Identification Of Fuzzy TS Neural Network Based On Second-Order Taylor Expansion

The fuzzy TS neural network combines with characteristics of both fuzzy TS systems and neural network, it is not only able to handle the language knowledge and large amounts of data, but also can be effectively carried out modeling and control of complex systems. Fuzzy TS system is a linear form, from the aspect of the numerical approximation, the system is the weight summation of several piecewise linear models, in other words, it approximates the original model with linear models in the local area. In order to further improve the approximation accuracy of the model, fuzzy TS system based on the Taylor expansion (Taylor-TS) is proposed, the original system is approximated with a polynomial in the local area, and neural network is applied to identify the parameters of the model, then the Taylor-TS system is used to simulate non-linear functions, power learning model and time series. The papers are as follows:Firstly, the paper presents a multi-input multi-output second-order Taylor-TS system model and second-order Taylor-TS fuzzy neural network structure;Secondly, second-order Taylor-TS fuzzy neural network is applied to model non-linear functions and dynamic model, the gradient descent algorithm (Taylor-TS-GD) is used. The simulation results are compared with other algorithms. The comparison shows that the second-order Taylor-TS fuzzy neural network can improve the approximation of the performance and accuracy effectively;Thirdly, the stepwise learning method is proposed to identify the second-order Taylor-TS fuzzy neural network. The PSO algorithm, the quasi-Newton algorithm and the gradient descent algorithm are used. Network parameters are identified separately. The PSO algorithm and gradient descent algorithm are used to initialize and modify the parameters of the membership functions, respectively, while the quasi-Newton algorithm is applied to adjust the consequent parameters. The stepwise learning method is applied to simulate the non-linear functions and differential equations, the simulation results are compared with other algorithms, the result of the comparison shows that the stepwise learning method can effectively improve the approximation performance and approximation precision;Lastly, second-order Taylor-TS fuzzy neural network is applied to predict the typical time series. In this part, the structure of second-order Taylor-TS fuzzy neural network is optimized, and the threshold is introduced to optimize the numbers of adjustable parameters, and then training errors and testing errors are compared with other algorithms, the result of the comparison shows that the second-order Taylor-TS fuzzy neural network can effectively improve the prediction performance of the nonlinear time series.