Fuzzy Model Identification Based On Tikhonov Regularization

This thesis studies the problems of parameter identification in the process of fuzzy system identification by using the Tikhonov regularization approach. Generally, the system parameter identification only considered the output noise, while the disturbances from the input data was ignored. For the parameter identification containing kinds of noises, this paper not only analyzes the case that the error occurs in the output data, but also gives a solution to solve the ill-posed problem of the input and output data both contaminated by noises.The work is done as follows:1. For the case of only the output noise, Bayes regularization with regular matrix is employed to solve such ill-posed problems. Many mathematical models are the inverse problems with ill-posedness. Tikhonov regularization is a key technique to solve such ill-posed problems. Bayes regularization developed from Tikhonov regularization can well handle the ill-posedness and the regularization parameter can be obtained by the method. The accuracy of solutions of the ill-posed problems is further improved for the existence of the regularization matrix.2. For the case that input and output sides of the system both contain noises, the Tikhonov regularization of total least squares is adopted to solve the ill-posed problems. Total least squares can well deal with the ill-posed problems of both sides with disturbance, and some better results can be obtained by the revise of Tikhonov regularization item. The regularization parameter is determined by using a choosing approach based on shuffled frog leaping algorithm.3. The Bayes regularization with regularization matrix and Tikhonov regularization of total least squares are applied in consequence parameters identification of T-S fuzzy systems, which has a better denoising effect. Simulation examples show that the feasibility and effectiveness of the proposed methods in this paper.The main innovations are:1. The optimal value of regularization parameter is calculated by shuffled frog leaping algorithm in total least squares algorithm. A better and stabilized algorithm to solve the parameter can be obtained by the algorithm combined shuffled frog leaping algorithm with total least squares.2. The article discusses the importance of regular matrix and obtains an algorithm based on Bayes theoretical framework having regularization regular matrix.The superiority of the proposed algorithms:In the process of parameter identification, it is can be seen that the accuracy and stability of the solutions obtained in this thesis are better, by comparison with Kalman filter, total least squares, singular value decomposition and recursive least squares.