| Statistical Learning Theory is based on the theory foundation and provides a uniform framework for learning subject of limited samples. Support Vector Machines (SVM) is a machine-learning algorithm based on statistical learning theory. This algorithm accomplishes the structural risk minimization principle. The fine performance of Support Vector Machines to limited samples attracts attention of investigators in fault diagnosis field. Fault diagnosis is a limited samples subject. The most predominance of SVM is proper for limited samples decision. The nature of the algorithm is acquiring connotative class information to great extent from limited samples. From the point of generalization, SVM is the more favorable for the practical engineering problem as fault diagnosis.SVM has eximious predominance in theory, but the research on application is comparatively delayed. Based on this, the problem of SVM in the application of fault diagnosis on the aspects of data pretreatment, fuzzy method with uncertain information, the realization of multi-class SVM and diagnosis based on model was developed in this paper. 1,Research and application on feature extraction for high-dimension dataFirstly, the relation between feature dimension and classify result was analyzed in this part, which shows that the increase of feature dimension will result in worse classify result. The reason for this mainly lies in the disturbance of false feature. In this paper, the longitudinal compression that applied to compressing feature dimensions was mainly researched, and this method can eliminate the false and retain the true, that is feature extraction. We introduced the typical algorithm -- Principal Component Analysis (PCA) in detail. As far as the turbine fault diagnosis is concerned, the data sample of some original group nine-dimension frequency was feature extracted, from the two-dimension principle component mapping we can conclude that the feature data after extracted is more separable, which suggests that data preprocessing in practical fault diagnosis is favorable to the realization of classify algorithm, and provide an effectively feasible data preprocessing method for the turbine fault diagnosis.2,The fuzzy judgment support vector machine algorithm based on loss function is proposed, and compared with fuzzy sample support vector machine algorithm.As for the uncertain information in fault diagnosis, FJ-SVM based on loss function was proposed in this paper, and fuzzy membership grades based on loss was also defined. Furthermore, we educed the optimal separating hyperplane after modified, and judge according to the maximum membership rules. Fuzzy support vector machine considered that different wrong judgment result in loss difference in practice. At the same time, it has preferable sensitivity for the slight fault of device and forepart fault diagnosis in productive process. Practically, the selection of fault sample is often typical sample with obvious feature. Therefore, the algorithm that using typical sample to form support vector machine is more practical. Just right, FJ-SVM is just based on this principle.In this paper, we also introduced FS-SVM. From the fuzzy grades we directly educed this algorithm. We use two kinds of algorithms to simulate experiment, compared the results, and analyzed the different emphasis in the application of these two algorithms.3,Discussing and analyzing the composing of multi-class support vectors, and researching these two typical algorithms.The method of conversion from two-class to multi-class was analyzed. Combining the decision tree, we studied the two kinds of multi-class algorithms: one is DAGSVM based on DDAG structure, and we discussed the selections of kernel function parameters. Second is multi-class algorithm based on hierarchical clustering and decision tree. We introduced the theory and concrete realization, and applied these two methods with the limited samples.4,Sensor fault diagnosis based on support vector regression is put forwardThe application form of...
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