Fuzzy Cluster Analysis And Its Application To Fault Diagnosis Of Power Transformer

Cluster analysis is an important method in the data analysis and one of the main research projects in data mining and knowledge discovery. Also, it is an important branch in unsupervised classification of pattern recognition. Clustering is a process of classification when only data available are unlabeled and no prior knowledge about it. According to a definition of metric of similarity (or dissimilarity), a set of objects are partitioned into a certain number of clusters, such that objects in the same clusters are as similar as possible and objects in different clusters are as dissimilar as possible in the sense of the definition. Cluster analysis has an extremely wide range of applications. A lot of fields have involved the study and application of cluster analysis, and many research results have achieved in theory and practice. Power Transformer is one of most important electric power equipment in power systems. Research on the fault diagnosis of power transformer is of important theoretical value and realistic significance. Widely used dissolved gas analysis (DGA) is the essence to evaluate the state of transformer insulation and analyze transformer insulation faults. Combining DGA with cluster analysis is one of effective methods to improve the reliability and precision of fault diagnosis of the power transformer. This paper mainly focuses on issues of the cluster validity problem, fuzzy clustering algorithm and genetic fuzzy clustering algorithm based on objective function. Also the above research results are applied to fault diagnosis of power transformer. The main contents of the dissertation are outlined as following:With an aim at the shortcoming of traditional cluster validity indices in evaluating some cluster properties such as compactness (or variation) and separation (or isolation), this paper puts forward the formal definition of cluster fuzzy set based on the basic theory of fuzzy set, which is subjected to the constraint condition of fuzzy c-means clustering algorithm. The cluster fuzzy degree and the lattice degree of approaching for the cluster fuzzy set are further defined. They are respectively used to measure the values of compactness and separation and better results have been obtained in our experiments. On the basis of the above work two new cluster validity indices are proposed. In the first index two factors such as the cluster fuzzy degree and the lattice degree of approaching are taken into comprehensive account. The notable advantage of the index is that it can adaptively adjust the relative significance levels of the two factors. In the other index the extreme values of the cluster fuzzy degree and lattice degree of approaching are used to improve its sensitiveness in judging process. The experimental results show the high evaluation ability of the indices we proposed.In static clustering algorithms the number of clusters is required to be given in advance. So there are some limitations in practical applications. To solve this problem we propose a dynamic fuzzy clustering algorithm based on genetic algorithms (GAs), in which the number of clusters can automatically be computed by using the cluster validity indices described above. We adopt a cluster prototype-based dynamic real-coding scheme, in which the chromosomes express cluster prototypes and different length of them corresponding to different numbers of cluster prototypes. Also, a new type of crossover operator and mutation operator are designed to adapt to the variable length chromosomes. In order to extend local search ability of the algorithm a clustering local optimization operator is proposed; The results show that the algorithm can obtain the optimal number of clusters and enhance clustering effect.Focusing on the problem of calculation and optimization of feature weights in weighted fuzzy cluster analysis, we propose a weighted fuzzy clustering algorithm based on objective function. The algorithm adopts the alternating optimization method to optimize the fuzzy partition matrix, cluster prototypes and feature weights respectively in the iteration. To utilize the global searching ability of GA, we also propose a fuzzy clustering algorithm based on double coding genetic algorithm, in which each chromosome consists of two segments of codes for cluster prototypes and feature weights. The two segments are evolved simultaneously in the clustering process. A weighted fuzzy c-means operator is designed to guide computing cluster prototypes and feature weights. We utilize the roulette selection strategy, the arithmetic crossover and the uniform mutation method to realize the usual genetic operations, and elitist strategy is adopted to guarantee the convergence of the algorithm, and good results have been obtained in our experiments.Dissolved Gas Analysis (DGA) is one of the most effective and popular method which can be used to discover insulation aging or the fault degree of power transformers. Theoretical analysis and practical application indicate that the insulative faults of power transformers are closely related with both the content and the ratio of component of various dissolved gas-in-oil. In this paper, a deep analysis is made of the above two types of influencing factors. The process of information fusion is realized by normalization and promotion & compression for the components content and the component ratio of various characteristic gases. In this way we have comprehensively utilized the two main information of fault. For this mixed-type data, we calculate the optimal number of faults by using the cluster validity indices proposed in this paper and also use the above dynamic fuzzy clustering algorithm to realize dynamic cluster analysis of insulative faults of power transformers. Also, we utilize the attribute weights to express the relative degree of the importance of various compositions of the mixed-type data. Experimental results show that the accurate judgement rate of our method is higher than that of the method of characteristic gas and improved three-ratio method in various degrees.