A Reweighted Overlapping Group Shrinkage Method for Bearing Fault Diagnosis

Abstract

Sparse regularization has received widespread attention in bearing fault diagnosis as it overcomes the limitation of the artificially constructed dictionary. However, the amplitude underestimation caused by different penalty functions reduces the precision of extracted fault features. To handle this difficulty, a Reweighted Overlapping Group Shrinkage (R-OGS) method for bearing fault diagnosis is proposed in this paper. The group property of the fault signal and the amplitude underestimation problem are considered simultaneously. A novel group weighting coefficient based on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm of the group is designed to mitigate the amplitude compression caused by the group penalty. Although a non-convex penalty function is used to improve the performance, the cost function can be convex with appropriate parameter selection. The convexity condition is given and the solution algorithm is derived based on the Majorization-Minimization (MM) algorithm. The setting strategy of the group size and the regularization parameter is given after in-depth analysis. Numerical simulation shows that the R-OGS method has stronger amplitude retention of fault feature signal and noise suppression capability than previous Overlapping Group Shrinkage (OGS). The bearing fault experiment signals verify that the proposed R-OGS method has superior performance in fault feature extraction compared to the Moreau-enhanced Total Variation Denoising (MTVD) and the Fast Kurtogram (FSK).