Enhanced sparsity via adaptive period estimation and Lp norm for rolling bearing fault feature extraction

The fault characteristics of rolling bearings are easily obscured by noise. To address the difficulty of extracting early weak faults of bearings, this paper proposes a novel enhanced sparsity via adaptive period estimation and L _p norm (AdaPELP) sparse representation method. First, the L _p norm is added to the periodic overlapping group shrinkage (POGS) model to enhance sparsity. Second, a Gini-Harmonic (GH) indicator based on the combination of the Gini index and the harmonic significance index (HSI) is proposed to evaluate fault characterization and dynamically update the periodic prior estimation. This approach addresses the limitation of the Gini index in distinguishing sparse patterns. Third, this model is solved by the majorization-minimization (MM) algorithm and the solution procedure is given. Meanwhile, GH is applied as the fitness function in the Grey Wolf Optimizer (GWO) algorithm to realize adaptive parameter selection, which addresses the difficulty of manual parameter tuning. The effectiveness of the AdaPELP method in rolling bearing fault feature extraction is verified through simulation and experiments.