Bearing fault signal detection based on non-negative matrix factorization and dual-feedback segmented unsaturated tristable stochastic resonance system

Stochastic resonance is widely used in bearing fault detection due to its ability to enhance weak signals. This paper proposes a fault detection method that combines noise reduction with stochastic resonance. Firstly, a segmented unsaturated potential function based on the classic potential function is constructed, and a dual-feedback structure is introduced to feed the system output back to the input, thereby enhancing system performance. Secondly, the theoretical expressions for the mean first passage time and the spectral amplification of the dual-feedback segmented unsaturated tristable stochastic resonance (DSUTSR) system are derived and analyzed. Additionally, a numerical simulation comparison using the fourth-order Runge–Kutta method is performed between the DSUTSR system and its predecessor systems to verify the improvements brought by the dual-feedback structure. Subsequently, non-negative matrix factorization (NMF) is introduced as a noise reduction method, with cross-validation used to determine the decomposition rank of NMF to guide the decomposition of the fault signal matrix. Finally, the combination of NMF and the DSUTSR system is used to detect bearing fault frequencies under white noise and Lévy noise backgrounds. Experimental results demonstrate the superiority and effectiveness of the proposed method in fault signal detection. This system holds significant potential for future weak signal detection, effectively enhancing and identifying fault signals hidden within noisy backgrounds.