Few-Shot Cross-Domain Fault Diagnosis via Wavelet Convolution Embedding and BDC-Based Metric Meta-Learning

Few-shot cross-domain bearing fault diagnosis is challenging because labeled fault samples are limited and signals collected by vibration sensors under different operating conditions often show significant distribution shifts. To improve bearing fault identification under limited-sample and cross-condition scenarios, this paper proposes a wavelet convolution (WC) and Brownian distance covariance (BDC)-based metric meta-learning framework, termed WCBDC. In this framework, the WC is inserted into the feature extraction process to capture multiscale time-frequency information from vibration signals. The BDC is then applied to model nonlinear inter-channel statistical dependencies and improve the discriminability of fault embeddings. The obtained feature embeddings are further organized within a prototypical-network-based classifier, in which category prototypes are estimated from support samples and query instances are assigned by prototype-distance comparison. The proposed method is evaluated on the Paderborn University (PU) and Beijing Jiaotong University (BJTU) bearing datasets under both 5-way 5-shot and 5-way 1-shot scenarios. On the PU dataset, WCBDC reaches average accuracies of 92.19% and 84.13%, while the corresponding results on the BJTU dataset are 77.24% and 62.57%. These results exceed those of representative meta-learning baselines, demonstrating that WCBDC provides improved diagnostic performance for sensor-based bearing fault recognition when labeled samples are scarce and operating conditions vary.