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Characterization of acoustic signals due to surface discharges on H.V. Glass insulators using wavelet radial basis function neural networks

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ContentslistsavailableatSciVerseScienceDirect

Applied

Soft

Computing

jo u r n al h om e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / a s o c

Characterization

of

acoustic

signals

due

to

surface

discharges

on

H.V.

glass

insulators

using

wavelet

radial

basis

function

neural

networks

Nasir

A.

Al-geelani

a,∗

,

M.

Afendi

M.

Piah

a

,

Redhwan

Q.

Shaddad

b aInstituteofHighVoltageandHighCurrent,UniversitiTeknologiMalaysia,81310Johor,Malaysia

bPhotonicTechnologyCenter,InfoCommResearchAlliance,UniversitiTeknologiMalaysia,81310Johor,Malaysia

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received2June2011 Receivedinrevisedform 14December2011 Accepted26December2011 Availableonline13January2012

Keywords:

Acousticsignal Drybands Glassinsulator RBF-NN Surfacedischarge Wavelettransform

a

b

s

t

r

a

c

t

Ahybridmodelincorporatingwaveletandradialbasisfunctionneuralnetworkispresentedwhichis usedtodetect,identifyandcharacterizetheacousticsignalsduetosurfacedischargeactivityandhence differentiateabnormaloperatingconditionsfromthenormalones.Thetestswerecarriedoutoncleaned andpollutedhighvoltageglassinsulatorsbyusingsurfacetrackinganderosiontestprocedureof inter-nationalelectrotechnicalcommission60587.Alaboratoryexperimentwasconductedbypreparingthe prototypesofthedischarges.Thisstudysuggestsafeatureextractionandclassificationalgorithmfor sur-facedischargeclassification,whichwhencombinedtogetherreducedthedimensionalityofthefeature spacetoamanageabledimension,by“marrying”thewavelettoradialbasisfunctionneuralnetwork veryhighlevelsofclassificationareachieved.Waveletsignaltreatmenttoolboxisusedtorecoverthe surfacedischargeacousticsignalsbyeliminatingthenoisyportionandtoreducethedimensionofthe featureinputvector.Aradialbasisfunctionneuralnetworkclassifierwasusedtoclassifythesurface dischargeandassessthesuitabilityofthisfeaturevectorinclassification.Thislearningmethodisproved tobeeffectivebyapplyingthewaveletradialbasisfunctionneuralnetworkintheclassificationofsurface dischargefaultdataset.Thetestresultsshowthattheproposedapproachisefficientandreliable.

©2012ElsevierB.V.Allrightsreserved.

1. Introduction

Atmosphericelementswhenaccumulatedoninsulator’s

sur-face,formalayerofpollutantovertime.Thedielectricpropertiesof

theinsulatordoesnotdiminishsignificantly,duetothepollutant

layerespeciallywhenthelayerisdry,butduetohighhumidity,

lightrainandevenfog,itgetswet,andgeneratesaleakage

cur-rentresultinginaflashoverwhicheventuallyleadstoadisasterin

servicereliability[1,2].

Theacoustictechnologyfortargetdetectionhasdevelopedvery

rapidlyinthepastfewyears.Sostrongtoolsarerequired,suchas

signalprocessingandfeatureextractionforthedetectionofsuch

acondition[3,4].Severalresearcherssuccessfullyusedamethod

ofacousticdetectionforstudyingthecharacteristicsofelectrical

dischargesoninsulators[5,6].Manytechniquesonsignalanalysis

havebeenusedsuchasFouriertransform,wavelettransform(WT)

aswellasneuralnetworkinordertocharacterizeandclassifythe

electricaldischargesignals[7,8].Butnoworkhasbeendoneupto

nowonthecombinedeffectofwavelettransformwithradialbasis

∗Correspondingauthor.Fax:+6075578150.

E-mailaddress:hondahonda750@yahoo.com(N.A.Al-geelani).

functionneuralnetworkforcharacterizationofsurfacedischarge

(SD).

Wavelettransform(WT)hasbeensuccessfullyemployedin

vari-ousfieldsofchemistryforsignalprocessingandshapeoptimization

forimprovingthequalitycharacteristicsoftheproducts.Alotof

researchhavebeendoneregardingWT,employedmainlyfor

sig-nalprocessinginvariousfieldsofanalyticalchemistry,including

flowinjectionanalysis(FIA),high-performanceliquid

chromatog-raphy(HPLC),capillaryelectrophoresis(CE),infraredspectrometry

(IR),ultraviolet–visiblespectrometry(UV–vis),massspectrometry

(MS),nuclearmagneticresonancespectrometry(NMR),

electroan-alyticalchemistry,andX-raydiffraction[9,10].

Some researchers developed the immune algorithm part of

theneuralnetworktooptimizemachiningparametersformilling

operations.Anewhybridoptimizationapproach wasdeveloped

by hybridizing the immune algorithm with hill climbing local

searchalgorithmtomaximizetotalprofitrateinmillingoperations

[11,12].

Amongdifferentstructuresofartificialneuralnetworks(ANNs),

themultilayerperceptronwiththeerror-back-propagation

train-ingalgorithmcalledbackpropagationnetwork(BPN)isthemost

popularone.However,duetoitsmultilayeredstructureandthe

greedynatureoftheback-propagationalgorithm,thetraining

pro-cessoftensettlesintheundesirablelocalminimaoferrorsurface

(2)

orconvergesslowly.Recentlyradialbasisfunctionneuralnetworks

(RBF-NNs)havebeenfoundtobeveryattractiveformany

prob-lems.AnimportantpropertyoftheRBF-NNsisthattheyforma

unifyinglinkamongmanydifferentresearchfieldssuchasfunction

approximation,regularization,noisyinterpolation,pattern

recog-nition,andmedicine.TheincreasingpopularityoftheRBF-NNsis

partlyduetotheirsimpletopologicalstructure,theirlocallytuned

neurons,andtheirabilitytohaveafastlearningalgorithmin

com-parisonwithothermultilayerfeedforwardneuralnetworks[13].

In some applications, electrical surface discharge detection

methodsarenotveryeffective,typicallyasaresultofexcessive

interferingsignal[14,15].Acousticmethodhasbeenusedwhich

hasadvantagesoverelectricalsurfacedischargedetection

meth-odsinthattheyareimmuneandnon-invasivetoelectromagnetic

noise.Forthesignalanalysis,waveletsignalprocessingwasused

tode-noisethesurfacedischargeacousticsignalbydiscardingthe

noise[16–18].

Furthermore,gatingtechniqueswereusedtoraisetheefficiency

ofsurfacedischargeacousticsignalextraction.Timeandfrequency

measurementswereconsideredinbothdomains.Acousticsignals

arefamiliarbytheirdominatingfeaturesthatarefrequency,phase

andamplitudeinwhich,keytomanysignalanalysissolutionsis

thefrequencyfeature.

Ortho-normalbasisfunctionlocalintimecanbeprovidedby

wavelettransforms.ThebeautyofWTisthatitcannearlygivea

sig-nalwithoutdistortion.TheWTcanalsoprovideamulti-resolution

concept,whichisusedinsignalprocessing,identificationof

acous-ticsignals,numericalanalysisandweaksignaldetection.

ThisworkdescribesandportraysthegreatcapabilitiesofWT

toextractuniquefeaturesfromthesignaloftheSDwhichwhen

combinedwithradialbasisfunctionneuralnetwork(RBF-NN)gives

highclassificationaccuracy.

Theorganizationofthispaperisasfollows.In Section2,the

conceptofWTappliedforSDdetectionisdescribedfirst.Although

therearemanytypesofANNs,wefocusourstudyonthecommonly

seenfeedforwardnetwork,namely,RBF-NN.Abriefintroduction

toRBF-NNisalsogiveninSection3.Section4reportsthe

exper-imentalsetupobtainedbydevelopingamodel todetecttheSD

acousticsignals.Thefeatureextractionandthefeaturevectorfrom

thenormalizedinputsisbeengeneratedinSection5.Theanalysis

ofresultsanddiscussionsaregiveninSection6.Section7presents

somecomparisonwithotherrelatedworksandtheconclusionis

madeinSection8.

2. Thewavelettransform

Theacousticsignalshavesomenon-linearcharacteristicsdueto

thesurfacedischargeandthatmakessomedifficultiestodealwith

becauseofnonlinearandtherandomlikebehaviorofsystem.The

problemofnon-linearityoftheacousticsignalisovercomebyusing

wavelettransformwhichisastrongtoolforfeaturepicking-up.It

isequivalenttofilters.Details(dn)areproducebyhighpassfilters

andapproximations(an)areproducedbylow-passfilters.Dueto

themultidimensionalcharacterswhichthewaveletspossess,there

areabletoadjusttheirscaletothenatureofthesignalfeatures

[19].Itcanzoominorzoomouttherequireddetailsjustlikea

microscope.

Furthermore,waveletscandecomposeasignaltogivedilations

andtranslationsparameters, sotheinformationin thesignalis

presentedbytheseparametersintheformoffrequencies.The

mat-labwavelettoolboxisusedtoverifythealgorithmwherediscrete

wavelettransform(DWT)isusedtoanalyzethesignals.The

coeffi-cientsaregeneratedandthefeaturesfromthesignalareextracted.

Waveletisagoodtooltoanalyzethenon-linearsignalsasit

repre-sentsthefeaturesbothintimeandfrequencydomains[20,21].The

WTanalysesthenon-periodicsurfacedischargesignalandadopts

theprincipleoflinkingoffrequencyscales.GenerallytheDWTis

usedforthismission.

Theequationfornon-staticsignalforaDWTisshownbelow

[22,23].

f(t)=

k

cj0,kj0,k(t)+

j>j0

k

wj,k2j/2 (2jt−k) (1)

where istheMotherwaveletfunction,jistheDilationorlevel

index,kistheTranslationorscalingindex,j0,kisthescaling

func-tionofthecoarsescalecoefficients,andCj0,k,Wj,k isthescaling

functionofdetail(fine)coefficients.

OneofthecapabilitiesofDWTisthat, itproducesdetailsto

showhigh frequency information and approximations toshow

lowfrequencyinformation.Themostsuitablemotherwaveletfor

detectingSDacousticsignalsistheDaubechies(Db)wavelets

trans-form,whichiscapableofdetectingshortduration,fastdecaying,

highfrequencyandlowamplitudesignals.Thedecomposition

pro-cessintheWTconsistsofmanynumbersoffiltersfromDb2to

Db44,sothemostpromisingnumberdependsuponhowthey

min-imizethealiasing.Basicallyinthefirststagethecapturedsignal

isdividedin totwo ofthefrequencybandwidth, which isthen

passedtohighpassandlowpassfilters[24].Afterthatthe

out-putsignalfromthelowpassfilterisfurthersubdividedintotwoof

thefrequencybandwidthandsenttothefollowingstage[25].This

procedurecontinuesuntilthepredeterminednumberoflevelsis

reached.Theoutputofthefinalstagerepresentsthesame

cap-turedsignalbutatdifferentfrequencybands[26,27].Thesuitable

selectionofmotherwaveletdependsontheapplication.Among

thevariousde-noisingtechniques,fromthepointofviewofthe

de-noisingeffectandthecomputingtimetheDWTmethodisthe

mostsuitable.

Finally, the Daubechies wavelet is the most appropriate for

treatingSD[28,29].Inthisstudy,theadaptabilityoftheDaubechies

waveletsoforders2hasbeenevaluated,andresultshaveshown

thesuperiority.Itisbefittingtoselectasuitablenumberofbreakup

levelsbasedonthenatureofthesignal.Basedonacousticsignal

fea-tures,itisseenthatsixlevelsofdecompositionisthebestchoice,

becauseithasdescribedtheSDacousticsignalinamoremindful

andsymptomaticway.Thisdecisionismainlyduetothelow

fre-quencyband(approximation),whichisthemostvaluablepartof

theacousticsignal[30].

3. Radialbasisfuctionnetworks

Radialbasisfunction(RBF)networkshavecertainadvantages

overothertypesofANNsandhavebeenwidelyappliedinmany

scienceandengineeringfields.Itisathreelayeredfeed-forward

andfullyconnectednetwork.Theoutputlayerhasnononlinearly

andtheconnectionsoftheoutputlayerareonlyweighted,the

con-nectionsfromtheinputtothehiddenlayerarenotweighted.Itis

afeed-forwardnetworkwithasinglelayerofhiddenunits,called

radialbasisfunctions(RBFs).RBFoutputsshowthemaximumvalue

atitscenterpointanddecreaseitsoutputvalueastheinputleaves

thecenter.Typically,theGaussianfunctionisusedforthe

activa-tionfunction.TheRBFnetworkisconstructedwiththreelayers:

inputlayer,hiddenlayerandoutputlayer.Ininputlayer,the

num-berofneuronsisthesamewiththenumberofinputdimension.

InthecaseofGaussianfunction,thisvaluerepresentsmeasurein

thequalityofthematchbetweentheinputvectorandlocationof

thecenterintheinputspace.Eachhiddennodetherefore,canbe

consideredasalocaldetectorintheinputdataspace[31,32].

OneoftheuniquefeaturesofRadialbasisnetworksisthatthey

canberepresentedbysimplefunctions.Theycouldcopetoany

(3)

ormulti-layer.AnRBF-NNissaidtobenonlinearifthereexistsmore

thanonehiddenlayerorifthebasisfunctionscanmoveorchange

thesize.Theactivationfunctionofahiddenunitispredictedbythe

distancebetweentheinputvectorandaprototypevector[33].

zk(x)= M

j−1

wkj(x)+wk0≡

M

j=0

wkjj(x) (2)

wherexistheinputvector,jistheactivationofoneoftheRBFs,

wkjistheweightofeachRBF,MisthenumberofRBFs,andzkisthe

output(linearsumofradialbasisfunction).

Ina3-layerRBF-NN,conversionfromtheinputroomtothe

hid-denroomusesanonlinearfunctionandlineartransformationtake

placebetweenthehiddenandtheoutputlayer.Thehiddenunits

usedinradialbasisfunctionsusuallytaketheformof[33]:

j(x− −→j) (3)

Thedistancebetweentheinputvectorxanda vectorjofthe

functionusuallydependsonEuclideandistance.

x− 2=

i

(xiji)2 (4)

ThemostordinaryformofbasisfunctionusedistheGaussian

func-tion.

j(x)=exp

−x− 2

22

j

(5)

and2

j arethejthcentervectorandthewidthparameter,

respec-tively.Ahiddenneuron ismoresusceptible todatapointsnear

itscenter.Thissensitivity maybeadjustedbytuningthewidth

, largerwidth leadstoless sensitivity. For a given input

vec-tor,typicallyonlyafewnumberofhiddenunitswillhavenotable

activations[34].RBFneuralnetworkscandesigncomplicated

map-pingscomparedtomultilayerperceptron.InadditionRBF-NNhas

twolayerweightsonlyandasimplelearningalgorithm,thatmakes

itveryfastintrainingspeedcomparedtomultilayerperceptron.

MATLABprovidestwo commandsthatcanbeusedtodesign

RBFneuralnetwork.Newrbandnewrbe.Newrbaddsneuronsstep

bystepuntilthegoalishit,withlongtrainingtime andalittle

error,whilenewrbeveryquicklydesignsanetworkwithzeroerror

[35,36].Forthetrainingprocessthefollowingstepsshouldbe ful-filled:

a. Thehiddenlayer’snumberofneurons.

b.ThecoordinatesofthecenterofRBFfunction.

c.Theradius(spread)ofeachRBFfunctionineachdimension.

4. Experimentalsetup

Thetestset-upconsistsoftwomainparts;thecircuitloop(AC

source,transformer,connectionsandinsulator),themeasurement

andacquisition system(earthresistor,wide bandantennas and

highresolutiondigitaloscilloscope,modelTektronixsTDS55000B

series).Fig.1showstheexperimentalset-upforgenerating

sur-facedischargeaswellasdetectingtheconsequentacousticsignal

ofsurface discharge.Thetestwasdesigned basedonthe

inter-nationalelectro-technicalcommission(IEC)60587standard test

procedures.A pointto planeelectrodesconfigurationwasused

andmountedatthetopandbottomsideoftheglassinsulator

sur-face.Thesurfacedischargesweregeneratedacrosstheelectrodes

byapplyinghighvoltagestressacrossthem.

Theglassinsulatorwasfixedonawoodenbaseandthe

elec-trodeswerefixedbysomearrangementontheinsulator.Aseries

ofexperimentswereperformedonH.V.glassinsulator,whichare

extensivelyusedintransmissionlines.Beforetests,theinsulator

surfacewascleanedbywashingwithisopropylicalcoholand

rins-ingwithdistilledwater,inordertoremoveanytraceofdirtand

grease.Toreproducesalinepollutiontypicalofcoastalareas,the

insulatorsweresprayedwithasolution,consistingofNaCland

dis-tilledwater,withdifferentdegreesofsalinity(from10g/lNaClto

30g/lNaCl).Aperistalticpumpwasusedtocontinuouslydeliverthe

electrolyteatafixedflow-rateof0.60ml/min.Eightlayersoffilter

paperwereusedbetweenthetopelectrodeandthesample,which

actasanelectrolytereservoirtoensureproperflowofelectrolyte

alongtheinsulatingmaterialsurface.Thecontaminantmustflow

fromthequillholeatthebottomofthetopelectrodeandshould

notsquirtoutofthesideortopofthefilterpaper.Thespecimen

wasadjustedsothattheelectrolyterandownasnearaspossible

tothecenterlineofthespecimen.

Anultrasounddetector(USD)withaparabolicantennawas

usedtodetecttheacousticsignalsresultedfromthesurface

dis-charge activity and was placed at a suitable position from the

specimen.TheUSDwasthenconnectedtoadigitaloscilloscope

tocaptureand recordtheacousticsignals.Therecordedsignals

werethenprocessedusingMATLABplateform.Manytrialswere

doneusingtheexperiment setupandthemostlogicaldatawas

finalized.

Fourtestconditionswereconductedinthelaboratoryincluding

firstconditioninwhichtheinsulatorwaskeptclean,second

con-ditioninwhichtheinsulatorwaslightlycontaminatedbyalayer

ofNaClsolution(10g/l),thirdconditioninwhichtheinsulatorwas

mediumcontaminatedbyalayerofNaClsolution(20g/l)andfourth

conditioninwhichtheinsulatorwasheavilycontaminatedbya

layerofNaClsolution(30g/l).Inthefirstconditiontheinsulator

waskeptcleanandtheresultisshowninFig.2(a).Thissignalis

beenprocessedbyusingwaveletanalysistoremovethenoise.It

canclearlybeenseenfromtheblackincoloursignalthattheclean

insulatorhasnoorverysmallsurfacedischargeactivity.Sothis

patterncouldbeconsideredtobethereference,defaultpatternor

thetargettoRBF-NN.Fig.2(b)–(d)showsthesecondcondition,the

thirdconditionandthefourthconditionanditsde-noisesignals

respectively.

5. Featureextraction

Thewavelettransformiswellsuitedinidentifyingsharpedge

transitions.Thedecompositionofasignalusingthewaveletbases

hasaninherentadaptationtothesignalsspatialcharacteristics.In

thiswork,theSDsignalsthatwerecollectedintheexperimental

processwereprocessedusingtheDWTtoobtainafeaturevector

thatwillbeusedinthenextstageofclassification.Theapproach

ofusingtheDWTtoextractafeaturevector,apartfromutilising

thepropertiesofthetransformitselfinrepresentingthesignal,has

theadvantagethatitcanbecombinedwithsensitivity

improve-mentandnoiserejectioninasinglestep.TheDWTduetoitstime

frequencylocalisation,unliketheFouriertransformwherealltime

informationaboutthesignalislost,isabletosuccessfullyhandle

suchrandomlyoccuringofSDs[37,38].

5.1. Processingthedata

1.Thegoalofpreprocessingistoreducethenumberofparameters

tofacethechallengeof“curseofdimensionality”.

2.Thepreprocessinghasahugeimpactonperformancesofneural

networks.

3. Theunwantedfieldnoiseandalltheinterferenceisfilteredoff,

(4)

Fig.1.Experimentalsetupforsurfacedischargedetection.

5.2. Decompositionofsurfacedischargesignals

Inthisworkthefeaturevectorisobtainedbyapplyingwavelet

transform.Forasingledecompositionthenumberofcoefficients

producedbyDb2 is7that is1approximationcoefficientand 6

detailed coefficients. Thisapproximation coefficient that is low

frequencycomponentisfurtherdecomposedintoapproximation

anddetailedcoefficients.InusingtheDWTcertainfeaturesofthe

signalthatisnotimmediatelyobviousinthetimedomainbecome

moreapparentthroughthismultiscaledifferentialoperator.The

featuresselectedtorepresentthemostimportantpartofthedata

areasfollows.

Mean,standarddeviation,normalizedskewnessand

nor-malizedkurtosisk,ateachdecompositionnode, wereusedasa

finger-print for SD and as an inputto theclassifier. The mean

,thestandarddeviation,thenormalizedskewness andthe

(5)

Fig.3.Theinputsoverlappingthetarget.

normalizedkurtosisk,wereestimatedfromthefollowing

equa-tions[37]:

= 1

N

N

n=1

(x[n]) (6)

=

1

N

N

n=1

(x[n])2

1/2

(7)

= 1

N3

N

n=1

(x[n]−)4 (8)

k= 1

N4

N

n=1

(x(n)−)

4

(9)

wherex[n]isthewaveletcoefficentatpostivenandNisthetotal

numberof waveletcoefficients usedateach scale.By taking

6-detailed coefficients and 1-approixmation coefficients fromthe

waveletanalysisforthe4-conditionsmentionedinSection5,we

willhavethefeaturevectorwhichusesfourdescriptorsforeach

scale,thereforeafeaturevectorofdimensionswasneededto

rep-resentthedata.Sothefeaturevectorisofdimension42×4,i.e.21

samplesforthe3-contaminatedconditionsandother21samples

forthecleanconditionthattotallygivesus42dimensional

vec-toreachhaving4-features.Thesecoefficientsareusedtotrainthe

RBFneuralnetwork,sothatitshoulddiscriminateSDactivityfrom

normaloperatingconditions.

6. Resultsanddiscussion

ThefourinputsshowninFig.3arethemainfeaturesofthe

sur-facedischargewhicharekurtosis,mean,standarddeviationand

skewnessextratedbyusingwavelettransformtechnique.The

tar-getvectorconsistsoftwoclassesthatareasfollows.

Thefirstclassisdenotedby(0)whichshowsnoorverysmallSD

activity.Thesecondclassisdenotedby(1)whichsshowshighSD

activity.Thenormalizedinputsandtargetsvectorsarerandomly

dividedintotwosets,60%ofthevectorsareusedtotrainthe

net-work,20%ofthevectorsareusedtovalidatehowwellthenetwork

generalized.Finally,thelast20%ofthevectorsprovidean

inde-pendenttestofnetworkgeneralizationtodatathatthenetwork

hasneverseen.BytrainingtheRBF-NNwiththenormalizedinputs

Fig.4. Thetrainingperformance.

wecanseetheresultinFig.3whichshowsusaveryperfect

over-lappingwhichmeansthattheneuralnetworkhadrecognizedthe

inputswitha100%accuracy.

Trainingperformancenearlyhitthegoalin25epochsonlyas

couldbeseeninFig.4givingaverygoodperformance,Thestopping

conditionsofRBF-NNweresettoaminimumerrorof0.0002or

maximumiterationof10000.Theerrorduringtrainingprocessin

Fig.5wasacceptableandverylow,whereitstartedwithaveryhigh

valueandduringthetrainingprocessreachedanaveragevalueof

0.0038within40iterations.Thecomputationaltimewas0.0795s,

thisistheabilityofWRBF-NNtohaveaveryfastlearningalgorithm.

Meansquarederror(mse)isanetworkperformancefunction.

Itmeasuresthenetwork’sperformanceaccordingtothemeanof

squarederrors.TheuniquefeatureofWRBF-NNisdepictedinFig.6

whichshowsthatthemeansquarederror(mse)requiredonly22

neuronstoattainzerovalue,thisisthebeautyofcombiningtheWT

withRBF-NNwaveletradialbasisfunctionneuralnetwork

(WRBF-NN).

TestingtheWRBF-NNbyunseendatashowshighclassification

accuracywhichisclearlyseeninFig.7.Thefourfeaturesofthedata

isaccumulatedat(1) whichmeansthisdatareferstodischarge

activity.

(6)

Fig.6. Themeansquareerror.

7. Comparisonwithotherresearchworks

InordertocheckthereliabilityoftheproposedWRBF-NNthe

modelisbeencomparedwiththepreviousworksconductedand

mentionedintheliteraturereview.ThesameSDdatasetisbeen

usedtocomparewiththeWaveletfeedforwardback-propagation

neuralnetwork(WFFBP-NN).

TheplotinFig.8hasthreelines,becausethenormalizedinputs

andtargetsvectorsarerandomlydividedintothreesets.60%ofthe

vectorsareusedtotrainthenetwork,20%ofthevectorsareusedto

validatehowwellthenetworkgeneralized.Finally,thelast20%of

thevectorsprovideanindependenttestofnetworkgeneralization

todatathatthenetworkhasneverseen.Trainingonthetraining

vectorscontinuesaslongthetrainingreducesthenetwork’serror

onthevalidationvectors.Afterthenetworkmemorizesthe

train-ingset(attheexpenseofgeneralizingmore poorly),training is

stopped.Thistechniqueautomaticallyavoidstheproblemof

over-fitting,whichplaguesmanyoptimizationandlearningalgorithms.

BytrainingtheWFFB-NNwiththenormalizedinputswecanseethe

resultwhichshowsustrainingperformancedidnotreachthegoal

perfectly.Thebestvalidationperformancewas0.00351atepoch

8,thismeansthattheneuralnetworkhadrecognizedtheinputs

withapproximately95%accuracy.Theresulthereisreasonable,

becausethetestseterrorandthevalidationseterrorhavesimilar

Fig.7.Testingtheinputdata.

Fig.8.Thetrainingperformance.

characteristics,anditdoesnotappearthatanysignificant

overfit-tinghasoccurred.TheerrorduringtrainingprocessinFig.9was

acceptable,which attained0.38in38iterations.Thetarget

vec-torconsistsoftwoclassesthataredesignatedas:thefirstclassis

denotedby(0)whichshowsnoorverysmallSDactivity.Thesecond

classisdenotedby(1)whichshowshighSDactivity.Testingthe

WFFB-NNisshowninFig.10wherethe4-inputsarethefeatures

oftheSDactivity,hencemostofthedataisaccumulatedat1that

meanshighdischargeactivitycanbefoundandasmallSDactivity

canbeseenat0.ItisworthnotingthattheConvergenceTimewas

0.61039s,thisisthedrawbackofFFB-NN,anupdatingalgorithm

usuallycausesthetrainingprocesstoconvergeslowly.Compared

withtheWRBF-NN,itcanupdatetheparameters,atthesametime

itdoesnotneedthepreviousupdatingvalues.Therefore,the

pro-posedWRBF-NNcanachievenumericalconvergenceandisfaster

thanWFFB-NNinthetrainingprocess.InadditiontothatFFB-NN

appliesaglobalsearchingmethod,whileRBF-NNappliesalocal

searchingmechanism.Itisfoundthatglobalsearchingmay

eas-ilybetrappedinthelocalminimum,therefore,thismannermakes

theestimationerrorsintheFFB-NNmodeldifficulttobeminimized

underthesamesystemparametersasthatinRBF-NN.ForRBF-NN.

Ontheotherhand,designingaradialbasisnetworkoftentakes

muchlesstimethantrainingaWFFB-NN,andcansometimesresult

infewerneurons.

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Fig.10. TestingofWFFB-NNbyunseendata.

8. Conclusion

Itisaninflatetosaythatwewillintroduceasmanyanalysis

algorithmsastherearesignals.Signalsaresocomplexandrich

thatasingleanalysismethodcannothandlethemall.Havingdone

alltheseanalysiswecanconcludethatacousticdetectionofsurface

dischargeispossiblebyobservingtheresultswhicharequitegood,

explainableandlogistical.Theproposedhybridmodelhasproved

tocharacterizetheSDactivitywithahighdegreeofintegritywhich

isattributedtothecombinedeffectoftheWTandRBF-NN.The

highrateofclassificationacquiredbytheRBF-NNisdue tothe

preprocessingofdatabytheWT.

Themodelisquiteversatileforawiderangeofapplicationsin

thefield ofpowersystemanalyses.Duetothepreprocessingof

thedatabyusingwavelettransformgavetheRBF-NNhighrateof

classificationaccuracy.Thisshowsthebeautyofwavelettransform

especiallywhencombinedinoneunitwithRBF-NN.Asfuturework

fourtypesofpartialdischargeswillbegeneratedinahighvoltage

laboratory,namelycoronadischargeinair,floatingdischargein

oil,internaldischargeinoilandsurfacedischargeinair,at

differ-entappliedvoltageswillberecordedandafeaturevectorwillbe

extractedbyusingwavelettransformwhichwillbeusedtotrain

theRBF-NN.

Acknowledgments

ThisworkissupportedbyUniversitiTeknologiMalaysia(UTM)

underResearchUniversityGrantSchemeofVote01J61.Theauthors

wouldliketothankResearchManagementCentre(RMC)Universiti

TeknologiMalaysia,fortheresearchactivities.Theauthorswould

alsoliketothanktheanonymousreviewerswhohavecontributed

sincerelyinthiswork.

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References

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