Smart Structures and Systems

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A wavelet finite element-based adaptive-scale damage detection strategy

  • He, Wen-Yu (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University) ;
  • Zhu, Songye (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University) ;
  • Ren, Wei-Xin (School of Civil Engineering, Hefei University of Technology)
  • Received : 2012.07.18
  • Accepted : 2013.06.24
  • Published : 2014.09.25
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Abstract

This study employs a novel beam-type wavelet finite element model (WFEM) to fulfill an adaptive-scale damage detection strategy in which structural modeling scales are not only spatially varying but also dynamically changed according to actual needs. Dynamical equations of beam structures are derived in the context of WFEM by using the second-generation cubic Hermite multiwavelets as interpolation functions. Based on the concept of modal strain energy, damage in beam structures can be detected in a progressive manner: the suspected region is first identified using a low-scale structural model and the more accurate location and severity of the damage can be estimated using a multi-scale model with local refinement in the suspected region. Although this strategy can be implemented using traditional finite element methods, the multi-scale and localization properties of the WFEM considerably facilitate the adaptive change of modeling scales in a multi-stage process. The numerical examples in this study clearly demonstrate that the proposed damage detection strategy can progressively and efficiently locate and quantify damage with minimal computation effort and a limited number of sensors.

Keywords

Acknowledgement

Supported by : Hong Kong Polytechnic University

References

  1. Amaratunga, K. and Sudarshan, R. (2006), "Multi-resolution modeling with operator-customized wavelets derived from finite elements", Comput. Method Appl. M., 195, 2509-2532. https://doi.org/10.1016/j.cma.2005.05.012
  2. Averbuch, A.Z., Zheludev, V.A. and Cohen, T. (2007), "Multiwavelet frames in signal space originated from Hermite splines", IEEE T. Signal Proces., 55(3), 797-808. https://doi.org/10.1109/TSP.2006.887569
  3. Bakhary, N., Hao, H. and Deeks, A.J. (2010), "Structure damage detection using neural network with multi-stage substructuring", Adv. Struct. Eng., 13(1), 95-110. https://doi.org/10.1260/1369-4332.13.1.95
  4. Balageas, D., Fritzen, C.P. and Guemes, A. (2006), Structural health monitoring, ISTE USA, Newport Beach, CA, USA.
  5. Chen, W.H. and Wu, C.W. (1995), "Spline wavelets element method for frame structures vibration", Comput. Mech., 16, 1-2l. https://doi.org/10.1007/BF00369880
  6. Chen, X.F., Zi, Y.Y., Li, B. and He, Z.J. (2006), "Identification of multiple cracks using a dynamic mesh-refinement method", J. Stain Anal. Eng., 41, 31-39. https://doi.org/10.1243/030932405X30911
  7. Chui, C.K. (2009), An introduction to wavelets, Posts and Telecom Press, Beijing, China.
  8. Clough, W. and Penzien, J. (1993), Dynamics of structures (3rd Ed.), McGraw-Hill, New York.
  9. Cornwell, P., Doebling, S.W. and Farrar, C.R. (1999), "Application of the strain energy damage detection method to plate-like structures", J Sound Vib., 224 (2), 359-374. https://doi.org/10.1006/jsvi.1999.2163
  10. Ding, Y.L., Li, A.Q., Du, D.S. and Liu, T. (2010), "Multi-scale damage analysis for a steel box girder of a long-span cable-stayed bridge", Struct. Infrastruct. E., 6(6), 725-739. https://doi.org/10.1080/15732470802187680
  11. Doebling, S.W., Farrar, C.R., Prime, M.B. and Shevitz, D.W. (1996), Damage identification and health monitoring of structural mechanical systems from changes in their vibration characteristics: a literature review, Report No. LA-13070-MS, Los Alamos National Laboratory, Los Alamos, NM, USA.
  12. Fan, W. and Qiao, P.Z. (2011), "Vibration-based damage identification methods: a review and comparative study", Struct Health Monit., 10(1), 83-111. https://doi.org/10.1177/1475921710365419
  13. Fox, R.L. and Kapoor, M.P. (1968), "Rate of change of eigenvalues and eigenvectors", AIAA J., 6(12), 2426-2429. https://doi.org/10.2514/3.5008
  14. Guan, H. and Karbhari, V.M. (2008), "Improved damage detection method based on element modal strain damage index using sparse measurement", J. Sound Vib., 309(3-5), 465-494. https://doi.org/10.1016/j.jsv.2007.07.060
  15. Han, J.G., Ren, W.X. and Huang, Y. (2005), "A multivariable wavelet based finite element method and its application to thick plates", Finite Elem. Anal. Des., 41, 821-833. https://doi.org/10.1016/j.finel.2004.11.001
  16. Han, J.G., Ren, W.X. and Huang, Y. (2006), "A spline wavelet finite-element method in structural mechanics", Int. J. Numer. Meth. Eng., 66, 166-190. https://doi.org/10.1002/nme.1551
  17. He, W.Y., Ren, W.X. and Yang, Z.J. (2012) "Computation of plane crack stress intensity factors using trigonometric wavelet finite element methods", Fatigue Fract. Eng. M., 35, 732-741. https://doi.org/10.1111/j.1460-2695.2011.01626.x
  18. He, W.Y. and Ren, W.X. (2012), "Finite element analysis of beam structures based on trigonometric wavelet", Finite Elem. Anal. Des., 51, 59-66. https://doi.org/10.1016/j.finel.2011.11.005
  19. He, W.Y. and Ren, W.X. (2013a), "Adaptive trigonometric hermite wavelet finite element method for structural analysis", Int. J. Struct. Stab. Dy., 1, 1350007.
  20. He, W.Y. and Ren, W.X. (2013b), "Trigonometric wavelet-based method for elastic thin plate analysis", App. Math. Model., 37, 1607-1617. https://doi.org/10.1016/j.apm.2012.04.030
  21. He, W.Y. and Zhu, S. (2013), "Progressive damage detection based on multi-scale wavelet finite element model: numerical study", Comput. Struct., 125, 177-186. https://doi.org/10.1016/j.compstruc.2013.05.001
  22. Ko, J., Kurdila, A.J. and Pilant, M.S. (1995), "A class of finite element methods based on orthonormal, compactly supported wavelets", Comput. Mech., 16, 235-244. https://doi.org/10.1007/BF00369868
  23. Kim, H.M. and Bartkowicz, T.J. (1997), "A two-step structural damage detection approach with limited instrumentation", J. Vib. Acoust., 119(2), 258-264. https://doi.org/10.1115/1.2889712
  24. Kim, J.T., Park, J.H., Hong, D.S. and Park, W.S (2010), "Hybrid health monitoring of prestressed concrete girder bridges by sequential vibration-impedance approaches", Eng. Struct., 32(1), 115-128. https://doi.org/10.1016/j.engstruct.2009.08.021
  25. Li, B., Chen, X.F., Ma, J.X. and He, Z.J. (2005), "Detection of crack location and size in structures using wavelet finite element methods", J. Sound Vib., 285, 767-782. https://doi.org/10.1016/j.jsv.2004.08.040
  26. Li, Z.X., Chan, T.H.T., Yu, Y. and Sun, Z.H. (2009), "Concurrent multi-scale modeling of civil infrastructures for analyses on structural deterioration, Part I: Modeling methodology and strategy", Finite Elem. Anal. Des., 45, 782-794. https://doi.org/10.1016/j.finel.2009.06.013
  27. Mallat, S. (1988), Multi-resolution representation and wavelets, Ph.D. Dissertation, University of Pennsylvania, Philadelphia, PA.
  28. Perera, R. and Ruiz, A. (2008), "A multistage FE updating procedure for damage identification in large-scale structures based on multi-objective evolutionary optimization", Mech. Syst. Signal Pr., 22, 970-991. https://doi.org/10.1016/j.ymssp.2007.10.004
  29. Ren, W.X. and De Roeck, G. (2002), "Discussion of "Structural Damage Detection from Modal Strain Energy Change" by z. Y. Shi, S. S. Law, and L. M. Zhang", J. Eng. Mech. - ASCE, 128, 376-377. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:3(376)
  30. Redjienski, M., Krawczuk, M. and Palacz, M. (2011), "Improvement of damage detection methods based on experimental modal parameters", Mech. Syst. Signal Pr., 25(6), 2169-2190. https://doi.org/10.1016/j.ymssp.2011.01.007
  31. Shi, Z.Y. and Law, S.S. (1998), "Structural damage localization from modal strain energy change", J. Sound Vib., 218 (5), 825-844. https://doi.org/10.1006/jsvi.1998.1878
  32. Shi, Z.Y., Law, S.S. and Zhang, L.M. (2000), "Structural damage detection from modal strain energy change", J. Eng. Mech. - ASCE, 126 (12), 1216-1223. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:12(1216)
  33. Shi, S.Y., Law, S.S. and Zhang L.M. (2002), "Improved damage quantification from elemental modal strain energy change", J. Eng. Mech.- ASCE, 128(5), 521-529. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:5(521)
  34. Sohn, H., Farrar, C.R., Hemez, F.M., Shunk, D.D., Stinemates, D.W. and Nadler, B.R. (2004), A review of structural health monitoring literature 1996-2001, Report No. LA-13976-MS, Los Alamos National Laboratory, Los Alamos, NM, USA.
  35. Sudarshan, R. and Amaratunga, K. (2003), "Hierarchical solution of eigenvalue problems using finite element multi-wavelets", Proceedings of the VII International Conference on Computational Plasticity (COMPLAS 2003), Barcelona.
  36. Sweldens, W. (1996), "The lifting scheme: a custom-design construction of biorthogonal wavelets", Appl Comput Harmon A., 3, 186-200. https://doi.org/10.1006/acha.1996.0015
  37. Wang, Y.M., Chen, X.F., He, Y.M. and He, Z.J. (2011), "The construction of finite element multi -wavelets for adaptive structural analysis", Int. J. Numer. Meth. Bio., 27, 562-584. https://doi.org/10.1002/cnm.1320
  38. Xiang, J.W., Chen, X.F., He, Y.M. and He, Z.J. (2006). "Identification of crack in a beam based on finite element method of B-spline wavelet on the interval", J. Sound Vib., 296,1046-1052. https://doi.org/10.1016/j.jsv.2006.02.019
  39. Xiang, J.W. and Liang, M. (2011), "Multiple damage detection method for beams based on multi-scale elements using Hermite cubic spline wavelet", Comp Model Eng., 73(3), 267-298.
  40. Yan, W.J., Huang, T.L. and Ren, W.X. (2010), "Damage detection method based on element modal strain energy sensitivity", Adv. Struct. Eng., 13, 1075-1088. https://doi.org/10.1260/1369-4332.13.6.1075
  41. Yan, W.J. and Ren, W.X. (2012), "Statistic structural damage detection based on the closed-form of element modal strain energy sensitivity", Mech. Syst. Signal Pr., 28, 183-194. https://doi.org/10.1016/j.ymssp.2011.04.011
  42. Zienkiewicz, O.C. and Taylor, R.L. (1961), The finite element method (4th Ed.), McGraw-Hill Book Company, London.

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