The characteristic analysis of stochastic resonance in a time polo-delayed tristable system and its application

Abstract

In the existing studies of stochastic resonance (SR) in time-delayed tristable systems, scholars have mainly studied the effect of time global delay on the system. Therefore, a time polo-delayed tristable system is studied in this paper. First, by using the small delay approximation method, the effective potential function Ueffx and steady-state probability density (SPD) are obtained. The influence of system parameters a, b, c, and time-delayed parameter τ on Ueffx is analyzed. The SPD plays an essential role in the research of particle motion state, and the effects of different system parameters on it are also analyzed by simulation. Then, by adiabatic approximation theory, the signal-to-noise ratio (SNR) is derived. The resonance characteristics of the time polo-delayed tristable stochastic resonance (TPTSR) system are studied by SNR. The simulation results show that the SNR is non-monotonic and SR can occur by adjusting the parameters. Finally, the TPTSR system is used to weak characteristic signal extraction and bearing fault diagnosis, and is compared with the high-order time-delayed feedback tristable stochastic resonance (HTFTSR) system. The results show that the weak signal can be detected and the failure frequency can be identified. In addition, the TPTSR system is better than the HTFTSR system in fault diagnosis, which shows that the system has important value in practical engineering applications.

Keywords

• Time polo-delayed
• Tristable system
• Stochastic resonance
• Bearing fault diagnosis