozdziale zaprezentowano wyniki eksperymentow, otrzymanych przy pomocy mechanicznego skanera. Pozwolißlo to na zilustrowanie interakcji roz nych, selektywnie wzbudzanych modow fal Lamba z roz nymi typami defektow. Na podstawie tych doswiadcze« zaproponowano metod

(57) e detekcji i lokalizacji uszkodze« w oparciu o analiz

(58) e tßlumienia fali.. ii.

(59) Abstract Nondestructive testing (NDT) techniques are widely used to ensure structural integrity and safety. Structural health monitoring (SHM) is an interdisciplinary eld that integrates NDT methods with structures to create smart self-diagnostic constructions. This thesis is concerned with NDT and SHM applied to plane-like structures based on the use of ultrasonic Lamb waves. The rst part of the thesis deals with the dispersive and multi-modal nature of these waves, providing methods that can be used for experimental evaluation of dispersion characteristics. Next, imaging of planar structures, by means of transducer arrays is outlined, and active and synthetic focusing techniques are compared. Furthermore, a coarray framework for eective design of sparse array apertures is presented. The following Chapter is concerned with algorithms capable of self-focusing wave energy at the scatterers' location. The self-focusing technique and its proposed extension are outlined in details. Both simulated and experimental results are provided. In the next part of the thesis, one of the most important problems with monitoring applications, i.e., temperature inuence on the waves' signals, is addressed. A new compensation method, based on instantaneous phase of the signals is proposed. The new technique is compared to other approaches using experimental data revealing superior performance. The nal study presented in the thesis is devoted to NDT of composite panels by means of air-coupled ultrasound techniques. Experimental results obtained using a precise mechanical scanner are outlined. The interaction of various selectively excited Lamb modes with dierent types of defects is illustrated in the form of B-scan images. Finally, a method for damage detection and localization based on wave attenuation is proposed.. iii.

(60) Contents. List of Figures. viii. Glossary. xvii. 1 Introduction. 1. 1.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2. 1.2. Nondestructive testing . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2. 1.3. Principles and concepts of SHM . . . . . . . . . . . . . . . . . . . . . . .. 4. 1.3.1. Classication of SHM systems . . . . . . . . . . . . . . . . . . . .. 6. Guided-waves-based SHM . . . . . . . . . . . . . . . . . . . . . . . . . .. 7. 1.4.1. Sensors and sensors networks . . . . . . . . . . . . . . . . . . . .. 8. 1.4.1.1. Transducers used in NDT inspections . . . . . . . . . .. 8. 1.4.1.2. Sensors for SHM . . . . . . . . . . . . . . . . . . . . . .. 9. 1.4.1.3. Sensors networks . . . . . . . . . . . . . . . . . . . . . .. 10. Processing of Lamb waves signals . . . . . . . . . . . . . . . . . .. 12. 1.4.2.1. Array signal processing . . . . . . . . . . . . . . . . . .. 12. 1.4.2.2. Distributed transducers . . . . . . . . . . . . . . . . . .. 14. 1.4. 1.4.2. 2 Aim and scope of the thesis. 16. 2.1. Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17. 2.2. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21. 3 Dispersion of Lamb waves. 24. 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25. 3.2. Rayleigh-Lamb equations. . . . . . . . . . . . . . . . . . . . . . . . . . .. 26. 3.3. Modeling Lamb wave propagation using structure transfer function . . .. 28. iv.

(61) CONTENTS 3.4. Dispersion compensation techniques. . . . . . . . . . . . . . . . . . . . .. 4 Experimental estimation of dispersive characteristics. 30. 33. 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34. 4.2. Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36. 4.2.1. Slant stack transform . . . . . . . . . . . . . . . . . . . . . . . . .. 36. 4.2.2. Two-dimensional Fourier transform . . . . . . . . . . . . . . . . .. 39. 4.2.3. MUltiple SIgnal Classication (MUSIC) . . . . . . . . . . . . . .. 40. Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41. 4.3.1. Non-dispersive waves . . . . . . . . . . . . . . . . . . . . . . . . .. 41. 4.3.2. Dispersive waves . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46. Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48. 4.4.1. MUSIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 49. 4.4.2. Isotropic plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51. 4.4.3. Composite laminate . . . . . . . . . . . . . . . . . . . . . . . . .. 52. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 54. 4.3. 4.4. 4.5. 5 Imaging using planar arrays. 56. 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57. 5.2. Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58. 5.2.1. Apertures and arrays . . . . . . . . . . . . . . . . . . . . . . . . .. 58. 5.2.2. Imaging using synthetic aperture . . . . . . . . . . . . . . . . . .. 61. 5.2.3. Eective aperture and coarray . . . . . . . . . . . . . . . . . . . .. 64. 5.2.3.1. Coarray reweighting . . . . . . . . . . . . . . . . . . . .. 66. Imaging schemes . . . . . . . . . . . . . . . . . . . . . . . . . . .. 67. 5.2.4.1. Array with single transmitter multiple receivers (STMR). 68. 5.2.4.2. Synthetic aperture . . . . . . . . . . . . . . . . . . . . .. 70. Examples of array design . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71. 5.3.1. STMR arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71. 5.3.1.1. Uniform linear array . . . . . . . . . . . . . . . . . . . .. 71. 5.3.1.2. 2D arrays . . . . . . . . . . . . . . . . . . . . . . . . . .. 72. Examples of coarray synthesis . . . . . . . . . . . . . . . . . . . .. 74. 5.3.2.1. Uniform linear array . . . . . . . . . . . . . . . . . . . .. 74. 5.3.2.2. Cross-like sparse array . . . . . . . . . . . . . . . . . . .. 77. 5.2.4. 5.3. 5.3.2. v.

(62) CONTENTS 5.3.2.3 5.4. Star-like array . . . . . . . . . . . . . . . . . . . . . . .. 78. Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82. 5.4.1. Simulation techniques . . . . . . . . . . . . . . . . . . . . . . . .. 82. 5.4.1.1. Structure transfer function (STF) . . . . . . . . . . . .. 82. 5.4.1.2. Local interaction simulation approach (LISA) . . . . .. 84. Imaging using STMR arrays . . . . . . . . . . . . . . . . . . . . .. 84. 5.4.2.1. Comparison of the simulation techniques . . . . . . . . .. 84. 5.4.2.2. Imaging using tone burst signals . . . . . . . . . . . . .. 86. 5.4.3. Inuence of the dispersion on directionality characteristics . . . .. 88. 5.4.4. Synthetic vs. active focusing. . . . . . . . . . . . . . . . . . . . .. 89. 5.4.5. Coarray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91. 5.4.5.1. Sparse cross array . . . . . . . . . . . . . . . . . . . . .. 92. 5.4.5.2. Star-like array . . . . . . . . . . . . . . . . . . . . . . .. 94. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96. 5.5.1. STMR arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 97. 5.5.2. Active and synthetic focusing . . . . . . . . . . . . . . . . . . . .. 99. 5.5.3. Using coarray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101. 5.4.2. 5.5. 5.5.3.1. Simulations of the sparse cross-array . . . . . . . . . . . 102. 5.5.3.2. Simulations of the star-like array . . . . . . . . . . . . . 103. 5.6. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104. 5.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106. 6 Array self-focusing techniques. 108. 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109. 6.2. Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . 110. 6.3. 6.4. 6.2.1. DORT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110. 6.2.2. DORT-CWT algorithm . . . . . . . . . . . . . . . . . . . . . . . 112. 6.2.3. Imaging with self-focused transmitting array . . . . . . . . . . . . 113. Numerical verication of the methods . . . . . . . . . . . . . . . . . . . . 114 6.3.1. Simulation algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 114. 6.3.2. Numerical backpropagation . . . . . . . . . . . . . . . . . . . . . 115. 6.3.3. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 116. Experimental validation of the DORT-CWT method . . . . . . . . . . . 120. vi.

(63) CONTENTS. 6.5. 6.4.1. Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 121. 6.4.2. Experimental results - numerical backpropagation. 6.4.3. Experimental verication of the backpropagation . . . . . . . . . 123. . . . . . . . . 121. Damage imaging using self-focused transmitting array . . . . . . . . . . 125 6.5.1. Damage imaging results. . . . . . . . . . . . . . . . . . . . . . . . 127. 6.6. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127. 6.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130. 7 Temperature compensation in SHM applications. 131. 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132. 7.2. Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.2.1. Temperature inuence on Lamb waves propagation . . . . . . . . 133. 7.2.2. Dierential features for evaluating signals similarity . . . . . . . . 134. 7.2.3. Instantaneous phase . . . . . . . . . . . . . . . . . . . . . . . . . 136. 7.3. Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137. 7.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139. 7.5. 7.4.1. Temperature inuence on time signals . . . . . . . . . . . . . . . 139. 7.4.2. Damage indices (DIs). 7.4.3. Damage indices ratio . . . . . . . . . . . . . . . . . . . . . . . . . 144. . . . . . . . . . . . . . . . . . . . . . . . . 142. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145. 8 Application of air-coupled ultrasound for damage detection. 147. 8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148. 8.2. Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . 148. 8.3. Experimental setup 8.3.1. 8.4. 8.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150. Phase velocity evaluation . . . . . . . . . . . . . . . . . . . . . . 151. Damage detection results . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.4.1. Interaction of Lamb waves with a crack. . . . . . . . . . . . . . . 152. 8.4.2. Lamb waves interaction with delaminations . . . . . . . . . . . . 155. 8.4.3. C-scan images based on attenuation analysis . . . . . . . . . . . . 156. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157. 9 Summary and future work. 158. References. 162. vii.

(64) List of Figures. 1.1. Through-transmission (a) and pulse-echo (b) setups for ultrasonic testing inspections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1.2. Pulse-echo (a) and pitch-catch (b) setups for guided waves-based inspections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1.3. 12. Phase (a) and group (b) velocity dispersion curves of an isotropic aluminum plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3.2. 10. Principles of imaging using an array of transducers (a) and example of distributed network of transducers (b). . . . . . . . . . . . . . . . . . . .. 3.1. 3. 26. Dispersion curves for an isotropic aluminum plate and dependence of phase velocity on the elastic constants: Young's modulus (a), mass density (b) and Poisson's ratio (c). . . . . . . . . . . . . . . . . . . . . . . .. 3.3. Dispersion curves of a 1mm aluminum plate and the spectrum of the excitation signal used to simulate Lamb wave response. . . . . . . . . . .. 3.4. 29. Responses of Lamb waves propagating in a 1mm-thick aluminum plate simulated for various distances. . . . . . . . . . . . . . . . . . . . . . . .. 3.5. 28. 30. Illustration of dispersion removal eect. The simulated time-signal consisting of 3 waves, which have traveled distances of 280, 300, 350mm (blue) was subject to dispersion removal technique which results in recompressed waveform (red). . . . . . . . . . . . . . . . . . . . . . . . . .. 32. 4.1. Linear array receiving a wave. . . . . . . . . . . . . . . . . . . . . . . . .. 37. 4.2. Synthetic data - a wave recorded using the array. A1. at N = 10 points. (a). The time-domain slant stack of the synthetic data (b).. viii. . . . . . . .. 42.

(65) LIST OF FIGURES 4.3. Results of the SL transform obtained using the synthetic data consisting of N signals captured at the points spaced with pitch d = 2.5mm, where:. N = 10, L = 22.5mm (array. A2) (b).. A1) (a), and N. = 20, L = 47.5mm (array. Cross-sections of the presented SL results at frequency 200kHz. (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. 43. Results of the 2DDFT obtained using the synthetic data consisting of. N signals captured at points spaced at distance d, where: N = 10, d = 2.5mm, L = 22.5mm (array 23.75mm (array. A3). A1). (a) and N = 20, d = 1.25mm, L =. (b). Dashed white lines denote spatial sampling. criterion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. 44. Results of the SL transform obtained using the synthetic data consisting of N signals captured at the points spaced at a distance of d, where: N =. 10, d = 2.5mm, L = 22.5mm (array L = 23.75mm (array. A3) (b).. at frequency 200kHz (c). 4.6. A1) (a) and N. = 20, d = 1.25mm,. Cross-sections of the presented SL results. . . . . . . . . . . . . . . . . . . . . . . . . . .. 45. Dispersion curves obtained from the data generated by the LISA transformed using the SL (a) and 2DDFT transform (c). Corresponding dispersion curves obtained from the Rayleigh-Lamb equations presented in the phase-velocity-frequency plane (b) and their wavenumber-frequency representation (d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.7. 47. Dispersion curves obtained from the simulated data using the SL (a) and 2DDFT (b) transform and the peak-nding operation. Solid lines denote the theoretical dispersion curves obtained from the Rayleigh-Lamb equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.8. 48. Experimental setup for laser measurement of Lamb waves used for an aluminium plate (a), laser measurement points used in the composite plate experiment (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.9. 49. Frequency-wavenumber spectra obtained using: 2D-DFT (a); MUSIC (b). 50. 4.10 Examples of cross-sections taken for the 2D spectra shown in g. 4.9 for: 0.4 MHz (a); 0.75 MHz (b). . . . . . . . . . . . . . . . . . . . . . . . . .. ix. 50.

(66) LIST OF FIGURES 4.11 Dispersion curves obtained for the inspected aluminum plate using the SL transform. Solid lines correspond to the theoretical dispersion curves obtained from the Rayleigh-Lamb equations. Dashed straight line denotes the spatial sampling criterion. . . . . . . . . . . . . . . . . . . . . . . . .. 51. 4.12 Dispersion curves obtained using laser measurements for the composite plate. Measurements captured along lines parallel (a) and perpendicular to the bers direction (b). Theoretical solutions obtained using partial wave approach parallel (c) and perpendicular to the bers direction (d).. 53. 4.13 Phase velocity proles of the CFRP sample at frequency of 100kHz (a) and 250kHz (b). Vertical axes coincide with the CFRP's ber direction.. 54. 5.1. Planar array in spherical coordinate system.. 59. 5.2. Beamforming using single receiver-transducer pair (a), Principle of syn-. . . . . . . . . . . . . . . .. thetic aperture imaging (b). . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. 62. Illustration of imaging under far-eld assumption using uniform linear sensing array: (a) synthetic aperture, (b) reections form a target localized at angle φ acquired by sensors of the uniform linear array. . . . . . .. 5.4. 68. Linear uniform array (a). Normalized beam pattern of a linear uniform array with M = 9 elements (b). . . . . . . . . . . . . . . . . . . . . . . .. 71. 5.5. Topology of a cross-shaped array. . . . . . . . . . . . . . . . . . . . . . .. 72. 5.6. The array pattern of an unsteered cross array in wavenumber plane (a) and the array pattern of the array steered in the 90◦ direction (b) and 45◦ direction (c). Beam patterns corresponding to these steered responses (d). (The array pattern magnitude is expressed in color scale -30dB dynamic range). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5.7. 73. Linear array with indicated elements excited in the subsequent rings and the corresponding coarrays (a). Coarrays obtained as a result of Nf = 6 rings (I + II+...+VI) (b) and only Nf = 2 rings (I+VI) (c).. 5.8. . . . . .. Example of the sparse array re-weighting to obtain a coarray apodized with triangle weighting function. . . . . . . . . . . . . . . . . . . . . . .. 5.9. 75 76. Beam patterns of the triangle-shaped and uncorrected coarray obtained according to the scheme presented in g. 5.7. . . . . . . . . . . . . . . .. x. 77.

(67) LIST OF FIGURES 5.10 Example of coarray synthesis. The elements of horizontal sub-array are used as emitters, the vertical sub-array is used as receivers which results in a square coarray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78. 5.11 Array patterns of the square coarray resulting from the sparse cross array. Uniform (rectangular window) weighting (a) and Hamming window weighting (b) (color scales used correspond to 60dB amplitude range). Coarray modulated by 2D Hamming window (c) and beam patterns obtained at points corresponding to white cycles presented in the array patterns (d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79. 5.12 Star-like array with outer elements used as emitters (a) resulting sum coarray (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 80. 5.13 Weighting functions of coarray presented in g. 5.12b. Uncorrected, resulting from data redundancy (a), corrected with Hamming window (b).. 80. 5.14 Steered responses of the star-like coarray with weighting: resulting from data redundancy, as presented in g. 5.13a (a), rectangular window (b), Hanning window as shown in g. 5.13b (c). Beam patterns obtained at points corresponding to white cycles presented in the gures (d). . . . .. 81. 5.15 Setup used to investigate array BPs. The central element in the array is a transmitter, R is a point-like reector in the plate, Si,α0 is the i-th element of the sensing array, Si,αn is the i-th element of an array rotated by an angle of n · α. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83. 5.16 Directionality characteristics of the cross-shaped array, presented in g. 5.5 obtained using dierent numerical tools: polar in linear scale (a) and linear plot in dB scale (b). . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85. 5.17 Star-like setups: single transmitter and multiple receivers (STMR) (a) multiple transmitters and multiple receivers (MTMR) (b). . . . . . . . .. 86. 5.18 Target images obtained in the star-like single transmitter and multiple receivers setup for the single A0 mode excited with windowed tone burst consisting of 3 a), and 30 sine cycles (b). Directionality characteristics obtained for the tone-burst excitation signals and for the monochromatic excitation (BP plot) c).. . . . . . . . . . . . . . . . . . . . . . . . . . . .. xi. 87.

(68) LIST OF FIGURES 5.19 Examples of damage imaging using the star-shaped array. Images obtained using the STF simulated raw data (a) and the data after dispersion compensation (b). Beam patterns obtained for the STF simulated raw signals and the signals after dispersion compensation (c). . . . . . .. 88. 5.20 Target image obtained using synthetic aperture MTMR-SA concept in the starlike setup(a). Comparison of the resulting beam pattern with that obtained with STMR (g. 5.18a), (b). . . . . . . . . . . . . . . . . .. 89. 5.21 Target images obtained in the simulations of the MTMR-PA mode for the following emission/reception sweeping steps: 10◦ /10◦ (a), 10◦ /1◦ (b), 1◦ /1◦ c). The beam patterns obtained using MTMR-SA and the MTMRPA mode with azimuth sweeping step 1◦ /1◦ d). . . . . . . . . . . . . . .. 91. 5.22 Imaging results of a far-eld reector, obtained using square coarray with uniform weighting (a) and apodization by 2D Hamming window (b). The beam patterns resulting form the theoretical array pattern (BP) and the structure's transfer function model (STF) for uniform (c) and the 2D Hamming window apodization. . . . . . . . . . . . . . . . . . . . . . . .. 92. 5.23 Comparison of the directional characteristics obtained from the STF model for uniform and Hamming apodization.. . . . . . . . . . . . . . .. 93. 5.24 Damage image of a far-eld reector obtained using the star-like coarray with weighting resulting from data redundancy, as presented in g. 5.13a (a). Beam patterns of the star-shaped coarray resulting form array pattern and as post processing of structure's transfer function image. (b) . .. 94. 5.25 Damage images of a far-eld reector obtained using the star-like coarray with uniform, rectangular window (a), Hanning window as shown in g. 5.13b (b). Directional characteristics obtained as angle-wise amplitudes of the images (c).. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 95. 5.26 Experimental setup to investigate imaging techniques (a) An example of laser vibrometer measurement points in: spiral-shaped conguration used in STMR setup (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 97. 5.27 Investigated topologies of the array: (a) star-shaped, (b) circular, (c) spiral. 98 5.28 BPs evaluated for the wave with incident angle 60◦ for: star-shaped (a), circular (b) and spiral (c) array. . . . . . . . . . . . . . . . . . . . . . . .. xii. 99.

(69) LIST OF FIGURES 5.29 Selected parameters of BPs obtained for the investigated topologies. Maximal main lobe-width (a), maximal side-lobe level (b). . . . . . . . . . . 100 5.30 Experimental results of damage imaging with the use of MTMR a), MTMR-PA excitation (b); Comparison of the beam patterns obtained for the experimental and simulated data c). . . . . . . . . . . . . . . . . 101 5.31 Images of the far-eld scatterer obtained using cross-shaped sparse array (a) and the multiple receivers square array consisting of 100 elements and a single-transmitter (STMR) (b). The cross-shaped sparse array apodized using Hamming window (c) and directional characteristics of three imaging methods: the cross shaped array with recatngular (Rect win) and Hamming apodization (Ham.) and the single transducer multiple receivers (STMR) (d). . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.32 Damage images of a far-eld reector obtained using the star-like coarray with weighting resulting from data redundancy, as presented in g. 5.13a (a), rectangular window (b), Hanning window as shown in g. 5.13b (c). Beam patterns obtained at points corresponding to white cycles presented in the gures (d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.1. The DORT (left) and the DORT-CWT (right) algorithm ow diagram. . 111. 6.2. Two scenarios of the damage location analyzed in simulations and experiments. Setup A (left) and setup B (right). . . . . . . . . . . . . . . . . . 114. 6.3. Numerical backpropgation performed for the data from the rst simulations (setup A) with use of 32-elements array. Wave focusing on the damage: a) M1 b) M2 c) N. Markers indicate damages locations. Dimensions of the backpropagated elds are in millimeters. . . . . . . . . . . . 116. 6.4. Backpropagation performed for the data from the rst simulations (setup A) using 8-elements array. Wave focusing on the damage: a) M1 b) M2 c) N. Markers indicate damages locations. Dimensions of the backpropagated elds are in millimeters. . . . . . . . . . . . . . . . . . . . . . . . . 117. 6.5. Subsequent normalized eigenvalues obtained with the DORT algorithm for the simulation data (setup B). . . . . . . . . . . . . . . . . . . . . . . 118. xiii.

(70) LIST OF FIGURES 6.6. Backpropagated elds calculated for the data from the second simulation (setup B) processed with the DORT. Backpropagation of the: a) rst eigenvector, b) second eigenvector; Beampatterns (c), (d), corresponding to the backpropagated elds a) and b), respectively; Markers indicate the damages locations; Dimensions of the backpropagated elds are in millimeters and beam azimuths are in degrees. . . . . . . . . . . . . . . . 118. 6.7. Normalized eigenvalues distribution obtained for the simulated data (setup B) processed with the DORT-CWT algorithm. Arrows point the peak eigenvalues used in the backpropagation. . . . . . . . . . . . . . . . . . . 119. 6.8. Numerical backpropgation of the eigenvectors obtained with DORT-CWT method for the second simulation (setup B). Wave focusing on the damages: (a) M1, (b) M2, (c) N; Beampatterns (d), (e) and (f) corresponding to the backpropagated elds a), b) and c) respectively. Markers indicate damage locations. Dimensions of the backpropagated elds are in millimeters and beam azimuths are in degrees. . . . . . . . . . . . . . . . 120. 6.9. Subsequent normalized eigenvalues calculated for the correctly resolved damages (g. 6.2 setup A). . . . . . . . . . . . . . . . . . . . . . . . . . 121. 6.10 Numerical backpropgation of the eigenvectors obtained with DORT method for the rst experiment (g. 2 setup A). Wave focusing on the damage: (a) M1, (b) M2, (c) N; Beampatterns (d), (e) and (f) corresponding to the backscattering elds a, b and c, respectively. Markers indicate damage locations. Dimensions of the backpropagated elds are in millimeters and beam azimuths are in degrees. . . . . . . . . . . . . . . . . . . . . . . . . 122 6.11 Subsequent normalized eigenvalues obtained with the DORT method in the second experiment (g. 6.2 setup B). . . . . . . . . . . . . . . . . . . 123 6.12 Backpropagated elds calculated for the data from the setup B in g. 2 processed with the DORT. Backpropagation of the: (a) rst eigenvector, (b) second eigenvector; Beampatterns (c) and (d), corresponding to the backpropagated elds a and b, respectively. Markers indicate damage locations. Dimensions of the backpropagated elds are in millimeters and beam azimuths are in degrees. . . . . . . . . . . . . . . . . . . . . . 124. xiv.

(71) LIST OF FIGURES 6.13 Eigenvalues distribution obtained for the data from the second measurement (g. 6.2 setup B) processed with the DORT-CWT algorithm. Arrows point the peak eigenvalues used in the numerical backpropagation.. 125. 6.14 Numerical backpropgation of the eigenvectors obtained with DORT-CWT method for the second experiment (g. 2 setup B). Wave focusing on the damage: (a) M1, (b) M2, (c) N; Beampatterns (d), (e) and (f) corresponding to the backpropagated elds a, b and c, respectively. Markers indicate damage locations. . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.15 Experimental setup for vibrometer measurements (right) and the arcshaped measurement points (left). The linear array is located under the arc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6.16 Beampatterns obtained using the scanning laser vibrometerfor monitoring physical backpropagation. The beams steered in the direction of damage denoted by (a) M1, (b) M2, and (c) N. . . . . . . . . . . . . . . . . . . . 126 6.17 Damage imaging results obtained with the star-shaped array for the transmitting -array steered in the direction of target denoted by M 1 (a), M 2 (b) and N (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.1. Inuence of temperature on dispersion curves of 1mm-thick aluminum plate (a), zoomed S0 mode (b). . . . . . . . . . . . . . . . . . . . . . . . 135. 7.2. The specimen used in the experiment. . . . . . . . . . . . . . . . . . . . 138. 7.3. Temperatures registered during the rst stage of the experiment. The damages were introduced at a room temperature. . . . . . . . . . . . . . 139. 7.4. Example of time signals acquired for an intact plate aected by temperature change (a) and the waveform zoomed at limits of 0.03 − 0.09ms (b). 0.13 − 0.19ms and 0.2 − 0.26ms. . . . . . . . . . . . . . . . . . . . . . . 140 7.5. Example of time signals acquired for an intact plate at dierent temperatures, presented in g. 7.4, after compensation of the temperature inuence (a) and the waveform zoomed at limits of 0.03 − 0.09ms (b). 0.13 − 0.19ms and 0.2 − 0.26ms. . . . . . . . . . . . . . . . . . . . . . . 141 7.6. Comparison of baseline and damaged signals acquired at room temperatures.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142. xv.

(72) LIST OF FIGURES 7.7. Comparison of normalized damage indices calculated using signal dierence coecient and local temporal coherence. The measurements marked by the dashed-line rectangle were taken for a damaged structure. . . . . 143. 7.8. Comparison of normalized damage indices calculated using local temporal coherence and the proposed method based on Hilbert and wavelet transform. The measurements marked by the dashed-line rectangle were taken for a damaged structure. . . . . . . . . . . . . . . . . . . . . . . . 144. 7.9. Ratio between the maximal DIs values obtained for the damaged and intact, temperature inuenced, structure. The color of the bars denotes corresponding emitter→receiver pair. Results obtained for the excitation frequency of 100kHz (a) and 300kHz (b). . . . . . . . . . . . . . . . . . 145. 8.1. Principles of Lamb waves generation and reception using air-coupled transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149. 8.2. Mechanical scanner used in the experiments (a), experimental setup at the rst plate (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150. 8.3. Experimental dispersion curves obtained using air-coupled transducers on a composite plate. Angle of the transducers set to enhance A0 (a) and. S0 mode (b). White lines denote sampling criterion. . . . . . . . . . . . 151 8.4. B-scan images illustrating the interaction of Lamb waves with a crack in a composite plate: S0 mode (a) and A0 mode (b) (note dierence in time scales). RMS amplitudes of the time-gained signals for S0 mode (c), and. A0 mode (d) (note dierence in amplitude scales) . . . . . . . . . . . . . 153 8.5. Mode conversion in the composite plate with a crack (a). Amplitude distribution of the signals from the B-scan (b) . . . . . . . . . . . . . . . 154. 8.6. B-scan images illustrating the interaction of Lamb waves with a crack in a composite plate: S0 mode (a) and A0 mode (b) (note dierence in time scales). RMS amplitudes of the time-gained signals for S0 mode (c), and. A0 mode (d) (note dierence in amplitude scales) . . . . . . . . . . . . . 155 8.7. Instantaneous amplitude of the signals obtained for the inspected surface (a). C-scan obtained for the composite plate with delamination (b).. xvi. . . 156.

(73) Glossary 2D-DFT. 2 dimensional discrete Fourier transform. BP. beam pattern. BSS. baseline signal stretch. CFRP. carbonber reinforced polymer. CT. computed tomography. CWT. continues wavelet transform. DAS. delay and sum. DI. damage index. DOA. direction of arrival. DORT. (fr.) décomposition de l'opérateur de retournement temporel, (ang.) decomposition of time-reversal operator. EMAT. electromagnetic acoustic transducer. ET. eddy current testing. IDT. Interdigital transducer. LRUT. long-range ultrasonic test. LSDV. laser scanning Doppler vibrometer. LTCD. local-time coherence dierence. MASW. multichannel analysis of surface waves. MTMR. multiple transmitters and multiple receivers. MUSIC. multiple signals classication. NDT/E. nondestructive testing/evaluation. OBS. optimal baseline subtraction. PA. phased array. POD. probability of detection. xvii.

(74) LIST OF FIGURES PSF. point spread function. PZT. piezoelectric lead zirconate titanate. RMS. root-mean-squared. ROI. region of interest. RT. radiographic testing. SA. synthetic aperture. SAFT. synthetic aperture focusing technique. SASW. spectral analysis of surface waves. SCA. sum coarray. SDC. signal dierence coecient. SF. synthetic focusing. SHM. structural health monitoring. SL. slant-stack (freq. domain). STF. structure's transfer function. STMR. single transmitter and multiple receiver. TFM. total focussing method. TFR. time-frequency representation. TOF. time-of-ight. TRM. time-reversal mirror. TRO. Time-reversal operator. ULA. uniform linear array. UT. ultrasonic testing. xviii.

(75) Chapter 1 Introduction. 1.

(76) 1.1 Background. 1.1 Background For a variety of engineering structures it is necessary to ensure quality from the raw materials phase, through fabrication, until the operation stage. Further, maintenance of these structures often requires regular inspections to secure their integrity and safety[1]. The schedule of these inspections is adjusted according to the predicted degradation time under assumed operational loads. For instance, airframes are subject to mandatory inspections to search for possible fatigue cracks. Other examples are composite structures made of carbon ber reinforced polymers (CRFP) and glass ber reinforced polymers (GFRP), that are widely used in structures requiring high safety standards. Some of the possible failure modes for composites, such as porosity and foreign object inclusion, may occur during manufacturing, others, e.g. disbonds and delaminations, may appear when the structure is in use. There is the need for both quality control and monitoring of such structures.. 1.2 Nondestructive testing Numerous nondestructive testing/evaluation (NDT/E) techniques have been developed for damage detection.. Eddy current (ET), radiographic (RT) and ultrasonic test-. ing (UT) are examples of well-established techniques, widely used in materials examination [2].. There is no single NDT method that can be used for the detection of all. types of aws. For instance, due to limited depth of penetration, ET can detect only surface and sub-surface cracks. An unfavorable orientation of non-volumetric discontinuities, with respect to the radiation or ultrasonic beam, can prevent their detection when using RT and UT methods. This, among other factors, is a strong incentive to develop new and/or upgrade existing techniques. Computed tomography (CT) is a remarkable example of RT technique advancement, which allows multiple cross-sections of the investigated object to be examined, revealing internal defects [3]. However, one of the main drawbacks of RT methods is the requirement of both-side access to the investigated object. CT requires, furthermore, a set of projections from dierent angles, thus, the sample must be placed on a rotation table or the radiation source and detector is rotated around the investigated element. Moreover, the ionizing radiation can pose a risk to human health [4].. 2.

(77) 1.2 Nondestructive testing The UT techniques utilize high frequency elastic waves of amplitudes that are not harmful for the inspecting personnel. Moreover, the inspections can be performed using dierent setups, including one-side access methods, which can yield superior damage detection capabilities. The basic, through-transmission setup, shown in g. 1.1a, involves two probes: a transmitter that is used to excite an elastic wave, which propagates through the sample, and a receiver to sense the wave on the other side. If there are no obstacles on the propagation path, the signal is received on the other side of the inspected object; a signal that fades away can be symptomatic of a defect that prevents wave transmission. This setup has several drawbacks, e.g. no depth of damage can be found and two-sides access is required. As mentioned above, the UT techniques also allow for one-side inspections. A single, transmitting/receiving probe can be used in a pulse-echo setup, illustrated in g. 1.1b. In this case the emitted wave propagates through the structure and after it is reected or scattered by a discontinuity it is sensed by the probe. The captured signals are analyzed in the time to search for damage-related echoes. The analysis allows for assessment of the aw's size and depth. Moreover, in this manner the thickness of the element can be found by measuring the time-of-ight (TOF) of the back wall-reected wave. Transmitter. Transducer. flaw. flaw. Receiver (a) Figure 1.1:. (b). Through-transmission (a) and pulse-echo (b) setups for ultrasonic testing. inspections.. Excitation and reception of ultrasonic waves by the means of contact transducers normally requires a coupling liquid, for instance water or an acoustic gel, which can be inconvenient and increase the probability of human error in the case of manual inspections. Therefore, in the automatized NDT systems immersion tanks [5] or squirters,. 3.

(78) 1.3 Principles and concepts of SHM that provide liquid ow between the probe and investigated object, are used. The use of immersion tanks limits the maximum size of elements that can be inspected, hence, this technique can be used almost only in the manufacturing stage for small structures or a structure's components.. 1.3 Principles and concepts of SHM Regardless of the NDT technique used, the inspections have to be carried out by trained and certied personnel [6]. The maintenance process often requires partial or complete disassemble of the structure, which is time-consuming. During this period the structure, e.g. an aircraft, cannot be operated, which increase the cost of the process. A possible solution to this issue is structural health monitoring (SHM), which is dened as integration of sensing and possibly also actuation devices in a way that NDT. becomes an integral part of the structure and material [7]. Although, the techniques used in NDT are often adopted in SHM, leading to a very close connection between them, the concept of SHM exceeds the denition of an embedded NDT. When a diagnostic system is capable of permanent monitoring, it is possible to collect the history of the structure and operational conditions, which includes not only information on the presence of damage, its size and localization, but also on loads. These data, together with a suitable material model, can be used for prognosis of the time-period within which the structure can be safely operated. Therefore, it is possible to evolve from schedule-driven to condition-based maintenance [1]. This progression can be particularly important for aircraft components, for which the spectrum of variable loads that aect the structure depends rst and foremost on the way the aircraft is operated. Hence, there is no chance of precisely dening the aircraft's life before it enters operational use [8]. Therefore, using SHM systems that are integrated with the structure can give considerable benets such as shortening maintenance times and increasing safety levels at the same time [1, 9, 10]. The above-mentioned features of the SHM concept were presented against NDT in tab. 1.1 [11]. The main dierence between these approaches is their implementation: NDT is performed oine, whereas SHM is implemented online, which makes monitoring tasks more complex when compared to NDT. In order to solve these problems, integration of various disciplines, such as mechanics, electronics, computer and material. 4.

(79) 1.3 Principles and concepts of SHM A comparison of basic features of NDT and SHM [11]. Table 1.1:. Feature. NDT. SHM. Time of inspections. Periodical. Permanent. Transducers. Coupled during the inspec-. Permanently mounted or. tions. embedded. Highly possible. Insignicant. Operation condition history. None. Possible. Remaining life prediction. Limited. Possible. Inspections. Schedule-driven. Condition-based. Range. Local. Local or global. Interference. with. struc-. ture's operation. science, strongly related to structures and their life-cycle is required. These areas are linked together to analyze and develop basic components of a SHM system, i.e., analyze possible damage scenarios in the monitored structure, develop sensors and instrumentation to obtain the data carrying information of the structure's condition and relevant signal analysis, capable of extracting damage-related information [12]. Taking into account these aspects, another denition of SHM can be formed as an interdisciplinary. approach enabling a diagnosis of the state and a prognosis of residual life, at any time in the structure's life [13]. SHM systems deal with tasks of diering complexity, which allows to classication of the systems into 6 groups, depending on their level of advancement [14]: 1. Damage detection 2. Damage localization 3. Damage type and size identication 4. Damage evaluation, prognosis 5. Self-diagnosis of a monitoring system 6. Self-repair The rst 3 levels can be achieved using NDT methods adopted for SHM. Level 4, however, involves additional sensors for operational conditions monitoring and models. 5.

(80) 1.3 Principles and concepts of SHM that allow for health prognosis based on these data. Level 5 is important for mature systems to prevent false alarms caused by sensor rather than structure's failure. The last, 6th level is a step towards smart structures capable of self-repairing.. 1.3.1 Classication of SHM systems Taking into account the range that SHM systems cover, they can be roughly classied into two groups: global and local SHM methods. The global techniques involve a global deformation or motion of the structures induced during their operation. These approaches are based on an assumption that changes in a structure's properties, e.g., eigen-frequencies, mode shapes and curvature, strain energy or damping, can be associated with damage parameters, e.g. local stiness reduction [2]. Vibration based methods are the most widely used global approaches [15]. These techniques allow for monitoring of the whole structure using only a rough sensor network, therefore, only limited knowledge about critical points is required. The main disadvantage of global techniques is their relatively low sensitivity to light damages and a limitted ability to estimate damage localization and size [12, 16]. In comparison with the global methods, local methods are used for monitoring small areas surrounding the sensors. Therefore, a dense network of transducers or knowledge of the critical damage location is required for these systems. There is a number of approaches that can be used in local SHM techniques, for instance, electro-mechanical impedance [17, 18, 19], static-parameter monitoring (displacement, strain), acoustic emission and elastic waves-based methods. Electro-mechanical-impedance-based techniques investigate changes in impedance resulting from the damage. The analyzes are performed in the high frequency range, normally higher than 30kHz [10]. The main drawback of these methods is that they only allow for detection of damage that is in close proximity of the sensor. The mechanism of the static parameters-based methods is based on the fact that damage inuences the displacement and strain distribution, compared to the intact condition. These approaches are relatively insensitive to undersized damages or defects that are distant from the sensor [10]. A rapid release of strain energy excites transient waves that can be used for damage detection and localization in an acoustic emission approach. However, due to the low. 6.

(81) 1.4 Guided-waves-based SHM energy of the generated waves the covering range of this technique may be limited, particularly in a high-damping medium. Last, but not least, elastic waves, excited in the structures using permanently installed emitters, permit inspections of large structures' areas in a short time, preserving sensitivity to small surface and internal defects. Using the wave-based approach it is possible to evaluate the size of a defect that is greater than half of its wavelength [20]. Even though the appearance of wave signals can be complicated due to the complex nature of the waves, the guided waves-based methods are one of the most often proposed local methods in SHM [12].. 1.4 Guided-waves-based SHM Isotropic elastic solid materials can support two types of bulk waves, i.e. longitudinal, in which the particles' displacement is in the direction of wave propagation, and shear, in which the oscillations occur in the direction perpendicular to the direction of waves propagation. In the case of uids, however, only longitudinal waves can exist [21]. When a wave has its wavelength of the order of dimensions of a medium, in which it propagates, the medium becomes a wave guide. The waves that travel in a wave guide are called guided waves [22].. Lamb waves are guided waves that propagate in plates of thickness comparable to their wavelength. Due to their ability to propagate over long distances and throughthickness displacement, which permits defect detection within and close to the surface of the plate, Lamb waves are a promising tool in applications, where large plate-like areas of the involved structure have to be assessed. Also other structures, such as rods [23] or pipes [24, 25, 26], can serve as a wave guide and, therefore, can be inspected using the guided waves. Longitudinal and shear waves are non-dispersive, i.e., their velocities are frequency independent. This means that the shape of the excited pulse is preserved during propagation. On the other hand, Lamb waves are dispersive, which means that their velocities depend on the excitation frequency. Moreover, multiple propagation modes, with different velocities can exist for a single frequency. Therefore, the structure's response can have a complex shape, even for an intact structure, something which is discussed more deeply in Chapter 3. The Lamb waves' nature becomes even more complex when. 7.

(82) 1.4 Guided-waves-based SHM the inspected plate is inhomogeneous, for instance, in the case of CFRPs the velocity depends also on the propagation direction with respect to the bers' alignment, which is illustrated in Chapter 4.. 1.4.1 Sensors and sensors networks There is a wide range of devices that can be used to excite and sense the Lamb waves. Some of them can be attached to or embedded into the monitored structure, others are not compact, cheap or lightweight enough, and therefore, are used only during the maintenance NDT [1] or the design phase of SHM systems [27].. 1.4.1.1 Transducers used in NDT inspections The most common devices that are used in guided waves-based inspections are ultrasonic probes with angle-adjustable perspex wedges [28, 29, 30], that allow, in accordance with Snell's law, for a selective generation and reception of a desired Lamb wave mode. The main problems in these inspections is that a layer of couplant agent between the investigated object and the probe has to be assured to permit the transmission of wave energy. Therefore, non-contact techniques are of great research interests and can be considered as a main innovation in the eld. Electromagnetic acoustic transducers (EMAT) can be used for non-contact generation of Lamb [31, 32, 33] and shear-horizontal [34] waves. A serious limitation for this technique is that the investigated object has to be conductive and, therefore, in order to investigate non-conductive composites a conductive, e.g. aluminum, foil has to be adhered to the investigated object [35]. The selective excitation and reception of Lamb modes, similar to using the contact variable-angle wedges, can be obtained in a contact-less manner using air-coupled ultrasonic transducers [36, 37]. The main problem to solve in the area of air-coupled ultrasound is a large impedance mismatch between solids and air, due to which only a small portion of acoustic energy can be passed between the transmitter and the investigated object. Therefore, applications of high-voltage excitation [38] and eective matching layers that reduce the impedance mismatch [39] have been proposed. The signal to noise ratio can be also improved using a pulse compression techniques, which assumes long frequency-modulated chirp signals that are correlated further with the response [40]. Two types of air-coupled transducers seem to be the most promising in. 8.

(83) 1.4 Guided-waves-based SHM imaging applications: the capacitive and piezoelectric [41]. A setup that combines these two types of transducers was used for the damage characterization of composite panels presented in Chapter 8. Ultrasonic Lamb waves can be also evoked and sensed using a laser [31, 42, 43]. In the waves generation, a pulsed laser beam incidents on a tested structure and is partially absorbed by it. The optical power is converted to heat, leading to a rapid local temperature increase. The thermal expansion of the heated region causes stress which excites the ultrasonic waves. To ensure the nondestructive character of this technique and prevent the material's melting and ablation, an adequately low power of the laser pulses has to be maintained [44]. Laser interferometers that are used for sensing of the waves [45, 46, 47], require much lower light energy than for the transmission. These measurements are, however, sensitive to the quality of the surface and often reective sprays or foils have to be used. One of the main problems with laser ultrasound is that it is dicult to control the modal content of the excited waves. One possible solution is to illuminate the structure through slits of dened shape [48]. Another approach involves processing the acquired data resulting from a relatively dense sensing point network in the frequency-wavenumber domain, which allows for selective mode ltration [49, 50].. 1.4.1.2 Sensors for SHM One of the most widely used sensors in guided wave SHM applications are piezoelectric lead zirconate titanate (PZT) elements [51]. Due to their small size, negligible mass, excellent mechanical strength, wide frequency responses, low power consumption, low cost and ability both for Lamb waves generation and sensing, these elements are particularly suitable for integration with the monitoring structure [52, 53]. PZTs excite, in principle, multiple Lamb wave modes. In order to inuence the modes' contents of the signal, a technique called single-mode tuning can be used [54]. The method relies on adequate size of the transducer selection for the parameters of the investigated plate. The shape of the transducer also inuences the directionality of the generated waves when its dimensions are signicant compared to the wavelength. However, when the transducer is relatively small, it can be considered as an omi-directional wave source [55, 56, 57]. Interdigital transducers (IDT) are capable of directional generation of a selected wave mode [58, 59, 60]. The control of the excited mode is achieved by adjusting the space between the interdigital electrodes to match the desired wavelength [61, 62, 63, 64]. The. 9.

(84) 1.4 Guided-waves-based SHM directionality characteristics of these transducers is set during manufacture, therefore, a set of IDTs, placed at dierent angles, is required to perform 360◦ coverage [59, 65]. 1.4.1.3 Sensors networks The guided waves oer capabilities for long-range ultrasonic tests (LRUT), that can be performed in two basic congurations illustrated in g. 1.2.. Emitter/receiver. Excited wave. Reflected wave. Defect. (a). Emitter. Excited wave. Scattered wave. Receiver. (b) Figure 1.2:. Pulse-echo (a) and pitch-catch (b) setups for guided waves-based inspections.. The pulse-echo setup, presented in g. 1.2a, can be compared to the conventional bulk waves-based NDT inspections, shown in g. 1.1a. Both approaches can be implemented, in principle, using a single transmit/receive probe. In some applications, however, an array of transmit/receive elements can be used. For instance, ring transducers, consisting of multiple elements that can be clamped around a pipe, are commonly used in LRUT inspections [66]. The main dierence between the bulk-waves and guided-waves-based tests is that only the area below the probe is examined in the case of bulk-waves inspections, whereas using the guided waves permits the detection of defects localized a signicant distance from the transducer. The test range of the LRUT reaches. 50m [66]. In pulse-echo inspections a wave is excited and propagates in the inspected waveguide, e.g. pipe. If any damage is present in the structure, it produces a reection that is captured at the source. From the analysis of the amplitude and TOF of the. 10.

(85) 1.4 Guided-waves-based SHM back-scattered signal's components it is possible to estimate the size and location of the defect. The pitch-catch setup, presented in g. 1.2b, involves a pair of transducers that are separated by a given distance. The wave that travels between the transducers interacts with defects, therefore, the received signal contains information on the condition of the structure. For example, TOF analysis of signals captured by a set of elements operating in the pitch-catch setup can be used to perform tomography that reveals the thickness changes resulting from corrosion [67]. The setups presented above are commonly used in the LRUT of pipes, but can be also applied for monitoring of planar structures using Lamb waves; however, damage localization has to be considered in 2 spatial dimensions. For instance, defects imaging in a plate requires a transducer that can determine not only the distance of the scatterer, but also its azimuth. An example of a probe that is capable of back scattered wave TOF and direction of arrival (DOA) estimation, is an array of transducers. An illustration of an imaging setup using an array consisting of transmit/receive elements can be seem in g. 1.3a. One or multiple array elements excite a wave that propagates through the plate. The array's receiving elements capture the backscattered signals enabling estimation of the location and size of a defect [22]. As will be discussed thoroughly in Chapter 5, the imaging of a 2D structure requires elements distributed among 2D array topology to permit omni-directional inspections. There is a number of other parameters that aect the performance of 2D imaging arrays, e.g., shape of the array, number of transducers and their spacing in terms of wavelength as well as the type of weighting function (apodization). Moreover, it is possible to use sparse arrays, which means that not all elements are used for transmitting and/or receiving. Using sparse arrays it is possible to decrease the time of data acquisition and processing [68], which results in signicant hardware simplication [69]. Another approach involves a network of transducers, operating in a pitch-catch mode, distributed on the investigated structure. As illustrated in g. 1.3b, a selected element of the network is used for the waves' excitation. Structural discontinuity (e.g. a damage) present in a plate scatters the incident Lamb waves in all directions and additional modes can be produced due to the mode conversion phenomena. The sensing elements capture the scattered and possibly mode-converted waves [10].. 11.

(86) 1.4 Guided-waves-based SHM. Emitters Receivers. Emitters Receivers. (a). (b). Principles of imaging using an array of transducers (a) and example of distributed network of transducers (b). Figure 1.3:. 1.4.2 Processing of Lamb waves signals From signals obtained using either of the measurement setups outlined in the previous section, it is possible to extract various features that can carry damage-related information. However, due to the complicated nature of Lamb waves and their complex interaction with defects [70], advanced signal processing algorithms are required [1, 9, 10].. 1.4.2.1 Array signal processing The signal processing technique implemented in the beamforming scheme is a critical factor that aects the performance of an array-based imaging SHM system. The most common approach used for processing snapshots captured by an array, mostly due to its simplicity and robustness, employs delay and sum (DAS) operations in the time domain [71]. More advanced methods, capable of angular resolution improvement can also be implemented in the Lamb waves sensed using arrays. These techniques rely on the statistical properties of the signals and can potentially achieve much higher resolution than the standard beamforming schemes [72, 73, 74]. The radial resolution improve-. 12.

(87) 1.4 Guided-waves-based SHM ment can be achieved using dispersion compensation techniques [75, 76], discussed more thoroughly in section 3.4. However, the advanced processing techniques require precise information on the modal content and dispersion characteristics of the investigated object, which can create limitations in practical applications, especially with anisotropic materials. As will be shown in Chapter 3, the dispersion characteristics can be predicted theoretically, however, the assumed material properties have to match precisely the actual parameters of the examined structure. If these data are not known, or nor accurate, the dispersion characteristic can be evaluated experimentally. As described in Chapter 4, the most commonly used approaches for experimental dispersion curves evaluation involve an emitter, used to excite a broadband signal, and a set of sensing points. The collected data are next processed using 2D discrete Fourier Transform (2D-DFT) yielding dispersion characteristics in frequency-wavenumber plane [77]. In Chapter 4 it is shown how the performance of the 2D-DFT technique can be improved further using multiple signals classication (MUSIC) [78, 79], moreover, an application of slant-stack (SL) transform [80] that leads explicitly to frequency-phase velocity is presented. Other techniques that can perform well without the information on wave velocities are self-focusing methods, for instance, time-reversal mirrors (TRM) introduced for ultrasonic waves [81, 82]. TRM is a powerful tool that enables signal to noise ratio improvement [83] and reducing the eect of dispersion [84, 85]. The iterative TRM enables obtaining selective focusing on the strongest reector in the region of interest [86]. In the SHM applications, however, focusing on targets with lower reexivity is also often desired. Decomposition of the time reversal operator (DORT) method has been introduced [87] with the aim to enable detecting and focusing waves on the multiple scatterers. DORT is a signal processing technique that is able to estimate, on the basis of the received data, time delays required for selectively focusing waves on a target. The method has been successfully applied in the NDT applications [88] as well as for Lamb wave characterization [89]. A in-depth description of the DORT technique and its proposed extension, using time-frequency representation (TFR) of the signals, can be found in Chapter 6.. 13.

(88) 1.4 Guided-waves-based SHM 1.4.2.2 Distributed transducers Using a pitch-catch setup for SHM normally involves a set of baseline signals captured on a healthy structure. The signals acquired during the operation are compared with the baselines and damage indices (DI), supposed to describe the condition of the monitored element, that are calculated [90]. If it is possible to extract the rst arriving wave packet from a signal, two basic features can be easily compared, namely amplitude, and TOF of the incident wave. Damage that exists on a wave's propagation path, can increase its attenuation, and hence, the decrease of the signal amplitude can be observed [91, 92]. Other defects, e.g. corrosion or delamination, change the thickness of the waveguide, which results in a change of the velocity of the Lamb wave [93, 94]. In monitoring of structures with complex geometries, for instance, testing of aircraft components with riveted joints and stringers, it is usually dicult to distinguish the incident and damage reected waves from the boundary reections. Therefore, diuse. elds signals, which have scattered many times from the defects and boundaries, are analyzed [95]. Although, this approach can be successfully used to remove reections from the unwanted boundaries and reveal damage scattered components, it becomes impractical when environmental or operational conditions change [96]. Therefore, approaches capable of compensating for these changes are of great interest [97, 98, 99]. The problem is presented in detail in Chapter 7, in which a new signal processing scheme is proposed. There are also baseline-free approaches that can be applied for a network of transducers operating in pitch-catch mode. For instance, a reconstruction property of the time reversed Lamb waves has been used to develop a technique in which a defect can be detected without historical baseline data captured for the untouched structure [100, 101]. A wave transmitted from the source to another point, captured there, time reversed and remitted is expected to be identical with the excited input signal. However, if a damage is present in the structure the reconstruction property breaks. Therefore a comparison of the snapshots of the emitted and reconstructed wave yields information about the damage. This approach has been applied to a composite [100, 101] and an aluminum plates [102]. The main drawback of this technique is that it requires rather complicated hardware and that sometimes the reconstruction property can be not fully lled even for an untouched structure.. 14.

(89) 1.4 Guided-waves-based SHM For a single emitter-receiver pair dierent DIs can be evaluated. In the case in which numerous DI are used simultaneously, multidimensional parameter space cannot be easily divided by arbitrary chosen classication threshold levels. Therefore, some techniques of dimensional reduction and classication need to be applied [53]. One of the most recognized methods for choosing the most ecient DIs is principal component analysis, from which the derived independent variables can be further used for structure assessment as inputs in classication models [103, 104]. Another possible approach is the application of an articial neural network feed on simple selected DIs [105, 106, 107, 108].. 15.

(90) Chapter 2 Aim and scope of the thesis. 16.

(91) 2.1 Aim. 2.1 Aim Flat or slightly curved plates are used in numerous engineered constructions, for example aircrafts, ships, and tanks. The application of SHM for these structures can bring benets in exploitation cost reduction while safety and performance are also improved. In recent years, Lamb waves have shown a great potential in such applications; however, due to their complex nature, complicated phenomena related to their interaction with defects and sensitivity to environmental conditions, the problem of Lamb-waves-based SHM still comprises many unsolved issues and new approaches are sought. The focus of this thesis is on development of damage detection strategies with the. use of Lamb waves, which can be applied for permanent SHM or which can be easily implemented for automated NDT inspections. The detailed objectives of the thesis are: 1. to develop tools that allow for the investigation and evaluation of dispersive characteristics of the investigated structure, 2. to propose a methodology for design and evaluate of 2D array topologies, 3. to develop a framework for 2D aperture synthesis in sparse array imaging, 4. to advance the self-focusing approach to improve its resolution, 5. to improve methods of temperature inuence on Lamb waves compensation, 6. to investigate the possibilities of composite testing using air-coupled ultrasound, 7. to propose a processing technique that can be used for damage detection and localization using the non-contact measurement method.. 17.

(92) 2.1 Aim Based on the above considerations the following theses have been formulated:. •. •. •. •. •. •. •. Non-contact ultrasound techniques can be used as an eective tool for estimation of the dispersive characteristics of plate-like structures, 2D array topologies make possible unequivocal imaging of defects in platelike structures, Lamb wave propagation can be modeled using frequency domain tools with an accuracy sucient for the analysis of 2D arrays performance, It is possible to design eective 2D arrays with a reduced number of elements, Self-focusing is capable of improving damage detection in plate-like structures, Compensation of temperature inuence on Lamb wave propagation is possible in practice, Air-coupled ultrasonic transducers can be used for investigation of composite structures.. To achieve the above-mentioned aims, the following tasks were undertaken: 1.. Literature study of the state of the art. Performed as the rst step of the research, this revealed increasing scientic interest in the SHM approaches. The selected literature references, that were used to frame the problems addressed in this thesis, were mentioned in Chapter 1 and are supplemented further in the introductions to the successive Chapters.. 2.. New tools for experimental evaluation of the dispersion characteristic were proposed. One of the most important problems to deal with in Lamb waves applications is the dispersive and multi-modal nature of Lamb waves. Exact knowledge of the dispersion characteristic is important for many signal processing algorithms. Therefore, there is a need for methods capable of experimental evaluation of these attributes. In Chapter 4 two signal processing techniques, i.e., SL transform and MUSIC, were introduced for experimental evaluation of Lamb waves' dispersion. 18.

(93) 2.1 Aim curves. Although the SL transform is widely used in geophysics, it is, to the author's best knowledge, the rst application of this technique for Lamb waves characterization. MUSIC is an approach that was used in Lamb waves beamforming applications, but as explained in Chapter 4, it can be also used to evaluate the dispersion curves. 3.. A methodology for 2D arrays' performance evaluation was proposed. 2D topologies are required to obtain an unequivocal damage localization in Lambwaves based array imaging applications. Since array performance depends, among other factors, on its topology, there is a demand for robust and numerically ecient tools for arrays design. To deal with this problem a method based on frequencydependent structure transfer function (STF), which can deal with multi-modal and dispersive nature of Lamb waves as well as with the arbitrary shape of the excitation bursts, was implemented. In addition, the proposed methodology assumes experimental evaluation of the investigated topology using a virtual array of sensors. The setup assumes waves excitation using a contact PZT emitter, and measurement of the structure's response using a laser scanning Doppler vibrometer (LSDV). Therefore, a number of topologies can be examined without the need for arrays prototypes. The approach, described in Chapter 5, was based on the author's following papers: [27, 109, 110, 111]. The STF approach was also applied for IDTs modeling [62, 63, 64]. This subject is, however, beyond the scope of this thesis.. 4.. A comparison of phased array and synthetic focusing imaging approaches was performed. Ultrasonic arrays in Lamb wave based SHM systems can operate in the phased array (PA) or synthetic focusing (SF) mode. In the real-time PA approach, multiple electronically delayed signals excite transmitting elements to form the desired wave-front, whereas receiving elements are used to sense scattered waves. Conversely, the SF mode assumes a single element excitation of subsequent transmitters and o-line processing of the acquired data. In the simplest implementation of the SF technique, a single multiplexed input and output channels are required, which results in signicant hardware simplication. In Chapter 5 a comparison. 19.

(94) 2.1 Aim of both approaches, using an example of a star-shaped array with one transmitting sub-array, was presented. The Chapter was based on the following papers: [112, 113, 114]. 5.. Coarray concept was introduced for synthesis of arrays apertures in Lamb waves imaging. The use of sparse arrays, i.e., not all array elements are used for transmission and/or reception, allows a signicant simplication of SHM systems with no or only minor reduction in their resolution. To facilitate the synthesis process of sparse arrays' apertures, used in the Lamb waves-based imaging systems, coarray concept was introduced. In the coherent imaging, performed in the transmit/receive mode, the sum coarray is a morphological convolution of the transmit/receive sub-arrays. It can be calculated as the set of sums of the individual sub-arrays' elements locations. Although, the coaray has been used in other branches of array processing, this thesis and [69] introduce the concept for the eld of Lamb waves.. 6.. DORT method was extended using TFR of the signals The DORT method enables selective focusing of the waveeld on scatterers, it appears, however, that in some cases resolving multiple scatterers with this method may fail. To deal with this problem a new method employing TFR of the signal has been proposed. Lamb waves propagation in a thin plate normally generates nonstationary responses due to the dispersive phenomenon; therefore the continuous wavelet transform (CWT) was used to calculate the TFR of the signals. The scatterers that could not be resolved correctly in the frequency domain could be resolved in the time domain. In this way it was possible to considerably improve resolution of the DORT method [115]. Based on the modied self-focusing method an imaging scheme leading to separate images of the scatterers was proposed [116].. 7.. A new strategy for temperature inuence on Lamb waves compensation was proposed. Variations of environmental conditions, such as temperature, aect the propagation of Lamb waves, which can severely limit their use for damage detection in SHM systems. Therefore, a novel technique which can be used to compensate. 20.