Physical effects of stochastic resonance in unsaturated Gaussian potential field and weak fault signal extraction

Abstract The fault features of rolling bearings in a time-varying rotational speed condition are often submerged in strong noise. In this paper, to address the issue that traditional stochastic resonance systems’ physical effects struggle to accurately extract weak fault features from strong noise backgrounds, an asymmetric unsaturated Gaussian stochastic resonance (AUGSR) mathematical model is proposed. The AUGSR model innovatively adopts a Gaussian decay function to construct an asymmetric term, whose core advantage lies in its simultaneous possession of functional global smoothness and strong localized decay. This combination ensures that the potential function remains continuously differentiable, physically realizable, and numerically stable, realizing the unsaturated nature of the model and thus breaking through the limitations of traditional symmetric models. First, the Signal-to-Noise Ratio (SNR) is utilized as an evaluation index for the stochastic resonance effect, and the Particle Swarm Optimization (PSO) algorithm is employed to optimize the model parameters, thereby verifying the accuracy of the AUGSR model. Next, for scenarios where SNR calculation requires a priori knowledge of the fault frequency, the Mainband Energy Ratio (MER) is proposed as an alternative evaluation index. The Hybrid Genetic Algorithm and Particle Swarm Optimization (HGAPSO) algorithm is employed to optimize the parameters under time-varying rotational speeds, which verifies the general applicability of the AUGSR model in fault feature extraction and the effectiveness of the MER index. Experimental results on rolling bearings confirm the superiority of the proposed mathematical model over conventional stochastic resonance systems.