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Parametric study and multi-parameter optimization of a generalized second-order tri-stable stochastic resonance system

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Abstract

The weak signal extraction methods based on stochastic resonance (SR) are extensively studied due to their ability of utilizing noise energy to enhance weak signals. Therefore, many SR-based methods have been proposed to extract characteristic signals from strong background noise. Among various SR models, the second-order tri-stable SR models have demonstrated their superiority in weak signal extraction with better output performance compared to other competitive SR models. However, the current studies have two main shortcomings including nonstandard forms of the system equation and insufficient investigations on the system parameters. Therefore, a generalized second-order tri-stable SR (GSTSR) system is proposed in this paper to address the aforementioned issues. In order to evaluate the output performance of the GSTSR system, the mean first-passage time (MFPT) of the system is derived, and the signal-to-noise ratio (SNR) and the so-called characteristic signal recognition rate (CSRR) are designed. On this basis, the effects of the parameters of the GSTSR (including the asymmetric parameters, the damping ratio and the scale-transformation parameters) on the system’s SR performance are fully investigated through numerical simulations. Furthermore, the multi-parameter optimization algorithm of the GSTSR system based on particle swarm optimization (PSO) is conducted, and the optimization results are analyzed. The research results can provide guidance for designing the tri-stable SR models with a superior SR performance.

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Data availability

To provide a reference for the multi-parameter optimization of the tri-stable stochastic resonance model established in this paper, we have uploaded the PSO algorithm programs for optimizing the target functions [the optimal output signal-to-noise ratio (SNR) and the optimal output characteristic signal recognition rate (CSRR)] when Signal 1 is input. The uploaded codes can be also used to process other signals besides signal 1. Moreover, it should be pointed out that as the particle swarm optimization (PSO) algorithm is a stochastic optimization algorithm, reproducing the exact numerical results of this paper in each optimization run is practically impossible. That is, using the uploaded algorithm programs may not precisely reproduce the numerical results shown in this paper. However, the uploaded algorithm programs can serve as a reference for the multi-parameter optimization of the tri-stable stochastic resonance system established in this paper.

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Acknowledgements

This work is supported by the Hainan Provincial Joint Project of Sanya Yazhou Bay Science and Technology City (Grant No. 2021JJLH0098), the National Natural Science Foundation of China (Grant Nos. 52375112 and 51905349) and Guangdong Key Laboratory of Electromagnetic Control and Intelligent Robots.

Funding

This work was supported by Hainan Provincial Joint Project of Sanya Yazhou Bay Science and Technology City grant number (2021JJLH0098), National Natural Science Foundation of China grant number (52375112, 51905349).

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Authors and Affiliations

  1. Ocean College, Zhejiang University, Zhoushan, 316021, China

    Cailiang Zhang, Yifan Zhao & Ronghua Zhu

  2. Shenzhen Key Laboratory of High-Performance Nontraditional Manufacturing, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, 518060, China

    Zhihui Lai

  3. Hannan Institute of Zhejiang University, Sanya, 572024, China

    Cailiang Zhang, Yifan Zhao & Ronghua Zhu

  4. Yangjiang Offshore Wind Power Laboratory, Yangjiang, 529500, China

    Cailiang Zhang, Yifan Zhao & Ronghua Zhu

  5. Guangdong Provincial Key Laboratory of Micro/Nano Optomechatronics Engineering, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, 518060, China

    Zhihui Lai

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  1. Cailiang Zhang
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Correspondence to Zhihui Lai or Ronghua Zhu.

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Zhang, C., Lai, Z., Zhao, Y. et al. Parametric study and multi-parameter optimization of a generalized second-order tri-stable stochastic resonance system. Nonlinear Dyn 112, 2661–2681 (2024). https://doi.org/10.1007/s11071-023-09211-1

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