Multi-class Classification Algorithm Research Based On Fuzzy Support Vector Machines

Support vector machines (SVMs), as a machine learning method based on statistical learning theory, have attracted more and more attention and become a hot issue in the field of machine learning, because they can well resolve such practical problems as non-linearity, high dimension and local minima. Research on the fault recognition of rotating machine is important for decreasing maintenance costs, reducing production costs, increasing economic and social benefits. Research on the rotating machine state monitoring and fault diagnosis is an important task of science and technology development nowadays. SVM method represents favorable advantages for limited samples learning, so it can better resolve this task. But at the same time, fault recognition of rotating machine also puts forward lots of challenging tasks for SVM, such as, difficulty of obtaining fault samples, noise data, and skewed training sets in fault classification. On the basis of research on fuzzy SVM classification methods and applications in the fault recognition of rotating machine, this paper mainly focus on directly constructing multi-class classification methods, fuzzy kenel SVM, SVDD-based classification method, and' its applications in the fault recognition of rotating machine. The main work is as follows:1. SVMs were originally designed for binary classification. How to effectively extend them for multi-class classification is still a hot research issue. Firstly, several existing multi-class classification SVM methods are compared and analyzed. Secondly, aiming at directly constructing multi-class classification methods, two novel directly constructing fuzzy SVM methods are presented in order to decreasing originally directly constructing methods' sensitivity to noise data, and overcoming disadvantages of the noise data for classification; results. The proposed methods integrate fuzzy throughts, introduce fuzzy compensation, and reconstruct and deduce corresponding optimal problems. Experimental results indicate the proposed methods have higher precision than originally directly constructing methods.2. How to find the best adaptive kenel function for a given problem is a key problem to SVMs from theories to practice. Kernel functions in SVMs sometimes; need to satisfy Mercer conditions, but some non positive semi-definite (non PSD) kernels, such as Sigmoid kernel, also apply to classification problems. Corresponding analysis indicates that despite Sigmoid kernel is non PSD, Sigmoid kernel is a conditional positive semi-definite kernel (CPD) when its parameters satify a > 0 and r < 0. This paper presents a novel fuzzy support vector machine based on vague-Sigmoid kernel by applying vague set theories into SVM's kernel function. The proposed method replaces traditional inner product with vague value similarity measurement of two samples, where vague value of a sample sufficiently depicts a case of a sample pertaining to a class, and vague value similarity measurement describes two samples' tightness degree pertatining to a class. Experimental results indicate that comapre to standard Sigmoid kernel SVM method, the proposed vague-Sigmoid kernel SVM method can obviously reduce training time in the condition of hardly affecting precision.3. Support vector data description (SVDD) was originally designed for one-class classification and novelty detection. Through analysis for its characteristic, SVDD is extended to multi-class classification problems. Firstly, a training sample's fuzzy value (weight) is computed by an improved probalbility c-mean clustering algorithm aiming at noise data of training sets. Then a classification decision formula is constructed and a weighted SVDD multi-class classification method is proposed. This method can decrease training time because the great masses of samples are only trained once. Bayesian theories analysis indicates the proposed classification decision-making formula satisfies Bayesian decision-making rules. Experimental results show that the proposed weighted SVDD multi-class classification method can get better classification precision than standard SVM and sphere-based classification methods do in a majority of standard data sets.4. Taking advantages of SVMs in limited samples learning and applying SVMs to fault recognition, an on-line intelligent fault diagnosis system based on SVMs is designed. However, in the large rotating machine, fault data samples obtain hardly, and usually spend higher costs. Combined with the former weighted SVDD multi-class classification method, a novel classification method based on positive and negative training samples is proposed. Experimental results show that this method can get higher classification precision in the fault recognition of rotating machine.