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

Gaigai Cai, Shibin Wang, Xuefeng Chen, Junjie Ye, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)320-334
Number of pages15
JournalISA Transactions
StatePublished - Oct 2020


  • Generalized minimax-concave penalty
  • Iterative reweight algorithm
  • Machinery fault diagnosis
  • Repetitive transient extraction
  • Squared envelope spectrum kurtosis

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Instrumentation
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


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