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Nonlinear identification of systems with parametric excitation

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Abstract

In this paper, the incremental harmonic balance nonlinear identification (IHBNID) is presented for modelling and parametric identification of nonlinear systems. The effects of harmonic balance nonlinear identification (HBNID) and IHBNID are also studied and compared by using numerical simulation. The effectiveness of the IHBNID is verified through the Mathieu-Duffing equation as an example. With the aid of the new method, the derivation procedure of the incremental harmonic balance method is simplified. The system responses can be represented by the Fourier series expansion in complex form. By keeping several lower-order primary harmonic coefficients to be constant, some of the higher-order harmonic coefficients can be self-adaptive in accordance with the residual errors. The results show that the IHBNID is highly efficient for computation, and excels the HBNID in terms of computation accuracy and noise resistance.

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References

  1. Ljung L. System Identification, Theory for the User. New Jersey: Prince-Hall, Englewood Cliffs, 1987

    MATH  Google Scholar 

  2. Billings S A. Identification of nonlinear systems-A survey. Proceedings IEEE, 1980, 127: 272–285

    MathSciNet  Google Scholar 

  3. Haber R, Unbehauen H. Structure identification of nonlinear dynamic systems—A survey in input/output approaches. Automatica, 1990, 26: 651–677

    Article  MATH  MathSciNet  Google Scholar 

  4. Casas R A, Jacobson C A, Rey G J, et al. Harmonic balance methods for nonlinear feedback identification. Allerton, 1997, 2: 230

    Google Scholar 

  5. Yasuda K, Kawamura S, Watanabe K. Identification of nonlinear multi-degree-of-freedom systems. JSME Int J, 1988, 31: 8–15

    MathSciNet  Google Scholar 

  6. Yuan C M, Feeny B F. Parametric identification of chaotic systems. J Vibr Control, 1998, 4: 405–426

    Article  Google Scholar 

  7. Thothadri M, Casas R A, Moon F C, et al. Nonlinear system identification of multi-degree-of-freedom systems. Nonlinear Dyn, 2003, 32: 307–322

    Article  MATH  MathSciNet  Google Scholar 

  8. Thothadri M, Moon F C. Nonlinear system identification of systems with periodic limit-cycle response. Nonlinear Dyn, 2005, 39: 63–77

    Article  MATH  MathSciNet  Google Scholar 

  9. Lau S L, Cheung Y K. Amplitude incremental variational principle for nonlinear vibration of elastic system. ASME J Appl Mech, 1981, 48: 959–964

    Article  MATH  Google Scholar 

  10. Cheung Y K, Chen S H, Lau S L. Application of the incremental harmonic balance method to cubic nonlinearity systems. J Sound Vibr, 1990, 140: 273–286

    Article  MathSciNet  Google Scholar 

  11. Lau S L. The incremental harmonic balance method and its application to nonlinear vibrations. In: Proceedings of International Conference on Structure Dynamics. Vibration, Noise and Control, Hong Kong, 1995. 50–57

  12. Shen J H, Lin K C, Chen S H, et al. Bifurcation and route-to-chaos analyses for Mathieu-Duffing oscillator by the incremental harmonic balance method. Nonlinear Dyn, 2008, 52: 403–414

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, 310027, China

    Min Ye, SuGuang Dou & ZhiGang Zeng

  2. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China

    Wei Zhang

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  1. Min Ye
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  2. SuGuang Dou
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  3. Wei Zhang
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  4. ZhiGang Zeng
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Correspondence to Min Ye.

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Ye, M., Dou, S., Zhang, W. et al. Nonlinear identification of systems with parametric excitation. Sci. China Technol. Sci. 54, 2080–2089 (2011). https://doi.org/10.1007/s11431-011-4485-y

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  • DOI: https://doi.org/10.1007/s11431-011-4485-y

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