Reweighted generalized minimax-concave sparse regularization and application in machinery fault diagnosis

• Published in: ISA transactions Vol. 105; pp. 320 - 334
• Main Authors: Cai, Gaigai, Wang, Shibin, Chen, Xuefeng, Ye, Junjie, Selesnick, Ivan W.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2020
• Subjects: Generalized minimax-concave penalty; Iterative reweight algorithm; Machinery fault diagnosis; Repetitive transient extraction; Squared envelope spectrum kurtosis; Iterative reweight algorithm; Squared envelope spectrum kurtosis; Generalized minimax-concave penalty; Machinery fault diagnosis; Repetitive transient extraction
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2020.05.043

The vibration signal of faulty rotating machinery tends to be a mixture of repetitive transients, discrete frequency components and noise. How to accurately extract the repetitive transients is a critical issue for machinery fault diagnosis. Inspired by reweighted L1 (ReL1) minimization for sparsity enhancement, a reweighted generalized minimax-concave (ReGMC) sparse regularization method is proposed to extract the repetitive transients. We utilize the generalized minimax-concave (GMC) penalty to regularize the weighted sparse representation model to overcome the underestimation deficiency of L1 norm penalty. Moreover, a new reweight strategy which is different from the reweight strategy in ReL1 for sparsity enhancement is proposed according to the statistical characteristic, i.e., squared envelope spectrum kurtosis. Then ReGMC is proposed by solving a series of weighted GMC minimization problems. ReGMC is utilized to process a simulated signal and the vibration signals of a hot-milling transmission gearbox and a run-to-failure bearing with incipient fault. The ReGMC analysis results and the comparison studies show that ReGMC can effectively extract the repetitive transients while suppressing the discrete frequency components and noise, and behaves better than GMC, improved lasso, and spectral kurtosis. •A reweighted generalized minimax-concave (GMC) sparse regularization method is proposed.•The weight is constructed according to the statistical characteristic of the wavelet coefficients.•GMC penalty is employed to regularize the weighted sparse representation model.•The proposed method has good anti-interference property and anti-noise property.•The proposed method is effective both for the gearbox and the bearing fault diagnosis.