Modeling And Control Of Type-2 Fuzzy System

The traditional fuzzy set has great limitations in expressing and dealing with uncertain problems.To solve this problem,Professor Zadeh,an expert in the field of fuzzy control in the United States,has extended and introduced the concept of type-2 fuzzy set for the first time.It is a fuzzy processing of the membership value in the traditional fuzzy set so that it has the characteristics of the three dimensional membership function,so it can extend the freedom degree of membership function and fuzzy reasoning,and can better deal with the uncertainty complex problems.However,the characteristics of the three dimensional membership function of type-2 fuzzy set also brings about the problem of complex calculation.Therefore,the concept of interval type-2 fuzzy set is proposed,which has the characteristics of easy expression,simple structure and low computational cost.The system composed of interval type-2 fuzzy set is called interval type-2 fuzzy system.At present,interval type-2 fuzzy system is a hot research topic of type-2 fuzzy system,and has been widely applied in many fields.Based on the theory of interval type-2 fuzzy system,this paper makes full use of its advantages in dealing with uncertainty complex problems,and takes the ethylene cracking process as the application background,and focuses on its theory and application of modelling and control of interval type-2 fuzzy system in complex industrial process.The main contributions of this paper are described as follows:(1)Aiming at the identification problem for the nonlinear system and the modeling problem of complex industrial process,an improved interval tyype-2 fuzzy neural network(IT2FNN)is presented in this article.The antecedent part in the improved IT2 FNN fuzzy rule uses interval type-2 membership function(IT2MF),and the consequent part adopts Mamdani model.In defuzzification,the design factor ? is learned to adaptively adjust the proportion of the left and right end-points of type-reduced set,which replaces the common mean sum calculation in order to increase the system precision.The improved IT2 FNN is developed by structure and parameter learning.The structure and antecedent parameters of the improved IT2 FNN is determined by utilizing a self-adaptive fuzzy c-means(FCM)algorithm.The consequent parameters are interval random number.The antecedent parameters,consequent parameters and weight coefficient ? of the improved IT2 FNN are tuned by utilizing an adaptive gradient descent method.Finally,the effectiveness of the improved IT2 FNN is demonstrated via the simulation results of nonlinear system case study and soft-sensing model for ethylene cracking furnace yield.(2)For the identification and modelling problems of a nonlinear system with complex uncertainties,a self-organising interval type-2 fuzzy neural network structure with asymmetric membership functions(SIT2FNN-AMF)is developed.First,a fuzzy c-means algorithm(FCM)with four fuzzifier parameters is used to partition the input data to obtain the uncertainty means and widths of the fuzzy rule antecedent;then,according to the cluster validity criterion,the number of fuzzy rules is determined.Thus,identifications of thestructure and rule antecedent parameters are automatically completed.The consequent part uses the Mamdani model and the initial value of the consequent parameter is an interval random number.The fuzzy rule parameters are tuned by the gradient descent method.Finally,the proposed SIT2FNN-AMF is applied to simulations of nonlinear system identification and soft-sensing model for ethylene cracking furnace yield.The comparison of simulation results obtained with a conventional fuzzy neural network and interval type-2 fuzzy neural network verifies the performance of the proposed SIT2FNN-AMF.(3)This study introduces a novel self-organizing recurrent interval type-2 fuzzy neural network(SRIT2FNN)for the construction of a soft sensor model for a complex chemical process.The proposed SRIT2 FNN combines interval type-2 fuzzy logic systems(IT2FLSs)and recurrent neural networks(RNNs)to prevent data uncertainties.The Gaussian interval type-2 membership function is used to describe the antecedent part of the SRIT2 FNN fuzzy rule,whereas the consequent part is a Mamdani-type rule,which is an interval random number.An adaptive optimal clustering number of fuzzy kernel clustering algorithms based on a Gaussian kernel validity index(GKVI-AOCN-FKCM)is developed to determine the structure of the SRIT2 FNN and fuzzy rule antecedent parameters,and the parameter learning of SRIT2 FNN used the gradient descent method.Finally,the proposed SRIT2 FNN is applied to the soft sensor modeling of ethylene cracking furnace yield in a typical chemical process.Comparisons between the SRIT2 FNN and conventional fuzzy neural network(FNN)and interval type-2 fuzzy neural network(IT2FNN)are presented via simulation experiments.The obtained results indicate that the proposed SRIT2 FNN performs better than the conventional FNN and IT2 FNN.(4)Multivariable coupling,nonlinear and large time delay exist in the coil outlet temperature(COT)control system of ethylene cracking furnace,which let it hard to achieve accurate control over the COT of the furnace in actual production.To solve these problems,an inverse controller based on interval type-2 fuzzy model control strategy is introduced.In this paper,the proposed control scheme is divided into two parts: one is the approach structure part of the interval type-2 fuzzy model(IT2FM),which is utilized to approach process output.The other is interval tyep-2 fuzzy model inverse controller(IT2FMIC)part,which is utilized to control the output process to achieve the target value.In addition,the actual industrial data are used to test and obtain the mathematical model of COT control system of ethylene cracking furnace.Finally,the proposed inverse controller based on IT2 FM control scheme has been implemented on the COT control system of ethylene cracking furnace,the simulation results show that the proposed method is feasible.(5)An improved interval type-2 fuzzy logic controller based on genetic algorithm is presented to deal with the problem of losing uncertain information in the type reduction process of interval type-2 fuzzy logic controller.The four uncertain boundary values of interval type-2 fuzzy output are obtained by using interval type-2 fuzzy reasoning and the Wu-Mendel uncertainty bound type reduction algorithm.Then the controller outputs are re-optimized.The quantization factor,scaling factor and membership functions of intervaltype-2 fuzzy logic controller are evolved by using genetic algorithm.By constructing the fitness function of genetic algorithm as performance index,which can be directly related with the system output in order to improve the performance of the whole control system.Finally,the proposed method is implemented on the outlet temperature control system of ethylene cracking furnace,the simulation results demonstrate the effectiveness of the proposed control scheme.