The Periodic Overlapping Group Sparsity: A Promising Technique for Extracting Sparse Fault Features in Rotating Machines

This paper introduces the periodic overlapping group sparsity (POGS) method, which is an effective tool for detecting faults in rotating machines. The POGS can estimate periodic-group-sparse features from measured noisy signals. Firstly, this paper presents the formulation of the optimization problem in the POGS method. Then, the derivation of the convexity conditions is introduced. Thus, the total cost function of the optimization problem formulated in the POGS method is guaranteed to be convex, while sparsity are maximally promoted using the non-convex regularization. Finally, a fast iterative algorithm is provided for its optimal solution. The effectiveness of the POGS is validated by analyzing numerical signals and experimental data.