Matching Parameter Design for Second-Order Stochastic Resonance

Stochastic resonance is a signal processing approach that converts noise energy to signal, enhancing the signal-to-noise ratio (SNR). Compared to classical stochastic resonance, second-order stochastic resonance (SSR) based on second-order nonlinear systems can achieve higher noise utilization. This research examines a normalized SSR system model with a bistable potential function. By solving the Fokker-Planck equation for the SSR system, the steady-state solution of the probability density function is found. The system’s Kramers escape rate and response characteristics are also examined using the two-state theory. The SNR of the system’s output is obtained according to the linear response theory. Then, a design method for the structural parameters that maximize the output SNR is given. Finally, the designed SSR system is applied to bearing fault diagnosis to verify the method’s effectiveness.