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Optimal Hilbert transform parameter identification of bistable structures

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Abstract

Nonlinear bistable structures have received significant attention in the field of energy harvesting and vibration absorption. Obtaining their precise nonlinear restoring force is of significance to predict and enhance the system's performance. However, it is difficult to measure their nonlinear restoring force in experiments due to the distinct characteristic of snap-through. Moreover, the traditional Hilbert transform-based method may have insufficient identification accuracy or even be incapable because numerical integration or differentiation procedure is sensitive to noise disturbance. To address these issues, an optimal Hilbert transform parameter identification is proposed to precisely estimate the parameters in the bistable dynamic equation. The Hilbert transform interval estimation of mass, damping and nonlinear restoring force coefficients are derived for obtaining the reasonable range of identified parameters. Furthermore, an optimization fitness function is established to obtain the optimal value of nonlinear parameters in bistable structures. Numerical simulation of an asymmetric bistable dynamic equation shows that the proposed method exhibits an NMSE value of 2.52% for free vibration and 1.64% for forced periodic oscillation under 20 dB noise level. Besides, the damping effects on identification results are discussed. Experimental measurements of a magnetic coupled bistable cantilever beam under different conditions are performed to identify the nonlinear system parameters. Results indicate that the proposed method can effectively identify the nonlinear bistable structures with an average NMSE value of 8.23% for free vibration and 6.39% for forced periodic responses, respectively.

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Availability of data and material

These data are collected by the experiment and can be provided upon request.

Code availability

The code is written according to the proposed model and can be provided upon request.

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Acknowledgements

This work is sponsored by the National Natural Science Foundation of China (Grant No. 51975453)

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Authors and Affiliations

  1. Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Qinghua Liu, Ying Zhang, Zehao Hou, Yuting Qiao, Junyi Cao & Yaguo Lei

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  1. Qinghua Liu
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  2. Ying Zhang
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  3. Zehao Hou
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Correspondence to Junyi Cao.

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Liu, Q., Zhang, Y., Hou, Z. et al. Optimal Hilbert transform parameter identification of bistable structures. Nonlinear Dyn 111, 5449–5468 (2023). https://doi.org/10.1007/s11071-022-08120-z

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