New Design of Robust Kalman Filters for Fault Detection and Isolation

Abstract

The results obtained recently using the reduced order observer (Koenig, 1998) are derived to obtain a fault detection and isolation (FDI) algorithm applicable to uncertain stochastic linearly discrete-time systems. The approach consists of decomposing the original system into several sub-systems, each being sensitive to a sub-set of faults defined beforehand, whilst remaining insensitive to the unknown inputs and other faults. Thereby the problem is reduced as the substate estimation of an unknown inputs-free reduced system (stochastic), which can be easily dealt with following the well-known Kalman filter theory (Graham, et al., 1984; Mehra, and Peschon, 1971). An extension of the chi-square test is proposed for FDI in dynamic systems with unknown inputs. A straightforward algorithm is developed, and the necessary and sufficient conditions for the convergence and stability of filters are established. The method developed has been applied to an illustrative example which shows that the optimal filters can give an excellent state and fault estimation with minimum variance.