DOI QR코드

DOI QR Code

Identification of nonlinear elastic structures using empirical mode decomposition and nonlinear normal modes

  • Poon, C.W. (Department of Civil Engineering, Hong Kong University of Science and Technology) ;
  • Chang, C.C. (Department of Civil Engineering, Hong Kong University of Science and Technology)
  • 투고 : 2006.02.20
  • 심사 : 2007.01.10
  • 발행 : 2007.10.25

초록

The empirical mode decomposition (EMD) method is well-known for its ability to decompose a multi-component signal into a set of intrinsic mode functions (IMFs). The method uses a sifting process in which local extrema of a signal are identified and followed by a spline fitting approximation for decomposition. This method provides an effective and robust approach for decomposing nonlinear and non-stationary signals. On the other hand, the IMF components do not automatically guarantee a well-defined physical meaning hence it is necessary to validate the IMF components carefully prior to any further processing and interpretation. In this paper, an attempt to use the EMD method to identify properties of nonlinear elastic multi-degree-of-freedom structures is explored. It is first shown that the IMF components of the displacement and velocity responses of a nonlinear elastic structure are numerically close to the nonlinear normal mode (NNM) responses obtained from two-dimensional invariant manifolds. The IMF components can then be used in the context of the NNM method to estimate the properties of the nonlinear elastic structure. A two-degree-of-freedom shear-beam building model is used as an example to illustrate the proposed technique. Numerical results show that combining the EMD and the NNM method provides a possible means for obtaining nonlinear properties in a structure.

키워드

참고문헌

  1. Donoho, D. L. (1995), "De-noising by soft-thresholding", IEEE Transactions on Information Theory, 41(3), 613-627. https://doi.org/10.1109/18.382009
  2. Farrar, C. R., Doebling, S. W. and Nix, D. A. (2001), "Vibration-based structural damage identification", Philosophical Transactions of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 359, 131-149. https://doi.org/10.1098/rsta.2000.0717
  3. Feldman, M. (1994a), "Non-linear system vibration analysis using Hilbert transform-I. Free vibration analysis method 'FREEVIB' ", Mechanical Systems and Signal Processing, 8(2), 119-127. https://doi.org/10.1006/mssp.1994.1011
  4. Feldman, M. (1994b), "Non-linear system vibration analysis using Hilbert transform-II. Forced vibration analysis method 'FORCEVIB' ", Mechanical Systems and Signal Processing, 8(3), 309-318. https://doi.org/10.1006/mssp.1994.1023
  5. Gurley, K. and Kareem, A. (1999), "Application of wavelet transform in earthquake, wind and ocean engineering", Eng. Struct., 21, 149-167. https://doi.org/10.1016/S0141-0296(97)00139-9
  6. Hahn, S. L. (1996), Hilbert Transforms in Signal Processing, Boston : Artech House, 442pp.
  7. 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. (1998a), "The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis", Proceedings of the Royal Society of London, Series A, 454, 903-995. https://doi.org/10.1098/rspa.1998.0193
  8. Huang, N. E., Shen, Z. and Long, S. R. (1998b), "A new view of nonlinear water waves: the Hilbert spectrum", Annual Review of Fluid Mechanics, 31, 417-457.
  9. Rilling, G., Flandrin, P. and Goncalves, P. (2003), "On empirical mode decomposition and its algorithms", IEEEEURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03.
  10. Shaw S. W. and Pierre C. (1993). "Normal modes for non-linear vibratory systems", J. Sound Vib., 164(1), 85-124. https://doi.org/10.1006/jsvi.1993.1198
  11. Schittowski, K. "NLQPL: A FORTRAN-subroutine solving constrained nonlinear programming problems", Annuals of Operations Research, 5, 485-500.
  12. Yang, J. N., Lei, Y., Pan, S. and Huang, N. (2003a), "Identification of linear structures based on Hilbert-Huang transform. Part 1: normal modes", Earthq. Eng. Struct. Dyn., 32(9), 1443-1467. https://doi.org/10.1002/eqe.287
  13. Yang, J. N., Lei, Y., Pan, S. and Huang, N. (2003b), "Identification of linear structures based on Hilbert-Huang transform. Part 2: complex modes", Earthq. Eng. Struct. Dyn., 32(10), 1533-1554. https://doi.org/10.1002/eqe.288
  14. Zhao, J. and DeWolf, J. T. (1999), "Sensitivity study for vibrational parameters used in damage detection", J. Struct. Eng., ASCE, 125(4), 410-416. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:4(410)

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  8. Experimental Identification of Nonlinearities under Free and Forced Vibration using the Hilbert Transform vol.15, pp.10, 2009, https://doi.org/10.1177/1077546308097270
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