Sparse Optimization Model Based on Sparse Matrix and Singular Value Vector for Fault Diagnosis of Rolling Bearings

The extraction and detection of weak faults of rolling bearings on rotating machinery are essential and crucial. However, traditional methods of Sparse Matrix Optimization have shortcomings of amplitude underestimation. Therefore, we propose a sparse optimization method based on sparse matrix and singular value vector. Due to the intrinsic features of the faulty bearing signals, we extract the sparsity and low-rank property from the matrix of time-frequency diagram. To improve the performance of the detection, we utilize the minimax concave penalty to both the elements and the singular value vector which respectively enhance the reconstruction accuracy of fault signal. Then, the convexity of the model is proved and the selection of the parameters is also discussed. To solve this convex optimization problem, an iterative algorithm based on Alternating Direction Method of Multipliers and Forward and Backward Splitting is adopted to attain the global optimal solution. Synthetic signals and experimental signals are utilized to verify the effectiveness and superiority of proposed method.