Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Damage detection of nonlinear structures with analytical mode decomposition and Hilbert transform

  • Wang, Zuo-Cai (School of Civil Engineering, Hefei University of Technology) ;
  • Geng, Dong (School of Civil Engineering, Hefei University of Technology) ;
  • Ren, Wei-Xin (School of Civil Engineering, Hefei University of Technology) ;
  • Chen, Gen-Da (Department of Civil, Architectural, and Environmental Engineering, Missouri University of Science and Technology) ;
  • Zhang, Guang-Feng (School of Civil Engineering, Hefei University of Technology)
  • Received : 2014.03.10
  • Accepted : 2014.05.15
  • Published : 2015.01.25
⟨ Previous Next ⟩

Abstract

This paper proposes an analytical mode decomposition (AMD) and Hilbert transform method for structural nonlinearity quantification and damage detection under earthquake loads. The measured structural response is first decomposed into several intrinsic mode functions (IMF) using the proposed AMD method. Each IMF is an amplitude modulated-frequency modulated signal with narrow frequency bandwidth. Then, the instantaneous frequencies of the decomposed IMF can be defined with Hilbert transform. However, for a nonlinear structure, the defined instantaneous frequencies from the decomposed IMF are not equal to the instantaneous frequencies of the structure itself. The theoretical derivation in this paper indicates that the instantaneous frequency of the decomposed measured response includes a slowly-varying part which represents the instantaneous frequency of the structure and rapidly-varying part for a nonlinear structure subjected to earthquake excitations. To eliminate the rapidly-varying part effects, the instantaneous frequency is integrated over time duration. Then the degree of nonlinearity index, which represents the damage severity of structure, is defined based on the integrated instantaneous frequency in this paper. A one-story hysteretic nonlinear structure with various earthquake excitations are simulated as numerical examples and the degree of nonlinearity index is obtained. Finally, the degree of nonlinearity index is estimated from the experimental data of a seven-story building under four earthquake excitations. The index values for the building subjected to a low intensity earthquake excitation, two medium intensity earthquake excitations, and a large intensity earthquake excitation are calculated as 12.8%, 23.0%, 23.2%, and 39.5%, respectively.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Bendat, J.S. and Piersol, A.G. (1993), Engineering applications of correlation and spectral analysis, 2nd Ed., John Wiley & Sons, New York.
  2. Brandon, J.A. (1997), "Structural damage identification of systems with strong nonlinearities: a qualitative identification methodology, structural damage assessment using advanced signal processing procedures", Proceedings of the International Conference on Damage Assess of Structures (DAMAS 97), University of Sheffield, UK.
  3. Brandon, J.A. (1999), "Towards a nonlinear identification methodology for mechanical signature analysis, damage assessment of structures", Proceedings of the International Conference on Damage Assess of Structures (DAMAS 99), Dublin, Ireland.
  4. Braun, S. and Feldman, M. (2011), "Decomposition of non-stationary signals into time varying scales: some aspects of the EMD and HVD methods", Mech. Syst. Signal Pr., 25(7), 2608-2630. https://doi.org/10.1016/j.ymssp.2011.04.005
  5. Chanpheng, T., Yamada, H., Katsuchi, H. and Sasaki, E. (2012), "Nonlinear features for damage detection on large civil structures due to earthquakes", Struct. Health Monit., 11(4), 482-488. https://doi.org/10.1177/1475921712437182
  6. Chen, G.D. and Wang, Z.C. (2012), "A signal decomposition theorem with Hilbert transform and its application to narrowband time series with closely spaced frequency components", Mech. Syst. Signal Pr., 28, 258-279. https://doi.org/10.1016/j.ymssp.2011.02.002
  7. Daubechies, I., Lu, J.F. and Wu, H.T. (2011), "Sychnrosqueezed wavelet transform: an empirical mode decomposition-like tool", Appl. Comput. Harmon. A., 30, 243-261. https://doi.org/10.1016/j.acha.2010.08.002
  8. Doebling, S.W., Farrar, C.R. and Prime, M.B. (1998), "A summary review of vibration-based damage identification methods", Shock Vib. Dig., 30(2), 91-105. https://doi.org/10.1177/058310249803000201
  9. Doebling, S.W., Farrar, C.R., Prime, M.B. and Shevitz, D.W. (1996), Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics. a literature review, LA-13070-MS, UC-900, Los Alamos National Laboratory, Los Alamos, NM.
  10. Feldman, M. (1997), "Non-linear free-vibration identification via the Hilbert transform", J. Sound Vib., 208(3), 475-489. https://doi.org/10.1006/jsvi.1997.1182
  11. Feldman, M. (2006), "Time-varying vibration decomposition and analysis based on the Hilbert transform", J. Sound Vib., 295(3-5), 518-530. https://doi.org/10.1016/j.jsv.2005.12.058
  12. Feldman, M. (2007), "Identification of weakly nonlinearities in multiple coupled oscillators", J. Sound Vib., 303(1-2), 357-370. https://doi.org/10.1016/j.jsv.2007.01.028
  13. Feldman, M. (2012), "Hilbert transform methods for nonparametric identification of nonlinear time varying vibration systems", Mech. Syst. Signal Pr., DOI: 10.1016/j.ymssp.2012.09.003.
  14. Ghanem, R. and Romeo, F. (2000), "A wavelet-based approach for the identification of linear time-varying dynamical systems", J. Sound Vib., 234(4), 555-576. https://doi.org/10.1006/jsvi.1999.2752
  15. Huang, N.E., Shen, Z. and Long, S.R. (1999), "A new view of nonlinear water waves: the Hilbert spectrum", Annu. Rev. Fluid Mech., 31, 417-457. https://doi.org/10.1146/annurev.fluid.31.1.417
  16. Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C. and Liu, H.H.(1998), "The empirical mode decomposition and Hilbert spectrum for nonlinear and non-Stationary time series analysis", P. Roy. Soc. Lond. - Series A, 454(1971), 903-995. https://doi.org/10.1098/rspa.1998.0193
  17. James, III, G.H., Carne, T.G. and Lauffer, J.P. (1995), "The natural excitation technique (NExT) for modal parameter extraction from operating structures", Int. J. Anal. Exper. Modal Anal., 10(4), 260-277.
  18. Kerschen, G., Vakakis, A.F., Lee, Y.S., McFarland, D.M. and Bergman, L.A. (2006), "Toward a fundamental understanding of the Hilbert-Huang transform in nonlinear structural dynamics", Proceedings of the IMAC-XXIV Conference & Exposition on Structural Dynamics, St. Louis, Missouri.
  19. Kerschen, G., Lee, Y.S., Vakakis, A.F., McFarland, D.M. and Bergman, L.A. (2006), "Irreversible passive energy transfer in coupled oscillators with essential nonlinearity", SIAM J. Appl. Math., 66(2), 648-679. https://doi.org/10.1137/040613706
  20. Kunnath, S.K., Mander, J.B. and Fang, L. (1997), "Parameter identification for degrading and pinched hysteretic structural concrete systems", Eng. Struct., 19(3), 224-232. https://doi.org/10.1016/S0141-0296(96)00058-2
  21. Li, H.N., Yi, T.H., Gu, M. and Huo, L.S. (2009), "Evaluation of earthquake-induced structural damages by wavelet transform", Prog. Natural Sci., 19(4), 461-470. https://doi.org/10.1016/j.pnsc.2008.09.002
  22. Lilly, J.M. and Olhede, S.C. (2010), "On the analytic wavelet transform", IEEE T. Inform. Theory, 56(8), 4135-4156. https://doi.org/10.1109/TIT.2010.2050935
  23. Mallat, S. (1998), A wavelet tour on signal processing, Academic Press, New York.
  24. Montejo, L.A. and Vidot, A.L. (2012), "Synchrosqueezed wavelet transform for frequency and damping identification from noisy signals", Smart Struct. Syst., 9(5), 441-459. https://doi.org/10.12989/sss.2012.9.5.441
  25. Pai, P.F. and Hu, J. (2006), "Nonlinear vibration characterization by signal decomposition", Proceedings of the IMAC-XXIV Conference & Exposition on Structural Dynamics, St. Louis, Missouri.
  26. Panagiotou, M., Restrepo, J. and Conte, J. (2011), "Shake table test of a 7-story full scale reinforced concrete structural wall building slice phase I: rectangular wall section", J. Struct. Eng. - ASCE, 137, 691-704. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000332
  27. Qian, S. and Chen, D. (1994), "Decomposition of the Wigner-Ville distribution and time-frequency distribution series", IEEE T. Signal Proces., 42(10), 2836-2842. https://doi.org/10.1109/78.324750
  28. Sohn, H., Farrar, C.F., Hemez, F.M., Shunk, D.D., Stinemates, D.W., Nadler, B.R. and Czarnecki, J.J. (2004), A Review of Structural Health Monitoring Literature: 1996-2001, Report LA-13976-MS, Los Alamos National Laboratory, Los Alamos, NM, USA.
  29. Ta, M.N. and Lardies, J. (2006), "Identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform", J. Sound Vib., 293(1-2), 16-37. https://doi.org/10.1016/j.jsv.2005.09.021
  30. Thakur, G. and Wu, H.T. (2011), "Synchrosqueezing-based recovery of instantaneous frequency from nonuniform samples", SIAM J. Math. Anal., 43(5), 2078-2095. https://doi.org/10.1137/100798818
  31. Vakakis, A.F., McFarland, D.M., Bergman, L.A., Manevitch, L.I. and Gendelman, O. (2004), "Isolated resonance captures and resonance capture cascades leading to single- or multi-mode passive energy pumping in damped coupled oscillators", J. Vib. Acoust., 126(2), 235-244. https://doi.org/10.1115/1.1687397
  32. Van Overschee, P. and De Moor, B. (1996), Subspace identification for linear systems: theory, implementation and application, Kluwer Academic Pulisher, Dordrecht, Netherlands.
  33. Wang, L., Zhang, J., Wang, C. and Hu, S. (2003), "Identification of nonlinear systems through time-frequency filtering technique", J. Vib. Acoust., 125(2), 199-204. https://doi.org/10.1115/1.1545769
  34. Wang, Z.C. (2011), Hilbert transform applications in signal analysis and non-parametric identification of linear and nonlinear systems, Ph.D dissertation, Missouri University of Science and Technology.
  35. Wang, Z.C. and Chen, G.D. (2012), "A Recursive Hilbert-Huang transform method for time-varying property identification of linear shear-type buildings under base excitations", J. Eng. Mech. - ASCE, 138(6), 631-639. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000357
  36. Wang, Z.C., Ren, W.X. and Chen, G.D. (2013a), "Time-varying linear and nonlinear structural identification with analytical mode decomposition and Hilbert transform", J. Struct. Eng. - ASCE, 139(12), 06013001, 1-5. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000832
  37. Wang, Z.C., Ren, W.X. and Liu, J.L. (2013b), "A Synchrosqueezed wavelet transform enhanced by extended analytical mode decomposition method for dynamic signal reconstruction", J. Sound Vib., 332(22), 6016-6028. https://doi.org/10.1016/j.jsv.2013.04.026
  38. Wen, Y.K. (1976), "Method for random vibration of hysteretic systems", J. Eng. Mech. - ASCE., 102(2), 249-263.
  39. Wu, Z.H. and Huang, N.E. (2009), "Ensemble empirical mode decomposition: a noise-assisted data analysis method", Adv. Adaptive Data Anal., 1(1), 1-41. https://doi.org/10.1142/S1793536909000047
  40. Yi, T.H., Li, H.N. and Sun, H.M. (2013), "Multi-stage structural damage diagnosis method based on energy-damage theory". Smart Struct. Syst., 12(3-4), 345-361. https://doi.org/10.12989/sss.2013.12.3_4.345
  41. Yi, T.H., Li, H.N. and Zhao, X.Y. (2012), "Noise smoothing for structural vibration test signals using an improved wavelet thresholding technique", Sensors, 12(8), 11205-11220. https://doi.org/10.3390/s120811205

Cited by

  1. Free and transient responses of linear complex stiffness system by Hilbert transform and convolution integral vol.17, pp.5, 2016, https://doi.org/10.12989/sss.2016.17.5.753
  2. Acoustic emission source location and noise cancellation for crack detection in rail head vol.18, pp.5, 2016, https://doi.org/10.12989/sss.2016.18.5.1063
  3. Detection and parametric identification of structural nonlinear restoring forces from partial measurements of structural responses vol.54, pp.2, 2015, https://doi.org/10.12989/sem.2015.54.2.291
  4. Time–frequency analysis and applications in time-varying/nonlinear structural systems: A state-of-the-art review 2018, https://doi.org/10.1177/1369433217751969
  5. Magnetic (ethylene-octene) elastomer composites obtained by extrusion vol.57, pp.5, 2017, https://doi.org/10.1002/pen.24446
  6. Damage Detection in Initially Nonlinear Structures Based on Variational Mode Decomposition vol.20, pp.10, 2015, https://doi.org/10.1142/s0219455420420092
  7. Review on the new development of vibration-based damage identification for civil engineering structures: 2010–2019 vol.491, pp.None, 2015, https://doi.org/10.1016/j.jsv.2020.115741
  8. Hilbert square demodulation and error mitigation of the measured nonlinear structural dynamic response vol.160, pp.None, 2015, https://doi.org/10.1016/j.ymssp.2021.107935