Dual-channel two-dimensional stochastic resonance and its application in bearing fault detection under alpha-stable noise

Coupled two-dimensional stochastic resonance (CTDSR) systems exhibit a higher quantity of steady-states and hold significant theoretical and practical value. However, the coupling between nonlinear systems generates multiplicative noise, which impairs signal transmission. In this paper, a novel dual-channel two-dimensional stochastic resonance (DCTDSR) model is proposed to harness multiplicative noise for enhancing system output. It is evident from the potential well analysis that multiplicative noise causes variations in the properties and amounts (from 2 to 4) of resonance peaks in the DCTDSR system. The steady-state probability density (SPD) of the novel system is derived by implementing the adiabatic approximation theory. In the background of alpha-stable noise, simulation results indicate that the DCTDSR system exhibits heightened detection capabilities for weak signals that are immersed in severe impulsive and heavy-tailed noise. Based on the stability of alpha-stable noise, an adaptive stochastic resonance fault diagnosis method that adjusts both parameters and multiplicative noise is designed to overcome the issue of insufficient single energy regulation. Experimental results have demonstrated that the DCTDSR system boosts noise energy transmission and offers improved bearing fault detection accuracy. Thus, effectively utilizing multiplicative alpha-stable noise can further enhance the practical applicability of stochastic resonance theory in engineering.