| In order to make up for the limitations of type-1 fuzzy sets in dealing with uncertainties, in 1975 Professor Zaheh originally presented the type-2 fuzzy sets, which is essentially "fuzzy fuzzy" sets where the fuzzy degree of membership is a type-1 fuzzy set. Since the type-2 fuzzy set is to use three-dimensional membership functions, with more than one dimensional degree of freedom for dealing with uncertainties compared with type-1 fuzzy set, it is more effective in solving the problems with high uncertainties in realistic environment, especially the interval type-2 fuzzy set with advantages of simple structure and high computation efficiency becomes a hot issue in the research and application of fuzzy theory. Based on the theory of the interval type-2 fuzzy system, this thesis focuses research on its theory and application in the field of system identification and image processing.Firstly, for the complicated problems of interval type-2 fuzzy system modeling caused by rules redundancy, rules reduction method of interval type-2 fuzzy system is studied. In order to solve the problem of rule reduction method based on Singular Value Decomposition-QR (SVD-QR) in determining the number of effective singular value, the concept of normalized difference of singular value is proposed.Through magnifying the difference of adjacent singular values to more clearly describe the mutation characteristics of singular values, the optimal choise of the number of effective singular values is realized. Comparing results with other methods show that the fuzzy model obtained by the instruction of the normalized difference of singular value maintains high approximation accuracy. Then, combined with statistical information criteria, the rules reduction method based on the pivoted QR (P-QR) decomposition is proposed. Experiments demonstrate that the simplifized model obtains less error and has better generalizing capabilities than the one with method based on SVD-QR.Secondly, combined with fuzzy reasoning and self-learning ability of neural network fuzzy neural network is widely used in system identification, the research is focused on structure identification and parameter identification. Therefore, a type-2 fuzzy neural network with self organizing structure and learning algorithm is proposed. The fuzzy C-means algorithm with two different weighting parameters is used for partition of input data and the number of fuzzy rules is determined with cluster validity criterion, so that the structure and parameters of rule antecedent identification are completed automatically. Then based on the gradient descent method and Lyapunov function, the adaptive learning algorithm for weight vectors of rules consequent is proposed. The experiment results of two nonlinear systems identification indicate that the proposed algorithm has faster convergence rate and more accurate approximate precision than other algorithms. Additional, based on the power load data of a city, a short-term load-forecasting model developed by the algorithm has high prediction precision and better generalization perfomance.Thirdly, image threshold segmentation method based on fuzzy entropy is an important method in the field of image processing, but it is facing problems of how to design effective membership functions, fuzzy entropy measure and reducing the running time. To overcome these problems, a novel image thresholding method based on entropy of interval type-2 fuzzy sets is proposed. On the basis of the axiom definition, a construction method of distance measure of interval type-2 fuzzy sets is given, then, according to axiomatic definition of entropy for interval type-2 fuzzy sets based on distance, a construction method of entropy measure of interval type-2 fuzzy sets is given so that some different formulas are derived to calculate this kind of entropy. Then, through theory justification the best formulae and threshold can be determined by minimum fuzzy entropy criterion. The experiments demonstrate that, compared with other fuzzy thresholding methods, improved 2-D Otsu’s methods and so forth, the new method can achieve accurate segmentation results and has excellent adaptive capability.Finally, due to the fault detection of pantograph slide is very important for the secure and stable operation of the electric locomotive, a novel method of pantograph slide crack detection based on fuzzy entropy and Hough transform is proposed. Based on the gray distribution of pixels in the neighborhood, an edge detection method based on entropy of interval type-2 fuzzy sets is proposed so that slide edge image with enhanced feature was obtained; then, the connected domain method is used to remove isolated noises. As a result, the slide edge image mainly includes four kinds of graphic elements such as the boundary line, joint, rivet and cracks. On this basis, the characteristics distribution of the various types of graphic elements in the parameter space are analyzed by Hough transform, and thus a method to extract the slide crack based on Hough transform with angle constraint is proposed. Through effectively excluding feature points of others graphic elements, the slide crack can be determined finally. The experiment results indicate that this edge detection method can obtain slide edge image with enhanced linear feature which is benefit for subsequent Hough transform; the crack extraction method can accurately identify and locate the slide crack. |
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