A Novel Fault Diagnosis Method for Rolling Bearing Based on Improved Sparse Regularization via Convex Optimization

Structural health monitoring and fault state identification of key components, such as rolling bearing, located in the mechanical main drive system, have a vital significance. The acquired fault signal of rolling bearing always presents the obvious nonlinear and nonstationary characteristics. Moreover, the concerned features are submerged in strong background noise. To handle this difficulty, a novel fault signal denoising scheme based on improved sparse regularization via convex optimization is proposed to extract the fault feature of rolling bearing. In this paper, the generalized minimax-concave (GMC) penalty is firstly researched to promote the sparsity of signal, which is based on traditional L1-norm and Huber function. It is designed to estimate the sparse solutions more accurately and maintain the convexity of the cost function. Then, the GMC penalty is extended to 1-D first-order total variation (TV) as nonseparability and nonconvex regularizer. Thus, a convex optimization problem, which involves a quadratic data fidelity term and a convex regularization term, is developed in this paper. To accelerate the convergence of the algorithm, it is solved by forward-backward (FB) iterative algorithm and thus the denoised signal can be obtained. In order to demonstrate its performance, the proposed method is illustrated for numerical simulation signal and applied in the feature extraction of the measured rolling bearing vibration signal.