Learning criteria of normalized regressor-based adaptive observer for actuator fault diagnosis of disturbed systems

Fault detection and diagnosis in dynamic systems are crucial for ensuring reliable performance, especially in complex industrial processes, intelligent vehicles, and large-scale systems. This paper presents an adaptive observer-based fault detection and diagnosis method for a class of multiple-input multiple-output linear dynamic systems subject to disturbances. Specifically, a novel output feedback fault detection scheme is proposed for systems with immeasurable states, which provides accurate alarm signals when actuator faults occur, and ensures that the state error of the detector converges to zero as faults vanish. An adaptive diagnosis observer is also designed, incorporating a new learning criterion for fault estimation, independent of the fault detector, and ensuring globally Lipschitz continuous fault estimations, even with unbounded control input regressors. Rigorous conditions are derived to guarantee the convergence of fault estimations. The robustness of the proposed method is analyzed, showing how the effects of disturbances can be mitigated by appropriate parameter selection. A principle for setting a minimum threshold in the fault detector is also provided to prevent false alarms for external disturbances. Simulation results are included to validate the effectiveness of the proposed approach, demonstrating its practical utility in fault diagnosis for dynamics systems.