Abstract:Aiming at the problem of less research on stochastic resonance (SR) in twodimensional potential field, the SR mechanism and application of twodimensional tetrastable potential system (TTPS) under the combined action of Gaussian white noise and external weak driving force are discussed. According to the linear response theory, the probability flow method is used to calculate the spectral amplification factor (SAF) of the TTPS to external periodic driving frequency. The theoretical analysis result shows that when the SAF is used as an indicator, a significant SR phenomenon will occur in the TTPS. The SAF can be further improved by increasing the coupling coefficient and asymmetry coefficient or lowering the driving frequency. Then, combining the Chambers MalllowaStuck algorithm and fourthorder RungeKutta method, using the optimization parameters of genetic algorithm (GA), the TTPS is applied to weak periodic signal detection and bearing fault diagnosis, and compared with the new onedimensional tristable potential system (NOTPS). The experiment results prove the correctness of the theoretical analysis conclusion, and indicate that the TTPS can effectively detect the weak periodic signal and diagnose the faults of the inner and outer rings of the bearings. The amplitudes at the fault frequencies of the two bearing inner rings can be increased to 4195 and 2971 with TTPS, respectively, while those can only be increased to 2506 and 1034 with NOTPS, respectively. The amplitudes at the fault frequencies of the two bearing outer rings can be increased to 4087 and 3429 with TTPS, respectively, while those can only be increased to 2693 and 1866 with NOTPS, respectively, which proves that the performance of the TTPS is better than that of NOTPS.