Cai Gaigai, Wang Shibin, Chen Xuefeng, Ye Junjie, Selesnick Ivan W
Key Laboratory of Ministry of Education for Electronic Equipment Structure Design, Xidian University, Xi'an, 710071, PR China; Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, NY 11201, USA.
State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China; Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, NY 11201, USA.
ISA Trans. 2020 Oct;105:320-334. doi: 10.1016/j.isatra.2020.05.043. Epub 2020 May 27.
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.
故障旋转机械的振动信号往往是重复瞬态、离散频率成分和噪声的混合。如何准确提取重复瞬态是机械故障诊断的关键问题。受用于增强稀疏性的重加权L1（ReL1）最小化启发，提出了一种重加权广义极小极大凹（ReGMC）稀疏正则化方法来提取重复瞬态。我们利用广义极小极大凹（GMC）罚函数对加权稀疏表示模型进行正则化，以克服L1范数罚函数的低估缺陷。此外，根据统计特征，即平方包络谱峭度，提出了一种不同于ReL1中用于增强稀疏性的重加权策略。然后通过求解一系列加权GMC最小化问题提出了ReGMC。利用ReGMC对模拟信号以及具有早期故障的热铣削传动变速箱和加速寿命试验轴承的振动信号进行处理。ReGMC分析结果和对比研究表明，ReGMC能够有效提取重复瞬态，同时抑制离散频率成分和噪声，并比GMC、改进的套索和谱峭度表现更好。
