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旋转机械设备关键部件故障诊断与预测方法研究

发布时间:2016-10-05 17:54

  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:

a6。∑商/L一%、JO

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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