Non-Linear System State Analysis via Takagi-Sugeno Fuzzy Modelling

Abstract: The fuzzy and neuro-fuzzy modeling approaches represent extremely powerful tool for non-linear dynamic systems approximation. By using this tool it is possible to overcome difficulties in conventional techniques for dealing with nonlinearity. This paper presents the design of the diagnostic system exploits these fuzzy modeling approximation abilities together with fault detection and isolation algorithm (FDI) to detect the presence of the fault at the system. The idea is based on using a Takagi-Sugeno fuzzy model to describe the non-linear dynamic system by its decomposition onto number of linear submodels. Having these submodels, the Kalman filters are designed for each of the local models to generate the fault indicating signals – residuals. Because of the assumption that the non-linear system under consideration is stochastic, the hypothesis testing technique (Generalized likelihood ratio test) is applied to the residuals along with the fuzzy regression to make a decision whether the system is subjected by the fault or not. The paper also provides the application study of the proposed approach using the three tank system example.