Adaptive multiscale wavelet-guided periodic sparse representation for bearing incipient fault feature extraction

Currently, accurately extracting early-stage bearing incipient fault features is urgent and challenging. This paper introduces a novel method called adaptive multiscale wavelet-guided periodic sparse representation (AMWPSR) to address this issue. For the first time, the dual-tree complex wavelet transform is applied to construct the linear transformation for the AMWPSR model. This transform offers superior shift invariance and minimizes spectrum aliasing. By integrating this linear transformation with the generalized minimax concave penalty term, a new sparse representation model is developed to recover faulty impulse components from heavily disturbed vibration signals. During each iteration of the AMWPSR process, the impulse periods of sparse signals are adaptively estimated, and the periodicity of the latest sparse signal is augmented using the final estimated period. Simulation studies demonstrate that AMWPSR can effectively estimate periodic impulses even in noisy environments, demonstrating greater accuracy and robustness in recovering faulty impulse components than existing techniques. Further validation through research on two sets of bearing life cycle data shows that AMWPSR delivers superior fault diagnosis results.