DWT based bearing fault detection in induction motor using noise cancellation

Availableonlineatwww.sciencedirect.com

ScienceDirect

JournalofElectricalSystemsandInformationTechnology3(2016)411–427

DWT

based

bearing

fault

detection

in

induction

motor

using

noise

cancellation

K.C.

Deekshit

Kompella

,

Venu

Gopala

Rao

Mannam

,

Srinivasa

Rao

Rayapudi

a_{DepartmentofElectrical&ElectronicsEngineering,KLUniversity,Guntur,A.P.,India} b_{DepartmentofElectrical&ElectronicsEngineering,PVPSIT,Kanuru,A.P.,India} c_{DepartmentofElectrical&ElectronicsEngineering,JNTUK,Kakinada,A.P.,India}

Received10February2015;receivedinrevisedform5June2016;accepted6July2016 Availableonline3August2016

Abstract

Thispaperpresentsanapproachtodetectthebearingfaultsexperiencedbyinductionmachineusingmotorcurrentsignature analysis(MCSA).Attheincipientstageofbearingfault,thecurrentsignatureanalysishasshownpoorperformanceduetodomination ofprefaultcomponentsinthestatorcurrent.Therefore,inthispaperdominationofprefaultcomponentsissuppressedusingnoise cancellationbyWienerfilter.Thespectralanalysisiscarriedoutusingdiscretewavelettransform(DWT).Thefaultseverityis estimatedbycalculatingfaultindexingparameterofwaveletcoefficients.Itisfurtherproposedthat,thefaultindexingparameter ofpowerspectraldensity(PSD)basedwaveletcoefficientsgivesbetterresults.Theproposedmethodisexaminedusingsimulation andexperimenton2.2kWtestbed.

©2016ElectronicsResearchInstitute(ERI).ProductionandhostingbyElsevierB.V.ThisisanopenaccessarticleundertheCC BY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Faultdetection;Motorcurrentsignatureanalysis(MCSA);Discretewavelettransforms(DWT);Powerspectraldensity;Wienerfilter

1. Introduction

Mostoftheindustriesdependonsquirrelcageinductionmotors,duetoitsstalwartstructure,highpowertoweight ratio,highreliabilityandeasydesign.Eventhoughthesemotorsareruggedinstructure,theyoftenfacemanyfaults, iftheyareoperatingforalongtimewithoutmonitoring(Report,1985a,b).Amongthefaultsexperiencedbyinduction motors,bearingfaultscontributeto41%ina200hpmotorasshowninFig.1(Soualhietal.,2015;Zhangetal.,2011). Thecontributionofbearingfaultmayvaryfrom40%to90%inlargetosmallrangemachines(ElHoussinetal.,2013). Asthesefaultsbecomesevere,theremaybeunexpectedinterruptionofindustrialprocess.Topreventthisunexpected damage,itisessentialtopredictthesefaultsatnascentstage.Conventionallyvibratingsensorsareusedtomonitorthese

∗_{Correspondingauthor.}

E-mailaddress:[email protected](K.C.D.Kompella).

PeerreviewundertheresponsibilityofElectronicsResearchInstitute(ERI).

http://dx.doi.org/10.1016/j.jesit.2016.07.002

2314-7172/©2016ElectronicsResearchInstitute(ERI).ProductionandhostingbyElsevierB.V.ThisisanopenaccessarticleundertheCC BY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Fig.1.Piediagramoffaultsexperiencedbyinductionmotor.

faults,whicharecostlyandsuitabletolargerangemachinesonly(Blodtetal.,2008).Incontrasttothis,thecurrent signatureanalysishasovercomethesedrawbacksandgivesgoodperformanceeveninnoisyatmosphere(Erenand Devaney,2004;Stacketal.,2004a;Filippettietal.,1995;Obaidetal.,2003;Bellinietal.,2008a).Theseadvantagesof motorcurrentsignatureanalysis(MCSA)haveattractedmanyresearchersinthelastfewyears.Conventionalcurrent spectralanalysisusingFFThasmanydrawbackslikespectralleakage,poorresolutionanddisablestoprovidetime frequencyrelationetc.ToovercomethedrawbacksinFFT,windowfunctionsarecommonlyemployed(Jungetal., 2006;Liuetal.,2008)inspectralanalysis.Faultdetectionusingtime–frequencytechniques,suchasshort-timeFourier transform(STFT)(Kimetal.,2007),theWigner–Villedistribution(WVD)(Vicenteetal.,2014;Kimetal.,2007) havefewdrawbacksliketheSTFTusesfixedwindowsforallfrequencieswhichgivespoorresolutionandWVDis complexduetocrossterms.Toovercomethesedrawbacksintime–frequencyanalysis,thewavelettransform(WT) basedfaultdetectionispresentedinLauandNgan(2010),Sunetal.(2013),Luoetal.(2013)andWeietal.(2011).

Basedonthelocationoffault,bearingdefectscanbeclassifiedintotwotypes:(1)singlepointdefect(Cyclic)and (2)generalizedroughness(NonCyclic).Further,thesinglepointdefectcanbesubclassifiedas(a)outerracefaults,(b) innerracefault,(c)balldefectand(d)cagefault(FrosiniandBassi,2010).Thesecyclicfaultswillgeneratedetectable vibrationsbyproducinganimpactbetweentheballandraceway.Thecharacteristicvibratingfrequenciesduetothese faultscanbecalculatedusingEqs.(1)–(4),(FrosiniandBassi,2010).

Thevibrationfrequencyduetoouterracefault,foutisgivenby

fout= n 2fr 1−BD PDcos∅ (1) Thevibrationfrequencyduetoinnerracefault,finnisgivenby

finn= n 2fr 1+BD PDcos∅ (2) Thevibrationfrequencyduetoballdefect,fballisgivenby

fball= PD 2BDfr 1− BD PD 2 cos2∅ (3) Thevibrationfrequencyduetocagefault,fcageisgivenby

fcage= 1 2fr 1−BD PDcos∅ (4) Wherenisthenumberofballs,∅isthecontactangle,PDisthepitchdiameter,BDistheballdiameterofthebearing, andfristherotorspeedinHzasshowninFig.2.

Fig.2.Geometryofbearing.

Thesevibratingfrequenciesduetobearingdefectwillreflectintothestatorcurrentspectrumbyaffectingtheairgap fluxdensity(Obaidetal.,2003).Thefaultfrequenciesinstatorcurrentcanbecalculatedfromvibratingfrequencies andfundamentalcomponentusingfollowingequation.

fbearing=|fs±m.fv| (5)

wherem=1,2,3...,fbearingisthecharacteristicfaultfrequencyinstatorcurrent,fsisthefundamentalfrequencyand

fvisthevibrationfrequencyfordifferentfaults.

Similarly,thegeneralizedroughnessfaultscanbeclassifiedinto(a)deformationofthesealand(b)corrosion(Frosini andBassi,2010).Thepredictionofgeneralizedroughnessfaultsisdifficult,becausetheyarenotvisibletounaided eyeandtheymaynotproducecharacteristicfaultfrequenciesinbothvibrationandstatorcurrent(Schoenetal.,1995; Stacketal.,2004c).

Manyof theresearchers(Sun etal.,2013; Luoetal.,2013;Weietal., 2011;Schoenetal., 1995;Stacketal., 2006;Zhongmingetal.,2001;Bellinietal.,2008b;Kiaetal.,2007;Garcia-Perezetal.,2011;Kimetal.,2013)have concentratedonthefaultlocationandseverity,whicharesuitabletofirstcategoryofthefaulti.e.singlepointdefect. Ontheotherhandthedetectionofgeneralizedfaultsisachallengingtasktotheresearchersduetotheirprogressive nature.EventhoughtheestimationofgeneralizedfaultspresentedinStacketal.(2004b),Zhouetal.(2009),Kompella etal.(2013)andElHoussinetal.(2013)havefewdrawbacks.ForexampleinStacketal.(2004b),itrequiresdetailed knowledgeaboutspectraldistribution,harmonicsandeccentricityetc.InZhouetal.(2009),thegeneralizedroughness faultscanbedetectedbycancellingthehealthycomponentsandthefaultcanbeestimatedbyRMSvalueofnoise cancelledstatorcurrent.Buttheauthorsdonotdiscussthefaultanalysisanditsclassificationunderthepresenceof noise.ThefaultclassificationandanalysisiscarriedoutusingFFTinKompellaetal.(2013)hasnoiseproblemsand faultcomponentissuppressedbynoiseespeciallyatearlystage.InElHoussinetal.(2013)discretewavelettransform (DWT)analysisispresentedwithfrequencysubtraction,itdoesnotgivegoodresultsduetospectral subtractionis performedwithoutanyfilter.

Incontrasttothese,thispaperpresentsthedetectionofbearingfaultsusingnoisecancellationwithDWTanalysis byanadaptivefilter(Wienerfilter).Thedominationof prefaultcomponentsinthestatorcurrentissuppressedby cancellingtheminarealtimefashionusingWienerfilter.Toimprovetheresolution,thespectralanalysisofstator currentafternoisecancellationiscarriedoutusingDWT.Inadditiontothis,thefaultseveritycanbeestimatedusing statisticalparametersnamelystandarddeviation(SD)andenergyofwaveletcoefficientsasfaultindexingparameters. Toelevatethefaultindexparametersforbetterindication,thepowerspectraldensityofwaveletcoefficientsispresented.

2. Systemmodeling

TheblockdiagramofproposedbearingfaultdetectiontopologyisshowninFig.3.Inthefirststage,thestatorcurrent underhealthyandfaultyconditionsofbearingisattainedusingcurrenttransducerandprocessedbydataacquisition system.Inthesecondstage,acquiredstatorcurrentprocessedfornoisecancellationusingWienerfiltertosuppress thedomination ofprefaultcomponents.Afterwards,thenoisecancelledstator currentisdecomposedusingDWT intosufficientlevelsdependingonsamplingfrequency,ratedspeedetc.Inthenextstagethepowerspectraldensity (PSD)ofwaveletcoefficientsiscalculatedandisusedtoestimatethefaultseverity.Inlaststageoffaultdetection,the statisticalparametersSDandenergyarecalculatedtoindicatethefaultseverity.

Fig.3.Blockdiagramofproposedbearingfaultdetectiontopology.

2.1. Noisecancellation

Underhealthyconditions(withrespecttobearingdefect)ofinductionmachine,thestatorcurrentusuallyconsist thefundamental component, harmonics,andthe noisecomponents (sensors andEMI) (Zhouetal., 2009).These componentswillremainevenafterthebearingfaultexistsandmaydominatethefaultcomponentatincipientstage. Therefore,thehealthycomponentsinthestatorcurrentispredictedandcancelledinarealtimefashionusingWiener filter.ThedesignofWienerfilterisdescribedinthefollowing.Themathematicalmodelofstatorcurrentisgivenby

x(n)=x0(n)+ M h=0 Aksin (hω0n)+xn(n) (6) where x0(n) fundamentalcomponent

xn(n) noisecomponentduetosensorsandEMI ωofundamentalfrequency

horderoftheharmoniccomponent b(n) bearingfaultcomponent

Xf(n) Statorcurrentwithbearingfault n0numberofdelayunits

PorderoftheWienerfilter W(z) Wienerfilter

Wheneverbearingfaultdevelops,afaultcomponentwillbeaddedinthestatorcurrentandtheEq.(6)becomes

xf(n)=x(n)+b(n) (7)

whereb(n) isbearingfaultcomponentandisestimatedbyeliminatingthehealthycomponentsofthemotorcurrent. Simplesubtraction of the healthycomponent fromthe faultycurrent (El Houssin etal.,2013) willnot givegood performanceduetorandomnatureofthenoise.Therefore,inthispaperthehealthycomponentsofthestatorcurrent aretreatedasnoiseandarecancelledinarealtimefashionbyusinganadaptivefilter(Wienerfilter).Theprocessof noisecancellationusingWienerfilterisshowninFig.4andisredrawninFig.5.

Fig.5.Wienerfilterbasednoisecancellation.

2.2. Filterdesign

Inthissection,thedesignofWienerfilterinZhouetal.(2009)hasbeenadoptedtoobtainthecoefficientsofthe filter.Thefiltercoefficientsaredesignedinminimummeansquaresensetominimizethepredictionerrorξ.Thiserror occursbecauseofthedeviationofestimatedcomponentsfromoriginalcomponentsof thestatorcurrent.Thefilter issaidtobeideal,ifthepredictedcomponentsaresameastheoriginalcomponentsunderhealthyconditionsofthe bearing.i.e.xˆ(n)≈x(n).Thepredictedcomponentsofnoiseisgivenby

ˆ x(n)= p k=0 w(k)xf(n−n0−k) (8)

wherepistheorderofthefilterandn0isthenumberofdelayunits.Thepredictionerrorisgivenby

e(n)=|x(n)−xˆ(n)| (9)

ThenthemeansquareerrorfromEqs.(8)and(9)isgivenby ξ=Ee(n)e∗(n)=E |e(n)|2 (10) ξ=E |e (n)|2 =E ⎧ ⎨ ⎩|x(n)− p k=0 w(k)xf(n−n0−k)| 2⎫_⎬ ⎭ (11)

whereE{.}standsforexpectation.TominimizethepredictionerrorinEq.(11),differentiateξwithrespecttow(k) andequatingtozero.Then

∂ξ ∂w(k)=E 2e(n) ∂e(n) ∂w(k) =0 (12) BysimplifyingtheEq.(12) E{e(n)x(n−n0−k)} =0, k=0,1,...p (13)

Thisisknownasprincipleoforthogonalityandcanbemodifiedasfollows

E ⎧ ⎨ ⎩ ⎡ ⎣_x(n)− p j=0 w(j)x(n−n0−j) ⎤ ⎦_x(n−n0−k) ⎫ ⎬ ⎭=0 (14)

Sincesignalx(n) isassumedtobewide-sensestationary,theautocorrelationsequenceofx(n) isgivenby p

j=0

Inmatrixform,(15)canbewrittenas ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ rx(0) rx(1) ··· rx(p) rx(1) rx(0) ··· rx(p−1) .. . ... ... rx(p) rx(p−1) ··· rx(0) ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ w(0) w(1) .. . w(p) ⎤ ⎥ ⎥ ⎥ ⎥ ⎦= ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ rx(n0) rx(n0+1) .. . rx(n0+p) ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (16)

Eq.(6)maybewrittenmorebrieflyas

RxW =rdx (17)

whereRxisaautocorrelationmatrix,Wisthefiltercoefficientsandrdxcrosscorrelationmatrixbetweendesiredsignal andtheobservedsignal.

Thefiltercoefficientscanbeobtainedas

W=R−_x1rdx (18)

2.3. Faultestimation

Wheneverbearingfaultdevelops,predictioncapabilityofthefilterdecreases.Thenthepredictionerrorafternoise cancellationwillincreaseandthebearingfaultfrequencycanbeeasilyextractedfromthestatorcurrentasgivenbelow.

b(n)=x(n)− p

k=0

w(k)xf(n−n0−k) (19)

UnderthehealthyconditionofthebearingtheEq.(19)hasminimumvalueduetopredictionerrorandwillincrease asthebearingfaultdevelops.Thisvaluebecomeshigh,ifseverefaultoccurs.Especiallyatthenascentstageoffault, thisvalueisverylowandalmostequaltohealthyconditionduetopredictionerrorinthefilterdesign.Atthisstage extractionoffaultcomponentfromstatorcurrentisverydifficult.Thereforethespectralanalysisofstatorcurrentafter noisecancellationispresentedinthefollowingsubsection.Afterevaluatingthefaultcomponentfrom(19),frequency analysiscanbedoneintwoways.

2.3.1. FFT

TheFFTanalysisofbearingfaultcomponentwillgivethecompletedetailsofthefaultlikefrequencyresponseand magnituderesponse.TheFFTanalysiscanbedoneusingbelowexpression.

B(ω)= N−1

n=0

b(n)e−jωn (20)

whereNisthelengthofthesignalb(n) andω=2πmn/N,m=0,1,...N−1.

2.3.2. DWT

Thebearingfaultsignalb(n) canbeexpressedasapproximationcoefficientsanddetailcoefficientsusingDWT, whichrepresentslowandhighfrequencycomponentsrespectively(HedayatiKiaetal.,2009).Inthiswork,Daubechies waveletistakentocalculatetheapproximationanddetailcoefficientsineachlevelusingbelowexpressions(Hedayati Kiaetal.,2009). A1(m)= n L(n−2m)b(n) (21) D1(m)= n H(n−2m)b(n) (22)

Table1 Machinedetails.

S.no. Nameplatedetail Rating

1 Powerrating 2.2kW

2 Ratedspeed 1435–1500rpm

3 Ratedvoltage 415V

4 Ratedcurrent 4.4A

whereA1,D1aretheapproximateanddetailcoefficientsatlevel1andL,Harethelowandhighpassfiltersrespectively.

TheapproximationanddetailscoefficientsatnextlevelcanbeobtainedusingA1,D1fromthebelowequations.

A2(m)= n L(n−2m)A1(n) (23) D2(m)= n H(n−2m)D1(n) (24)

Similarlythejthlevelcoefficientscanbeobtainedfromj−1thlevelcoefficientsasbelow. Aj(m)= n L(n−2m)Aj−1(n) (25) Dj(m)= n H(n−2m)Dj−1(n) (26)

Thedecompositionleveljcanbeobtainedbyusing

j=integer ⎡ ⎣ln Fs 8srf ln2 −1 ⎤ ⎦ (27)

wheresrisslipandfisthefundamentalcomponent.Aftercomputingthejthlevelcoefficients,faultestimationcriteria

canbedoneusing twoparameters.Thesecriteriaaretheratioof standarddeviationoffaultycoefficienttohealthy coefficientsλandenergyratiooffaultycoefficienttohealthycoefficientsϕ.

λ= _N m=1(D(m)−Dmean(m))2 _N m=1(Dh(m)−Dhmean(m))2 (28) ϕ= _N−1 m=0|D(m)|2 _N−1 m=0|Dh(m)|2 (29) Theseparametershavealsobeenusedtoindicatethefaultseverity.

3. Experimentalsetup&bearingfaultfrequencies

TheexperimentalsetupisshowninFig.6.ThenameplatedetailsoftheinductionmotortakenaregiveninTable1. The machinewasmade torun via3 phaseauto transformer.Thismotorismechanicallyloadedtoobtain current samplesatthetimeofhealthyaswellasfaultyconditions.Thedata-acquisitionsystem(NIMYDAQ)alongwiththe currentsensorLEMLA55Pisusedtotakethestatorcurrentunderbothconditions.Thesamplingfrequencyistaken as10KHz.ThesensedstatorcurrentfromDAQisprocessedtoMATLABfortestingthealgorithmpractically.Inthe presentexperiment,SKF6206ZZsinglerowdeepgroveisusedastestbearing.Thetestbearing6206ZZismounted ontheshaftatdrivingend.Thespecificationsofthebearingare:PD=1.83in.,BD=0.375in.,n=9and∅=00.The faultfrequenciescalculatedusing(1)–(5)fortheabovetestmachineareshowninTable2.

Fig.6.Experimentalsetupforbearingfaultdetection.

Table2

Bearingfaultfrequencies.

No-loadfrequencies(Hz) Full-load(12.73N-M)frequencies(Hz)

fout finn fball fcage fout finn fball fcage

fr 24.8 24.8 24.8 24.8 23.9 23.9 23.9 23.9

m=1 138.8 184.6 108 70 135 179.6 106 64.4

m=2 227.7 319.2 166 80 221 309.3 161.8 78.8

m=−1 38.8 84.6 8 35 35 79.6 6 35.5

m=−2 127.7 219.2 66 20 121 209.3 61.8 21.8

4. Results&discussion

Inthissection,simulationandexperimentalresultofbearingfaultsdetectionin3phaseinductionmotorhasbeen presented.TheflowgraphofproposedtopologyisshowninFig.7.Firstthestatorcurrentistakenfromdataacquisition systemandisprocessedforconstantfrequencychecking.Ifithasconstantfrequency,thenthecurrentisusedtodesign theWiener filter coefficientsfor first timeandinthenextit isprocessedfor noisecancellation.Otherwise, stator currentissensedagainuntilconstantfrequency. Afterwards,the noisecancelled statorcurrentisdecomposedinto approximatedanddetailed coefficientsusingwaveletanalysisandpowerspectraldensityof theeachcoefficientis computed.ThePSDoftherequiredlevelcoefficientsareusedtocalculatethefaultindexingparameterstoestimate faultseverity.

Fig.7.Flowgraphofproposedfaultdetectiontopology.

4.1. Simulationresults

Inthissimulationwork,theprefaultcomponentsofstatorcurrentismodeledusing(6)withfundamentalfrequency 50Hzandits5th,7th,and11thharmonic componentsof 250Hz,350Hzand550Hzfrequenciesrespectively.The sensorandEMInoiseismodeledbymeansofwhiteGaussiannoise(WGN)withalesssignaltonoiseratio(SNR). TheWienerfilterisdesignedusing(18)withorderp=2000andtrainedwithawiderangeoffaultfrequencies.

4.1.1. FFTanalysis

Inthis,theFFTanalysisofhealthystatorcurrentwithandwithoutnoisecancellationisperformedandcompared withfaultyconditionofthebearing.ThebearingfaultfrequenciesforthesinglepointdefectistakenfromTable2and introducedintothestatorcurrenttotestthefilterperformance.Thegeneralizedroughnessfaultistestedwithdifferent faultseverities.

ThehealthystatorcurrentbeforeandafternoisecancellationisshowninFig.8(a)&(b)respectively.Thecurrent spectrumafter noisecancellation underhealthyconditionshowsthat, aminimum noisefloor ismaintaineddueto the performanceof the filter coefficients. Thisnoise floor will become severeespeciallyat incipient stageof the fault.

(a)

(b)

Fig.8. Healthystatorcurrentspectrum(a)beforenoisecancellation(b)afternoisecancellation.

4.1.1.1. Singlepointdefect. FFTanalysisof bearingfaultafter noisecancellationwithsinglepointdefecttypeis performedundernoloadcaseinTable2.Thefaultfrequenciesofouterrace,innerrace,cagefaultandballdefects areintroducedintothestatorcurrentoneafterotherwithdifferentmagnitudesandextractedfromcurrentspectrum bynoisecancellationasshowninFig.9(a)–d).Itshowsthat,theFFTanalysishavegoodperformancewithlessvalue ofnoisefloorforseverefaults.Atnascentstageoffault,thenoisefloordominatesfaultcomponent.Thisisthemajor issueinFFTanalysisespeciallyatearlystageofthefault.

4.1.1.2. Generalizedroughness. Estimationof non cyclic (Generalizedroughness)fault usingFFT analysishasa limitationthat,thesefaultsdoesnotimposeanycharacteristicfaultfrequenciesintostatorcurrentspectrum.Thesefaults willimposebroadbandandunpredictablefrequenciesintostatorcurrent.Therefore,inthissectionfaultfrequencies withrandomvaluesareintroducedwithdifferentmagnitudestotesttheproposedmethodforvariousfaultseverities. Thefaultmagnitudes0.1%,1%and5%areusedfortesting.FFTanalysisofstatorcurrentspectrumforgeneralized faultafternoisecancellationisshowninFig.10(a)–(c).TheseresultsareevidentthattheFFTanalysisissuitablefor thefrequencieswhichareveryfarfromthehealthycomponentsandhavesomeresolutionproblemsforthefrequencies nearertohealthycomponentslikefundamentalandharmonics.Fig.10(b)&(c)showsthat,thenoisefloordominates thefaultcomponentespeciallyatthenascentstageoffault.ThisproblemcanbeovercomebyDWTanalysis,which ispresentedinthenextsection.

4.1.2. DWTanalysis

Inthissection,thewavelettransformbased noisecancellation isperformedbyDaubechieswaveletfunctionof family8(db8)andbearingfaultsignalb(n)isdecomposedintolevel8usingEq.(27).Afterward,theapproximation anddetail coefficientsatthelevel 8are takenandperformed thetwocriteria proposedinthispaper.Theratios of standarddeviationλandenergyϕarecalculatedandcomparedwiththeratiosofPSDvalues.Thedecompositionof healthystatorcurrentandcagefaultafternoisecancellationareshowninFigs.11–12.FromFigs.11–12itisobserved that,directvisualizationofwaveletcoefficientsdoesnotgiveanyinformationregardingfaultexistenceanditsseverity. Therefore,the faultindexingbasedfault estimationispresented inthe following.Fig.13showsthebar graphsof faultindexingparametersfor4 categoriesof faultswithdifferentmagnitudes.Thefaultfrequencieswithdifferent magnitudesvisually,0.1%,1%and5%areintroducedintostatorcurrentandexaminedusingproposedmethodof bearingfaultdetection.Forincipientstagefaulti.e.faultwith0.1%magnitudehaslessindicationinbothparameters.

(a)

(b)

(c)

(d)

Fig.9.Statorcurrentafternoisecancellation.(a)Outerrace(b)innerrace(c)cagefault(d)balldefect.

ThisisduetodominationofnoiseafterWienerfiltering.Directcalculationoffaultindexingparameterswillhavepoor resolutionandhaveless informationregardingfaultespeciallyatearlystage.Therefore,thepowerspectraldensity basedfaultindexingparametercalculationisproposedandpresentedinthefollowing.

The power spectral density based fault indexing parametersare shownin Fig.14.The power spectral density haselevatingthewaveletcoefficientsandfaultindexingparameters. Consequently,theindicationoffaultindexing parametersisraisedandgivesclearinformationregardingfaultespeciallyatearlystage(0.1%).Thebargraphsin Fig.14(a)&(d)areraisedcomparedtoFig.13(a)&(d).Thisshowstheimportanceofpowerspectraldensityinwavelet decomposition.Inthesimilarway,thegeneralizedroughnessfaultwithsamevariationsinthemagnitude(0.1%,1%, and5%)isexaminedwithproposedtopologyandshowninFig.15.Fromthisfigureitisobservedthat,theparameter

0 500 1000 1500 0 0.5 1x 10 -5 Frequency (Hz)

(c)

(b)

(a)

Fig.10.FFTanalysisofstatorcurrentwithdifferentmagnitude,(a)with5%faultmagnitude,(b)with1%faultmagnitudeand(c)0.1%fault magnitude. 0 2000 4000 6000 8000 10000 -1 0 1x 10 -3 b(n) 0 20 40 60 -5 0 5x 10 -4 ca8 0 2000 4000 6000 -1 0 1x 10 -3 cd1 0 1000 2000 3000 -5 0 5x 10 -4 cd2 0 500 1000 1500 -5 0 5x 10 -4 cd3 0 200 400 600 800 -5 0 5x 10 -4 cd4 0 100 200 300 400 -5 0 5x 10 -4 cd5 0 50 100 150 200 -5 0 5x 10 -4 cd6 0 20 40 60 80 100 -5 0 5x 10 -4 cd7 0 20 40 60 -5 0 5x 10 -4 cd8

Fig.11.Waveletdecompositionofhealthysignalafternoisecancellation.

SDhasshowngoodvariationsinPSDbasedcalculationwhereastheparameterenergywillremainunaffectedeven afterPSD.ThesamewillbeexaminedusingexperimentalsetupproposedinSection3andtheresultsarepresentedin followingsubsection.

4.2. Experimentalresults

Inthe experimentalarrangement ofbearing faultdetection topology,the statorcurrent istaken from induction machineunderhealthyconditionofthebearingusingcurrenttransducerandprocessedfornoisecancellationbyNI MYDAC.Thestatorcurrentissampledatafrequencyof10kHzandnormalizedtoprocessinMATLABprogramming. AfterwardsthestatorcurrentisprocessedfornoisecancellationusingWienerfiltercoefficientsanddecomposedinto 8levelsusingDWTdecomposition.Thewaveletcoefficientsareusedtocalculatethefaultindexingparametersusing withoutpowerspectraldensity(PSD).AfterthatforwithPSDcase,thedecomposedDWTcoefficientsareprocessed forpowerspectraldensitycalculationandthenusedtocalculatethefaultindexingparameters.Thesevaluesoffault indexingparameterusingwithandwithoutPSDaresavedforcalculationoffaultratiosproposedinprevioussection.

0 2000 4000 6000 8000 10000 -2 0 2x 10 -3 _b(n) 0 20 40 60 -2 0 2x 10 -3 _ca8 0 2000 4000 6000 -1 0 1x 10 -3 _cd1 0 1000 2000 3000 -1 0 1x 10 -3 _cd2 0 500 1000 1500 -5 0 5x 10 -4 _cd3 0 200 400 600 800 -1 0 1x 10 -3 _cd4 0 100 200 300 400 -5 0 5x 10 -3 _cd5 0 50 100 150 200 -5 0 5x 10 -3 _cd6 0 20 40 60 80 100 -5 0 5x 10 -3 cd7 0 20 40 60 -1 0 1x 10 -3 _cd8

Fig.12.Waveletdecompositionofouterracefaultafternoisecancellation.

1 2 3 0 0.5 1 1.5 2

(a)

(b)

(c)

(d)

(e)

(f)

Outer Race Fault Inner Race Fault Cage fault Ball Defect

Fig.13.FaultindexingparameterswithoutPSD(1#CD6,2#CD7and3#CD8).(a)SDof0.1%fault,(b)SDof1%fault,(c)SDof5%fault,(d) energyof0.1%fault,(e)energyof1%faultand(f)energyof5%fault.

Nowtotesttheproposedalgorithmforbearingfault,thefaultybearings(outerrace,cageandgeneralizedroughness) areinsertedintothemachineoneafterotherandrepeattheentireprocesstoobtainfaultindexingparametersforeach case. Theratiosfor faultytohealthyparametersareplottedinFig.16.InFig.16theimpactof outerracefault is lesscomparedtocagefault.Thatmeans,theouterracefaultisatearlystageandcagefaultisatseverestage.The standarddeviationandenergyinFig.16(a)&(b)forboththefaultsshowsthestandarddeviationhaspoorperformance comparedtoenergy.Especially forouterracefault,thestandarddeviation givespoorindicationandisdifficultto estimatethefault.InthecaseofenergyparameterallthecoefficientsofDWThavegoodindicationanditiseasyto predictthefaultcomponentatearlystage.Butaftercalculationofpowerspectraldensityforthewaveletcoefficients, theindicationsforincipientfaultaregreatlyimprovedinboththeparametersandhaveagoodsignforfaultasshown inFig.16(c)–(d).Therefore,thepowerspectraldensityofwaveletcoefficientsgreatlyhighlightsthefaultindication inboththeparametersforallcategoriesoffault.

Inthecaseofgeneralizedroughnessfault,theratiosoffaultindexingparametersareshowninFig.17.Inthiscase also,thefaultindexingparametersaregreatlyimprovedusingpowerspectraldensityasmentionedinsimulationpart.

1 2 3 0 1 2 3 4

(a)

(b)

(c)

(d)

(e)

(f)

Outer Race Fault Inner Race Fault Cage Fault Ball Defect

Fig.14.FaultindexingparameterswithPSD(1#CD6,2#CD7and3#CD8).(a)SDof0.1%fault,(b)SDof1%fault,(c)SDof5%fault,(d) energyof0.1%fault,(e)energyof1%faultand(f)energyof5%fault.

1 2 0 1 2 3 4 5

(a)

(b)

Fig.15.Faultindexparametersforgeneralizedroughnessfaultwithdifferentfaultseverities(1#SD,2#energy)(a)withoutPSDand(b)withPSD.

1 2 3 0 5 10 15

(a)

(b)

(c)

(d)

Fig.16.Experimentalfaultindexingparametersusingwith&withoutpowerspectraldensity(1#CD6,2#CD7and3#CD8).(a)SDwithoutPSD, (b)energywithoutPSD,(c)SDwithPSDand(d)energywithPSD.

1 2 0 5 10 15 20 25

Healthy Condition STD

ENERGY

Fig.17.Experimentalfaultindexingparametersforgeneralizedroughnessfaultusingwith&withoutpowerspectraldensity(1#withoutPSD,2# withPSD).

ThestandarddeviationandenergyofwithandwithoutPSDareshowninFig.17.Theparametersaregreatlyimproved afterPSDbasedcalculationasshowninFig.17.Therefore,thebearingfaultdetectionusingnoisecancellationwith powerspectraldensityofDWTanalysisgivesgoodresultscomparedtoconventionalanalysisofDWT.

5. Conclusions

Thispaperhaspresented anapproachtodetectthe incipientstatebearingfaultsininduction motorusingstator currentsignatureanalysisvianoisecancellationusingDWTdecomposition.Thehealthycomponentsofstatorcurrent areestimatedandcancelledusingWienerfiltercoefficients.Thestandarddeviationandenergyratiosoffaultytohealthy statorcurrentarecalculatedasfaultindex.Twotypesoffrequencydomainanalysishavebeenpresentedtodetectthe bearingfaults.DWTanalysisofstatorcurrentafternoisecancellationhasovercomethedrawbacksoftheFFTanalysis forearlystagefaults.TheproposedmethodhasshownimprovedperformanceusingpowerspectraldensitybasedDWT analysis.ThefaultindexingparametersSDandenergyhaveshownalmostequalperformanceatseverestageoffault. Atincipientstage,SDshownsomegoodindicationcomparedtoPSDanalysis.ThoughtheSDhavemaintainsame indicationevenafterPSDcalculation,theenergyindicationhaveraisedabruptlytomaximum.Therefore,theenergy withPSDbasedfaultdetectionhasgivengoodresultscomparedtoother.Theresultshaveconfirmedtheeffectiveness oftheproposedtechnique.

InFuture,theeffectofseverenoisemaybereducedbyproperde-noisingtechniqueslikeWaveletDe-Noisingand deconvolutionandtheWienerfiltercoefficientsmaybedesignedusingbettererrorminimizationtechniques.

Acknowledgement

TheauthorsgratefullyacknowledgethecontributionofR.NagaSreenivasu,IRSE,IndianRailways,forhissupport inresearchwork.

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Mr.K.K.C.DeekshitiscurrentlyworkingtowardsDoctoraldegreeinElectrical&ElectronicsEngineering,JNTUK, Kakinada,A.P.,India.PreviouslyheworkedforK.L.University,Guntur,India.HeiscurrentlyanAssistantprofessor intheDepartmentofElectricalandElectronicsEngineering,PVPSIT,Kanuru,A.P,India.Hiscurrentresearchinterest includePowerElectronicsInductionmotordrivesandSignalProcessing.

Dr.VenuGopalaRao.M.,FIE,MIEEEatpresentisProfessorandHead,DepartmentofElectrical&Electronics Engi-neering,PVPSIT,Kanuru,A.P.,India.PreviouslyheworkedforK.L.University,Guntur.Hepublishedmorethan20papers invariousNational,InternationalConferencesandJournals.HisresearchinterestsaccumulateintheareaofPowerQuality, DistributionSystem,HighVoltageEngineeringandElectricalMachines.

Dr.R.SrinivasaRao,MIEEEatpresentisaProfessorinElectricalandElectronicsEngineeringDepartment,Jawaharlal NehruTechnologicalUniversityKakinada,Kakinada,A.P.,India.Hisareaofinterestincludeselectricalpowerdistribution systemsandpowersystemoperationandcontrol.