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基于核算法的故障智能诊断理论及方法研究摘要设备故障诊断与监测技术是一门正在不断发展和完善的新技术，它具有保障安全生产，防止突发事故，节约维修费用等特点，在现代化大生产中发挥着重要的作用。然而正是因为生产设备结构日趋复杂及内部关系日益密切，造成了设备运行状态监测和故障诊断的难度不断增大，迫使人们需要不断探索新的理论或方法来解决实际中所遇到的问题。自20世纪60年代以来，以Vapnik为代表的研究人员致力于统计学习理论的研究，并在此基础上创建出一类新的机器学习算法：支持向量机(SupportVectorMachine，SVM)。正是核函数在SVM的成功应用，基于核函数的学习方法(简称核算法)的研究受到重视。将核算法应用到故障诊断中有望解决其中的非线性、不精确性和不确定性等问题，为该领域的研究提供了全新且可行的研究途径。基于核算法的故障智能诊断技术，在国际上都属于一个全新的研究领域，这一方法在实际应用中还有许多问题值得进行深入的研究和探讨。本论文围绕核算法在故障智能诊断中的应用，对故障诊断中不确定信息的处理、故障诊断实时性的实现、核函数的选择和参数优化、多类故障诊断、早期故障的发现以及样本数据的压缩等几个方面进行了较为系统深入的研究，为核算法应用于故障诊断提供了理论依据，促进了故障诊断技术的发展。论文的主要工作及创新之处为：针对故障诊断中两类误判造成损失不等的情况，提出一种基于几何距离的后验概率计算方法；在定义基于风险的诊断可信度的基础上，将SVM与贝叶斯决策理论相结合，提出一种基于最小风险的SVM方法；并且将该方法应用于电液伺服阀故障诊断实例，证实了该方法的可行性。针对单值SVM只训练单类别样本的特点，证明了径向基核函数的参数s→0和s→∞时两个定理；探索了两种支持向量(边界支持向量或非边界支持向量)与目标识别率的关系，提出一种改进的“留一法”模型参数选择方法，该方法在确保分类器泛化性能的前提下，大大减少模型参数选择的时间，可针对性地确定目标识别率或非目标识别率。面对时变系统的故障诊断，提出了一种基于滚动时间窗的单值SVM学习算法，为将单值SVM实用化作出了努力。提出了将单值SVM推广到多故障诊断的两种方法，并将之应用到基准数据库和液压泵多故障识别中，不仅解决了目前存在的SVM多值分类方法存在的不属于任何一类以及同时属于多类的情况，同时提高了算法的训练与决策速度。针对支持向量回归机(SupportVectorRegression，SVR)模型参数选择难的问题，探究了SVR各参数对其性能的影响，提出了一种基于遗传算法的SVR参数自动优化的方法；并且通过建立SVR预测模型，用于实现早期故障诊断以及强混沌背景下微弱信号的检测。仿真验证，该方法比径向基神经网络更具有稳健性和泛化性。最后，详细讨论了核矩阵维度缩减问题，给出了残差估计的界定理；在综合考虑选取列的独立性和残差范数大小两者关系的基础上，提出了解决核矩阵维度缩减的启发性算法－贪心算法。并在此基础上，在再生核Hilbert空间又提出一种稀疏性回归算法。关键词：故障诊断；机器学习；支持向量机；核算法；多类故障；早期故障诊断；核矩阵Subject:StudyonTheoryandMethodsofIntelligentFaultDiagnosisBasedonKernelAlgorithmSpecialty:SafetyTechnologyandEngineeringName:DuJing-yi(signature)Instructor:HouYuan-bin(signature)AbstractThenewtechniqueoffaultdiagnosisandmonitoringofequipmentsisdevelopingandperfectingcontinuously.Itplaysanimportantroleinthemodernduplicateproductionswiththecharacteristicsthatsafeguardsthesafetyproductionandpreventsfromtheaccidentsandsavesthemaintenancecosts.However,themorecomplexstructuresofthefacilitiesanditscloserinnerconnectionincreasethedifficultiesindiagnosingfaultandmonitoringtherunningstateoftheequipments.Thenewtheoriesandmethodshavetobeinvestigatedinordertosolvetheproblemsencounteredinreality.Since1960s,researchersrepresentedbyVapnikhavedevotedthemselvestothestudyonstatisticlearningtheory.Theyestablishedanewtypeoflearningalgorithm,supportvectormachine(SVM),basedonthestatisticlearningtheory.ItisthesuccessfulapplicationofkernelfunctiontoSVMthatthestudyonlearningalgorithmbasedonkernelfunctionsorkernelalgorithmforsimplificationhasattractedgreatinterest.Applyingthekernelalgorithmtofaultdiagnosiswillsolvethenon-linear,impreciseanduncertainproblems.Thisprovidesacompletelynewandfeasibleapproachinthedomain.Manyproblemsareworthdeeplystudyinganddiscussingaboutthepracticeoftheapproachforthetechniqueofintelligentfaultdiagnosis,basedonkernelalgorithm,isabrandnewfieldintheworld.Thispaperprovidesthetheoreticalfoundationsfortheapplicationsofkernelalgorithmtofaultdiagnosesthoughthedeepandsystematicalstudyontheapplicationofkernelalgorithmtointelligentfaultdiagnosis,theprocessingoftheuncertaininformationinthediagnosis,thereal-timerealizationoffaultdiagnoses,thechoiceofkernelfunctionandparameteroptimization,multipleclassesoffaultdiagnoses,andincipientfaultdiagnosis,andthesampledatacompaction.Thus,itpromotesthedevelopmentoffaultdiagnosestechnique.Themaintasksandtheinnovationsworksareasthefollows.Aposteriorprobabilityalgorithmispresentedbasedonthegeometricdistancetosolvetheproblemthatthemiscarriageofjusticeintwoclassescausesthedifferentlossinthefaultdiagnosis,Furthermore,aSVMmethodonthebaseoftheminimumriskisproposedbycombiningtheSVMwiththeBayesiandecisiontheoryafterthedefinitionofthedegreeofdiagnosisconfidence.Finally,themethodisvalidatedbyapplyingittothepracticalfaultdiagnosisofelectro-hydraulicservovalve.Twotheoremsabouttheradialbasisfunctionontheparameterconditionofs→0ors→∞arepresentedandprovedaimingatthecharacteristicsthattheone-classofsamplesistrainedbytheone-classSVM.Thispaperexplorestherelationbetweenthetwotypesofsupportvectors(boundarysupportvectorsandnon-boundarysupportvectors)andtherecognitionrateofobject;proposesanimprovedmethodofthemodelparameterchoiceof“leaveoneout”;whichdramaticallydecreasesthetimeofmodelparameterchoiceinthepreconditionofgeneralizingperformanceofclassifier,sothattherecognitionratesoftheobjectsandthenon-objectsaredeterminedonpurpose;presentsanewone-classSVMlearningalgorithmbasedontime–rollingwindowforthefaultdiagnosisofdynamicsystem,whichwillcontributetothepracticalapplicationofone-classSVM.Inaddition,twomethodsarepresentedthoughwhichtheoneclassSVMisextendedintomultiplefaultsdiagnoses.Ifthemethodsareappliedtothefiduciallydatabaseandthehydraulicpressurepumprespectively,wecansolvetheproblemexistinginthemethodoftheavailableSVMmulti-classclassificationthattheobjectdoesnotbelongtoanyclassortheobjectbelongstomorethanoneclasssimultaneouslyandspeedupthetraininganddecisionmakingofthealgorithm.Aimingatthedifficultyofchoosingtheparametersofsupportvectorregression(SVR)model,anautomaticallyoptimizedmethodofSVRparameterispresentedbasedonthegeneticalgorithmaftertheinfluenceofeachSVRparameteronSVRperformance.Inaddition,incipientfaultdiagnosisa