Adaptive conditional kernel Bures metric learning for bearing cross-device fault diagnosis under small and unbalanced samples

Abstract To address the prevalent issues of data distribution shift and class imbalance in cross-device bearing fault diagnosis under industrial environments, this paper proposes a novel adaptive conditional kernel Bures (ACKB) metric learning framework. The method aims to learn domain-invariant features by explicitly aligning the conditional distributions of the source and target domains, while adaptively coping with the challenges brought by small and unbalanced data. The three core contributions of this study include: firstly, the design of an adaptive multi-scale kernel fusion mechanism that can automatically learn and integrate kernel functions of different scales, thereby enriching the representation ability of complex fault features; Secondly, a dynamic category aware reweighting strategy is introduced to continuously balance the alignment effects of minority classes and weakly separated classes by evaluating category frequency and feature discrimination; finally, implementing a progressive domain alignment strategy enables the model to smoothly transition from feature extraction to cross domain adaptation during the training phase, ensuring a stable and efficient training process. A comprehensive experiment conducted on six cross device diagnostic tasks covering three types of bearings showed that ACKB can still maintain an average accuracy of 93.12% under severe data imbalance conditions. Its performance is significantly better than existing methods. These results strongly demonstrate that ACKB is a reliable and effective fault diagnosis solution in industrial environments where labeled samples are scarce and unevenly distributed.