An extraction method for early fault features of rolling bearings based on resonance sparse signal decomposition and non-convex second-order total variation denoising

A primary challenge in the field of fault diagnosis is extracting weak fault characteristics of bearings under large background noise and non-stationary conditions. Due to significant noise interference in the signals of rolling bearings, resonance sparse signal decomposition (RSSD) cannot efficiently extract the transient impact components in the early failure stage and the total variation denoising (TVD) method distorts signal waveforms. In this study, a combined extraction method for early fault features of rolling bearings based on RSSD and non-convex second-order total variation denoising (NCSOTVD) is proposed. Firstly, a non-convex function is introduced to define the regularisation term in the second-order TVD method, and the regularisation parameter and the convexity parameter in the NCSOTVD method are respectively screened using the noise standard deviation and the permutation entropy value to enhance the impact characteristics of signals and induce signal sparsity. The NCSOTVD model is solved using the optimisation-minimisation algorithm, so as to achieve noise reduction and feature enhancement of the vibration signals. Then, the low-resonance components of RSSD are denoised using the NCSOTVD method to highlight periodic pulse signals and extract the fault features of the rolling bearings. The simulation results and experimental data show that the method largely suppresses the noise interference, highlights the fault characteristics and reduces the problems of waveform distortion and poor sparsity of the TVD method in the denoising process.