  This paper addresses the problem of noise reduction with simultaneous
components extrac- tion in vibration signals for faults diagnosis of bearing.
The observed vibration signal is modeled as a summation of two components
contaminated by noise, and each component composes of repetitive transients. To
extract the two components simultaneously, an approach by solving an
optimization problem is proposed in this paper. The problem adopts convex
sparsity-based regularization scheme for decomposition, and non-convex
regularization is used to further promote the sparsity but preserving the
global convexity. A synthetic example is presented to illustrate the
performance of the proposed approach for repetitive feature extraction. The
performance and effectiveness of the proposed method are further demonstrated
by applying to compound faults and single fault diagnosis of a locomotive
bearing. The results show the proposed approach can effectively extract the
features of outer and inner race defects.
