Fault detection and isolation based on robust Kalman filter for discrete-time systems with stochastic and norm-bounded uncertainties

This paper deals with the problem of fault detection and isolation for discrete time-varying systems with stochastic and bounded uncertainties, and in presence of noises in the plant and sensors. Faults can occur simultaneously or sequentially, so the designed filter has the ability to detect and isolate these faults, and handle the challenges posed by uncertainty and the effects of noises. In solving the problem of fault diagnosis, fault detection and isolation filter based on the robust Kalman filter are presented. For this purpose, a time-varying threshold is defined based on the upper bound of covariance of the residuals. This threshold helps in better performance and prevents misdiagnosis. In the design of the fault detector, due to the number of outputs, fault detectors are designed. Moreover, by examining the residuals of the system, some conditions are obtained, which, by applying these conditions, a robust fault isolator is achieved. Finally, using three examples, the efficiency and performance of the proposed method are shown. In the first example, the performance of the proposed method is studied in the presence of uncertainty and noise, and in the second and third examples, the performance of the method is compared with other methods and the superiority of the proposed approach in the presence of uncertainties is shown.