Theoretical and Numerical Analyses and Application of Novel Underdamped Tri-Stable Stochastic Resonances under Symmetric Trichotomous Noise

Abstract

In this paper, a novel underdamped tri-stable stochastic resonance (NUTSR) is presented in order to overcome the low out-performance of weak signal reinforcement in the classical tri-stable stochastic resonance (CTSR). The two systems are compared using the input and output amplitude as a measure when noiseless. NUTSR improves the output saturation characteristics and has more outstanding signal enhancement capability. In the background of Gaussian noise, the expressions of mean first-pass time (MFPT), steady-state probability density (SPD) and signal-to-noise ratio (SNR) are derived. The fourth-order Runge–Kutta algorithm and genetic algorithm (GA) is used for numerical simulations. Then the numerical simulation results of the two systems are compared comprehensively, and the theoretical deduction and numerical simulation results of NUTSR are also compared. Moreover, the two systems are applied in two bearing fault types of 6205-2RS JEM SKF and HRB 6205-2Z. Finally, the feasibility of NUTSR is verified under different noise, which is simulated numerically under symmetric trichotomous that NUTSR has better noise immunity and the increase in signal amplitude is more pronounced.