State and fault estimation based on interval type-2 fuzzy inference system optimised by genetic algorithms

Abstract

In this paper, an optimisation method is proposed for state and fault estimation in a non-linear system that is described by interval type-2 fuzzy model. The method concerns the development of an optimised interval type-2 fuzzy Kalman observer (IT2 FKO). At each fuzzy rule, a local fuzzy observer is associated. As the main advantage is to obtain an unbiased estimation, the membership functions (MFs) parameters of IT2 fuzzy logic system were adjusted using genetic algorithms (GAs). These MFs are interval type-2 fuzzy sets which represent an extension version of typical type-1 fuzzy sets and provide additional degrees of freedom to directly handle uncertainties and external disturbances. To illustrate the performance of the developed observer, comparison with an IT2 FKO before tuning their MFs parameters and an optimised type-1 fuzzy Kalman observer is performed on a three-tank system for estimating their states under faults. Simulation results demonstrate the superiority of the proposed approach in spite of the presence of faults.