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

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.