DOI QR코드

DOI QR Code

Identification of nonlinear systems through statistical analysis of the dynamic response

  • 투고 : 2019.06.01
  • 심사 : 2020.08.09
  • 발행 : 2020.09.25

초록

In this paper an extension to the method for the identification of mechanical parameters of nonlinear systems proposed in Breccolotti and Materazzi (2007) for MDoF systems is presented. It can be used for damage identification purposes when damage modifies the linear characteristics of the investigated structure. It is based on the following two main features: the solution of the Fokker-Planck equation that describes the response probabilistic properties of the system when it is excited by external Gaussian loads; and a model updating technique that minimizes the differences between the response of the actual system and that of a parametric system used to identify the unknown parameters. Numerical analysis, that simulate virtual experimental tests, are used in the paper to show the capabilities of the method and to analyse the conditions required for its application.

키워드

참고문헌

  1. Belenky, V., Glotzer, D., Pipiras, V. and Sapsis, T.P. (2019), "Distribution tail structure and extreme value analysis of constrained piecewise linear oscillators", Probab. Eng. Mech., 57, 1-13. https://doi.org/10.1016/j.probengmech.2019.04.001
  2. Bernal, D. and Beck, J. (2004), "Special Structural Health monitoring benchmark, Section: Phase I of the IASC-ASCE", J. Eng. Mech., 130(1).
  3. Boujo, E. and Noiray, N. (2017), "Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473, 2200.
  4. Breccolotti, M. and Materazzi, A.L. (2007), "Identification of a nonlinear spring through the Fokker-Planck equation", Probab. Eng. Mech., 23, 146-153. https://doi.org/10.1016/j.probengmech.2007.12.018
  5. Breccolotti,M., Materazzi, A.L. and Venanzi, I. (2008), "Identification of the nonlinear behaviour of a cracked RC beam through the statistical analysis of the dynamic response", Struct. Control Health Monit., 15, 416-435. https://doi.org/10.1002/stc.245
  6. Cacciola, P. and Muscolino. G. (2002), "Dynamic response of a rectangular beam with a known non-propagating crack of certain or uncertain depth", Comput. Struct., 80, 2387-2396. https://doi.org/10.1016/S0045-7949(02)00255-9
  7. Cacciola, P., Impollonia, N. and Muscolino, G. (2003), "Crack detection and location in a damaged beam vibrating under white noise", Comput. Struct., 81, 1773-1782. https://doi.org/10.1016/S0045-7949(03)00201-3
  8. Chatzi, E.N. and Smyth, A.W. (2009), "The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing", Struct. Control Health Monit., 16, 99-123. https://doi.org/10.1002/stc.290
  9. Chen, J. and Rui, Z. (2018), "Dimension-reduced FPK equation for additive white-noise excited nonlinear structures", Probab. Eng. Mech., 53, 1-13. https://doi.org/10.1016/j.probengmech.2018.03.002
  10. Doebling, S.W., Farrar, C.R., Prime, M.B. and Shevitz, D.W. (1996), Damage identification and health monitoring of structural and mechanical system from changes in their vibrational characteristic: a literature review. Los Alamos National Laboratories, Report LA-13070-MS, Los Alamos, New Mexico.
  11. Erazo, K. and Nagarajaiah, S. (2018), "Bayesian structural identification of a hysteretic negati ve stiffness earthquake protection system using unscented Kalman filtering", Struct. Control Health Monit., 25, e2203. https://doi.org/10.1002/stc.2203
  12. Goldberg, D.E. (1989), Genetic Algorithms in Search, Optimization and Machine Learning Addison-Wesley.
  13. Green, PL. (2015), "Bayesian system identification of a nonlinear dynamical system using a novel variant of Simulated Annealing", Mech. Syst. Signal Pr., 52-53, 133-146. https://doi.org/10.1016/j.ymssp.2014.07.010
  14. Hadjileontiadis, L.J., Douka, E. and Trochidis, A. (2005), "Crack detection in beam using kurtosis", Comput. Struct., 83, 909-919. https://doi.org/10.1016/j.compstruc.2004.11.010
  15. Hoon S, Farrar CR, Hemez FM, Czarnecki JJ, Shunk DD, Stinemates DW, Nadler BR. A review of Structural Health Monitoring Literature: 1996-2001. Los Alamos National Laboratories, Report LA-13976-MS, 2003, Los Alamos, New Mexico.
  16. Hughes, T.J.R. (1987), The Finite Element Method Prentice Hall.
  17. Iourtchenko, D.V., Mo, E. and Naess, A. (2006), "Response probability functions of strongly nonlinear system by the path integration method", Nonlinear Mech., 41, 693-705. https://doi.org/10.1016/j.ijnonlinmec.2006.04.002
  18. Kim, J.T. and Stubbs, N. (2003), "Crack detection in beam-type structures using frequency data", J. Sound Vib., 259, 145-160. https://doi.org/10.1006/jsvi.2002.5132
  19. Lai, Z .and Nagarajaiah, S. (2019), "Sparse structural system identification method for nonlinear dynamic systems with hysteresis/inelastic behavior", Mech. Syst. Signal Pr., 117, 813-842. https://doi.org/10.1016/j.ymssp.2018.08.033
  20. Lai, Z. and Nagarajaiah, S. (2019), "Semi-supervised structural linear/nonlinear damage detection and characterization using sparse identification", Struct. Control Health Monit., 26, e2306.
  21. Lei, Y. and Xia, D. and Erazo, K. and Nagarajaiah, S. (2019), "A novel unscented Kalman filter for recursive state-input-system identification of nonlinear systems", Mech. Syst. Signal Pr., 127, 120-135. https://doi.org/10.1016/j.ymssp.2019.03.013
  22. Li, H.N., Yi, T.H., Ren, L., Li, D.S. and Huo, L.S. (2014), "Reviews on innovations and applications in structural health monitoring for infrastructures", Struct. Monit. Maint., 1, 1-45. https://doi.org/10.12989/smm.2014.1.1.001
  23. Lin, H.P., Chang, S.C. and Wu, J.D. (2002), "Beam vibrations with an arbitrary number of cracks", J. Sound Vib., 258, 987-999. https://doi.org/10.1006/jsvi.2002.5184
  24. Mosbah, H. and Fogli, M. (2003), "An original approximate method for estimating the invariant probability distribution of a large class of multi-dimensional nonlinear stochastic oscillators", Probab. Eng. Mech., 18(2), 165-170. https://doi.org/10.1016/S0266-8920(03)00002-X
  25. Neild, S.A., Williams, M.S, and McFadden, P.D. (2001), "Nonlinear vibration characteristic of damaged concrete beams", J. Struct. Eng., 129(260), 260-268.
  26. Owen, J.S., Eccles, B.J., Choo, B.S. and Woodings, M.A. (2001), "The application of auto-regressive time series modeling for the time-frequency analysis of civil engineering structures", Eng. Struct., 23(5), 521-536. https://doi.org/10.1016/S0141-0296(00)00059-6
  27. Patil, D.P. and Maiti, S.K. (2003), "Detection of multiple cracks using frequency measurements", Eng. Fract. Mech., 70, 1553-1572. https://doi.org/10.1016/S0013-7944(02)00121-2
  28. Petryna, Y.S. and Kratzig, W.B. (2005), "Compliance-based structural damage measure and its sensitivity to uncertainties", Comput. Struct., 83(14), 1113-1133. https://doi.org/10.1016/j.compstruc.2004.11.020
  29. Piszczec, K. and Niziol, J. (1986), Random Vibration of Mechanical System Ellis Horwood Limited: Chichester.
  30. Saavedra, P.N. and Cuitino, L.A. (2001), "Crack detection and vibration behaviour of cracked beams", Comput. Struct., 79(16), 1451-1459. https://doi.org/10.1016/S0045-7949(01)00049-9
  31. Shinozuka, M. and Jan, C.M. (1972), "Digital simulation of random processes and its application", J. Sound Vib., 25, 111-128. https://doi.org/10.1016/0022-460X(72)90600-1
  32. Von Wagner, U. and Wedig, W.V. (2000), "On the calculation of stationary solutions of multi-dimensional Fokker-Planck equations by orthogonal functions", Nonlinear Dymam., 21, 289-306. https://doi.org/10.1023/A:1008389909132
  33. Wimarshana, B., Wu, N. and Wu, C. (2017), "Crack identification with parametric optimization of entropy & wavelet transformation", Struct. Monit. Maint., 4(1), 33-52. https://doi.org/10.12989/smm.2017.4.1.033
  34. Wu, M. and Smyth, A.W. (2007), "Application of the unscented Kalman filter for real-time nonlinear structural system identification", Struct. Control Health Monit., 14, 971-990. https://doi.org/10.1002/stc.186