A New Family of Model-Based Impulsive Wavelets and Their Sparse Representation for Rolling Bearing Fault Diagnosis

• Published in: IEEE transactions on industrial electronics (1982) Vol. 65; no. 3; pp. 2716 - 2726
• Main Author: Qin, Yi
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-03-2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Background noise; Computational geometry; Computer simulation; Convex optimization; Convexity; dictionary; fault detection; Fault diagnosis; Feature extraction; Harmonic analysis; Impulses; inverse wavelet transform; Iterative methods; iterative shrinking algorithm; Kurtosis; Matching pursuit algorithms; Optimization; Representations; Roller bearings; Rolling bearings; Shrinkage; Simulated annealing; Transient analysis; Vibrations; Wavelet analysis; Wavelet transforms; weak impulsive feature extraction
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2017.2736510

The localized faults of rolling bearings can be diagnosed by the extraction of the impulsive feature. However, the approximately periodic impulses may be submerged in strong interferences generated by other components and the background noise. To address this issue, this paper explores a new impulsive feature extraction method based on the sparse representation. According to the vibration model of an impulse generated by the bearing fault, a novel impulsive wavelet is constructed, which satisfies the admissibility condition. As a result, this family of model-based impulsive wavelets can form a Parseval frame. With the model-based impulsive wavelet basis and Fourier basis, a convex optimization problem is formulated to extract the repetitive impulses. Based on the splitting idea, an iterative thresholding shrinkage algorithm is proposed to solve this problem, and it has a fast convergence rate. Via the simulated signal and real vibration signals with bearing fault information, the performance of the proposed approach for repetitive impulsive feature extraction is validated and compared with the noted spectral kurtosis method, the optimized spectral kurtosis method based on simulated annealing, and the resonance-based signal decomposition method. The results demonstrate its advantage and superiority in weak repetitive transient feature extraction.