基于径向基函数神经网络的滚动轴承故障模式的识别

2004262EngineeringScienceFeb.2004Vol16No12[]2003-08-21;2003-10-23[](9910)[](1957-),,,,,,(,130025)[](RBF)3,,,AR,AR,,[];;AR;RBF;[]TH133133;TP183[]A[]1009-1742(2004)02-0056-051,[1,2],,131031,,,,,,,,,,,PQ,2AR(P)AR(P)x(n)=-a1x(n-1)-a2x(n-2)--ap(x-P)+w(n),(1)w(n),2W[3]:(ARMA)(MA),ARMAMA,AR(P)P©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(i=1,2,,P),AR(P)AR(P0)[4]x(n)=-6P0k=1akx(n-k)+w(n)(2)x(n)P^x(n)=-6Pk=1^akx(n-k)(3)e(n)=x(n)+6Pk=1^akx(n-k)(4)P=6e(n)2=6x(n)+6^akx(n-k)2(5)P^ak3(RBF),[58],()BPRBFyi=fi(x)=6Nk=1Wikk(x-ck2)(6)Guassian,752:©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(x)=exp-x-ck222k(7)Guassian,xc,x,,c,x-cc,(x-c)[7]:Guassian3,RBFckkWk1ck,ck2:=dmaxK,(8)dmaxEucilidean;Kck34x(n)^yi(n):^y(n)=6Nk=1Wk(x(n),ck,k)(9)5RBF:W(n+1)=W(n)+We(n)(n),(10)ck(n+1)=ck(n)+ce(n)Wk(n)2k(n)(x(n),ck(n),k)(x(n)-ck(n)),(11)k(n+1)=k(n)+e(n)Wk(n)2k(n)(x(n),ck(n),k)x(n)-ck(n)2(12):(n)=(x(n),c1,1),(x(n),c2,2),L,(x(n),cN,N)T;e(n)=^yi(n)-yd(n);yd(n);W,c,36,,44RBFARRBF,,,22Fig12Recognizingnetworkmodeloffaultpatternofrollingbearing2,RBF,,,AR,^aRBF,,,AR^a,5RBF3103,136,12,5,10247,9,8,RBFAR20,20,3()015%,25,20,20RBF,,1RBF,234234,12,14,12,70%;32,30,33,70%;22856©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[9],,1RBFTable1PartdataofRBFnettrainingandrecognizingresults31012AR(20)123456789101112a1-010450011756016451010455013711-014279016421014607-011442-012410-012288019647a2-010681-012765010884011531013904019462016698016129110797018895019735013203a3010919-010979-010780010061-010905-019944-012985010403-010282-011105011016010614a4-010122010564-011747010992014630112489-012156013082016068012702013386010936a5-010017011839-011279-010228010614-111650-012782-012232012100012163013752-010078a6010533-012205-011200010114010875113291010298-011054011963010247-010606-010554a7-010838-010096-010775010617-012833-110379011067-012867012835012284013966-010083a8010138011720010987010044014609110183011040-010427012409010474-010229-010166a9011388011816011142011442011092-018075010792-011990011876011754010464-010387a10010241011149010658010603013042015072-010462-011823011473010416011876-010256a11010144-011295-010459-010091-011397-011977-010816010645011451-010046-011051-011645a12-010013-010880-011062010216012632010606-011374010326011437-010023012056-010026a13010124011030-011056010047010023011416010003012043011426010005-010741013075a14010155010592010571-010413010992-012256010368010708010745010877010397013517a15010737-011170010662-010671-010959013751011533012627010645-010205010334013111a16-010298-010488011391-010180012170-012787-010363010736-010151010530-010742011896a17010612011453-010176-010686010199013258-010902011205-010420-010215010769010799a18-010569010208-011079010037011345-011631-010732-010637-011119-010699010036-010749a19-011045010856-010027010524-010294012336010159010363-010192010430010855-011192a20-010346-010489-010649-011368011265-011553010272-010430-011011-011257011017-01006231122333,1,2,32Table2Amountoftrainingsamplesandaccuraterecognizingresultsofnormalbearings1012141618202224262830323401420157017101730172018101890192019301870182016701573Table3Amountoftrainingsamplesandaccuraterecognizingresultsofbearingswithouterringsfault101214161820222426283032340135016701650191019401930193019101890174016501610161952:©1994-2006ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[1],,,.[M].:,2001[2],,,.[M].:,2001[3]ManolakisDG,IngleVK,KogonSM.[M].:,2003[4],.[M].:,1986[5]ChenS,CowanCFN,GrantPM.Orthogonalleastsquareslearningalgorithmforradialbasisfunctionnetworks[J].IEEETransNeuralNetworks,1991,(2):302309[6]HaykinS.NeuralNetworks:AComprehensiveFoundation(SecondEdition)[M].PrenticeHall,1999[7]HamFM,KostanicI.PrinciplesofNeuroComputingforScience&Engineering[M].McGrawHill,2001[8]HushDR,HorneBG.Progressinsupervisedneuralnetworks:whatpsnewsinceLippmann?[J].IEEESPMagazine,1993,10(1):839[9],.[M].:,2003FaultPatternRecognitionofRollingBearingBasedonRadialBasisFunctionNeuralNetworksLuShuang,ZhangZida,LiMeng(CollegeofMachineryandEngineering,JilinUniversity,Changchun130025,China)[Abstract]Radialbasisfunctionneuralnetworkisatypeofthree-layerfeedforwardnetwork.Ithasmanygoodproperties,suchaspowerfulabilityforfunctionapproximation,classificationandlearningrapidly.Inthispaper,inthelightofthemeritofradialbasisfunctionneuralnetworkandonthebasisofthefeatureanalysisofvibrationsignalofrollingbearing,ARmodelispresentedbyusingtimeseriesmethod.RadialbasisfunctionneuralnetworksisestablishedbasedonARmodelparameters.Inthelightofthetheoryofradialbasisfunctionneuralnetworks,faultpatternofrollingbearingisrecognizedcorrespondingly.Theoryandexperimentshowthattherecognitionoffau