Adaptive detection of impact signals with two-dimensional piecewise tri-stable stochastic resonance and its application in bearing fault diagnosis

In this paper, we introduce an innovative method known as Adaptive Two-Dimensional Piecewise Tri-Stable Stochastic Resonance (TDPTSR) and discuss its applicability in extracting weak fault features. Initially, addressing the saturation issue of the Standard Tri-Stable Stochastic Resonance (STSR) system, we construct a novel piecewise tri-stable potential function. This function independently adjusts the depth and width of potential wells. We explore the particle output characteristics of the Piecewise Tri-Stable Stochastic Resonance (PTSR) system using the fourth-order Runge-Kutta algorithm. Subsequently, we delve into the performance analysis of the TDPTSR system. Leveraging adiabatic approximation theory, we derive the equivalent potential function, steady-state probability density (SPD), mean first-pass time (MFPT), and output signal-to-noise ratio (SNR) of the TDPTSR. We also investigate the impact of changes in system parameters on these metrics. Additionally, drawing from kurtosis and cosine similarity properties, we introduce a Modified Kurtosis Index (MKC) as a measurement index for impact signal detection. We propose a method for impact signal feature extraction by integrating MKC with the TDPTSR system. Simulation analysis demonstrates the suitability of MKC as an index for quantifying Stochastic Resonance and the superior detection capability of the TDPTSR system. Finally, we apply TDPTSR to the fault diagnosis of two types of bearings, optimizing system parameters using a genetic algorithm (GA). Comparative analysis with STSR and PTSR confirms that our proposed method in this paper yields further improvements in Signal-to-Noise Ratio Improvement (SNRI), higher spectral peak magnitude (Amout) at characteristic frequencies, and increased recognition quantity (Delta).