A fusion non-convex group sparsity difference method and its application in rolling bearing fault diagnosis

Bearing fault is a common factor leading to machine failures. How to extract the periodic transient signal due to bearing faults submerged in strong noise is a challenging problem for bearing fault diagnosis. Total variation denoising is a method used to remove noise and extract features. However, it solely relies on the sparsity of the first-order difference of the signal, resulting in the loss of important features and underestimation of amplitude. Additionally, it fails to capture the periodicity of the signal. To address these issues, a novel approach called fusion non-convex group sparsity difference (FNC-GSD) method is proposed for bearing fault diagnosis. Firstly, it is recognized that noise does not exhibit sparsity in the difference domain, while transient signal exhibits group sparsity in the difference domain. This grouping property enhances the feature selection ability of sparse model. Inspired by this, the group sparsity of the transient signal in the difference domain is used to preserve the fault features as much as possible. Additionally, in order to promote sparsity of the signal itself in the time domain to preserve the potential impulse component, a l 1-norm regularization term is introduced. Furthermore, a non-convex sparsity-inducing penalty function strategy is employed to prevent amplitude underestimation. The proposed sparse model considers both the group sparsity in the difference domain and the sparsity in the time domain of the transient signal, and its solution is derived according to the majorization-minimization algorithm. And the particle swarm optimization algorithm is used to adaptively search the regularization parameters of FNC-GSD. Finally, multiple bearing fault diagnosis experiments are conducted to demonstrate the performance of the FNC-GSD. The results show that it has advantages in fault feature extraction compared with some other methods.