Adaptive two-dimensional coupled bistable stochastic resonance and its application in bearing fault diagnosis

The effective detection of weak fault signals with extremely low signal-to-noise ratios (SNR) remains a critical issue in engineering applications. Traditional one-dimensional stochastic resonance (SR) methods for weak signal detection exhibit limitations in extracting and enhancing feature signals. In this study, an adaptive two-dimensional coupled bistable stochastic resonance (TDCBSR) system is proposed based on the classical bistable SR model to enhance the performance of SR systems. The system can switch flexibly among monostable, bistable, and quad-stable states. The model is utilized to analyze the effects of system parameters and coupling coefficients on the dynamic characteristics of particle transitions. This investigation is conducted from two perspectives: changes in the system structure and variations in the steady-state probability density distribution. It is observed that the controlling subsystem parameters and controlled subsystem parameters can induce the particle in periodic motion between adjacent wells, while the coupling coefficients of the two subsystems can induce the particle in periodic motion between opposite wells, indicating higher flexibility of the TDCBSR system. The BSO algorithm is combined with the two-dimensional coupled bistable stochastic resonance model to achieve multi-parameter adaptive co-optimization, which enables the nonlinear system to detect input noisy signals with even lower SNR. Simulation experiments for weak periodic signal detection under an α-stable noise background, as well as engineering application experiments for bearing fault signal detection, demonstrates that the proposed method effectively detects signals with lower SNR.