Bearing Fault Diagnosis Using Hyper-Laplacian Priors and Non-convex Optimization

Bearing fault diagnosis is one of the most important topics in the condition-based maintenance and is also a challenging problem because of the heavy noise interference. Sparse representation methods have been proven effective to solve such a challenging problem, especially through L1 norm regularization (Laplacian). In this paper, we analyze the sparse signal model deeply in the Bayesian aspect and conclude that the distribution of the wavelet coefficients (transforming by TQWT) is well modeled by a hyper-Laplacian. However, such a prior makes the optimization problem non-convex. We adopt an effective algorithm called the generalized shrinkage algorithm (GISA) to solve this non-convex problem. Furthermore, we use the k-sparsity strategy to replace the regularization parameter for adaptivity. Finally, a simulation study and a bearing fault experiment demonstrate the performance of the proposed GISA with k-sparsity, and the comparison study shows that the hyper-Laplacian distribution can estimate the bearing fault information more accurately than the Laplacian distribution.