旋转机械设备关键部件故障诊断与预测方法研究
本文关键词:旋转机械设备关键部件故障诊断与预测方法研究,由笔耕文化传播整理发布。
CHAP‘IER5AGENERICSUPPORT;min要11w112+c宝(专+六+),_f2l;IJ,,一W?工,一b≤占+六(5.8);sj.\w?Xi+b—yl§s+考:.;【缶,缶+≥0;InEq.(5.8),卣and茧+denote;errorstheslackvariable,C;follow:largerthan±£;l孝I;Fig?5?4(
CHAP‘IER5AGENERICSUPPORTVECTORREGRESSIVECLASSIFIER
min要11w112+c宝(专+六+),_f2l
IJ,,一W?工,一b≤占+六(5.8)
sj.\w?Xi+b—yl§s+考:.
【缶,缶+≥0
InEq.(5.8),卣and茧+denote
errorstheslackvariable,Cisusings—insensitiveapositiveconstantwhichlossfunctiongivenaSpenalizesthe
follow:largerthan±£
l孝I。={苫Jif—s,。『tfhIe<rw占ise.
Fig?5?4(a)shows
5.4(b)showsthe占一insensitivelossfunction.(5.9)theregressionline,theupperandlowerboundarylines.Fig.
Fig?5.4TheregressionlineofSVRisshownin(a)andthelossfunctionofSVRisshownin(b).
Tosolvetheoptimizationproblemprovidedby
equationisrequiredtobeconstructed:Eq.(5.8),thefollowingLagrange
上=吾nol,2+喜c(专嘲一喜(仍戋+矿占)
一,(5.10)。∑闰口,LS+毒一y+W■+6、,一●
。∑脚口I,LF十占+M—W一一6、J
whereQl,Z,,ql,戎areLagrangemultiplierswhichhavetosatisfythefollowingconstraints:
口,,Ofi+,r/i,叩≥0,
65(5.11)
CHAPTER5AGENERICSUPPORTVECToRREGRESSIVECLASSIFIERThepartialderivativesoftheLagrangeequationLwithrespecttotheprimalvariables(co,b,毒,等)havetovanishforoptimality:
砚
a6。∑商/L一%、JO
钇
0co=∞一∑(%一西ki=1
I’0(5.12)q1:o要:c8{;
詈一ct徊
Bysubstituting
asEq.(5.12)intoEq.(5.10),thedualoptimizationproblemisgivenfollow:
maX一昙窆(%一口顶哆一巧)(一
‘i,j=l
●●0、J一占。∑H/Lq+口\J+。∑Ⅲy/L口一ocl),(5.13)
S。∑褂,L口一口、J0and%,口^[o,C】
ByexploitingKarush.Kuhn-Tucker(KKT)conditions(Smolaetal?2004),the
thefollowingformula:computationofbisdoneby
一w
w一S6lI"M一t薯+Sf弦or≥嚣三,
regression@均functionisThen.by
presentedaslinearsolvingtheoptimizationproblem,afollows:
厂(功=∑(%一Z)(薯,曲+6,
I-l(5.15)
Thelinearregressionfunctionisnotsufficient
toenoughtoprocessthenon-linearvectorintoahigh
aSproblem.Thekernelfunctionisappliedheremaptheinputdimensionalfeaturespaceandthustheregressivefunctionisderivedfollow:
厂@)=∑(%一西)K(一,x)+6,(5.16)
i=1
whereK(薯,x)=烈t)?p(x)is
SVM,theasymmetricpositivedefinedkernelfunctiongivenbytheMercer’Stheorem[146].Similartothe
thiswork.RBFkernelfunctionwritteninEq.(5.6)isadoptedin
5.3Proposedhealthstatusidentificationscheme
Fig?5.5TheframeworkoftheproposedintelligentmachinefaultdiagnosisschemeTheproposednCWintelligentmachinefaultdiagnosisschemesteps:faultfeatureextraction,sensitivefaultfeatureselectionandrecognition.Eachstepincludesthreefaultpatternindetailsisillustratedinthefollowingsubsections.TheframeworkoftheproposedschemeisdepictedinFig5.5.
5.3.1Faultfeatureextraction
Thevibrationsignalscollectedbyaccelerometers
packetarefirstprocessedbyawavelettransformatdifferentdecompositiondepthstoenhancethesignal..to..noiseratio.ThewaveletpacketcoefficientsatdifferentdecompositiondepthsarereferredtoastheWPTpaving.Thepavingofwaveletpacketsatamaximumdepthof3isplottedinFig.5.6.67
NodeNode
(1,0)(1,1)
NodeNodeNOdeNode
(2,0)(2,1)(2,2)(2,3)
NodeNodeNOdeNodeNodeNodeNodeNode
(3,0)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(3,7)
Fig.5.6TIlepavingofwaveletpacketsatthemaximumdepthof3
A11waveletpacketcoefficientsatdifferentdepthsareconsideredbecauseitIS
todeclaredefinitivelythatthoseatacertaindeptharebetterthanthoseat
another.Thetypicalexampleisthekurtosisofwaveletpacketcoefficientpaving,
Leieta1.[147]referredtoasanimprovedkurtogram.Theirresultsshowedthatmaximumkurtosisofthecoefficientsofwaveletpacketscouldbeobtainedatdifferentdepths.Hence,itismorereasonabletoextractthefaultfeaturesfromthe
ofwaveletpackets(thewaveletpacketcoefficientsatdifferentdepths).The
ninestatisticalparameterslistedinTable5.1areextractedfromthepavingofwaveletpacketsatdifferentdecompositiondepths.Ingeneral,themaximumwaveletpacketdecompositionlevelof3iseffectiveforfeaturesextractionpurpose[104,105].Asaresult,afeaturesetcontaining126featuresforeachsampleisobtained.
Table5.1Theninestatisticalfeatureparameters.
K…i8:专∑#,』Vl=t:ssenwekS专∑i=l#,』T
Crestfactor:max(I—1)
√专酽斤—广’Cle一鼬r:爵max(而Ix,1),
Shapefactor:√专善#max(I五1)Impulseindicator:
●一ⅣⅣ∑斟●一ⅣⅣ∑Ⅲ
Ⅷ一:专缸squareroot蛐pltmaeVa?u“专喜佩)2,舳烈—…删ituaeva?ue:专磐1.difficultwhichthepaving
CHAPTER5AGENERICSUPPORTVECToRREGRESSIVECLASSIFIER
5.3.2Faultfeatureselection
Theninestatisticalfaultfeaturesbasedonwaveletpacketcoeffieientshavetheirownparticularmeaningsindescribingthedifferentaspectsofamachine’Shealthstatus.Thewaveletpacketsatamaximumdepthof3produce126faultfeatures.Itshouldbenotedthatthepacketshavedifferemsensitivitycontributionsforclassification[103].Inotherwords,toomanyinputparametersforaclassifiercangreatlydecreaseitsidentificationaccuracyandgreatlyincreasethecomputationalburden.Hence,itisnecessarytocarryoutsensitivefaultfeatureselection.Sensitivefaultfeaturesusuallyexhibitasmalldegreeofvarianceforsamplesbelongingtothesameclassandarelativelylargedegreeforthosebelongingtodifferentclasses.OneofthemosteffectivemethodsformeasuringthedifferentsensitivitiesofthesefeaturesistheDET,andtheproceduresofthismethodarepresentedasfollow.
Assumefeatureparameterset{厶,c’,,m=1,2,...,必;c=1,2,...,C;j=1,2….,J},wherefm,。,』isdenotedasthejthfeatureparameterinthecaseofthemthsamplecollectedunderthe础condition.Here,尥,CandJarethemaximumnumberofsamplesunderthecthcondition,themaximumnumberofconditionsa11dt11emaximumnumberofstatisticsforeachsample,respectively.Obviously,thereareMcxCxJfaultfeatureparametersina11.ThefeatureselectionprocedureproceedsinthefollowingsteDs.
Stepl?Calculatetheaveragedistancedc,Jofthesamecondition
而1×隧k,吒,1]一嘶∽samplesby
Step2.CalculatetheaveragedistanceofCconditionsby:
1c
∥=I,X∑吃,(5.18)LC=I
Step3.Calculateaveragedistancebetweendifferentconditionsby:
巧∞=云≮i甚二面xC;J”。,,一心,,『],c≠P,(5.?9)
where
%,=瓦1×弘∥‰=击x弘,@2。,
Step4.CalculatetheratioAitoevaluatethejthfeatureby69
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本文关键词:旋转机械设备关键部件故障诊断与预测方法研究,由笔耕文化传播整理发布。
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