T-S fuzzy modeling for predicting chaotic time series based on unscented Kalman filter approach

This paper presents a hybrid approach to fully train T-S model for predicting chaotic time series. The approach consists of a sequence of steps aiming at developing a optimal fuzzy model structure. In a first step, fuzzy c-means (FCM) and least squares (LS) techniques are used to derive initial parameters of membership functions and consequent part of the fuzzy model. In a second step, unscented Kalman filter (UKF) parameter estimation is employed to tune those parameters of the constructed fuzzy model in order to obtain a more precise fuzzy model from the given input-output data. Finally, the number of fuzzy rules is determined by iterative implementation of the first two steps. A classical Lorenz chaotic time series is used to illustrate the effectiveness of the proposed approach.