Design and Application of Weak Signal Detection Method Based on the Four-Dimensional Bistable Stochastic Resonance System

Classical low-dimensional stochastic resonance (SR) systems often exhibit limitations in complex engineering signal processing due to their restricted output channels and narrow parameter tunability. Building upon existing research on multi-dimensional SR, this paper constructs a four-dimensional bistable stochastic resonance system. By establishing inter-dimensional coupling relationships, the system achieves multi-channel parallel output and coordinated resonance responses. The dynamical behavior of the system is analyzed, with its equilibrium points and stability criteria derived. Moreover, the effect of input amplitude on the system's dynamical response is investigated across different types of signals. Furthermore, to alleviate the frequency limitations imposed by the adiabatic approximation in conventional SR, a time-scale transformation method is applied. By adjusting the sampling frequency and integration step size, this technique is utilized to broaden the applicable frequency range of the multi-dimensional system. Case studies on image restoration and mechanical bearing fault diagnosis demonstrate that the proposed 4DSR system can effectively extract weak signal features under strong background noise, indicating its promising application potential in relevant weak signal detection tasks.