文献翻译-NED效果的评估方法

英语论文PerformanceEvaluationofNDEMethodsByHyung-SeopShim*AbstractMathematicalbasisfortheperformanceevaluationofNondestructiveEvaluation(NDE)methodsispresented.InstructuralinspectionwithNDEmethods,NDEdataarenotdirectlyusedfortheconditionassessment.Instead,NDEdatamustbeinterpretedasconditionofinspectedelement.CorrectassessmentsofconditionsdependonmanyfactorssuchastheinaccuracyandthevariabilityinNDEmeasurementsandtheuncertaintyincorrelationbetweenattributes(whatismeasured)andconditions(whatissoughtintheinspection).InaccuracyandvariabilityarethevulnerablenatureofNDEmethods,whereasuncertaintyistheinevitableerrorintroducedfromattributesusedbytestdevice.DespiteallthevulnerabititiesusingNDEmethods,areliableNDEmethodshouldprovidecorrectassessmentofcondition,whichmaybethecorrectpercentareadamagedinaninspectedelement.TomakethedecisionontheperformanceofNDEmethods,thispaperpresentsmathematicalbasistomeasurethereliabilityofNDEmethods.Keywords:interpretationofNDEdata,NDEmethods,NDEinspection,reliabilityoftest1.IntroductionTheusefulnessofNDEmethoddependsonhowwellthemethodindicatestheconditionofaninspectedelementcomparedtoitsactualcondition.TheperformanceevaluationofNDEmethodsisperformedbycomparingindicationsoftheconditionmadebytheNDEmethodtothetreeconditionoftheelement.Theindicationsofconditionsmadebypoint-wiseinspectionmethodsarefunctionofboththeaccuracymadthevariabilityofthemethodandtheuncertaintyincorrelationbetweenattributesandconditions.Accuracyandvariabilityhereentailtheperformanceofthedevice.AnoutcomefromNDEtestcanbeexpressedasaYesorNoindicationofdamage,orasaprobabilityoftheexistenceofdamage.Anassessmentcanbeexpressedasthepercentageofareainaninspectedelement,whichisdamaged.Theprobablevalueofassessmentiscalculatedthroughtheseveralconsiderations.Theseincludethelocationoftests,relationofphysicalquantitymeasuredtoexistenceofdamage,accuracyandvariabilityinmeasurements,andinterpretationofindividualtests.Thetermofdamageinthisstudyisconsideredtobebinary.Anelementinspectedisdamagedoritisnotdamagedatanytestlocation.Thereisnodegreeofdamage.Uncertainlyexistsonlyinthedetectionofdamagebyaninspectionmethod.ThispaperdevelopsthemathematicalbasisfortheinterpretationofNDEdataandtheperformanceevaluationofNDEmethods.Theapproachdevelopedinthispaperisapplicableanyinstrument-basedinspectionmethod,whichusespointapplicationsoftests.AprocedureforthecalculationofanassessmentandtheevaluationoftheperformanceofNDEmethodsispresentedwhichusesthefoursteps:Applicationoftest,Formationofprobabilitydensityfunctions,Formationofpopulations,andInterpretation.Thisevaluationprocesswilldeterminetrueandfalseindicationsofconditioninaninspectedelementforinstrument-basedinspectionmethods.Fortheclarityinunderstanding,severaltermsusedinthispaperaredefined.NDEmethodisameansofmeasuringaphysicalquantity(attribute)inaninspectedelementfordeterminationofthecondition;Testisanindividual,point-wiseapplicationofNDEmethod;Surveyisanensembleoftests;Outcomeisaninterpretationofasingletest;Assessmentisanensembleofoutcomes.2.InterpretationofNDEDataTheconditionassessmentofaninspectedelementistheinterpretationofmeasuredattributes.Attributeshereareemployedasindicatorsofcondition.Theyarethemeasurablephysicalquantityinaninspectedelementwhosemagnitudegivesevidenceoftheexistenceorseverityofdamageinanelement.Attributesarenotinthemselvesadirectindicationofdamage.Attributesmustbecorrelatedwiththeexistenceorseverityofdamageinaninspectedelement.Voidsinconcrete,forexample,affectsoundvelocityandscatterultrasoundwavespassingthrough.Voidscanalsoaffectthenatureoftransmissionsandreflectionofradarpulses.Electricalpotentialsorelectricalcurrentsmaybetheevidenceofcorrosionofreinforcingsteelwhichoftenleadstodelaminationofconcrete.Theformofmagneticfieldsanddisruptionofeddycurrentpatternsmaybecorrelatedwiththepresenceofvoids,cracksorotherdiscontinuities.Attributesareusefulforinspection,onlyifthereisacorrelationbetweenthephysicalquantitymeasuredandtheconditionofinspectedelement.Interpretationofmeasuredattributesfollowssimple,thresholdbasedinterpretation.NDEmeasurementsofattributesareeitherhigherorlowerthanthreshold,andsoYesorNodeterminationonexistenceofdamagecanbemade.Usingthresholds,continuousNDEdataarereducedtobinaryassessments.Inexistingpractice,thresholdsarenormallydeterminedbyperformingcompaniontests.NDEandcompaniontestsarecardedoutforthesamespecimensinlaborfield.ThetrueconditionofelementsandthresholdforNDEmethodaredeterminedbycomparingresultsoftests.Inthisway,thresholdsforNDEmethodscanbeselected.2.1ProbabilityDensityFunctions(PDF)ofNDEDataMeasurementsofattributesfromNDEmethodsarevariable,inadditiontobeinginaccurate.Higherandlowerdatavaluesareobtained,evenforelementsinidenticalcondition.EachofattributesmeasuredbyNDEmethodscanbeseenmfollowaprobabilitydistributionofmagnitude.ForoneNDEmethodseekingtothedamageinelementtwoprobabilitydistributionscanbeformed.OnedistributionofmagnitudeofNDEdatafrominspectedelementswhereelementsaredamaged,andaseconddistributionofNDEdatafromelementswhereelementsaresound.AnattributemeasuredbyNDEmethodisusefulindicator,iftheprobabilitydistributionsfromsoundandfromdamagedelementsarcdifferent.Thatis,iftheprobabilitydistributionofNDEdatafromsoundanddamagedelementshavedifferentmeansandiftwodistributionsdonotoverlaptoomuch.Toillustratethesepoints,considertwocasesshowninFig.1.Thefirstexampledistributionsarewell-seperated,therebyuniqueinterpretationofdataispossible.However,theseconddistributionsshowconsiderableoverlaps.Infact,thisleadstoanambiguousinterpretationofdata.TheoverlapofthedistributionsofaphysicalquantityinsoundandindamagedelementsisofprimaryimportanceintheperformanceofanNDEmethod.Itshouldbepossibletoevaluatetheperformanceofaninspectionmethodbasedonthedistributionsofitsmagnitudeinsoundandindamagedelements.Theamountofoverlapofthedistributionsinsoundandindamagedelementsisindicatedby/3.Largevaluesofcorrespondtoalittleoverlapoftwodistributionswhilesmallvaluesof/Jcorrespondtoasignificantoverlapoftwodistributions,canbecalculatedas:WherethesubscriptsSandDdenotetheparametersfortheprobabilitydistributionsofmagnitudeofNDEdatainsoundandindamageelements,respectively.2.2PopulationsofNDEDataNDEtestsareusuallyappliedinpoint-wisemannerinaninspectedelement.Moreover.methodsareperformedonevenlyspacedgridlineacrossthetestedelement.Thisfactcanmaketheonepossibleassumptionaboutassessmentofteststhatinterpretationofnumberoftestsresultsinaninterpretedamountofdamagedelement.Thatis,thefractionofalltestsinterpretedasdamagedelementwillequalthefractionofarea,whichisdamaged.Evenfurther,thepopulationsofNDEdatainsoundandindamagedelementswillbeproportionaltothetractionofelementwhichareactuallysoundanddamagedelements.Therefore,thepopulationofNDEdatacanbeobtainedbymultiplicationoffractionofelementwhichisinsoundorindamagedelementstotheprobabilitydistributionsofNDEdatainsoundandindamagedelements.Fig.2showstheexampleofpopulationsfromelementwhichisdamagedabout20%byarea.ThesepopulationsofNDEdataareobtainedfromprobabilitydistributionsmultipliedbyfractionofdamagedportionandofsoundportionofelements.TheprobabilitydistributionsandthepopulationsofNDEdataplayimportantrolewhentheperformanceofNDEmethodsareevaluated.3.PerformanceEvaluationofNDEMethodsTheperformanceevaluationofNDEmethodsisthemeasurementofdifferencebetweeninterpretedconditionandtrueconditionofinspectedelement.AnusefulNDEmethodshouldprovidethesmalldifference.Thatis,trueconditionofelementshouldbedetectedwithrelativeaccuracy.FortheperformanceevaluationofNDEmethod,twoprobabilitydistributionsofNDEdataandsimple,threshold-basedinterpretationareusedthroughout.ConsiderNDEmethodwithtwoprobabilitydensityfunctions(PDF)ofNDEdatainsoundandindamagedelements.Ifthethresholdvalue,fortheinterpretationisgiven,theprobabilitythatatestisinterpretedasdamageisusualtotheprobabilitythatthemeasuredvalueoftheNDEdataisgreaterthanthethresholdvalue.Bothsoundanddamagedareasmayhavemagnitudesofdatawhicharegreaterthanthethreshold.Therefore,theprobabilitythatthemeasureddataisgreaterthanthethresholdisthesumoftwoparts:Trueindicationsofactualdamagedareaandfalseindicationsofactualsoundarea.Fig.3showstrueandfalseindications.where,jj(x)ispdfofmagnitudeofNDEdataindamagedclement,./fx)ispdfofmagnitudeofNDEdatainsoundelement,Pt)isprobabilityoftrueindicationsofactualdamagedarea,andPsz)isprobabilityoffalseindicationsofactualsoundarea.Similarly,theprobabilitythatameasureddataisinterpretedassoundisusualtotheprobabilitythatthemeasuredvalueislessthanthethreshold.Bothsoundanddamagedareasmayhavemagnitudesofdatawhicharelessthanthethreshold.Therefore,theprobabilitythatthemeasuredvalueislessthanthethresholdisthesumoftwoparts:Trueindicationsofactualsoundareasandfalseindicationsofactualdamagedareas.Fig.4showsthetrueandfalseindications.（4）（5）WherePssisprobabilityoftrueindicationsofactualsoundarea,andPdsisprobabilityoffalseindicationsofactualdamagedarea.Ingeneral,therearefourpossibleoutcomesinthreshold-basedinterpretation.IfNDEdeviceisplaceondamagedelement,onlyEq(2)and(4)arepossible,whereasifNDEdeviceisplacedonsoundelement,onlyEq(3)and(5)arepossible.Thesumoftheprobabilitiesofthesetwooutcomesalwaysequalsone.Bymakinganassumptionthattheinterpretationofnumberoftestsresultsininterpretedamountofdamagedareainanelement,theinterpretedpercentareadamagediseasilycomputedfrompopulationsofNDEdata.PopulationsareobtainedfromPDFsandfractionofareainanelementdamaged。（6）where,PsandP,arethepopulationsofNDEdatainsoundandindamagedareasinanelementandnisthefractionofactualareadamagedinanelement.ForgivenpopulationsofNDEdataandthresholdvalue,7;fortheinterpretation,therearefourpossibleinterpretedpercentareas,TheseareshowninTable1.UsingTable1,theinterpretedpercentareadamagedinanelementiscalculatedas:（7）whereadistheinterpretedpercentareadamagedinanelement.Notethatthefirsttermin.(7)isthetrueinterpretationandthesecondtermisthefalseinterpretationofdamage.ForanyNDEmethodseekingtothedamageinanelement,interpreteddamageisthesumoftwoparts,ThefalseinterpretationforNDEmethodis:where,ErristhefalseinterpretationforNDEmethod.WiththeaidofEq.(6)and(7),theinterpretedpercentareadamagedinanelementcanbecomputedasafunctionofactualpercentareadamagedinanelement.Thatis,foranygivenactualpercentareadamagedinanelement,theinterpretedpercentareadamagediscomputedbyformationofpopulations,Eq(6)andcalculationusingEq(7).Iftheinterpretedpercentareadamagedinanelementisplottedinxvplaneasactualpercentareadamagedinanelementbeingxaxis,theaccurateNDEmethodshouldprovide45lineinx-yplane.4.DeterminationofThresholdThechoiceofathresholdvalueforinterpretationaffectsperformanceofNDEmethods.Dependingonthresholdvalue,theinterpretedpercentareadamagedandthefalseinterpretationinanelementissignificantlyaffected.Possiblecriteriaforthechoiceofathresholdmaybetominimizethenumberoffalseinterpretationsoftests,ortoinsurethattheactualamountofdamagedareaisaccuratelydetermined.Tounderstandhowthevalueofathresholdaffectsanassessment,fourdifferentcriteriaofchoiceofthresholdareselected.Thefourdifferentcriteriaare:1.IntersectionofPDFsofmagnitudeofNDEdatainsoundandindamagedareasinanelement.2.IntersectionofpopulationsofmagnitudeofNDEdatainsoundandindamagedareasinanelement.3.Minimizetheprobabilityoffalselyinterpretedtests.4.Insurethattheactualamountofdamageisaccuratelydetermined.TheintersectionofPDFsofmagnitudeofNDEdatainsoundandindamagedareasinanelementleadstoauniquethreshold.Thisthresholdcanbeobtainedbyfollowingequation.where,TisthethresholdattheintersectionofPDFs.OncelimitationinusingathresholdattheintersectionofPDFsisthatitdoesnotrespondtothechangeinsoundandindamagespopulationsasanelementbecomesmoredamaged.Tosolvethisproblem,anothercriterionistochooseathresholdsuchthatitliesontheintersectionofthesoundanddamagedpopulations.ThresholdattheintersectionofpopulationsisobtainedfromfollowingequationIftheprimaryconcernofNDEinspectionisthatthelocationofdamagedareasisaccuratelydetermined,itwouldbeimportantthatathresholdinterpretationischosensuchthatspatialerrorsareminimized.Spatialerrorsareminimizedbyminimizingfalseinterpretations,whichisthethirdcriterionforchoosingathresholdvalue.Thethresholdwhichminimizestheprobabilityoffalseinterpretationsdependsontheamountofactualdamage.Therefore,thevalueofthethresholdisafunctionoftheactualareadamaged.Foranyamountofdamage,thethresholdwhichminimizesfalseinterpretationsisidentifiedbysearchingforfilethresholdwhichminimizesthesumoftwoequations,Eq(3)and(4).Itturnsoutthatthresholdswhichminimizethefalseinterpretationsareidenticaltothresholdsattheintersectionsofpopulations.ThegoalofsomeNDEinspectionistoaccuratelydeterminetheamountofdamagedareainaninspectedelement.Forexample,thedecisionofwhethertoreplaceabridgedeckisgenerallybasedonthetotalamountofdamagedarea.Thelocationsofdamagearenotimportant.Allthatisneededisanaccurateinterpretedamountofdamageisequaltotheactualamountofdamage.Thisiscalledinterpretationaccuracyandisthefourthcriterionforchoosingathresholdvalue.Toinsureinterpretationaccuracy,athresholdmustbechosensuchthatthenumberoffalselyinterpretedtestsindamagedareainanelementexactlyequalsthenumberoffalselyinterpretedtestsinsoundareainanelementinthismanner,thedamagedareafalselyinterpretedassoundisreplacedbythesoundareafalselyinterpretedasdamaged,resultinginacorrectinterpretationofthetotalamountofdamage.Thenumberoftestsfalselyinterpretedinsoundandindamagedareainanelementdependsontheamountofactualdamage.Sincethelocationofthethresholddeterminesthenumberoffalseinterpretationsofsoundandofdamagedareas,thethresholdmustalsobeafunctionoftheamountofactualdamage.Thedeterminationofathreshold,whichinsuresinterpretationaccuracyiscalculatedfromthefollowingequation.WhereYisthethresholdtoinsureinterpretationaccuracy.5.ComparisonofThresholdsFouruniquecriteriauponwhichachoiceofthresholdcanbebasedisintroduced,ToclearlyunderstandhoweachofthiscriteriainfluencestheperformanceofNDEmethod,thesecriteriaareappliedtoexampleNDEofhalf-cellpotentialmethod.Theperformanceofhalf-cellpotentialmethodusingeachofthesecriteriaisevaluatedintermsofthefalseinterpretation.Halt-cellpotentialtestdetectcorrosionactivityofreinforcingsteelinconcrete.Electricalpotentialsofreinforcingsteelinconcreteshiftabruptlytomorenegativevalueswhencorrosionbegins.Inlaboratorystudies,historiesofelectricalpotentialsovertimeexhibitjumpswhencorrosionbegins.Jumpsunambiguouslyrevealonsetofcorrosion.Infielduse,singlepoint-in-timereadingsarecollected,andcorrosionactivityisinferredfromthemagnitudeofhalf-cellpotential.HearnandMarshallHearnandMarshall,1996havecollecteddatafromhalf-cellpotentialsurveysofreinforcedconcretebridgedecksinUnitedStates.Inregionofdeckswherereinforcingsteelisnotcorroding,half-cellpotentialhaveanormaldistributionwithameanvalue207mVandastandarddeviationof80mV.Inregionsofdeckswherecorrosionisactive,half-cellpotentialvaluehaveameanvalueof354mVandastandarddeviationof70mV.Fig.5showsPDFsofhalfcellpotentialinsoundandincorrodedareas.TheBvalueofhalf-cellpotentialmethodis1.38,whichindicatelargeoverlapoftwodistributions.Fig.6showsthethresholdforhalf-cellpotentialmethod.NoticethatthresholdattheintersectionofPDFsdoesnotdependonactualamountofdamage,whereasthresholdsbyothercriteriado.Thresholdsbyothercriteriaapproachnegativeandpositiveinfiniteaspercentareacorrodedinanelementapproaches0%and100%.Giventhresholdvaluesfortheinterpretationofhalt-cellpotentialmethodandfractionofareacorroded,interpretedpercentareacorrodedcanbeplottedasafunctionofactualpercentareacorrodedusingEq.(7).ThiskindplotisrecognizedasperformancecurveforNDEmethod.Performancecurveofhalf-cellpotentialmethodisshowninFig.7.PerformancecurvebythresholdattheintersectionofPDFsshowsthathalf-cellpotentialmethodoverestimatescorrodedareaupto56%actualdamage(corrodedarea).Between56and100percentareaactuallycorroded,thisNDEmethodunderestimatesthedamage.:orathresholdattheintersectionofpopulations,andwhichminimizethefalseinterpretation,theinterpretedandtheactualamountofareacorrodedareequalat0,42,and100percentareaactuallycorroded.Thetrendofslightoverandunder-estimationsisalsoshownforthisthreshold.Forathresholdofinterpretationaccuracy,interpretedamountofcorrodedareaisexactlyequaltoactuallycorrodedareaasexpected.However,noticethattheinterpretationbythisthresholdstillcontainsspatialerrorSimilartotheperformancecurveofhalf-cellpotentialmethod,falseinterpretationcanalsobeplottedasafunctionofactualpercentareacorrodedusingEq.(8).ThisisshowninFig.8.ThefalseinterpretationforathresholdattheintersectionofPDFsreachesthemaximumvaluesof18%at0percentofactuallycorrodedareaanddecreasesto15%.Forathresholdattheintersectionofpopulationsandathresholdwhichinsureinterpretationaccuracyareverysimilar,coincidingatzero,100,andapproximately43percentactuallycorrodedarea.Foractualamountsofcorrodedareadifferentfromthese,athresholdinterpretationattheintersectionofpopulationsresultsintheleastfalseinterpretations.Sincethistypeofthresholdinterpretationminimizesthefalseinterpretations,thiscurveisessentiallyanenvelopdefiningthelowestfalseinterpretationswhichcanbeachievedforthehalf-cellpotentialmethod.Interpretationofhalf-cellpotentialsaccordingtorecommendationsofASTM【Annual,1992】identifiesprobablecorrosionwherepotentialsaremorenegativethan350mV.ForthisASTMthreshold,falseinterpretationincreaseslinearlyfrom4%to50%.Thismeansthatforanelementseverelycorroded,thereisalargerprobabilitythatahalf-cellpotentialtestwillbefalselyinterpretedthancorrectlyinterpreted.6,PerformanceofNDEby16ValuesPerformanceofNDEmethodisinvestigatedaccordingtothechoiceofthresholdinprecedingsection.Since,oneexampleofhalf-cellpotentialmethodisillustrated,theeffectof/3valueontheperformanceofNDEcannotbeseen.TheflvaluedefinesamountofoverlapbetweentwoPDFsofmagnitudeofNDEdata.Dependingon/3value,theperformanceofNDEmethodissignificantlyaltered.TheeffectofBvalueontheperformanceofNDEisinvestigatedintermsoffalseinterpretation.ThefalseinterpretationininterpretationofNDEdataisbothfunctionof/3valueandofthresholdvalue.Since,thresholdforNDEmethodisalsofunctionofactualamountofdamageinaninspectedelement,thefalseinterpretationofNDEisnowplottedinthreedimensions.Thecontourplotoffalseinterpre