Two combination methods of piecewise unsaturated tri-stable stochastic resonance system and bearing fault detection under different noise

Abstract

In this paper, a piecewise unsaturated tri-stable stochastic resonance (PUTSR) system is proposed to address the issue of output saturation. Firstly, the unsaturated characteristics of the PUTSR system are verified, followed by a discussion on the system performance of PUTSR under two different combinations of coupled and cascaded systems. The two-dimensional coupled piecewise unsaturated tri-stable stochastic resonance (TCPUTSR) system and cascaded piecewise unsaturated tri-stable stochastic resonance (CPUTSR) system are proposed. By implementing the adiabatic approximation theory, the steady-state probability density (SPD) of TCPUTSR system and spectral amplification (SA) coefficient of TCPUTSR and CPUTSR systems are derived respectively. The impact of different system parameters on the SPD and SA are also investigated. Finally, PUTSR, TCPUTSR and CPUTSR systems are applied to detection on the fault signal of bearing. Gaussian white noise and color noise are used to simulate actual noise environments in the experiments, while the adaptive genetic algorithm (AGA) is used to optimize the parameters and measure the system performance via signal-to-noise ratio improvement (SNRI). Results indicate that both coupled and cascaded systems demonstrate better detection capabilities than individual systems, with the CPUTSR system offering better enhancement and detection of bearing fault signals. Under Gaussian white noise, the SNRI of the CPUTSR system is 1.449 dB ~ 3.198 dB higher than that of the PUTSR and TCPUTSR systems, while under color noise it is 1.566 dB ~ 2.849 dB higher. This paper mainly compares the spectral amplification capability and fault signal detection capability of the same system under two different combinations of coupled and cascaded. The theoretical and numerical simulations further verify that the designed cascaded system outperforms the coupled system and proves the great superiority of CPUTSR system. These findings provide crucial theoretical support and practical application prospects for engineering purposes.