支持向量机在电缆故障分类中的应用
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摘要
支持向量机是一种专门针对小样本的模式识别方法,它建立在统计学习理论的VC维和结构风险最小化原理的基础上,较好地解决了非线性、高维数、局部极小点等问题,具有良好的推广性。经典的支持向量机是一种两类分类器,随着应用范围的扩展,支持向量机被广泛地用于解决多类分类问题。如何针对具体的问题建立较好的支持向量机多分类模型,是近几年支持向量机研究的热点之一。
本文在统计学习理论相关原理及支持向量机理论基础上,对支持向量机多类分类算法及核函数的参数选择问题进行了分析与研究。论文概述了统计学习理论、支持向量机的分类原理、支持向量机集成的最优分类面、分类间隔、最优化理论等技术,介绍了支持向量机的重要模块——核函数,并对不同核函数的性能进行了比较;分析和总结了现有的几种支持向量机多类分类方法,包括一次性求解算法、“一对多”、“一对一”、有向无环图算法等,比较了它们的性能及优缺点;针对现有的支持向量机多类分类算法中存在错分或拒分区域问题和二叉树支持向量机结构的生成问题,在定义了较小邻近距离和构造类间相异度矩阵的基础上,提出了基于类间相异度矩阵的支持向量机多类分类算法,并通过仿真实验,与传统的一对一、一对多及有向无环图支持向量机算法结果进行比较,验证了该算法的正确性和有效性。
论文最后部分将基于类间相异度矩阵的支持向量机多分类算法用于对电缆故障类型的识别分析中,通过尝试不同的核参数选择出较优的核参数以建立支持向量机多类识别模型,实现了对故障类型有效的识别。
Support vector machine is a pattern recognition method specially for small samples, which is based on the VC dimensions of the statistical learning theory and the structural risk minimization principle. It well sloves the problems of nonlinear, high dimensions and local minimum. It has a good generalization performance. The classical support vector machine is a two classs classifiers. With the expansion of its application,it is widely used to solve the multi-class classification problems. For a special problem, how to build a better support vector machine multi-classification model has become one of the spots of support vector machines in recent years.
The multi-class support vector machine algorithm and the selecting problem of kernel parameters are analyzed and researched in the thesis based on the statistical learning theory and the support vector machine theory. First, the statistical learning theory, the support vector machine classification principle and the techniques which the support vector machine has integrates including the optimal hyperplane, the classification interval, the optimization theory are summarized. At the same time, the kernel function, which is an important module of the support vector machine is described and the performance of differnt kernel functions are compared. Then, several existing multi-class support vector algorithms including the one-time algorithm, one versus rest algorithm, one versus one algorithm and the acyclic graph algorithm are analyzed and their performance, advantages and disadvantages are compared. Aming at the problem that there exsits some wrongly classified region or refused region in the above algorithms and the difficulty to determine the structure of the binary tree in the binary tree support vector machine algorithm, a support vector machine algorithm based on the between-class dissimilarity matrix is presented after the two novel concepts of the shorter neighboring distance and the between-class dissimilarity matrix are defined. In the simulation, the results of the new algorithm are compared with that of one versus one algorithm, one versus rest algorithm and the acyclic graph algorithm, which verifies that the alogrithm is correct and effective.
In the last part of the thesis, the support vector machine algorithm based on the between-class dissimilairity matrix is applied to the recognition for the types of cable fault. The fault types are finally effectively recognized after selecting a better parameter by trying differernt kernel parameters to build the multi-class support vector machine model.
本文在统计学习理论相关原理及支持向量机理论基础上,对支持向量机多类分类算法及核函数的参数选择问题进行了分析与研究。论文概述了统计学习理论、支持向量机的分类原理、支持向量机集成的最优分类面、分类间隔、最优化理论等技术,介绍了支持向量机的重要模块——核函数,并对不同核函数的性能进行了比较;分析和总结了现有的几种支持向量机多类分类方法,包括一次性求解算法、“一对多”、“一对一”、有向无环图算法等,比较了它们的性能及优缺点;针对现有的支持向量机多类分类算法中存在错分或拒分区域问题和二叉树支持向量机结构的生成问题,在定义了较小邻近距离和构造类间相异度矩阵的基础上,提出了基于类间相异度矩阵的支持向量机多类分类算法,并通过仿真实验,与传统的一对一、一对多及有向无环图支持向量机算法结果进行比较,验证了该算法的正确性和有效性。
论文最后部分将基于类间相异度矩阵的支持向量机多分类算法用于对电缆故障类型的识别分析中,通过尝试不同的核参数选择出较优的核参数以建立支持向量机多类识别模型,实现了对故障类型有效的识别。
Support vector machine is a pattern recognition method specially for small samples, which is based on the VC dimensions of the statistical learning theory and the structural risk minimization principle. It well sloves the problems of nonlinear, high dimensions and local minimum. It has a good generalization performance. The classical support vector machine is a two classs classifiers. With the expansion of its application,it is widely used to solve the multi-class classification problems. For a special problem, how to build a better support vector machine multi-classification model has become one of the spots of support vector machines in recent years.
The multi-class support vector machine algorithm and the selecting problem of kernel parameters are analyzed and researched in the thesis based on the statistical learning theory and the support vector machine theory. First, the statistical learning theory, the support vector machine classification principle and the techniques which the support vector machine has integrates including the optimal hyperplane, the classification interval, the optimization theory are summarized. At the same time, the kernel function, which is an important module of the support vector machine is described and the performance of differnt kernel functions are compared. Then, several existing multi-class support vector algorithms including the one-time algorithm, one versus rest algorithm, one versus one algorithm and the acyclic graph algorithm are analyzed and their performance, advantages and disadvantages are compared. Aming at the problem that there exsits some wrongly classified region or refused region in the above algorithms and the difficulty to determine the structure of the binary tree in the binary tree support vector machine algorithm, a support vector machine algorithm based on the between-class dissimilarity matrix is presented after the two novel concepts of the shorter neighboring distance and the between-class dissimilarity matrix are defined. In the simulation, the results of the new algorithm are compared with that of one versus one algorithm, one versus rest algorithm and the acyclic graph algorithm, which verifies that the alogrithm is correct and effective.
In the last part of the thesis, the support vector machine algorithm based on the between-class dissimilairity matrix is applied to the recognition for the types of cable fault. The fault types are finally effectively recognized after selecting a better parameter by trying differernt kernel parameters to build the multi-class support vector machine model.
引文
[1]肖健华.智能模式识别方法[M].广州:华南理工大学出版社,2006.
[2]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):32-42.
[3]章兢,张小刚等编著.数据挖掘算法及其工程应用[M].北京:机械工业出版社,2006.
[4]魏丹.支持向量机多分类预测技术研究[D].西安科技大学,2008,1-3.
[5]张南,刘军杰,刘志军.基于支持向量机的模式识别方法研究[J].舰船科学技术,2006,28 (5): 94-95.
[6]杨雪.支持向量机多类分类方法的研究[D].哈尔冰工程大学,2006,2-4.
[7]宋召青,崔和,胡云安.支持向量机理论的研究与进展[J].海军航空工程学院学报,2008,23(2):143-145.
[8]李晓宇,张新峰,沈兰荪.支持向量机(SVM)的研究进展[J].测控技术,2006,25(5):7-9.
[9]肖燕彩.支持向量机在变压器状态评估中的应用研究[D].北京交通大学, 2008,14-15.
[10] XIAN Guang-lin.Statistical learning theory and support vector machine[J].China Science and Technology Information,2005,4(2):21-23.
[11] ZHENG Yongtao.An analysis of multi-class support vector machines[J].Computer Engineering and Applications,2005,41(23):19-19.
[12]朱燕飞,谭洪舟,章云.基于LS-SVM的非线性系统盲辨识[J].广东工业大学学报,2007,24(2):76-78.
[13]刘伟华,李峰.基于支持向量机分数等级融合的虹膜识别方法[J].计算机工程与应用,2008,44(27):184-186.
[14]吴进军,杜树新.SVM在车牌字符识别中的应用[J].电路与系统学报,2008,13(1):84-85.
[15]万涛,邹维,万谦,何晓庆.结合无监督聚类的SVM二叉树在SAR自动目标识别系统中的应用[J].成都大学学报(自然科学版),2008,27(2):134-136.
[16]吴德会.基于支持向量机的非线性动态系统辨识方法[J].系统仿真学报,2007, 19(14):3170-3172.
[17]何学文,孙林,付静.基于小波分析和支持向量机的旋转机械故障诊断方法[J].中国工程机械学报,2007,5(1):86-90.
[18]邹淑雪.基于支持向量机的蛋白质结构域预测方法研究[D].吉林大学,2009,31-33.
[19]祁亨年.支持向量机及其应用研究综述[J].计算机工程,2004,30(10):6-8.
[20]黄勇,宋忠虎.多类支持向量机算法综述[J].计算机技术与自动化,2005,24(4):61-62.
[21]郭世杰.基于支持向量机的多分类问题的研究[D].上海师范大学,2005,4-9.
[22] Burges CJC.A tutorial on support vector machines for pattern recognition[J]. Data Miningand Knowledeg Discovery,1998,2(2):121-167.
[23] LI Kunlun,HUANG HouKuan,TIAN Shengfeng.A novel multi-class SVM classifier based on DDAG[J].Pattern Recognition and Artificial Intelligence,2003,16(2):164-168.
[24]边肇祺,张学工.模式识别[M].北京:清华大学出版社,2002.
[25]白鹏,张喜斌,张斌等.支持向量机理论及工程应用实例[M].西安:西安电子科技大学出版社,2008.
[26]李焕荣,林健.基于一类分类方法的多类分类及其应用[J].华南理工大学学报,2004,32 (8):83-84.
[27] Jiang ZQ,Fu H G,LiL J.Support Vector Machine for Mechanical Faults Classification[J]. Journal of Zhejiang University Science,2005,6 (5):433-439.
[28] Keerthi S S,Lin C J. A symptotic behaviors of support vector machines with gaussian Kernel[J].Neural Computation,2003.
[29]荆双喜,华伟.基于小波-支持向量机的齿轮故障诊断研究[J].山东科技大学学报,2008.
[30]刘丙状.最优化问题的Lagrangian对偶理论与SQP方法[D].曲阜师范大学,2005,20-25.
[31] Nello Cristianini,John Shawe-Taylor著,李国正译.支持向量机导论[M].北京:电子工业出版社,2004.
[32] M.Anitescu.On the rate of convergence of sequential quadratic programming with nondifferentiable exact penalty function in the presence of constraint degeneracy[J]. Mathematical Programming,2002,92:359-386.
[33] A.M.Rubinov,B.M.Glover,and X.Q.Yang.Modified Larange and penalty functions in continuous optimization[J].Optimization,1999,46:327-351.
[34]李昆仑.一种基于有向无环图的多类SVM分类器[J].模式识别与人工智能,2003,16 (2):164- 168.
[35] Sergios Theodoridis,Konstantino Koutroumbas.Pattern Recognition[M].北京:机械工业出版社,2003.
[36] .A.Smola,B.Scholkopf,K.R.Muller.The Connection Between Regularization Operators and Support Vector Kernels[J].Neural Network,1998,11:637-649.
[37] Vapnik V,Levin E and Le Cun Y.Measuring the VC Dimension of a Learining Machine[J].Neural Computation,1994,6:851-876.
[38] Ying Tan,Jun Wang.A Support Vector Machine with a Hybrid Kernel and Minimal Vapnik-Chervonenkis Dimension[J].IEEE Transaction on Knowledge and Data Engineering,2004,(4):385-395.
[39] Suykens JAK and Vandewalle J.Least Squares Support Vector Machine Classifiers[J]. Neural Processing Letters,1999,9(3):293-300.
[40]张冰,孔锐.一种支持向量机的组合核函数[J].计算机应用,2007,27(1):44-46.
[41]王国胜.核函数的性质及其构造方法[J].计算机科学,2006,33(6):172-174.
[42]袁玉波,杨传胜,等.数据挖掘与最优化技术及其应用[M].北京:科学出版社,2007.
[43]魏朗,余强.现代最优化设计与规划方法[M].北京:人民交通出版社,2005.
[44]侯媛彬,杜京义,汪梅.神经网络[M].西安:西安电子科技大学出版社,2007.
[45]黄琼英.支持向量机多类分类算法的研究与应用[D].河北工业大学,2005.
[46]刘志刚,李德仁,秦前清,史文中.支持向量机在多类分类问题中的推广[J].计算机工程与应用,2004(7).
[47]唐发明等.支持向量机多类分类算法研究[J].控制与决策,2005,20(7):746- 749.
[48]潘继斌.核函数的概念、性质及其应用[J].湖北师范学院学报(自然科学版),2007, 27(1):10-12.
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[53]赵春晖,陈万海,郭春燕.多类支持向量机方法的研究现状与分析[J].智能系统学报,2007,2(2):12-13.
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[55] Wang Mei,Tania Stathaki.Online fault recognition of electric power cables in coal mine based on a minimum risk neural network[C].Journal of Coal Science&Engineering.2008, 14(3):492-496.
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[57]何仰赞,温增银.电力系统分析[M].武汉:华中科技大学出版社,2002,95-96.
[2]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):32-42.
[3]章兢,张小刚等编著.数据挖掘算法及其工程应用[M].北京:机械工业出版社,2006.
[4]魏丹.支持向量机多分类预测技术研究[D].西安科技大学,2008,1-3.
[5]张南,刘军杰,刘志军.基于支持向量机的模式识别方法研究[J].舰船科学技术,2006,28 (5): 94-95.
[6]杨雪.支持向量机多类分类方法的研究[D].哈尔冰工程大学,2006,2-4.
[7]宋召青,崔和,胡云安.支持向量机理论的研究与进展[J].海军航空工程学院学报,2008,23(2):143-145.
[8]李晓宇,张新峰,沈兰荪.支持向量机(SVM)的研究进展[J].测控技术,2006,25(5):7-9.
[9]肖燕彩.支持向量机在变压器状态评估中的应用研究[D].北京交通大学, 2008,14-15.
[10] XIAN Guang-lin.Statistical learning theory and support vector machine[J].China Science and Technology Information,2005,4(2):21-23.
[11] ZHENG Yongtao.An analysis of multi-class support vector machines[J].Computer Engineering and Applications,2005,41(23):19-19.
[12]朱燕飞,谭洪舟,章云.基于LS-SVM的非线性系统盲辨识[J].广东工业大学学报,2007,24(2):76-78.
[13]刘伟华,李峰.基于支持向量机分数等级融合的虹膜识别方法[J].计算机工程与应用,2008,44(27):184-186.
[14]吴进军,杜树新.SVM在车牌字符识别中的应用[J].电路与系统学报,2008,13(1):84-85.
[15]万涛,邹维,万谦,何晓庆.结合无监督聚类的SVM二叉树在SAR自动目标识别系统中的应用[J].成都大学学报(自然科学版),2008,27(2):134-136.
[16]吴德会.基于支持向量机的非线性动态系统辨识方法[J].系统仿真学报,2007, 19(14):3170-3172.
[17]何学文,孙林,付静.基于小波分析和支持向量机的旋转机械故障诊断方法[J].中国工程机械学报,2007,5(1):86-90.
[18]邹淑雪.基于支持向量机的蛋白质结构域预测方法研究[D].吉林大学,2009,31-33.
[19]祁亨年.支持向量机及其应用研究综述[J].计算机工程,2004,30(10):6-8.
[20]黄勇,宋忠虎.多类支持向量机算法综述[J].计算机技术与自动化,2005,24(4):61-62.
[21]郭世杰.基于支持向量机的多分类问题的研究[D].上海师范大学,2005,4-9.
[22] Burges CJC.A tutorial on support vector machines for pattern recognition[J]. Data Miningand Knowledeg Discovery,1998,2(2):121-167.
[23] LI Kunlun,HUANG HouKuan,TIAN Shengfeng.A novel multi-class SVM classifier based on DDAG[J].Pattern Recognition and Artificial Intelligence,2003,16(2):164-168.
[24]边肇祺,张学工.模式识别[M].北京:清华大学出版社,2002.
[25]白鹏,张喜斌,张斌等.支持向量机理论及工程应用实例[M].西安:西安电子科技大学出版社,2008.
[26]李焕荣,林健.基于一类分类方法的多类分类及其应用[J].华南理工大学学报,2004,32 (8):83-84.
[27] Jiang ZQ,Fu H G,LiL J.Support Vector Machine for Mechanical Faults Classification[J]. Journal of Zhejiang University Science,2005,6 (5):433-439.
[28] Keerthi S S,Lin C J. A symptotic behaviors of support vector machines with gaussian Kernel[J].Neural Computation,2003.
[29]荆双喜,华伟.基于小波-支持向量机的齿轮故障诊断研究[J].山东科技大学学报,2008.
[30]刘丙状.最优化问题的Lagrangian对偶理论与SQP方法[D].曲阜师范大学,2005,20-25.
[31] Nello Cristianini,John Shawe-Taylor著,李国正译.支持向量机导论[M].北京:电子工业出版社,2004.
[32] M.Anitescu.On the rate of convergence of sequential quadratic programming with nondifferentiable exact penalty function in the presence of constraint degeneracy[J]. Mathematical Programming,2002,92:359-386.
[33] A.M.Rubinov,B.M.Glover,and X.Q.Yang.Modified Larange and penalty functions in continuous optimization[J].Optimization,1999,46:327-351.
[34]李昆仑.一种基于有向无环图的多类SVM分类器[J].模式识别与人工智能,2003,16 (2):164- 168.
[35] Sergios Theodoridis,Konstantino Koutroumbas.Pattern Recognition[M].北京:机械工业出版社,2003.
[36] .A.Smola,B.Scholkopf,K.R.Muller.The Connection Between Regularization Operators and Support Vector Kernels[J].Neural Network,1998,11:637-649.
[37] Vapnik V,Levin E and Le Cun Y.Measuring the VC Dimension of a Learining Machine[J].Neural Computation,1994,6:851-876.
[38] Ying Tan,Jun Wang.A Support Vector Machine with a Hybrid Kernel and Minimal Vapnik-Chervonenkis Dimension[J].IEEE Transaction on Knowledge and Data Engineering,2004,(4):385-395.
[39] Suykens JAK and Vandewalle J.Least Squares Support Vector Machine Classifiers[J]. Neural Processing Letters,1999,9(3):293-300.
[40]张冰,孔锐.一种支持向量机的组合核函数[J].计算机应用,2007,27(1):44-46.
[41]王国胜.核函数的性质及其构造方法[J].计算机科学,2006,33(6):172-174.
[42]袁玉波,杨传胜,等.数据挖掘与最优化技术及其应用[M].北京:科学出版社,2007.
[43]魏朗,余强.现代最优化设计与规划方法[M].北京:人民交通出版社,2005.
[44]侯媛彬,杜京义,汪梅.神经网络[M].西安:西安电子科技大学出版社,2007.
[45]黄琼英.支持向量机多类分类算法的研究与应用[D].河北工业大学,2005.
[46]刘志刚,李德仁,秦前清,史文中.支持向量机在多类分类问题中的推广[J].计算机工程与应用,2004(7).
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