Interpolative Bayesian Formulation to Improve Transfer Learning for Anomaly Detection in Rotating Machinery

Anomaly detection in rotating machinery is vital for maintaining industrial reliability, safety, and operational efficiency. However, developing accurate anomaly detection systems remains a significant challenge, particularly in scenarios where labeled anomalous data are limited or entirely absent during training. To address this issue, prior work introduced a transfer learning framework that estimates a key order---a weight vector over features that prioritizes certain dimensions in the anomaly scoring process---from a source domain and applies it to a target domain lacking any anomalous labels. In this study, we extend that framework to more complex and realistic scenarios where the target domain contains a limited number of known anomalous samples. Our enhanced approach estimates the key order within the target domain and integrates it with the source domain’s key order through both Bayesian-based and heuristic methods. We demonstrate that in scenarios with very limited anomalous data in the target, Bayesian-based methods for combining source and target key orders are prone to inaccuracies in estimating the variance of the target key order, leading to suboptimal performance. To mitigate this limitation, we propose a weighted linear combination strategy that improves robustness in regimes with extremely few anomalies. In contrast, when abundant anomalous data are available, the Bayesian-based approach remains preferable due to its capacity to model uncertainty more effectively. Furthermore, we introduce a heuristic based on the Kullback–Leibler (KL) divergence for source domain selection when the optimal source-target pairing is not known \textit{a priori}. Comprehensive experiments conducted on several benchmark datasets for rotating machinery validate the effectiveness of our approach. Results indicate that our proposed method of combining source and target key orders consistently outperforms source-only and target-only key orders across varying levels of anomaly availability. This work underscores the critical role of uncertainty-aware transfer learning and adaptive integration strategies in advancing anomaly detection capabilities in industrial settings characterized by scarce labeling.