Noise-Robust Bearing Fault Diagnosis via Soft-VMD and Hierarchical Feature Fusion

To address information loss and imbalanced feature contributions in bearing fault diagnosis under strong noise and limited training samples, this paper proposes a diagnostic method combining modal soft-suppression reconstruction (Soft-VMD) with discriminative-ability-driven hierarchical soft weighting. Following standard variational mode decomposition (VMD), Soft-VMD retains suppressed modes with small nonzero weights, providing continuous adjustment between noise suppression and information utilization. Hierarchical soft weighting uses bootstrap-averaged Fisher estimates from training source recordings to jointly adjust the scale contributions of refined composite multiscale fluctuation-based dispersion entropy (RCMFDE) and the distance contributions of different feature domains, together with grouped parameter selection within the training set and global distance normalization. In recording-disjoint Paderborn experiments, four conditions were classified: healthy, artificially induced outer-race damage, combined inner- and outer-race damage caused by real fatigue, and artificially induced inner-race damage, using 10, 20, and 30 training windows per class, respectively. Soft-VMD improved mean accuracy over fixed hard truncation under six white-noise conditions; full hierarchical weighting improved performance over unweighted features in three small-sample scenarios. All these comparisons remained significant after Holm correction within their respective exploratory testing families. Experiments with synthetic pink noise further demonstrated the improvement of soft reconstruction over hard truncation, while both the pink-noise and CWRU leave-one-load-out experiments supported the performance gains of full weighting over unweighted features. The findings support soft reconstruction over fixed hard truncation in the Paderborn white- and pink-noise experiments, and full hierarchical weighting over unweighted features in the evaluated Paderborn and CWRU settings, providing a useful approach to diagnosis with limited training samples under these experimental conditions.