Regulated Kalman filter based training of an interval type-2 fuzzy system and its evaluation

Abstract

Most industrial systems are non-linear and prone to different sources of uncertainties. Accordingly, data generated by these systems for their model development can contain noise and outliers, which consecutively affect the approximation accuracy of their models. Hence, there is a need to use robust approaches, such as fuzzy systems. The type-2 fuzzy system is characterized by a foot print of uncertainty (FOU), which enables it to handle the impreciseness in non-linear systems. In this paper, a strategy for optimizing the membership function (MF) parameters of an interval type-2 fuzzy system using the Kalman gain and error covariance of its constant consequent parameter is presented. In the proposed strategy, the MF parameters are not a part of the input to the extended Kalman filter (EKF) algorithm, which reduces the computational cost of optimization. The proposed strategy was used to identify a robot hand path, Mackey–Glass Chaotic Series, dynamic system, and the inverse kinematics of a 6-PSS parallel robot. The proposed strategy was compared with an interval type-2 fuzzy system having only the consequent parameters being optimized by the extended Kalman filter (KFT2FS). The performance characteristic considered was the root mean square error between the desired output and the model output. The comparison results showed that the proposed model outperformed the KFT2FS, with an improved performance of 85%, 15.7%, 11.25%, and 3.6% for the robot hand path, Mackey–Glass Chaotic Series, dynamic system, and 6-PSS parallel robot respectively and also 7.3%, 17.5%, and 37.1% for 20 dB, 15 dB, and 10 dB corrupted 6-PSS parallel robot data respectively.