Study On Fuzzy Model Identification Based On Kernel Method

Fuzzy model identification is one of the most important research branches in intelligent control theory. Traditional mathematical modeling approaches are always not amenable to various complex research objects which come up with the developing information technology. However, fuzzy model possesses some advantages such as expressing structural knowledge easily and being able to combine mathematical function approximators with process information, etc. Many new approaches based on fuzzy model have been successfully applied in fields such as system identification, intelligent control and pattern recognition, etc. Thus, fuzzy model identification has become one of the key issues in basic theory research of intelligent control.In the past two decades, scholars at home and abroad have done a lot of work about the theory research of fuzzy model identification. But identification algorithms in existence are still faced with some tough questions, such as how to avoid"the curse of dimensionality", and how to improve the generalization ability of fuzzy model. Generally, fuzzy model identification is composed of two main parts: structure identification and parameter estimation. The former is not only a difficulty, but also is a key to the whole identification process. However, it remains a pity that structure identification has not developed into a perfect theory. Moreover, how to make a tradeoff between multiple performance indexes (such as complexity and accuracy) to provide reasonable criterions for parameter estimation is still short of effective theory guidance. In addition, there also exist many difficulties in applying fuzzy model identification approaches to real industrial processes, such as the excessive fuzzy rules and the huge computational cost. So, how to design simple and effective identification algorithms, improve generalization ability and cut down computational complexity become the main goals of our research.This dissertation focuses on developing a novel and effective identification algorithm which can overcome some shortages existing in conventional methods by introducing kernel methods to the field of fuzzy model identification. Kernel method is a general appellation for the class of learning algorithms using kernel mapping techniques. It is one of the most active research issues in the machine learning field at present. In this dissertation, we firstly develop a new support vector machine (SVM)-based fuzzy identification algorithm, which uses SVM to achieve structure identification to improve generalization capability, and utilizes Kalman filtering to implement the parameter estimation. Then for the problem of selecting a proper kernel function and optimizing kernel parameters, we develop an improved genetic algorithm (GA) to tackle with it. The tradeoff between multiple performance indexes is achieved by designing an objective function in GA which simultaneously concerns accuracy and complexity. For the purpose of cutting down computational cost of identification, this dissertation proposes a new identification algorithm based on incremental kernel-based learning. Finally, to overcome the rule redundancy which probably exists in the support vector fuzzy system, we develop a novel identification algorithm based on dual kernel-based learning machines (kernel fuzzy clustering and support vector regression), and propose a combination strategy for support vectors to guarantee the conciseness. This approach simultaneously avoids the shortcoming that the performance of traditional clustering-based identification algorithm is sensitive to the initial clustering number,Specifically, the main contributions of this dissertation are as follows:1. The selection of proper kernel function and the optimization of kernel parameters are always difficult and critical to the use of kernel method. We combine two typical kernel functions by means of convex combination. The weighting coefficient and other kernel parameters are optimized by an improved GA. So, the selection of kernel functions is converted into a parameter optimization problem. By introducing the concept of the insensitive variance step of parameters, we improve the genetic operators to speed up evolution speed. In the optimization objective function, we simultaneously consider the identification accuracy and the model complexiy to meet the requirement of multiple performance indexes of fuzzy model.2. For the fuzzy identification approaches based on SVM, the computational cost of identification assumes the exponential growth along with the number of training samples. We use the kernel Mahalanobis distance to define an ellipse area to pick up some samples which are candidates for support vectors. By this means, the scale of training samples can be effectively decreased. Then the training of SVM is achieved by using incremental learning, finally the fuzzy rules can be directly extracted from the results of support vector learning. This approach provides a good solution to developments of online identification techniques.3. The rule number of support vector fuzzy system is determined by the number of support vectors. Once too many support vectors are produced, the fuzzy rules will probably appear redundant. For this, this dissertation proposes a new simplification strategy for the fuzzy rule base by using dual kernel-based learning machines. Firstly, a new kernel fuzzy clustering is proposed to partition the sample set. Then support vector regression is further used to locate support vector points in each cluster. A combination strategy for these obtained support vectors is developed to cut down the number of support vectors. Finally, these compressed support vectors are used to determine the structure of fuzzy model. The simplification strategy can effectively assure the conciseness of fuzzy model. In addition, this algorithm is not only insensitive to initial clustering number just like traditional methods, but also free of the optimization process for kernel parameters due to the use of conditionally positive definite kernel.