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Nonlinear time-varying vibration system identification using parametric time–frequency transform with spline kernel

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Abstract

In real-life applications, mechanical vibration systems are not linear time invariant. Time-varying pattern arise, for instance, during deployment, aging, deformation, load variation, etc. In the absence of a complete physics-based description of a system, system identification (SI) is able to obtain the missed information of nonstationary pattern for the unknown system. The SI will face difficulty when the time-varying system involves the nonlinearity, which makes the system solution have both the nonlinear and nonstationary time–frequency patterns. This paper aimed to identify the system with linear and nonlinear time-varying characteristics using parametric time–frequency transform with spline kernel, which is known for offering great energy concentration in time–frequency domain and allows the accurate extraction of model feature. The efficacy of the proposed method is demonstrated on SDOF systems comprised of three types of nonlinear time-varying stiffness, including time-varying periodic modulation of stiffness, time-varying piecewise modulation of nonlinear stiffness and time-varying periodic modulation of nonlinear stiffness. Comparisons with the conventional time–frequency methods and the Hilbert transform-based SI validated that the proposed method is more robust in characterizing the nonlinear time-varying stiffness of the system with the presence of noise.

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Abbreviations

SI:

System identification

TFA:

Time–frequency analysis

TFR:

Time–frequency representation

LTI:

Linear time invariant

NTV:

Nonlinear time varying

PTFT:

Parametric time–frequency transform

IF:

Instantaneous frequency

STFT:

Short-time Fourier transform

WT:

Wavelet transform

WVD:

Wigner–Ville distribution

SDOF:

Single degree of freedom

MDOF:

Multiple degree of freedom

PTFT_S:

Parametric time–frequency transform with spline kernel

IA:

Instantaneous amplitude

HT:

Hilbert transform

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Acknowledgments

This research was supported by the NSFC for Distinguished Young Scholars (11125209) and the NSFC (11402144, 51121063).

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Authors and Affiliations

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

    Y. Yang, Z. K. Peng, X. J. Dong, W. M. Zhang & G. Meng

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  1. Y. Yang
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  2. Z. K. Peng
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  3. X. J. Dong
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  4. W. M. Zhang
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  5. G. Meng
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Correspondence to Z. K. Peng.

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Yang, Y., Peng, Z.K., Dong, X.J. et al. Nonlinear time-varying vibration system identification using parametric time–frequency transform with spline kernel. Nonlinear Dyn 85, 1679–1694 (2016). https://doi.org/10.1007/s11071-016-2786-1

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  • DOI: https://doi.org/10.1007/s11071-016-2786-1

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