Abstract: Localized faults in rotating machinery parts tend to result in transient impulse responses in the vibration signal and thus present a potential approach for fault feature extraction. Sparse representation is one of the effective methods for weak feature extraction. A method incorporating Laplace wavelet basis function into sparse representation theory is proposed and applied to identify weak features of bearing fault. With the matched basis function by correlation filtering, the split augmented Lagrangian shrinkage algorithm is introduced to solve the basis pursuit denoising (BPD) problem. The transient impulse responses can be intuitively represented in the sparse coefficients. Both the simulation study and the real applications of rolling bearings with weak fault demonstrate that the weak transients can be effectively obtained through the proposed method.

Key words: basis function, bearing fault diagnosis, feature extraction, Laplace wavelet, sparse representation