Support Vector Machine Based on Possibility Degrees and Fault Diagnosis

Despite many benefits of support vector machine (SVM), all the data points are treated identically in the learning process of conventional SVM, which causes the algorithm extremely sensitive to the outliers and the noise data. For this problem, a new SVM algorithm based on possibility degrees (PDSVM) is proposed. Considering the variation of the geometric significance among different classes in a training data set, the possibility degrees of samples are defined in this paper. To reflect the geometric shape of one class, the possibility degrees of the samples of the class are calculated according to the Mahalanobis distances between the samples and the centroid of the pattern class. Then the training samples and their possibility degrees are trained together with the SVM, so as to make the important samples are classified exactly and the negligible samples are ignored. Based on the numerical experiment, the algorithm is applied to the servo valve fault diagnosis and gains a good effect. According to the theoretical analysis and the experiment, the algorithm is effective and robust.