Fuzzy Kalman observer for fault detection in nonlinear discrete systems based on type-2 fuzzy logic

Abstract

This paper presents an approach to design a fuzzy augmented state Kalman observer based on interval type-2 fuzzy logic for state estimation and fault detection in nonlinear stochastic systems. The main idea consists of combining interval type-2 Takagi-Sugeno-Kang (IT2 TSK) fuzzy model with the Kalman filter theory. The IT2 TSK fuzzy model presents an extension of the type-1 TSK fuzzy logic systems. It can well approximate the nonlinear system by its decomposition into a number of linear submodels using interval type-2 fuzzy sets that provide additional degrees of freedom and offer the capability to directly handle uncertainties. At each local linear model of the IT2 TSK fuzzy model, Kalman filter equations are used to develop an interval type-2 fuzzy augmented state Kalman observer (IT2 FASKO). The performance of The IT2 FASKO is compared with the traditional fuzzy Kalman filter to estimate both faults and faulty system states. Single and multiple actuator faults are considered. The simulation results performed on three tank systems illustrate the effectiveness of the proposed approach.