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A semi-automatic approach for thermographic inspection of electrical installations within buildings

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A semi-automatic approach for thermographic inspection of electrical installations within buildings
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  EnergyandBuildings55(2012)585–591 ContentslistsavailableatSciVerseScienceDirect Energy   and   Buildings  j   ournalhomep   age:www.elsevier.com/locate/enbuild A   semi-automatic   approach   forthermographic   inspection   of    electricalinstallations   within   buildings A.S.   Nazmul   Huda a ,Soib   Taib a , ∗ ,Mohd   Shawal    Jadin b ,   Dahaman   Ishak a a SchoolofElectricalandElectronicEngineering,UniversitiSainsMalaysia,14300NibongTebal,PulauPinang,Malaysia b FacultyofElectrical&ElectronicEngineering,UniversitiMalaysiaPahang,26600Pekan,Pahang,Malaysia a   r   t   i   c   le   i   nf   o  Articlehistory: Received20June2012Receivedinrevisedform4September2012Accepted17September2012 Keywords: ElectricalinstallationInfraredimageMultilayeredperceptronStatisticalfeaturesConditionsclassificationBuilding ab   s   t   ra   ct Maintaining   the   reliability   of    electrical   installationhasbecome   partof    the   energy   efficiency   practices   inbuilding.   Thedegradation   of    electrical   installations   can   cause   overheating,which   canlead   tosubsequentfailure   of    the   equipments   that   can   potentially   result   inunplanned   power   outages,   possibleinjury   andfire   hazard.   In   addition,   the   efficiency   of    an   electrical   systembecomeslowprior   to   failure,   thusenergyisspent   generating   heatand   causing   unnecessaryenergy   loses.   Therefore,earlyprevention   is   requiredtoavoid   thissituation   by   monitoring   the   reliabilityof    the   electricalinstallations   through   energyauditpractices.   Thisarticle   proposesa   semi-automatic   approach   for   evaluating   thethermal   condition   of    elec-tricalinstallations   within   thebuildinginMalaysia   by   analyzing   its   infrared   image.   Initially   the   interestregions   of    the   images   are   manuallysegmented.   Thenthe   statistical   featuresof    first   orderhistogram   andgray   levelco-occurrence   matrix   featuresas   well   asthedifferencesof    feature   parameters   between   hotand   referenceregionsare   extracted   from   segmented   regions.   Principle   component   analysis   is   applied   forthe   bestfeaturesselection   and   atthe   final   stage,the   condition   of    electrical   equipmentswill   be   classifiedusingmultilayered   perceptron   neuralnetwork.Theperformances   of    multilayeredperceptron   networkshavebeen   compared   and   testedwith   varioustrainingalgorithms.Theclassification   accuracy   of    mul-tilayered   perceptron   networks   are   also   compared   with   discriminant   analysis   classifier   and   itisfoundthatthe   multilayeredperceptron   networkusing   Levenberg–Marquardt   algorithm   givesthe   besttestingperformance.   Theresult   showsthatthemaximumtesting   accuracy   78.5%   wasobtained.©2012   ElsevierB.V.Allrights   reserved. 1.Introduction Accordingtothelatestreport[1]of    FireandRescueDepartmentofMalaysiaaboutthecausesoffirein   buildings,2317firerelatedincidentshaveoccurredbetweenJanuary2012andJune2012,mak-ingtheaveragenumberof    incidentsaround387a   month.Inthisreport,1049offireswerecausedbyelectricalproblemswhichwasabout46%ofthetotalcausesoffirein   buildingandweremainlyinvolvedtheelectricalwiringproblems(809cases)andfailureof electricalequipments(240cases).Failurein   electricaldistributionequipmentscanpotentiallyproduceanignitionandfire.Oneof thecausesofignitionis   excessiveohmicheatingin   electricaldis-tribution[2].   Thisconditioncanoccurespeciallyforoldbuildingswithoutdatedelectricalwiringthatis   deteriorating,inappropri-atelyamended,orinsufficientfortheelectricalloads.However,newconstructionsalsoare   notprotectedfromthiscondition.If thequalityoftheconnectiondegrades,ineffect,moreenergywilldissipatefromthedevicesasitselectricalresistanceincreases[3]. ∗ Correspondingauthor.Tel.:+6045996012. E-mailaddress: soibtaib@eng.usm.my (S.Taib). Therefore,periodicalmonitoringanddiagnosisofequipmentscon-ditionareessentialforearlyfaultdetectionandmaintainingtheenergyefficiencyinbuildings.Infraredthermography(IRT)isthebestandusefultooltomonitoranddeterminetheheatrelatedproblems[4–8].   Vari-ousproblemscanalsobedetectedwithinthemonitoringsuchaspoorconnections,short-circuits,overloads,loadimbalances,andimproperlyinstalledelectricalcomponents[9].   Thesystemallowson-linemaintenanceprocesswithoutinterruptionof    service,mini-mizesdowntime,reducesoutageandmanpowercost,avoidssuddenfailureof    theequipmentsthatcouldbecatastrophic,injur-ingandlosingoflife[10–12].Applyingautomaticconditionmonitoringsystemcanimprovethefaultdetectiontechniqueandthelevelof    abnormalitiesinelectricalequipmentscanbeevaluatedevenwhentheexpertorexperiencedpersonnelarenotpresent[13,14].Forinstance,Almeidaetal.proposedanintelligentfaultsdiagnosissystembasedonthermographyforsurgearrestorsusingtwokindsof    variablesasinputsof    neuro-fuzzynetwork[15].Thissystemwas   designedtoclassifyfaultsintotwoclasseswhicharenormalor   faultyandtheindexof    wrongclassificationresultisfoundtobelowerthan10%.Shafi’iandHamzahusedRGBcolourscaledataandtemperature 0378-7788/$–seefrontmatter©2012ElsevierB.V.All   rightsreserved.http://dx.doi.org/10.1016/j.enbuild.2012.09.014  586  A.S.NazmulHudaetal./    EnergyandBuildings55(2012)585–591  Table   1 Classificationofconditionsof    electricalequipments.PriorityTypeof    condition  T  betweensimilarcomponents( ◦ C)Recommendedaction1Critical  T  ≥ 15Majordiscrepancy;repairimmediately2 Warning 5   <    T  <   15 Indicatesprobabledeficiency;repairastimepermits3 Normal  T  ≤ 5Minoroverheating;warrantsinvestigation dataastheinputfeaturesof    artificialneuralnetworktodetectfaultsinelectricalequipments[16].   Rahmanietal.developedanintel-ligentsystemtodetectfaultsof    electricalequipmentsin   groundsubstationsusingsupportvectormachine(SVM)asaclassifierand22imagefeaturesof    Zernikemoments[17].Inthisresearchwork,anautomaticclassificationsystemfordeterminingtheconditionsof    electricalequipmentswas   imple-mented.Initiallytheinfraredimagesofelectricalequipmentsweremanuallysegmentedintotwodifferentregionof    interest(ROI)forthesameloadandcondition.OneoftheROIis   thesuspectedfaultycomponentwhiletheotheroneis   thenormalcomponentwhichisusuallyassignedasthereferencecomponent.Mostoftheelectricalequipmentsandcomponentsareinstalledsidebyside;thereforeitiseasytosegmentallthecomponentswiththesamesize.Asym-metryanalysisof    thesetwoROIsisfoundtobetheappropriatewaytoanalysetheconditionsof    theequipments.Twokindsofsta-tisticalbasedfeatureextractionmethodsnamelyhistogrambasedfirstorderstatisticalandsecondordergreylevelco-occurrencematrix(GLCM)statisticaltextureanalysismethodarewidelyusedtodescribetheasymmetrybetweenthesetworegions[18].   Sevenordersofthefirstorderstatisticalapproachandfourordersof theGLCMtextureanalysismethodwereused.Total22featuresareextractedforbothreferenceandhot   componentasaseparateparameternamelyreferenceandhotparameterrespectively.Suitablefeatureselectionis   animportanttaskforensuringbet-terperformanceof    classifierespeciallyin   highbuilding.Because,someinputfeaturesarehighlyuncorrelatedor   irrelevantthosecandecreasetheclassifierperformanceandthiscancauseincor-rectanalysisofenergyeditingprocess.Forreducingthefeatures,variousfeatureselectionmethodssuchasprinciplecomponentanalysis(PCA),anddiscriminantanalysis(DA)canbeused.Inthisarticle,PCA[19]is   usedtoselectthesuitablefeaturesforconditionmonitoringof    equipments.ItisfoundthatPCAis   thesimplest,easytoapplyandprovidetrueeigenvectorbasedmul-tivariateanalysistool.Atthefinalstage,multilayeredperceptron(MLP)neuralnetworksareusedforclassifyingtheconditionsofelectricalequipmentswhichweredividedinto3classesi.e.normal,warningandcritical.TheperformanceofMLP   networkswerecomparedusingtwelvedifferenttrainingalgorithmsnamelyLevenberg–Marquardt(LM),Broyden–Fletcher–Goldfarb–Shannoquasi-Newton(BFG),resilientbackpropagation(RP),scaledconju-gategradient(SCG),conjugategradientwithPowell-Bealerestarts(CGB),ConjugategradientwithFletcher-Reevesupdates(CGF),conjugategradientwithPolak-Ribiereupdates(CGP),Onestepsecant(OSS),Bayesianregularisation(BR),Gradientdescent(GD),Gradientdescentwithmomentumandadaptivelearningrate(GDX)andGradientdescentwithmomentum(GDM)algorithm.Detailsofthesealgorithmscanbefoundin[20].Theperformancesofclassificationareevaluatedbasedonoverallpercentageaccu-racy.Performanceof    MLPneuralnetworkisalsocomparedwithdiscriminantanalysisclassifier. 2.Infraredimageacquisitionandmanualclassificationapproach Infraredimagesof    electricalequipmentsarecapturedfrommainswitchboards(MSB)fromdifferentlocationsof    oldofficebuildingsandfactories.FlukeTi25thermalcamerawithfusiontechnologywasusedtocapturetheimages.Thethermalimagerconsistedof a160 × 120focalplanearray,uncooledmicrobolometerdetectorandoperatedintheinfraredspectralbandof7.5–14  m.Thether-mallenscaptureimagesof320 × 240pixelswhiletheordinarylensproduced640 × 480pixels(visualimages).All   theinfraredimagesof    electricalequipmentswerecollectedatthemainswitchboardwhichissupplyingtheelectricitytoanofficebuilding.Forcaptur-ingtheimage,thethermalimagerorientationis   directlyfacingtothetargetelectricalequipmentinordertogetanaccuratemeasure-ment.Thedistancebetweenthetargetelectricalequipmentandthethermalimagerisintherangeof    0.5–1.0m.   Emissivitymeas-ureshowwellthesurfaceemitsenergy.Inthisstudy,thethermalpictureofelectricalequipmentswascapturedfrommainswitchboardsinbuildings.Themetalsurfaceof    equipmentswaspaintedoroxidizedandalsosomeof    themwerecoveredbyhigh-qualityelectricaltape.Thestandardemissivityofmostorganicmateri-als   andpaintedor   oxidizedsurfacesis0.95[21].   Mostlowvoltageandmanymediumvoltageswitchgearandcomponentshavehighemissivitymaterialsneartheconnectionpoints.Frommoldedcasebreakerstocableinsulation,anemissivityof    0.95shouldperformbetter[22].Itwas   notedthattheambienttemperaturearoundtheequipmentsisbetween30and33 ◦ C   duringtheinspection.Atotalof500infraredimageswithdifferentelectricalequipmentswerecaptured.Conventionally,theconditionofelectricalequipmentiseval-uatedbycomparingthetemperaturevaluebetweenabnormal(hot)andreference(normal)components.Thistechniqueisknownasqualitativemeasurementwhichisanalysedbymeasuringthetemperaturedifference,  T  betweennormalandabnormalcompo-nents.Usually,thetemperatureofnormal(reference)componentisassignedasminimumtemperatureandthetemperatureof    abnor-mal(hot)componentisassignedasmaximumtemperature. Severalstandardsfor    measuring   T    arefoundsuchasInterNationalElectri-calTestingAssociation(NETA)[23],   AmericanSocietyforTesting&Materials(ASTM)–E[24]andNationalFireProtectionAssociation(NFPA)– NFPA70-B[25].Inthepresentstudy,basedontheexpe-riencefrominspectionsresults,theconditionsof    equipmentsareclassifiedinsteadof    usingtheavailablestandards.Foranaccuratetemperaturemeasurement,someimportantparametersrelatedtoenvironmentaleffect,targetequipmentconditionsaswellasthetechniqueusedforcapturingtheimagehavetobe   considered[26].Inthisresearch,theconditionsof    equipmentsareclassifiedintothreeclasseswhichwasnormal,warningandcriticalcondition.ThisspecificationisillustratedinTable1withtheircorrespondingrecommendedauditactions.Basedonoursurveyon500elec-tricalequipments125equipmentsare   classifiedascritical,193equipmentsaswarningand182equipmentsasnormalcondition.Thisresultsshowthat25%of    theequipmenthadto   berepairimmediatelyand38%indicateprobabledeficiency.Ahugesav-ing   of    energyisexpectediftheequipmentsarebeingreplacedimmediately.Forexample,thermalinsulationsurveyof    a   460MWthermalpowerstationwithfourunitsin   Indiashowsthat   about1.02millionkcal/henergylosseswas   occurringduetobaresur-faces,inadequate/damagedinsulationoropencladdingconditioninall   fourunits.Furtheranalysisshowsthatifthesefaultyinsu-latedareasareattendedtherewouldbe   energysavingof    around0.774millionkcal/h[27].   Alltheseequipmentswereevaluatedmanuallyusinginfraredimageanalysissoftware.Someexamplesof theconditionsaredepictedinFig.1,wheretheabnormalconditionisclearlyshownbytheredcolour.   A.S.NazmulHudaetal./EnergyandBuildings55(2012)585–591 587 Fig.1. Thermalimageof    (a)abnormalcondition,(b)warningcondition,and(c)   normalconditionof    electricalequipments.(Forinterpretationofthereferencestocolorintext,   thereaderisreferredtothewebversionof    thearticle.) Fig.2. (a)Originalinfraredimageof    a   three-phasecable,and(b)greyscaleimagewithreferenceandhotregionselections. 3.   Infraredimageprocessingandautomaticfeaturesextraction Infraredimagesareconvertedintogreyscaleimagewheretheblackpixelsandwhitepixelsimplythelowestandhighestpixelintensityregionrespectively.Therefore,hotspotoftheelectricalequipmentwithrespecttothereferencespotcarriesmorebrightpixels.Fig.2illustratesanexampleofinfraredimageanditscorre-spondinggreyscaleimageof    athree-phasecableconnection.Thesuspectedcomponent(hot)is   locatedatmostrightwhilereferencecomponentis   attheleft.TheequalsizeROIsaremanuallyselectedforbothreferenceandhot   components.ThenfirstandsecondorderstatisticalfeaturesareextractedfromtheseROIs.Thefeaturesarethenusedastheinputsof    MLPnetworksforautomaticconditionclassificationofelectricalequipments.  3.1.Histogrambasedfirstorderstatisticalfeatures Histogrambasedfirstorderstatisticalfeaturesare   verycommonto   describetheasymmetryin   infraredimages.Imagehistogramisdefinedasthegraphicalrepresentationof    numberof    pixelval-uesatdifferentintensitieslevelofthatimage[18].   Thehistogrambasedfirstorderstatisticalfeaturesusedinthisstudyareaveragegreylevelintensity,variance,skewness,kurtosis,entropy,standarddeviationandmaximumgreyintensity.Theformulasofthesefea-turesaresummarizedinTable2:InTable2, n  x and n  y denotethenumberofpixelscolumns(widthof    ROI)andnumberofpixelsrows(heightof    ROI),respectively. i isthenumberof    distinctgreylevelin   thequantizedimage.  p(i) isthe   histogramof    thepixelintensityand l   is   thepossibleintensitylevelof    theimage.Averageintensityistheaveragepixelsvaluewhichdeterminesthebrightnessordarknessof    thegraylevelimage.Skewnessdeterminestheasymmetricalpropertyofthehis-  Table2 Firstorderstatisticalfeatures.FeaturesFormulaMaximumintensitymax l − 1  i = 0 ip ( i )Averageintensity,   1 n  x n  y l − 1  i = 0 ip ( i )Variance,   2 1 n  x n  y l − 1  i = 0 ( i −    ) 2  p ( i )Skewness  1   3 n  x n  y l − 1  i = 0 ( i −  ) 3  p ( i ) − 3Kurtosis  1   4 n  x n  y l − 1  i = 0 ( i −  ) 4  p ( i )Entropy  −  1 n  x n  y l − 1  i = 0 i log( i )Standarddeviation    1 n  x n  y l − 1  i = 0 ( i −    ) 2  p ( i )  588  A.S.NazmulHudaetal./    EnergyandBuildings55(2012)585–591 togramwithrespecttoaverageintensity.If    skewnessis   negative,thegreypixelintensityofentireimageislessthantheaveragegreylevelpixelintensity.Thezerovalueofskewnessmeanstheequalnumberofgreypixelintensitywithrespecttomeanintensity.Thekurtosismeasuresvariationof    intensitydistributionpeaknessorflatnesswithrespectto   thenormaldistribution(kurtosis=3).Entropymeasuresthedisorderlinessof    theimageandmaximumgreyintensitydefinesthemaximumpixelintensityof    thegreyscaleimage.Variancedeterminesthedispersionofgreylevelpixelsfromthemeanandstandarddeviationofpixelintensitiesisaslike   asvariance,butdifferentinvalue.Theaveragegreyintensity,entropy,maximumgreyintensity,kurtosis,skewness,standarddeviationandvariancefortheregionofhotcomponentaredenotedas  x 1 ,    x 2 ,    x 3 ,    x 4 ,  x 5 ,    x 6  and  x 7 ,respectively.Similarly,thesimilarparametersalsoappliedforthereferencecomponentwhichcanberepresentedas h 1 , h 2 ,   h 3 , h 4 , h 5 , h 6  and h 7 .Besides,mutualparametersi.e.thedifferencesbetweenhotandreferenceparametersarecalculatednamelyas d 11 ( h 1 −  x 1 ), d 12 ( h 2 −    x 2 ), d 13 ( h 3 −  x 3 ), d 14 ( h 4 −    x 4 ), d 15 ( h 5 −  x 5 ), d 16 ( h 5 −    x 5 ),and d 17 ( h 7 −  x 7 ).  3.2.StatisticalfeaturesusingGLCM  Thebasicdifferencebetweenfirstandsecondorderstatisticalapproachisthatthefirstorder   statisticsestimateonlytheproper-tiesofindividualpixelvalues,whilesecondorder   statisticsestimatespatialrelationshipsbetweenpixelgreylevelsof    theimageoccur-ringatspecificlocationsrelativeto   eachother[28].A   GLCMis   asquarehavingnumberofrowsandcolumnsequalto   thenumberofgreylevelsintheimagethatis   formedontheprobabilitiesthatpairsofpixels,separatedbyacertainpixeldistanceanda   specificdirection[29].Inthisresearch,a   distanceof1pixelis   consideredi.e.neighbouringpixelsinthepair.Mostlysmalldistancesproducethebestresults[30],   sincetheyareappropriatefortexturesthatarefine,aswellasforthosethatarecoarse.Foragivendistanced,therearefourangularco-occurrencematricesalongfourdirections:0 ◦ (horizontal),45 ◦ (diagonal),90 ◦ (vertical)and135 ◦ (anti-diagonal).Selectionofappropriatedirectionisverydifficult.Themostcom-mon   choiceforthedirectionbetweenpixelsis   0.   Inthiswork,co-occurrencematrixalong0 ◦ iscalculated.Thismeansthatthepixelsinthepairare   locatedhorizontallywithrespecttoeachother.ThusatfirstROIsare   selectedandGLCMfeaturesareevaluatedfromboththehottestandreferencecomponents.Haralicketal.suggestedthat14featurescanbederivedfromGLCM[31].Thesta-tisticalfeaturesusingGLCMutilizedinthisstudyarehomogeneity,energy,entropyandcontrast.Theformulasof    thesefeaturesarelistedinTable3.Where, i denotesthegreylevelof    thereferencepixel,  j   isthegreylevelofneighbouringpixeland  p ( i ,  j )is   thenormalisedGLCM.  Table3 GLCMfeatures.FeaturesFormulaHomogeneity l − 1  i = 0 l − 1   j = 0  p ( i,j )1 +| i −  j | Energy l − 1  i = 0 l − 1   j = 0  p 2 ( i,j )Entropy − l − 1  i = 0 l − 1   j = 0  p ( i,j )log 2  p ( i,j )Contrast l − 1  n = 0 n 2 l  i = 1 l   j = 1  p ( i,j ) , | i −  j |   = n Homogeneitymeasurestheclosenessofthedistributionof    ele-mentsin   theco-occurrencematrixwithrespecttoitsdiagonal.Energyisthesumof    squareelementsintheco-occurrencematrix.Contrastis   ameasureof    theintensitycontrastbetweena   pixelanditsneighbouroverthewholeimageandentropyusedtocalcu-latestatisticalrandomness.Thehomogeneity,energy,entropyandcontrastfortheROIof    thehot   componentaredenotedas  p 1 ,  p 2 ,    p 3 ,  p 4 ,respectively.Similarlyforthereferencecomponent:  g  1 ,  g  2 ,    g  3 ,  g  4  arerepresentedforhomogeneity,energy,entropyandcontrastofitsregion.Themutualparametersare calculatedbytakingthedifferencebetweenhotandreferenceparameters.Theseparametersaregivenas   d 21 (  p 1 −  g  1 ), d 22 (  p 2 −    g  2 ), d 23 (  p 3 −    g  3 ),and d 24 (  p 4 −  g  4 ).Buttheconditionsof    equipmentsaremainlyinfluencedbythecharacteristicsofthehotcomponentanddifferenceof    parametersbetweenhotandreference.Therefore,total22featuresareprimar-ilyselectedneglecting11featuresof    referenceparameterswhichare   highlightedinboldasshownin   Table4. 4.Suitablefeaturesselection Featuresselectionis   usedforreducingdatadimensionality.Allextractedfeaturesfrom500infraredimagesofelectricalequip-mentsinbuildingaretabulatedintothreecategories.Principlecomponentanalysis(PCA)toolwas   employedforfeaturesselectionfromtheabovementionedof    22features.Theprinciplecompo-nentsarecalculatedusingcorrelationmatrix.Theresultof    PCAisshowninscreeplotwhichis   usedtojustifyrelativemagnitudeof eigenvalues.Fig.3showsthescreeplotfor22featuresof    allthedataset.TheresultsofscreeplotandeigenvaluesasillustratedinTable5.   EigenanalysisofthecorrelationmatrixforelectricalequipmentsconditionsclassificationdataTable5.Itis   foundthatthemostappropriatenumberof    principlecomponentisfourforthefirstprinciplecomponent(PC1)untilfourthprinciplecomponent  Table4 Featuresextractedfrombothhotandreferenceregion.FeaturetypeListofparametersReferenceparameterHotparameterDifferencebetweenhotandreferenceHistogrambased1storderfeatures Averagegreyintensity h 1  x  1  d 11 Entropy h 2  x  2  d 12 Maximumgreyintensity h 3  x  3  d 13 Kurtosis h 4  x  4  d 14 Skewness h 5  x  5  d 15 Standarddeviation  h 6  x  6  d 16 Variance h 7  x  7  d 17 Statisticalfeaturesusing   GLCM Homogeneity  g  1  p 1  d 21 Entropy  g  2  p 2  d 22 Energy  g  3  p 3  d 23 Contrast  g  4  p 4  d 24   A.S.NazmulHudaetal./EnergyandBuildings55(2012)585–591 589 Fig.3. Screeplotsof    conditionsclassificationdata. (PC4).PC1hasvariance(eigenvalue)of    6.8786andaccountsfor31.3%ofthetotalvariance.Ontheotherhand,PC2,PC3andPC4havetheeigenvaluesof    4.9777,2.7349and1.9782producingtheirrespectedtotalvarianceof    22.6%,12.4%and9.0%.Therefore,thefirstfourprinciplecomponentsgive75.3%ofthetotalvariance.Theremainingprincipalcomponentsproduceverysmallvarianceandthustheseareassumedasunimportant.Theeigenvectorsofthefourprinciplecomponents(PC1–PC4)areshowninTable6.ThevariablesthathavestronglycorrelatedwithPC1–PC4are   tabulatedinTable7. 5.ClassificationusingMLP   network Afterchoosingthebestfeatures,thenextstepistoclassifytheconditionsofequipmentsusingMLP   neuralnetwork.InMLParchitecture,thenetworkcontainsthreelayersi.e.inputlayer,hid-denlayerandoutputlayerasillustratedin   Fig.4[32].   Thefirstandthelastlayersarecalledasinputandoutputlayers,respec-tively.Intheinputlayer,thenumberofnodescorrespondstothenumberofinputfeaturesandthenumberofnodesin   theoutputlayercorrespondstothenumberof    targetclasses.Neuronsare   the  Table5 Eigenanalysisofthecorrelationmatrixforelectricalequipmentsconditionsclassi-ficationdata.PrinciplecomponentEigenvalueProportionCumulativePC16.87860.3130.313PC2   4.97770.2260.539PC3   2.73490.1240.663PC4   1.97820.0900.753PC5 1.28640.0580.812PC6   0.95670.0430.855PC7   0.75870.0340.890PC8   0.61250.0280.917PC9   0.46270.0210.938PC10 0.36150.0160.955PC11   0.27190.0120.967PC12   0.21600.0100.977PC13   0.13190.0060.983PC14   0.11490.0050.988PC15 0.09580.0040.993PC16   0.07610.0030.996PC17   0.03500.0020.998PC18   0.01680.0010.998PC19   0.01550.0010.999PC20 0.01210.0011.000PC210.00330.0001.000PC220.00270.0001.000  Table6 Eigenvectorsof    PC1–PC4forelectricalequipmentsconditionsclassification.VariablePC1   PC2PC3PC4  x 1  − 0.229 − 0.054 − 0.313 − 0.077  x 2  0.1320.1370.2590.020  x 3  − 0.0840.182 − 0.2990.071  x 4  − 0.222 − 0.175 − 0.147 − 0.315  x 5  0.2300.1780.2080.258  x 6  0.1120.317 − 0.2750.260  x 7  0.1130.314 − 0.2720.244 d 11  − 0.1240.244 − 0.231 − 0.339 d 12  0.0740.1910.352 − 0.282 d 13  0.0160.324 − 0.013 − 0.318 d 14  0.062 − 0.151 − 0.3420.099 d 15  0.0080.1510.380 − 0.125 d 16  0.0580.405 − 0.028 − 0.119 d 17  0.0790.403 − 0.124 − 0.002  p 1  − 0.320 − 0.0550.023 − 0.064  p 2  0.342 − 0.013 − 0.104 − 0.214  p 3  − 0.3550.0210.0300.187  p 4  − 0.2370.0800.1980.369 d 21  − 0.2710.1580.040 − 0.269 d 22  0.324 − 0.174 − 0.076 − 0.012 d 23  − 0.3430.1570.0150.034 d 24  − 0.2510.1430.1330.260  Table7 VariablesthathavestrongrelationshipforPC1–PC4.PC1PC2PC3PC4  p 1  x 6  d 12  x 4  p 2  d 13  d 14  d 11  p 3  d 16  d 15  p 4 d 22  d 17  –– d 23  ––– information-processingunitthat   isthefundamentalto   theopera-tionof    a   neuralnetwork.Consider,a   standardMLP   networkwithinputs  z  1 ,    z  2 , ... ,    z  ni ,predictedoutputs  y 1 ,    y 2 , ... ,    y m  and   n h  hiddennodes.Connectionweightsbetweeninputandhiddenlayeraredenotedas w 1 ij  while w 2  jk  denotestheconnectionweightsbetweenhiddenandoutputlayer.Thenetworkisfullyconnectedinthesensethat   everyneu-ronineachlayerof    thenetworkis   connectedto   everyotherneuronintheadjacentforwardlayerbytheweightedconnection.Also b  j denotesthethresholdsinthehiddennodes.Thenthepredictedoutputof    the  j thneuronsof    the k thnodein   theoutputlayerofthe Fig.4. StandardMLP   architecture.
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