Intra and Inter Wavelet-Subband Sparse Model for Bearing Fault Diagnosis

Extracting fault components from heavy noise is one of the key challenges in bearing fault diagnosis. This article proposes an intra and inter wavelet-subband sparse model (I2WSM) that introduces a hierarchical sparsity prior tailored to the distribution character of bearing fault signals. Specifically, intra-subband regularization is constructed based on the oscillatory behavior of fault impulses, while inter-subband regularization is designed according to the resonance band characteristics. These two constraints work collaboratively to enhance feature extraction capability. An optimization algorithm is developed to directly solve the l₀ -constrained optimization problem while preserving signal amplitude. Extensive simulations and two experimental cases based on vibration acceleration sensors were conducted, one with an outer race defect and the other with an inner race defect. Quantitative analysis using the failure characteristic energy ratio (FCER) index demonstrates that the proposed method achieves superior noise suppression and enables more accurate fault impulse extraction compared with conventional wavelet-based sparse denoising methods.