Physics-Enhanced Fault Detection Framework for Nonlinear Distributed Parameter Systems Under Limited Sensor Data

Fault detection in distributed parameter systems (DPSs) is crucial for ensuring the reliability and safety of industrial processes. However, DPSs are governed by complex nonlinear partial differential equations (PDEs), making full-state measurement impractical, particularly in scenarios with limited sensor availability. Traditional methods often struggle to achieve accurate fault detection under such conditions. This paper proposes a novel physics-enhanced fault detection framework to monitor state variables and capture spatiotemporal nonlinearities in DPSs under limited sensing. First, a physics-enhanced neural network is developed to model the system dynamics. This method integrates system spatiotemporal patterns with machine learning techniques, enabling the framework to extract meaningful representations from available data while maintaining consistency with physical laws. Then, temporal variation features are extracted from the estimated state variables and used to construct a dynamic temporal graph representation, which captures intrinsic temporal correlations to improve early fault detection. Experimental evaluations on nonlinear DPS applications demonstrate that the proposed framework outperforms conventional methods in both the effectiveness (fault detection rate, FDR) and robustness (false alarm rate, FAR).