Optimization algorithm for bearing fault diagnosis based on composite non-convex sparse constraints and ADMM

In response to the weak early fault signals of rolling bearings and their susceptibility to strong background noise, the research proposes a sparse domain bearing fault diagnosis optimization algorithm based on the alternating direction method of multipliers (ADMM) and composite non-convex constraints. The algorithm framework consists of two core innovation stages. Firstly, in the feature enhancement stage, the lp (0 < p < 1) norm is innovatively combined with the ADMM framework. This method yields sparser solutions compared to the traditional L1 norm—a superiority that is experimentally demonstrated—thereby more effectively enhancing the transient impulse characteristics of fault signals. Secondly, in the fault diagnosis stage, a Laplace wavelet dictionary is constructed that integrates discrete cosine transform (DCT) and composite non-convex regularization, achieving robust extraction and high-precision classification of key fault features. The results on the Case Western Reserve University (CWRU) public dataset showed that the method significantly outperformed baseline models, with an average diagnostic accuracy of 98.0% and an F1-Score of 0.973. Crucially, the method demonstrated strong generalization by maintaining a high accuracy of 95.2% on the more challenging industrial XJTU-SY dataset, a scenario where baseline models faltered. It also exhibited excellent robustness across diverse industrial noise types and superior computational efficiency, proving significantly faster than competing deep learning models. This research delivers an efficient, accurate, and physically interpretable solution, establishing a new and robust paradigm for mechanical fault diagnosis in complex, real-world industrial environments.