Optimal filtering and robust fault diagnosis of stochastic systems with unknown disturbances

The paper studies the optimal filtering and robust fault diagnosis problems for stochastic systems with unknown disturbances. An optimal observer is proposed, which can produce disturbance decoupled state estimation with minimum variance for time varying systems with both noise and unknown disturbances. The existence conditions and the observer design procedure are presented. The output estimation error with disturbance decoupling and minimum variance properties is used as a residual signal. A statistical testing procedure is applied to examine the residual and is used to diagnose faults. The method developed is applied to an illustrative example, and simulation results show that the optimal observer can give good state estimation; the fault detection approach taken is able to detect faults reliably in the presence of both modelling errors and noise