Koopman-based Anomaly Detection for Industrial Processes under Non-stationary Dynamics

Detecting anomalies in industrial processes is crucial for ensuring the safety and reliability of complex industrial systems. However, the prominent non-stationary characteristics in real industrial processes, such as multi-scale variations and rapid dynamic changes, present significant challenges for time-series anomaly detection. To address this issue, we propose a novel anomaly detection method specifically designed for complex industrial processes under non-stationary dynamics, using the Koopman high-dimensional space prediction model. Initially, non-stationary time series data is decomposed into time-variant and time-invariant components through Fourier decomposition, and a specialized neural Koopman operator is employed to model and predict each component. Subsequently, a squared prediction error (SPE) control limit is established based on normal data and dynamically updated under new operating conditions using KL divergence, enabling real-time anomaly detection by comparing the real-time SPE values against the updated control limits. Experimental results on the SKAB dataset demonstrate that the proposed method significantly outperforms various traditional techniques in detection performance, highlighting its effectiveness and adaptability in industrial anomaly detection applications.