Weighted multiscale convolutional sparse representation and its application in rolling bearing compound fault diagnosis

Accurate fault feature extraction is an important part of achieving bearing fault diagnosis. The convolutional sparse representation can characterize the shift-invariant property of features, which is very suitable for rolling bearing fault feature extraction. However, the convolutional sparse representation ignores the periodicity of fault impulse features and the difference of signal characteristics at different scales, which restricts its feature extraction ability under the interference of harmonic components and background noise. Therefore, a weighted multiscale convolutional sparse representation is proposed for separating the periodic fault impulse features in vibration signals to achieve bearing fault diagnosis. Specifically, in the constructed sparse representation model, the original signal is converted to different scales using multiscale transformation, and different weights are utilized in different scales to suppress the interferences such as harmonic components. Meanwhile, to promote fault impulse features, a regularization term that constrains the periodicity of the sparse coefficient of fault features is established to improve fault feature separation ability. In addition, the alternating direction method of multipliers and the majorization-minimization method are introduced to derive an iterative solving algorithm. Finally, by analyzing the waveform and envelope spectrum of extracted features and two quantitative evaluation indicators of fault information, the excellent capability of the proposed method in fault feature extraction and diagnosis of bearing compound faults is verified. © 2024 Science Press. All rights reserved.