Data-Driven Probabilistic Fault Detection and Identification via Density Flow Matching

Abstract

Fault detection and identification (FDI) is critical for maintaining the safety and reliability of systems subject to actuator and sensor faults. In this paper, the problem of FDI for nonlinear control-affine systems under simultaneous actuator and sensor faults is studied. We model fault signatures through the evolution of the probability density flow along the trajectory and characterize detectability using the 2-Wasserstein metric. In order to introduce quantifiable guarantees for fault detectability based on system parameters and fault magnitudes, we derive upper bounds on the distributional separation between nominal and faulty dynamics. The latter is achieved through a stochastic contraction analysis of probability distributions in the 2-Wasserstein metric. A data-driven FDI method is developed by means of a conditional flow-matching scheme that learns neural vector fields governing density propagation under different fault profiles. To generalize the data-driven FDI method across continuous fault magnitudes, Gaussian bridge interpolation and Feature-wise Linear Modulation (FiLM) conditioning are incorporated. The effectiveness of our proposed method is illustrated on a spacecraft attitude control system, and its performance is compared with an augmented Extended Kalman Filter (EKF) baseline. The results confirm that trajectory-based distributional analysis provides improved discrimination between fault scenarios and enables reliable data-driven FDI with a lower false alarm rate compared with the augmented EKF.