Structural Monitoring and Maintenance

  • 제4권4호
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  • Pages.381-396
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  • 2017
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  • 2288-6605(pISSN)
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  • 2288-6613(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Harnessing sparsity in lamb wave-based damage detection for beams

  • Sen, Debarshi (Department of Civil and Environmental Engineering, Rice University) ;
  • Nagarajaiah, Satish (Department of Civil and Environmental Engineering, Rice University) ;
  • Gopalakrishnan, S. (Department of Aerospace Engineering, Indian Institute of Science)
  • 투고 : 2017.11.06
  • 심사 : 2017.11.23
  • 발행 : 2017.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

Structural health monitoring (SHM) is a necessity for reliable and efficient functioning of engineering systems. Damage detection (DD) is a crucial component of any SHM system. Lamb waves are a popular means to DD owing to their sensitivity to small damages over a substantial length. This typically involves an active sensing paradigm in a pitch-catch setting, that involves two piezo-sensors, a transmitter and a receiver. In this paper, we propose a data-intensive DD approach for beam structures using high frequency signals acquired from beams in a pitch-catch setting. The key idea is to develop a statistical learning-based approach, that harnesses the inherent sparsity in the problem. The proposed approach performs damage detection, localization in beams. In addition, quantification is possible too with prior calibration. We demonstrate numerically that the proposed approach achieves 100% accuracy in detection and localization even with a signal to noise ratio of 25 dB.

키워드

과제정보

연구 과제 주관 기관 : Texas Instruments

참고문헌

  1. Alleyne, D.N., Lowe, M.J.S. and Cawley, P. (1998), "The reflection of guided waves from circumferential notches in pipes", J. Appl. Mech., 65(3), 635-641. https://doi.org/10.1115/1.2789105
  2. Baraniuk, R.G. (2007), "Compressive sensing", IEEE Sign. Proc. Mag., 24(4), 118-120, 124. https://doi.org/10.1109/MSP.2007.4286571
  3. Boller, C. (2000), "Next generation structural health monitoring and its integration into aircraft design", J. Syst. Sci., 31(11), 1333-1349. https://doi.org/10.1080/00207720050197730
  4. Candes, E. and Romberg, J. (2005), ${\ell}_1$ MAGIC: Recovery of Sparse Signals via Convex Programming, Technical Report, Caltech, California, U.S.A.
  5. Chakraborty, A. and Gopalakrishnan, S. (2006), "A spectral finite element model for wave propagation analysis in laminated composite plate", J. Vibr. Acoust., 128(4), 477-488. https://doi.org/10.1115/1.2203338
  6. Demma, A., Cawley, P., Lowe, M.J.S., Roosenbrand, A.G. and Pavlakovic, B. (2004), "The reflection of guided waves from notches in pipes: A guide for interpreting corrosion measurements", NDT E Int., 37(3), 167-180. https://doi.org/10.1016/j.ndteint.2003.09.004
  7. Doyle, J.F. (1997), Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, Springer.
  8. Eybpoosh, M., Berges, M. and Noh, H.Y. (2016), "Sparse representation of ultrasonic guided-waves for robust damage detection in pipelines under varying environmental and operational conditions", Struct. Contr. Health Monitor., 23(2), 369-391. https://doi.org/10.1002/stc.1776
  9. Farrar, C.R., Doebling, S.W. and Nix, D.A. (2001), "Vibration based structural damage identification", Philosoph. Transac. Roy. Soc. A, 359, 131-149. https://doi.org/10.1098/rsta.2000.0717
  10. Farrar, C.R. and Worden, K. (2007), "An introduction to structural health monitoring", Philosoph. Transac. Roy. Soc. A, 365, 303-315. https://doi.org/10.1098/rsta.2006.1928
  11. Giurgiutiu, V. (2008), Structural Health Monitoring: with Piezoelectric Wafer Active Sensors, Academic Press.
  12. Gopalakrishnan, S., Martin, M. and Doyle, J.F. (1992), "A matrix methodology for spectral analysis of wave propagation in multiple connected Timoshenko beams", J. Sound Vibr., 158(1), 11-24. https://doi.org/10.1016/0022-460X(92)90660-P
  13. Gopalakrishnan, S. and Doyle, J.F. (1995), "Spectral super-elements for wave propagation in structures with local non-uniformities", Comput. Meth. Appl. Mech. Eng., 121(1-4), 77-90. https://doi.org/10.1016/0045-7825(94)00686-H
  14. Gopalakrishnan, S., Chakraborty, A. and Mahapatra, D.R. (2007), Spectral Finite Element Method: Wave Propagation Diagnostics and Control in Anisotropic and Inhomogenous Structures, Academic Press.
  15. Gopalakrishnan, S. (2009), Modeling Aspects in Finite Elements", Encyclopedia of Structural Health Monitoring, John Wiley and Sons.
  16. Gopalakrishnan, S. and Mitra, M. (2010), Wavelet Methods for Dynamical Problems: With Applications to Metallic, Composite and Nano-Composite Structures, CRC Press.
  17. Graff, K.F. (1991), Wave Motion in Elastic Solids, Dover Publications.
  18. Hastie, T., Tibshirani, R. and Friedman, J. (2009), The Elements of Statistical Learning: Data Mining, Inference and Prediction, Springer.
  19. Hernandez, E.M. (2014), "Identification of isolated structural damage from incomplete spectrum information using ${\ell}_1$-norm minimization", Mech. Syst. Sign. Proc., 46, 59-69. https://doi.org/10.1016/j.ymssp.2013.12.009
  20. Hu, N., H Fukunaga, H., Kameyama, M., Mahapatra, D.R. and Gopalakrishnan, S. (2007), "Analysis of wave propagation in beams with transverse and lateral cracks using a weakly formulated spectral method", ASME J. Appl. Mech., 74(1), 119-127. https://doi.org/10.1115/1.2188015
  21. Igawa, H., Komatsu, K., Yamaguchi, I. and Kasai, T. (2004), "Wave propagation analysis of frame structures using the spectral element method", J. Sound Vibr., 277, 1071-1081. https://doi.org/10.1016/j.jsv.2003.11.026
  22. Kandel, B.M., Wolk, D.A., Gee, J.C. and Avants, B. (2013), textitPredicting Cognitive Data from Medical Images Using Sparse Linear Regression, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, Germany, 7197.
  23. Kim, S.J., Koh, K., Lustig, M., Boyd, S. and Gorinevsky, D. (2007), "A method for large-scale ${\ell}_1$-regularized least squares", IEEE J. Select. Top. Sign. Proc., 1(4), 606-617. https://doi.org/10.1109/JSTSP.2007.910971
  24. Kumar, D.S., Chakraborty, A. and Gopalakrishnan, S. (2004), "A spectral finite element for wave propagation and structural diagnostic analysis of composite beam with transverse crack", Fin. Elem. Analy. Des., 40(13-14), 1729-1751. https://doi.org/10.1016/j.finel.2004.01.001
  25. Levine, R.M. and Michaels, J.E. (2013), "Model-based imaging of damage with Lamb waves via sparse reconstruction", J. Acoust. Soc. Am., 133(3), 1525-1534. https://doi.org/10.1121/1.4788984
  26. Liu, Z. and Kleiner, Y. (2012), "State-of-the-Art Review of Technologies for Pipe Structural Health Monitoring", IEEE Sens. J., 12(6), 1987-1992. https://doi.org/10.1109/JSEN.2011.2181161
  27. Liu, C., Harley, J.B., Berges, M., Greve, D.W. and Oppenheim, I.J. (2015), "Robust ultrasonic damage detection under complex environmental conditions using singular value decomposition", Ultrason., 58, 75-86. https://doi.org/10.1016/j.ultras.2014.12.005
  28. Lowe, M.J.S., Alleyne, D.N. and Cawley, P. (1998), "Defect detection in pipes using guided waves", Ultrason., 36(1-5), 147-154. https://doi.org/10.1016/S0041-624X(97)00038-3
  29. Lu, Y., Ye, L., Su, Z., Zhou, L. and Cheng, L. (2007), "Artificial neural network (ANN)-based crack identification in aluminum plates with lamb wave signals", J. Intell. Mater. Syst. Struct., 20, 39-49.
  30. Lu, Y.and Michaels, J.E. (2008), "Numerical implementation of matching pursuit for the analysis of complex ultrasonic signals", IEEE Trans. Ultrason. Ferroelectr. Freq. Contr., 55(1), 173-182. https://doi.org/10.1109/TUFFC.2008.626
  31. Murthy, M.V.V.S., Gopalakrishnan, S. and Nair, P.S. (2011), "Signal wrap-around free spectral element formulation for multiply connected finite 1-D waveguides", J. Aerosp. Sci. Technol., 63(1), 72-88.
  32. Na, W.B. and Kundu, T. (2002), "Underwater pipeline inspection using guided waves", Trans. ASME, 124, 196-200. https://doi.org/10.1115/1.1398292
  33. Nagarajaiah, S. and Yang, Y. (2017), "Modeling and harnessing sparse and low-rank data structure: A new paradigm for structural dynamics, identification, damage detection, and health monitoring", Struct. Contr. Health Monitor., 24(1), e1851. https://doi.org/10.1002/stc.1851
  34. Ostachowicz, W., Kudela, P., Krawczuk, M. and Zak, A. (2012), Guided Waves in Structures for SHM: The Time-Domain Spectral Element Method, Dover Publications.
  35. Ou, J. and Li, H. (2010), "Structural health monitoring in mainland China: Review and future trends", Struct. Health Monitor., 9(3), 219-241. https://doi.org/10.1177/1475921710365269
  36. Packo, P., Bielak, T., Spencer, A.B., Staszewski, W.J., Uhl, T. and Worden, K. (2012), "Lamb wave propagation modelling and simulation using parallel processing architecture and graphical cards", Smart Mater. Struct., 21, 13.
  37. Park, M.H., Kim, I.S. and Yoon, Y.K. (1996), "Ultrasonic inspection of long steel pipes using lamb waves", NDT E Int., 29(1), 13-20. https://doi.org/10.1016/0963-8695(95)00030-5
  38. Patera, A.T. (1984), "A spectral element method for fluid dynamics: Laminar flow in a channel expansion", J. Comput. Phys., 54, 468-488. https://doi.org/10.1016/0021-9991(84)90128-1
  39. Raghavan, A. and Cesnik, C.E.S (2007), "Review of guided-wave structural health monitoring", Shock Vibr. Dig., 39(2), 91-114. https://doi.org/10.1177/0583102406075428
  40. Rose, J.L. (1999), Ultrasonic Waves in Solid Media, Cambridge University Press.
  41. Rose, J.L. (2004), "Ultrasonic Guided Waves in Structural Health Monitoring", Key Eng. Mater., 270-273, 14-21. https://doi.org/10.4028/www.scientific.net/KEM.270-273.14
  42. Rytter, A. (1993), "Vibration based inspection of civil engineering structures", Ph.D. Dissertation, Aolborg University, Denmark.
  43. Tibaduiza, D.A., Torres-Arredondo, M.A., MUjica, L.E., Rodellar, J. and Fritzen, C.P. (2013), "A study of two unsupervised data driven statistical methodologies for detecting and classifying damages in structural health monitoring", Mech. Syst. Sign. Proc., 41(1-2), 467-484. https://doi.org/10.1016/j.ymssp.2013.05.020
  44. Tibshirani, R. (1996), "Regression shrinkage and selection via the LASSO", J. Roy. Stat. Soc. B, 58(1), 267-288.
  45. Tse, P.W. and Wang, X. (2013), "Characterization of pipeline defect in guided-waves based inspection through matching pursuit with the optimized dictionary", NDT E Int., 54, 177-182.
  46. Worden, K. and Manson, G. (2007), "The application of machine learning to structural health monitoring", Philosoph. Trans. Roy. Soc. A, 365, 515-537. https://doi.org/10.1098/rsta.2006.1938
  47. Yang, Y. and Nagarajaiah, S. (2013), "Output-only modal identification with limited sensors using sparse component analysis", J. Sound Vibr., 332(19), 4741-4765. https://doi.org/10.1016/j.jsv.2013.04.004
  48. Yang, A., Ganesh, A., Zhou, Z., Sastry, S. and Ma, Y. (2010), textitFast ${\ell}_1$ minimization algorithms and an application in robust face recognition: a review, Technical Report, UC Berkeley, California, U.S.A.
  49. Yang, Y. and Nagarajaiah, S. (2014), "Structural damage identification via a combination of blind feature extraction and sparse representation classification", Mech. Syst. Sign. Proc., 45(1), 1-23. https://doi.org/10.1016/j.ymssp.2013.09.009
  50. Yang, Y. and Nagarajaiah, S. (2014), "Blind identification of damage in time-varying systems using independent component analysis with wavelet transform", Mech. Syst. Sign. Proc., 47(1-2), 3-20. https://doi.org/10.1016/j.ymssp.2012.08.029
  51. Ying, Y., Garrett Jr, J.H., Harley, J., Oppenheim, I.J., Shi, J. and Soibelman, L. (2013), "Damage detection in pipes under changing environmental conditions using embedded piezoelectric transducers and pattern recognition techniques", J. Pipeline Syst. Eng. Prac., 4(1), 17-23. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000106
  52. Ying, Y., Garrett Jr, J.H., Oppenheim, I.J., Soibelman, L., Harley, J., Shi, J. and Jin, Y. (2013), "Toward data-driven structural health monitoring: Application of machine learning and signal processing to damage detection", J. Comput. Civil Eng., 27(6), 667-680. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000258
  53. Yu, L., Giurgiutiu, V., Wang, J. and Shin, Y.J. (2011), "Corrosion detection with piezoelectric wafer active sensors using pitch-catch waves and cross-time-frequency analysis", Struct. Health Monitor., 11(1), 83-93.

피인용 문헌

  1. Predicting crack in a beam-like structure through an over fitting verified regression model vol.15, pp.6, 2017, https://doi.org/10.1108/mmms-12-2018-0213