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Modal identification of multi-degree-of-freedom structures based on intrinsic chirp component decomposition method

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Abstract

Modal parameter identification is a mature technology. However, there are some challenges in its practical applications such as the identification of vibration systems involving closely spaced modes and intensive noise contamination. This paper proposes a new time-frequency method based on intrinsic chirp component decomposition (ICCD) to address these issues. In this method, a redundant Fourier model is used to ameliorate border distortions and improve the accuracy of signal reconstruction. The effectiveness and accuracy of the proposed method are illustrated using three examples: a cantilever beam structure with intensive noise contamination or environmental interference, a four-degree-of-freedom structure with two closely spaced modes, and an impact test on a cantilever rectangular plate. By comparison with the identification method based on the empirical wavelet transform (EWT), it is shown that the presented method is effective, even in a high-noise environment, and the dynamic characteristics of closely spaced modes are accurately determined.

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References

  1. YIN, T., LAM, H., and ZHU, H. P. Statistical detection of structural damage based on model reduction. Applied Mathematics and Mechanics (English Edition), 30(7), 875–888 (2009) https://doi.org/10.1007/s10483-009-0707-7

    Article  Google Scholar 

  2. FENG, K., LI, Z., GAO, G. Y., and SU, X. Y. Damage detection method in complicated beams with varying flexural stiffness. Applied Mathematics and Mechanics (English Edition), 32(4), 469–478 (2011) https://doi.org/10.1007/s10483-011-1431-x

    Article  MathSciNet  Google Scholar 

  3. CALVI, A. and ROY, N. Spacecraft Mechanical Loads Analysis Handbook, ESA Requirements and Standards Division, Noordwijk (2013)

    Google Scholar 

  4. ZHAO, Y. C., YUAN, S. Q., XIAO, Z. H., and XU, Q. Y. The fractional dimension identification method of critical bifurcated parameters of bearing-rotor system. Applied Mathematics and Mechanics (English Edition), 21(2), 141–146 (2000) https://doi.org/10.1007/BF02458514

    Article  Google Scholar 

  5. YUAN, T. C., YANG, J., and CHEN, L. Q. Nonparametric identification of nonlinear piezoelectric mechanical systems. Journal of Applied Mechanics, 85, 111008 (2018)

    Article  Google Scholar 

  6. NEILD, S. A., MCFADDEN, P. D., and WILLIAMS, M. S. A review of time-frequency methods for structural vibration analysis. Engineering Structures, 25, 713–728 (2003)

    Article  Google Scholar 

  7. JAWERTH, B. and SWELDENS, W. An overview of wavelet based multiresolution analysis. Society for Industrial and Applied Mathematics, 36, 377–412 (1994)

    MATH  Google Scholar 

  8. CHUI, C. K. An Introduction to Wavelets, Academic Press, Boston (1992)

    MATH  Google Scholar 

  9. PRIEBE, R. D. and WILSON, G. R. Wavelet applications to structural analysis. IEEE International Conference on Acoustics, Speech, and Signal Processing, 3, 205–208 (1994)

    Google Scholar 

  10. STASZEWSKI, W. J. Identification of damping in MDOF systems using time-scale decomposition. Journal of Sound and Vibration, 203, 283–305 (1997)

    Article  Google Scholar 

  11. LARDIES, J. and GOUTTEBROZE, S. Identification of modal parameters using the wavelet transform. International Journal of Mechanical Sciences, 44, 2263–2283 (2002)

    Article  Google Scholar 

  12. PENG, Z., MENG, G., and CHU, F. Improved wavelet reassigned scalograms and application for modal parameter estimation. Shock and Vibration, 18, 299–316 (2011)

    Article  Google Scholar 

  13. HUANG, C. S. and SU, W. C. Identification of modal parameters of a time invariant linear system by continuous wavelet transformation. Mechanical Systems and Signal Processing, 21, 1642–1664 (2007)

    Article  Google Scholar 

  14. CHEN, S., LIU, J., and LAI, H. Wavelet analysis for identification of damping ratios and natural frequencies. Journal of Sound and Vibration, 323, 130–147 (2009)

    Article  Google Scholar 

  15. SLAVIČ, J., SIMONOVSKI, I., and BOLTEŽAR, M. Damping identification using a continuous wavelet transform: application to real data. Journal of Sound and Vibration, 262, 291–307 (2003)

    Article  Google Scholar 

  16. RUZZENE, M., FASANA, A., GARIBALDI, L., and PIOMBO, B. Natural frequencies and dampings identification using wavelet transform: application to real data. Mechanical Systems and Signal Processing, 11, 207–218 (1997)

    Article  Google Scholar 

  17. KIM, Y. S. and CHEN, L. Q. Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition. Applied Mathematics and Mechanics (English Edition), 34(7), 801–810 (2013) https://doi.org/10.1007/s10483-013-1708-9

    Article  MathSciNet  Google Scholar 

  18. FELDMAN, M. Time-varying vibration decomposition and analysis based on the Hilbert transform. Journal of Sound and Vibration, 295, 518–530 (2006)

    Article  Google Scholar 

  19. YANG, J. N., LEI, Y., PAN, S., and HUANG, N. System identification of linear structures based on Hilbert-Huang spectral analysis, part 2: complex modes. Earthquake Engineering and Structural Dynamics, 32, 1533–1554 (2003)

    Article  Google Scholar 

  20. YANG, J. N., LEI, Y., PAN, S., and HUANG, N. System identification of linear structures based on Hilbert-Huang spectral analysis, part 1: normal modes. Earthquake Engineering and Structural Dynamics, 32, 1443–1467 (2003)

    Article  Google Scholar 

  21. CHEN, J. and XU, Y. L. Identification of modal damping ratios of structures with closely spaced modal frequencies. Structural Engineering and Mechanics, 14, 417–434 (2002)

    Article  Google Scholar 

  22. RILLING, G., FLANDRIN, P., and GONCALVES, P. On empirical mode decomposition and its algorithms. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, Grado (2003)

    Google Scholar 

  23. PENG, Z. K., TSE, P. W., and CHU, F. L. A comparison study of improved Hilbert-Huang transform and wavelet transform: application to fault diagnosis for rolling bearing. Mechanical Systems and Signal Processing, 19, 974–988 (2005)

    Article  Google Scholar 

  24. CHEN, S., PENG, Z., YANG, Y., DONG, X., and ZHANG, W. Intrinsic chirp component decomposition by using Fourier series representation. Signal Processing, 137, 319–327 (2017)

    Article  Google Scholar 

  25. YAN, B. and MIYAMOTO, A. A comparative study of modal parameter identification based on wavelet and Hilbert-Huang transforms. Computer-Aided Civil and Infrastructure Engineering, 21, 9–23 (2006)

    Article  Google Scholar 

  26. YANG, Y., PENG, Z., DONG, X., ZHANG, W., and MENG, G. General parameterized time-frequency transform. IEEE Transactions on Signal Processing, 62, 2751–2764 (2014)

    Article  MathSciNet  Google Scholar 

  27. ZHANG, H., BI, G., RAZUL, S. G., and SEE, C. M. S. Robust time-varying filtering and separation of some nonstationary signals in low SNR environments. Signal Processing, 106, 141–158 (2015)

    Article  Google Scholar 

  28. DJUROVIĆ, I. and STANKOVIĆ, L. An algorithm for the Wigner distribution based instantaneous frequency estimation in a high noise environment. Signal Processing, 84, 631–643 (2004)

    Article  Google Scholar 

  29. GILLES, J. Empirical wavelet transform. IEEE Transactions on Signal Processing, 61, 3999–4010 (2013)

    Article  MathSciNet  Google Scholar 

  30. LI, Y., XUE, B., and HONG, H. Instantaneous pitch estimation based on empirical wavelet transform. Digital Signal Processing (DSP), 19th International Conference on IEEE, 250–253 (2014)

    Google Scholar 

  31. LIU, W., CAO, S., and CHEN, Y. Seismic time-frequency analysis via empirical wavelet transform. IEEE Geoscience and Remote Sensing Letters, 13, 28–32 (2016)

    Article  Google Scholar 

  32. PEETERS, B., AUWERAER, H. V. D., GUILLAUME, P., and LEURIDAN, J. The PolyMAX frequency-domain method: a new standard for modal parameter estimation. Shock and Vibration, 11, 395–409 (2004)

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, 200240, China

    Sha Wei, Shiqian Chen, Zhike Peng, Xingjian Dong & Wenming Zhang

Authors
  1. Sha Wei
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  2. Shiqian Chen
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  3. Zhike Peng
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  4. Xingjian Dong
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  5. Wenming Zhang
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Corresponding author

Correspondence to Zhike Peng.

Additional information

* Citation: WEI, S., CHEN, S. Q., PENG, Z. K., DONG, X. J., and ZHANG, W. M. Modal identification of multi-degree-of-freedom structures based on intrinsic chirp component decomposition method. Applied Mathematics and Mechanics (English Edition), 40(12), 1741–1758 (2019) https://doi.org/10.1007/s10483-019-2547-9

Project supported by the National Natural Science Foundation of China (Nos. 11702170, 11320011, and 11802279) and the China Postdoctoral Science Foundation (No. 2016M601585)

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Wei, S., Chen, S., Peng, Z. et al. Modal identification of multi-degree-of-freedom structures based on intrinsic chirp component decomposition method. Appl. Math. Mech.-Engl. Ed. 40, 1741–1758 (2019). https://doi.org/10.1007/s10483-019-2547-9

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  • DOI: https://doi.org/10.1007/s10483-019-2547-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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