Flexible Analytical Wavelet Transform Enhanced Sparse Representation with Nonconvex Penalty and Its Application to Weak Fault Feature Extraction of Rolling Bearings

To address the problem of early-stage weak fault feature extraction of rolling bearings, non-convex penalty enhanced sparse representation method based on flexible analytical wavelet transform is proposed. The flexible analytical wavelet transform possesses tunable time-frequency frame and atom oscillation, and optimal flexible analytical wavelet transform frame is selected to match the impulsive fault feature to be extracted. Further, sparse representation model based on generalized min-max concave penalty is established, in which the non-convex penalty could induce sparsity of the solutions and the optimization function could remain convex. Thus, the forward-backward splitting method is adopted for solving the optimization problem of sparse representation model. The effectiveness of the proposed non-convex penalty enhanced sparse representation method based on flexible analytical wavelet transform is validated via simulated vibration signals, and the results show that the proposed method could extract the weak, impulsive fault signals of rolling bearings from strong background noise with high fidelity