Long-tailed multi-domain generalization for fault diagnosis of rotating machinery under variable operating conditions

As the operating conditions (also known as domains) of rotating machinery become increasingly diverse, fault diagnosis has garnered growing attention. However, fault diagnosis frequently encounters challenges such as long-tailed data distributions, domain shifts in monitoring data, and the unavailability of target-domain data. Existing approaches can only address some of these challenges, limiting their applications. To address these challenges concurrently, we introduce a novel learning paradigm called long-tailed multi-domain generalized fault diagnosis (LMGFD) and propose a two-stage learning framework for LMGFD, comprising domain-invariant feature learning and balanced classifier learning. In the first stage, we leverage a balanced multi-order moment matching (BMMM) module to align subdomains with long-tailed distributions. Additionally, a balanced prototypical supervised contrastive (BPSC) module is developed to effectively alleviate the contrastive imbalance. The combination of BMMM and BPSC enables the effective learning of long-tailed domain-invariant features. In the second stage, we extend the focal loss to a multi-class version and re-weight it using effective sample numbers to strengthen tailed-class loss, thereby mitigating the overfitting problem. Experimental results on both a public dataset and a private dataset support the competitiveness and effectiveness of the proposed method. The findings suggest that we present a promising solution for fault diagnosis of rotating machinery under variable operating conditions.