Physics-Enhanced NMF Toward Anomaly Detection in Rotating Mechanical Systems

With the advancements in sensor technology, it is now possible to measure and record a multitude of features that reflect the health condition of complex systems. These measurements are stored in a sizable data matrix, enabling the detection of anomalies. Nevertheless, the presence of this large data matrix poses a significant computational burden. The dimension-reduction methods, such as non-negative matrix factorization (NMF), can efficiently reduce computational burden. However, their pure data-driven nature can lead to overfitting and biases in anomaly detection results. To address this shortcoming, we propose a physics-enhanced NMF (PNMF) method by incorporating physical knowledge into NMF with the help of graph technique. The graph technique organizes measurements and features into two graph objects, respectively, and the physical knowledge guides the formation of edges between nodes in the graph. This allows the PNMF to capture not only the data-driven patterns but also the physical structure inherent in the system. The closed-form update algorithm is developed for the PNMF model, which can guarantee the convergence of parameters estimation. The superior performance of the PNMF model in detecting anomalies is demonstrated by comparing prevailing methods in both public datasets and real-world applications.