T-S Fuzzy Model Identification Based On Differential Evolution

Constructing a fuzzy system based on the fuzzy rule sets,which are directly extracted from data without prior knowledge,is an efficient way of pattern recognition.The Takagi-Sugeno(T-S)model is a semilinear fuzzy system that divides the input space into several fuzzy subspaces.When construct a T-S model,the estimations of the number of IF-THEN rules and the parameters of the antecedent and consequent parts become very significant.Fuzzy clustering algorithm is often used in extracting the fuzzy rule antecedents.However,Fuzzy clustering has two main problems: sensitive to the initial value;lacking stability and robustness in noisy environments.So it need optimizing strategies to improve the procedure of rule extraction.Differential evolution(DE)is an evolutionary algorithm that offers outstanding global optimization performance and numerical stability.This paper introduces DE with a new parameter strategy to improve the identification of T-S fuzzy system based on fuzzy clustering.There is another evolutionary algorithm called particle swarm optimization(PSO)broadly introduced to deal the problems of sensitivity to initial values in fuzzy clustering-based T-S fuzzy system.However,PSO is easy to be trapped around local optimum,and lacks the capacity of processing noise data.Instead,using DE,the search capability and robustness of which,can provide a better initiation for fuzzy clustering avoid the influence of noise data,and improve the identification of T-S system.In this paper,An improved initialization optimization methodology based on DE is proposed to construct a stronger fuzzy clustering-based T-S fuzzy model.Further analysis of the T-S fuzzy model identifying algorithms show that the whole identifying process is always discretely divided into antecedents part and consequent part with the pre-set number of rules.Actually,identifying a fuzzy models is equivalent to an optimization problem in multidimensional space,whereby each position relates to a potential fuzzy model having its own structure and parameters.Thus,the number of rules,the structure of input,and antecedent parameters of the T-S model can be co-encoded into a particle of DE and evolve together.However,theoriginal DE algorithm was highly susceptible to becoming trapped around local optima when tackling complex problems.This paper proposes a improved DE method with two alternative external archives and a new replacement strategy,called SubReDE(sub-population and replacement differential evolution)to identify T-S fuzzy model.The favorable effectiveness and efficiency of these algorithms are demonstrated through comparison experiments against previous techniques using three different kinds of datasets(function,multi-attribute data,and time series data).