A fuzzy modeling method via Enhanced Objective Cluster Analysis for designing TSK model

Abstract

This paper proposes a fuzzy modeling method via Enhanced Objective Cluster Analysis to obtain the compact and robust approximate TSK fuzzy model. In our approach, the Objective Cluster Analysis algorithm is introduced. In order to obtain more compact and more robust fuzzy rule prototypes, this algorithm is enhanced by introducing the Relative Dissimilarity Measure and the new consistency criterion to represent the similarity degree between the clusters. By these additional criteria, the redundant clusters caused by iterations are avoided; the subjective influence from human judgment for clustering is weakened. Moreover the clustering results including the number of clusters and the cluster centers are considered as the initial condition of the premise parameters identification. Thus the traditional iteration modeling procedure for determining the number of rules and identifying parameters is changed into one-off modeling, which significantly reduces the burden of computation. Furthermore the decomposition errors and the approximation errors resulted from premise parameters identification by Fuzzy c-Means clustering are decreased. For the consequence parameters identification, the Stable Kalman Filter algorithm is adopted. The performance of the proposed modeling method is evaluated by the example of Box–Jenkins gas furnace. The simulation results demonstrate the power of our model.