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Probabilistic Modeling of Condition-Based Maintenance and Quantification of Its Benefits for Airliners

Permanent Link: http://ufdc.ufl.edu/UFE0043955/00001

Material Information

Title: Probabilistic Modeling of Condition-Based Maintenance and Quantification of Its Benefits for Airliners
Physical Description: 1 online resource (104 p.)
Language: english
Creator: Pattabhiraman, Sriram
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: cbm -- conditionbasedmaintenance -- fuselagefatigue -- maintenanceprediction -- savings -- shm -- structuralhealthmonitoring
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Airplane fuselage structures are designed with the concept of damage tolerance, wherein small damage are allowed to remain on the airplane, and damage that otherwise affect the safety of the structure are repaired. The damage critical to the safety of the fuselage are repaired by scheduling maintenance at pre-determined intervals. Scheduling maintenance is an interesting trade-off between damage tolerance and cost. Tolerance of larger damage would require less frequent maintenance and hence, a lower cost, to maintain a certain level of reliability. Alternatively, condition-based maintenance techniques have been developed using on-board sensors, which track damage continuously and request maintenance only when the damage size crosses a particular threshold. This effects a tolerance of larger damage than scheduled maintenance, leading to savings in cost. This work quantifies the savings of condition-based maintenance over scheduled maintenance. The work also quantifies converting the cost savings into weight savings. Structural health monitoring will need time to be able to establish itself as a stand-alone system for maintenance, due to concerns on its diagnosis accuracy and reliability. This work also investigates the effect of synchronizing structural health monitoring system with scheduled maintenance. This work uses on-board SHM equipment skip structural airframe maintenance (a subsect of scheduled maintenance), whenever deemed unnecessary while maintaining a desired level of safety of structure. The work will also predict the necessary maintenance for a fleet of airplanes, based on the current damage status of the airplanes. The work also analyses the possibility of false alarm, wherein maintenance is being requested with no critical damage on the airplane. The work use SHM as a tool to identify lemons in a fleet of airplanes. Lemons are those airplanes that would warrant more maintenance trips than the average behavior of the fleet.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sriram Pattabhiraman.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Kim, Nam Ho.
Local: Co-adviser: Haftka, Raphael T.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0043955:00001

Permanent Link: http://ufdc.ufl.edu/UFE0043955/00001

Material Information

Title: Probabilistic Modeling of Condition-Based Maintenance and Quantification of Its Benefits for Airliners
Physical Description: 1 online resource (104 p.)
Language: english
Creator: Pattabhiraman, Sriram
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: cbm -- conditionbasedmaintenance -- fuselagefatigue -- maintenanceprediction -- savings -- shm -- structuralhealthmonitoring
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Airplane fuselage structures are designed with the concept of damage tolerance, wherein small damage are allowed to remain on the airplane, and damage that otherwise affect the safety of the structure are repaired. The damage critical to the safety of the fuselage are repaired by scheduling maintenance at pre-determined intervals. Scheduling maintenance is an interesting trade-off between damage tolerance and cost. Tolerance of larger damage would require less frequent maintenance and hence, a lower cost, to maintain a certain level of reliability. Alternatively, condition-based maintenance techniques have been developed using on-board sensors, which track damage continuously and request maintenance only when the damage size crosses a particular threshold. This effects a tolerance of larger damage than scheduled maintenance, leading to savings in cost. This work quantifies the savings of condition-based maintenance over scheduled maintenance. The work also quantifies converting the cost savings into weight savings. Structural health monitoring will need time to be able to establish itself as a stand-alone system for maintenance, due to concerns on its diagnosis accuracy and reliability. This work also investigates the effect of synchronizing structural health monitoring system with scheduled maintenance. This work uses on-board SHM equipment skip structural airframe maintenance (a subsect of scheduled maintenance), whenever deemed unnecessary while maintaining a desired level of safety of structure. The work will also predict the necessary maintenance for a fleet of airplanes, based on the current damage status of the airplanes. The work also analyses the possibility of false alarm, wherein maintenance is being requested with no critical damage on the airplane. The work use SHM as a tool to identify lemons in a fleet of airplanes. Lemons are those airplanes that would warrant more maintenance trips than the average behavior of the fleet.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sriram Pattabhiraman.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Kim, Nam Ho.
Local: Co-adviser: Haftka, Raphael T.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0043955:00001


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PROBABILISTICMODELINGOFCONDITION-BASEDMAINTENANCE STRATEGIESANDQUANTIFICATIONOFITSBENEFITSFORAIRLINER S By SRIRAMPATTABHIRAMAN ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2012

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c r 2012SriramPattabhiraman 2

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Tomylovingparents,PattabhiramanandUsha,andtomybelov edsister,Harini 3

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ACKNOWLEDGMENTS Firstandforemost,Iwouldliketothankmyadvisors,Dr.Nam HoKimandDr. RaphaelHaftka,forgivingthisopportunitytopursueadoct oratedegree.Mysincere thanksforthemotivation,andallthecommentsandsuggesti onsonallaspectsof research,youprovidedduringmyentirelengthofstudy.The experienceswithyoudid shapemetobecomeabetterperson.Iamhighlyindebtedtoyou forthat. Iwouldliketothankmycommitteemembers,Dr.NagarajArake re,andDr.Panos Pardalos,fortheircontinuedsupportandvaluedsuggestio nsonmywork.Aspecial thanksforDr.Pardalosforagreeingtobeonmycommitteeons uchashortnotice. Iwouldliketothankallmypastandpresentlabmatesandfrie nds,Shriram,Matt, Alex,Diane,Anirban,Felipe,Taiki,Chanyoung,Saad,Kyle ,Jinuk,Jinsang,JianLi,for theirmuchvaluedsupportduringacourseofmystudy.Yourva luablecommentsduring thegroupmeetingshelpedhonemyinter-personalandpresen tationskills. IwouldliketothankDr.ChristianGoguandDr.ChristianBes ,attheUniversitede PaulSabatier,Toulouse,France,fortheinternshipopport unity.Iwouldliketothankthem forthevaluableinsightintomyresearchandforallthelogi sticshelpduringmytimein France. LifeinGainesvillewouldhavebeenincomplete,ifnotformy belovedfriends.For thoseendlessdiscussiononfootball,music,andpractical lyeverythingunderthesun, formakingmefeelcompletelyathomeinanalienland,formak ingmylife,practically voidofdullmoments,Iamthankfultoallmyfriends,andinpa rticular,totheesteemed membersofJFJgroupandrev.Sanagam,The. Tomyparentsandsister,fortheircontinuedsupportduring everysignicant momentinmylife,rightfrommybirth.Asimplethankswillne verdojusticetowhatyou allmeantome. IwouldalsoliketothankNASAandAirForceforthenanciala ssistanceduringthe courseofmystudy. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 11 CHAPTER 1INTRODUCTIONANDLITERATUREREVIEW .................. 13 1.1Introduction ................................... 13 1.2Background ................................... 15 1.2.1DamageToleranceDesign ....................... 15 1.2.2ScheduledMaintenance ........................ 17 1.2.3Condition-basedMaintenance ..................... 20 1.2.4StructuralHealthMonitoring ...................... 22 1.3ResearchObjective .............................. 24 2METHODOLOGY .................................. 26 2.1Introduction ................................... 26 2.2CorrectiveMaintenanceProcedure ...................... 26 2.2.1ScheduledMaintenance ........................ 28 2.2.2Condition-basedMaintenanceProcedure .............. 29 2.3ModelingDamageGrowthandInspectionProcess ............. 31 2.3.1FatigueDamageGrowthduetoFuselagePressurization ...... 32 2.3.2InspectionModel ............................ 35 2.4MonteCarloSimulation ............................ 35 3COMPARINGSCHEDULEDMAINTENANCEAND CONDITIONBASEDMAINTENANCE ....................... 37 3.1DamageGrowthParameters ......................... 37 3.2ComparisonBetweenMaintenanceProcesses ............... 38 3.3WeightSavings ................................. 42 3.3.1MinimumThickness .......................... 42 3.3.2EffectofVaryingThickness ...................... 43 3.4Summary .................................... 46 4SKIPPINGUNWANTEDPREVENTIVEMAINTENANCEUSINGCBM ..... 48 4.1Introduction ................................... 48 4.2MaintenanceStrategiestoSkipUnnecessaryStructural Airframe Maintenance ............................... 49 5

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4.2.1Sched-SHM ............................... 49 4.2.2ConditionbasedMaintenanceProcedure-skip(CBM-sk ip) .... 51 4.3ComparisonBetweenDifferentMaintenanceProcesses .......... 51 4.4CostComparisons ............................... 54 4.5EffectofParametersAffectingCBM-skiponMaintenance Cost ...... 58 4.6Summary .................................... 60 5MAINTENANCEPREDICTION ........................... 62 5.1Introduction ................................... 62 5.2MaintenancePrediction ............................ 63 5.3ChoosingOptimalValueof(m,C) ...................... 65 5.4Summary .................................... 68 6EFFECTOFDAMAGEQUANTIFICATIONERROROFONBOARD SHMSYSTEM .................................... 70 6.1ClassifyingManagementErrorArisingfromDamageQuant icationError 70 6.1.1Condition-basedMaintenance ..................... 71 6.1.2ConstantRatiobetweenDetectedandActualCrackSize ...... 71 6.1.3ConstantDifferencebetweenDetectedandActualCrac kSize ... 75 6.2CounteringDamageQuanticationError ................... 76 6.3Summary .................................... 78 7CONCLUSIONS ................................... 79 APPENDIX AIDENTIFYINGPARAMETERSFORPARISLAW ................. 81 BCOSTMODELFORSHORTRANGEAIRPLANE(A320) ............ 83 CDIRECTINTEGRATIONPROCEDURE ...................... 85 DIDENTIFYINGANOMALIESINAFLEETOFAIRPLANES ............ 87 D.1Introduction ................................... 87 D.2Methodology .................................. 87 D.3ErrorQuantication ............................... 90 D.4ModelingLemon ................................ 90 D.4.1ModelingLemonbyInitialCrackSize ................. 91 D.4.2ModelingLemonbyPressureDifferential ............... 92 D.5Summary .................................... 93 REFERENCES ....................................... 94 BIOGRAPHICALSKETCH ................................ 104 6

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LISTOFTABLES Table page 3-1Parametersofdamagegrowthmodelandinspectionmodela ndtheirvalues .. 37 3-2ParametersofCBMprocessesandtheconstraintssettode terminethem ... 38 3-3Comparingscheduledandcondition-basedmaintenanceo nreliabilityand criteriacontributingtolifecyclecostwithsamereplacem entthreshold(=12mm) forbothmaintenancestrategies ........................... 39 3-4ComparingthebestandworstcasecostsofCBMwiththecos tofscheduled maintenance ..................................... 41 3-5Dimensionsandmaterialpropertiesoffuselagecylinde r ............. 43 3-6Costandweightsavingsfromtheoriginalfuselagedesig n,tothefuel+maintenance costofscheduledmaintenance ........................... 46 4-1Comparisonofdifferentmaintenanceprocessesonthenu mberofmaintenance trips,percentageofpanelsreplacedperairplane,andprob abilityoffatigue failureofasinglepaneluntiltheendoflife ..................... 53 4-2ComparingthebestandworstcasecostsofdifferentCBMp rocesseswith thecostforscheduledmaintenance ........................ 57 4-3LifetimeFuelcost(basedon$/gal)forscheduledmainte nanceandCBM,for differentcasesoffuselagemassincreaseduetoon-boardse nsorsandactuators. Fuelcostbasedon$126.1/barrel[1] ....................... 57 6-1Effectofthresholdforrequestingmaintenanceonthenu mberofmaintenance trips,percentageofpanelsreplaced,andtheprobabilityo ffailureofapanel untiltheendoflifeofaA320airplane,withalifeof60,000 ightcycles ..... 72 6-2Managementerrorresultingfromdamagequanticatione rrorforvariouscombinations ofthresholdforrequestingmaintenance,a maintandtheCOVofdamagequantication (DQ)errorwhenaconstantratioismaintainedbetweenthede tectedandactual cracksizes ...................................... 74 6-3Managementerrorresultingfromdamagequanticatione rrorforvariouscombinations ofthresholdforrequestingmaintenance,a maintandtheCOVofdamagequantication (DQ)errorwhenaconstantdifferenceismaintainedbetween thedetected andactualcracksizes ................................ 76 6-4Managementerrorresultingfromconsideringdetectedc racksize(aDet)to beofavaluegreaterthanthatquantied(aQuant)byon-boar dSHMsystem, whenthresholdforrequestingmaintenance,a maint=70mmandtheCOVof damagequantication(DQ)error=10%whenaconstantratioi smaintained betweenthedetectedandactualcracksizes ................... 77 7

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B-1Airplaneparametersaffectingcost ......................... 84 8

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LISTOFFIGURES Figure page 2-1Theeffectofinspectionandreplacementprocessoncrac klengthdistributions 28 2-2Exampleofthescheduledmaintenanceprocess ................. 29 2-3Flowchartofmaintenanceschedulingandassessmentpro cedureforSHM basedinspection ................................... 31 2-4PossibleregionofParismodelparameters .................... 34 3-1Changeincostfromthatofcostatthickness=2mm,forvar iouscontributors forlifecyclecost,forchangeinfuselagethicknesstomain tainsamelevelof probabilityoffailure ................................. 44 3-2Comparingvariationoffuel+maintenancecostforCBMwi thfuselagethickness, withfuel+maintenancecostforscheduledmaintenanceatfu selagethickness =2mm,fordifferentcasesofweightincreaseduetoonboardS HMequipment 45 4-1FlowchartoftheSched-SHMmaintenanceprocess ................ 50 4-2Flowchartdepictingmaintenanceschedulingandassess mentprocedurefor CBM-skip ....................................... 52 4-3Fractionofairplanesundergoingstructuralairframem aintenance(i.e.repair) ateachscheduledmaintenance .......................... 55 4-4Effectofparameters,a thskipanda repontheno.ofstructuralairframemaintenance trips,theno.ofunscheduledmaintenancetrips,andtheper centageofpanels replacedforCBM-skipmaintenancestrategy ................... 59 4-5Theeffectoftheparameters,a thskipanda rep,onthemaintenancecost,asa functionofparameters,k SHMandk unsch,andpanelreplacementcostforCBM-skip maintenancestrategy ................................ 60 4-6Paretofrontconstructedbasedonparametersaffecting maintenancecost ... 61 5-1Predictionplotconsideringtheextremitiesandmeanva luesofjointdistribution of(m,C) ........................................ 64 5-2Idealpredictionplot ................................. 66 5-3Predictionplotswhen(m,C)wereoptimizedconsidering rmsoftheareadifference untilthenthmaintenance .............................. 66 5-4Optimalvaluesof(m,C)forcasesconsideredinFigure53 ........... 67 5-5Predictionplotwhenoptimalvaluesof(m,C)untilendof ascheduledmaintenance isusedtopredictthemaintenanceforthenextscheduledmai ntenance .... 67 9

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5-6Plotoferrorsinthepredictionplot ......................... 68 6-1Explainingtheeffectofdamagequanticationerror ................ 73 A-1Comparingthesensitivityofinspectionintervalforop timalsetofparameters andthetrendobservedinreality .......................... 82 C-1Regionsof(C,m)forN=50,000anda 0=1mm .................. 86 D-1ExplainingHierarchicalclusteringanddifferentways tocomputedistancebetween clusters ........................................ 89 D-2VariationofTypeIandIIerrorswithmaintenanceassess ments,forvarious casesofimmediatehistoryconsideredtoclassifyalemon ............ 92 D-3VariationofTypeIandIIerrorswithmaintenanceassess ments,forvarious casesofimmediatehistoryconsideredtoclassifyalemonba sedondifference inpressuredifferential ................................ 93 10

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AbstractofdissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy PROBABILISTICMODELINGOFCONDITION-BASEDMAINTENANCE STRATEGIESANDQUANTIFICATIONOFITSBENEFITSFORAIRLINER S By SriramPattabhiraman May2012 Chair:Dr.NamHoKimCochair:Dr.RaphaelT.HaftkaMajor:MechanicalEngineering Airplanefuselagestructuresaredesignedwiththeconcept ofdamagetolerance, whereinsmalldamageareallowedtoremainontheairplane,a nddamagethat otherwiseaffectthesafetyofthestructurearerepaired.T hedamagecriticaltothe safetyofthefuselagearerepairedbyschedulingmaintenan ceatpre-determined intervals. Schedulingmaintenanceisaninterestingtrade-offbetwee ndamagetoleranceand cost.Toleranceoflargerdamagewouldrequirelessfrequen tmaintenanceandhence, alowercost,tomaintainacertainlevelofreliability.Alt ernatively,condition-based maintenancetechniqueshavebeendevelopedusingon-board sensors,whichtrack damagecontinuouslyandrequestmaintenanceonlywhenthed amagesizecrosses aparticularthreshold.Thiseffectsatoleranceoflargerd amagethanscheduled maintenance,leadingtosavingsincost.Thisworkquantie sthesavingsofcondition-based maintenanceoverscheduledmaintenance.Theworkalsoquan tiesconvertingthecost savingsintoweightsavings. Structuralhealthmonitoringwillneedtimetobeabletoest ablishitselfasa stand-alonesystemformaintenance,duetoconcernsonitsd iagnosisaccuracyand reliability.Thisworkalsoinvestigatestheeffectofsync hronizingstructuralhealth monitoringsystemwithscheduledmaintenance.Thisworkus eson-boardSHM 11

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equipmentskipstructuralairframemaintenance(asubsect ofscheduledmaintenance), wheneverdeemedunnecessarywhilemaintainadesiredlevel ofsafetyofstructure. Theworkwillalsopredictthenecessarymaintenanceforae etofairplanes,based onthecurrentdamagestatusoftheairplanes.Theworkalsoa nalysesthepossibility offalsealarm,whereinmaintenanceisbeingrequestedwith nocriticaldamageonthe airplane.TheworkuseSHMasatooltoidentifylemonsinaee tofairplanes.Lemons arethoseairplanesthatwouldwarrantmoremaintenancetri psthantheaverage behavioroftheeet. 12

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CHAPTER1 INTRODUCTIONANDLITERATUREREVIEW 1.1Introduction Traditionally,aircraftstructureshavebeendesignedusi ngtheconceptofdamage tolerance,inwhichthestructureisdesignedtowithstands mallcracks,andlargecracks arerepairedthroughscheduledinspectionsandmaintenanc e.Thisconceptturnsoutto bemorecost-effectivethansafe-lifedesign,whereinthes tructureisdesignedsothatit doesn'tfailuntiltheendofitslife.Theconceptiscost-ef fectivethansafe-lifebecause airplanesdesignedbasedonthelatterwouldbemuchheavier ,andthus,morecostly. Indamagetolerancedesign,itisimportanttoinspectastru ctureregularlysothatall damagethatcanpossiblythreatenthesafetycanberepaired Selectinginspectionintervalforscheduledinspectionsd ependonsizeoftolerated damageandlifecyclecost.Tomaintainthesamelevelofsafe tyofstructure,frequent inspectionsmayallowtolerationofalargercrack.But,fre quentinspectionswouldcause ahigherlifecyclecost.Similarly,lessfrequentinspecti onsleadstolowerlifecyclecost, buttoleratesonlyasmallcracksizetoremainonthestructu re.Butthetoleranceof smallcrackislimitedbytheinspectioncapability.Thesch eduleofmaintenanceisoften optimizedonthecostwhilemaintainingadesiredlevelofre liability. Alternativetoscheduledmaintenance,thereisongoingres earchoncondition-based maintenance.Inthisapproach,damageiscontinuouslymoni tored,andmaintenanceis requestedwhenthedamagesizecrossesacertainthreshold. Continuousmonitoring toleratesamuchlargercracktoremainonthestructure,the rebyleadingtoalower lifecyclecost.But,therecouldbesubstantialcostinvolv edininstallingacondition-based maintenancesystem,causinghigherlifecyclecost.Butongoingresearchwork suggestscondition-basedmaintenancetobecostefcient( [ 2 ],[ 3 ]).Acondition-based maintenancesystemcouldbeoptimizedtomatchacertainlev elofreliabilityofasystem orforcost. 13

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Recently,structuralhealthmonitoring(SHM)systemshave becomeavailableusing on-boardsensorsandactuators.Thesesystemscanperformd amageassessmentas frequentlyasneeded,andtheycouldbeagoodtoolforcondit ion-basedmaintenance. Hence,inspectionbystructuralhealthmonitoringwouldwa rrantahigherdamage tolerancethanscheduledmaintenance,butcouldmonitorda magemorefrequentlyand inlesstimethannon-destructiveinspection.Theymayhave asignicantinstallation cost,butonceinstalled,theoperationalcostisquitenegl igible.Condition-based maintenanceusingstructuralhealthmonitoringcouldbeav alidcandidateforsavingsin lifecyclecostofanairplane. Savingsinlifecyclecostofanairplanecouldbetradedagai nstsavingsonthe weightoftheairplane,whilemaintainingthesamelevelofr eliabilityoftheairplane structure.Athinnerairplanestructurewouldwarrantafas tercrackgrowthandhence, wouldcausemoremaintenancetrips,therebycausinganincr easeinlifecyclecost. Butthinnerairplanedecreasesthefuelcostspenttoythea irplane.Theeffectof condition-basedmaintenancebystructuralhealthmonitor ingsystemontheweightand lifecyclecosttrade-offisaninterestingpossibilitytol ookat. On-boardstructuralhealthmonitoringequipmenthassomeu n-resolvedissuesto functionasastand-alonedeviceforinspectionpurpose.Th ereareconcernsonthe reliabilityoftheon-boardSHMsystem,andalsoontheaccur acyofitsdiagnosis.These concernsmustbeironedoutbeforetheSHMsystemismadeapar tofmaintenance schedule.ThereisahighpossibilityofSHMsystemintegrat edwithtraditionalscheduled maintenance,complementingit,beforecondition-basedma intenanceschemeis acceptedintothedesignofmaintenanceschedule. Oncethecondition-basedmaintenanceschemeisintegrated withtheexisting maintenancescheme,condition-basedmaintenancecouldbe usedasatooltopredict thetimeofnextstructuralairframemaintenance(asubseto fscheduledmaintenance). Condition-basedmaintenancecouldalsobeusedasatooltoi dentifylemonsina 14

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eetofairplanes.Lemons,arethoseairplanesthatrequire morestructuralairframe maintenancethantherestoftheeet. 1.2Background 1.2.1DamageToleranceDesign Structuresaretraditionallydesignedwithaconceptofsaf e-life.Safe-lifedesign methodologyreliesontheuseofsafetyfactorsonloadandma terialpropertiesto preventfailureuntiltheendoflifeofthestructure.Safelifedesignmethodologywas laterreplacedbyfail-safedesignmethodologywhereinast ructuremayfailbeforeits endoflife,andinspectionandmaintenancetechniquesareu sedtorepairthestructure beforeitfails.Mcbreaty[ 4 ]comparedsafe-lifeandfail-safemethodologyonairframe designandconcludedthatthesafe-lifemethodisgenerally inadequatewhilefail-safe methodispracticalandsound.Kennethb[ 5 ]concludedthatfail-safedesignreduced weightandcostonUSArmy sLHX,ascomparedtosafe-lifedesignwhilereducingthe probabilityofcatastrophicfailure. Designingstructuresusingfail-safemethodologyisveryw elladdressedinliterature. David[ 6 ]presentedthegeneralapproachtoafail-safeproblem,and thevariousexisting method,andtheirshortcomings.QueslatiandSankar[ 7 ]usedfail-safemethodology todesignactiveandpassivesuspensionontractorandsemit railermodel.Breeseand Gordaninejad[ 8 ]usedfail-safemethodologyonmountainbicycledampertom aintain minimumrequireddampingcapacityincaseofelectronicsys temsfailure. Forstructuralapplications,Sunetal.[ 9 ]solvedafail-safeoptimaldesignproblem forathreemembertrussunderstress,bucklingformultiple loadingconditions.Moses [ 10 ]usedreliabilityanalysistodesigntrussesbasedonthefa ilureoftheweakestlink. Inmetallicstructuresinvolvingfatigue,fail-safedesig nisusedwiththeconcept ofdamagetolerance.Anestablishedwayistoallowsmalldam agetoremainonthe structureandreplace/repairthedamage,onlywhenitgrows largeenoughtoaffect thereliabilityofthestructure.Thisapproachistermedas damagetolerance.Broek 15

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[ 11 ]describedthedamagetolerancerequirementsapplicablet ocommercialairplanes, ships,offshorestructuresandnuclearpressurevesselsan dRudd[ 12 ]presentedthe analyticalandexperimentaldamagetolerancerequirement sforaircraftstructures. Designingstructureswiththeconceptofdamagetolerancet opreventfatigue failureisverywelladdressedinliterature.Lind[ 13 ]gaveanintroductiononthe damagetoleranceconcept.Hedeneddamagetoleranceappro achasareciprocal ofvulnerabilityofthestructure,i.eadamagetolerantstr ucturewillnotbevulnerableto unforseenfuturedamage.Margery[ 14 ]advocatedtheuseofprobabilisticmethodology fordamagetolerancemethods.Lazzeri[ 15 ]comparedsafelifeandprobabilisticdamage tolerantapproachesontheriskoffailureandcostsforairc raftstructuraldesign.Alam andJenkins[ 16 ]realizedtheconceptofdamagetolerancebyperformingan ite elementanalysis(staticanddynamic)ofaspiderweb. Ingeneral,damagetoleranceanalysisisusedtodeterminet heeffectofcrackson thestrengthofastructureandcrackgrowthasafunctionoft ime.Broek[ 17 ]computed theremaininglifeofatenmemberstructureinstructuralbe nding.Henotedthetolerable awsizesfordifferentaluminiumalloys.Toor[ 18 ]summarizeddifferentmethodologies tondtheresidualstrengthofastructure.Healsosummariz edthevariouscrackgrowth lawsusedinpractice.Swift[ 19 ]predictedtheresidualstrengthofdamaged,stiffened fuselagepanelsofDC-10,basedonmatrixforcesolutionona nidealizedstructure. Theconceptofdamagetoleranceisprevalentinvariousappl ications.Gravesand Lagace[ 20 ]assesseddamagetoleranceapproachtopreventfractureof pressurized graphite/epoxycylinders.Russelletal.[ 21 ]discussedvariousmethodologiesfor damagetolerancedesignwithspecicfocusonthefail-safe tyofcompositesandwich structures.O Brien[ 22 ]ensuredthedamagetolerancedesignofcompositeoff-axis pliesbypredictingthede-laminationgrowthinthestructu re.Hayman[ 23 ]discussed damagetolerancedesignandcorrectivemeasurestoprevent failureforanavalship.He 16

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considereddamagepresentinsandwichstructurestohaveb erreinforcedplasticface sheets. Forapplicationofconceptofdamagetolerancetometallics tructures,Lazzeri andMariani[ 24 ]presenteddifferentmethodologiesofdamagetolerance,c urrentlyin practice,forhelicopterindustry.Zerbstetal.[ 25 ]gaveabriefoverviewofapplications basedondamagetoleranceapproachintherailwayindustry. Theyalsomentioned issuesonusingdamagetoleranceapproachesforaxles,whee lsandrails.Mistree etal.[ 26 ]useddamagetoleranceapproachestodesignoffshorestruc tures.Chamis [ 27 ]useddamagetoleranceanalysisforturbineenginecompone nts.Hepropagated uncertaintyinmaterialpropertiesusingcomputationalme thodstoevaluatethereliability andremainingusefullifeofthestructure. Formetallicaircraftstructures,ZhangandLi[ 28 ]useddamagetoleranceapproach topreventfatiguefailurewithaskincrackunderabrokenst inger.SalgadoandAliabadi [ 29 ]useddamagetoleranceconceptfordesignofstiffenedpane ls.Theyalsoused dualboundaryelementmethodforcrackpropagationanalysi s.Alibadetal.[ 30 ]also useddualboundaryelementmethodforcrackpropagationana lysisinstiffenedfuselage toanalyzeeffectofmembraneandoutofplanebendingloads. Theirworkfocuses ondamagetoleranceapproachonmetallicfuselageofanairp lane,topreventfatigue failure.Thisdissertationfocusondamagetoleranceappro achtopreventfatiguefailure infuselageofairplane,causedduetoexcessivedamageprop agation. 1.2.2ScheduledMaintenance Fatiguefailureonmetallicfuselagepaneliscausedbyexce ssivedamage propagation.Inthedamagetoleranceapproach,smallcrack sareallowedtoremainon theairplane,whilelargecracks,thatmayaffectthesafety oftheairplanearerepaired. Therepairofthelargecracksisdonebymaintenance.During maintenance,the airplaneistakenoffserviceandsenttohangar,whereinthe correctivemaintenance actionsareperformed.EastinandMowery[ 31 ]examinedthedamagetolerancedesign 17

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requirementsforlargetransportationairplanesinthelas t30yearswithrespectto operationallifeanddamagetolerancethreshold.Sincethe semaintenanceprocedures arescheduledatpre-determinedtimestopreventfatiguefa ilureofairplanes,itistermed asscheduledmaintenance. Maintenanceisusuallyscheduledtopreventfailureofasys tem.SherifandSmith [ 32 ]reviewedvariousoptimalmaintenanceschedulingmethodo logycurrentlyused inliteratureforsystemssubjectedtofailure.Wang[ 33 ]presentedasurveyofvarious maintenancepoliciesinvolvingsingleunitandmultiunitd eterioratingsystems.Bea [ 34 ]summarizedaseriesoftechnologicaldevelopmentsinmain tenancetobetterthe integrityanddurabilityoflargecrude-oilcarriers.Stya rtandLin[ 35 ]demonstrateda methodologyforprobabilisticdamagetolerancebasedmain tenanceschedulingfor compositestructuresbasedonatheoryofoptimalstatistic aldecisions. Schedulingmaintenanceveryoftenwillguaranteeahighlev elofsafety,butcould beveryexpensive.Breen[ 36 ]reviewedvariousmethodologiesfordesigningstructural maintenanceschedule,inpracticeinUnitedStatesmilitar yandcommercialairplanes andalsonotedthedifferencesinthemethodologieswithRoy alAustralianAirforce airplanes.Theoptimalmaintenancescheduleforasystemus uallyinvolvesminimizing costwhilemaintainingthedesiredlevelofsafety.Mainten anceisscheduledusuallywith emphasisonbothsafetyandcost. Baeketal.[ 37 ]optimizedinspectionscheduleforendbeamofuncoveredfr eight train(brake)tomaintainadesiredlevelofsafety.Manning etal.[ 38 ]optimizedthe inspectionscheduletomaintainacertainlevelofreliabil itywhenthecrackgrowthis governedbystochasticmodels.Yangetal.[ 39 ]developedanoptimummaintenance schedulefordeterioratingbridgestructuresinprobabili sticframeworkwiththeobjective ofminimizinglife-cyclemaintenancecost.OkeandCharles -Owabe[ 40 ]optimizedthe scheduledmaintenanceschedule,whileconsideringaperio d-dependentcostfunction forthemaintenance.Jingetal.[ 41 ]optimizedmaintenancecostfornon-periodic 18

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inspectionintervalwhentheinspectionisimperfect.Brot [ 42 ]usedprobabilistic simulationstominimizefatiguefailureswithspecialemph asisontherelativemeritsof multipleinspectionsoveraterminatingaction.Okashaand Frangnopol[ 43 ]usedgenetic algorithmtosolvemulti-objectiveoptimizationproblemi nvolvingsystemreliability, redundancyandlifecyclecosttoschedulestructuralmaint enance. Inairplane,maintenanceisscheduledtomaintaintheairwo rthinessoftheairplane inservice.Airworthinessisatermtodescribewhetheranai rcrafthasbeencertied bynationalaviationauthority,suitableforasafeight.A kdeniz[ 44 ]discussedneed forstructuralmaintenanceprogramtochecktheairworthin essofairplanes.Ahmadiet al.[ 45 ]describedtrendsinaircraftmaintenanceinthepast50yea rs.Hagemaier[ 46 ] statedthatinadditiontocorrosionassessment,repairass essmentandservicebulletin complianceprogramsforthestructuralsafetyoftheaginga ircraft,theaircraftisalso protectedbymanufacturer'sextendedairframefatiguetes tingprogramsandindustries' advancementinnon-destructiveinspectiontechnology. Thereisalotofworkinliteratureonschedulingtheoptimum inspectioninterval forairplanes,usingdamagetoleranceapproach.Goranson[ 47 ]notedthevarious challengesinschedulingmaintenanceusingdamagetoleran ceapproach,considering theuncertaintyindamagedetectionandthevarioustypesof fatiguethataffectthe airworthinessoftheairplane.SinghandKoenke[ 48 ]optimizedtheinspectionschedule withatradeoffbetweensafetyandmaintenancecostandplac edemphasisonthe inspectiontechniquesandtheirimportanceindamagetoler ancedesign.Nechvaletal. [ 49 ]useddamagetoleranceapproachtofocusontheinspections chemeofafatigued multi-statesystem(MSS)withdecreasingintervalsofinsp ections.KaleandHaftka[ 50 ] useddamagetoleranceapproachtohaveatrade-offbetweenw eightandinspection costforaircraftstructuressubjecttofatiguedamagegrow th. Advancementinthedamagetoleranceapproachforschedulin gmaintenance forairplanesinvolvesincorporatingrealtimedegradatio nofthestructureintoaircraft 19

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design.SimpsonandBrooks[ 51 ]providedprocessesforincorporatingdegradation aspectsofaircraftintoexistinginfrastructureofaircra ftsystemdesign,manufacturing andmaintenance.Theyalsodiscussedtheeffectofthesestr ucturalintegrityprocesses oncostandsafety.Tsaietal.[ 52 ]optimizedinspectionintervalconsideringtheeffectof mechanicalservice,repairandreplacementduringapartic ularmaintenanceoperation. Repairrestoresthedegradedstrengthpartly,whilereplac ementissettorecoverthe componenttoitsoriginalcondition.Theinspectioninterv alisoptimizedonavailability maximization. Incidentally,Grimsleyetal.[ 53 ]notedthatagreatdealofprogresshasbeenmade inprobabilisticdamagetoleranceapproachforaircraftst ructuressothatthefuture workismorefocusedonthesavingsincostratherthanonsafe ty.Adifferenttypeof maintenanceprocess,termedcondition-basedmaintenance isgaininginpopularityover scheduledmaintenanceastheformerisfoundtobemoreecono mical(Starr[ 54 ]than thelatter.1.2.3Condition-basedMaintenance Condition-basedmaintenance,asthenamesuggests,hasato olthatrequests maintenancewhenaparticularconditionissatised.Jardi neetal.[ 55 ]summarized therecentdevelopmentsindiagnosticsandprognosticsofm echanicalsystems implementingcondition-basedmaintenancewithemphasiso nmodels,algorithms andmaintenancedecisionmaking. Condition-basedmaintenancetechniquetracksacontinuou slydeterioratingsystem andrequestmaintenancewhenthedeteriorationlevelcross esapre-determined threshold.Differentapproacheshavebeenconsideredinth eliteraturetomodelthe deteriorationanddecisionprocesses.Dieulleetal.[ 56 ]usedamaintenancescheduling functiontochoosethenextinspectionandmaintenancetime foracontinuously deterioratingsystem.Marseguerraetal.[ 57 ]usedgeneticalgorithmforamulti-component systemfordeterminingtheoptimaldegradationlevelbeyon dwhichmaintenancehas 20

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tobeperformed.ChenandTrivedi[ 58 ]usedasemi-Markovdecisionprocessforthe maintenancepolicyoptimizationofcondition-basedmaint enanceschedule.Ghasemi etal.[ 59 ]usedproportionalhazardsmodeltorepresentthesystem's degradationand Markovdecisionprocesstomodeloptimalmaintenancesched ule. Castaineretal.[ 60 ]consideredacondition-basedmaintenancepolicyforatwo -unit deterioratingsystem.Eachunitissubjecttogradualdeter iorationandismonitored bysequentialnon-periodicinspections.ChenandTrivedi[ 61 ]derivedclosedform expressionsofsystemavailabilitywhenthedeviceundergo esbothdeteriorationas wellasPoissontypefailures.Theseclosedformsolutionse nabledthemtondfaster algorithmstodeterminetheoptimalinspectionschedule. Workhasalsobeendoneinliteraturetomodelcondition-bas edmaintenancewith emphasisonminimizingcost.Grailetal.[ 62 ]modeledcondition-basedmaintenance processschedule,analytically,forastochasticallyandc ontinuouslydeterioratingsingle unitsystem,withanobjectivetominimizecostperunittime .Hontelezetal.[ 63 ]found theoptimummaintenancepolicywithcostforcontinuouslyd eterioratingprocess,by formulatingthedecisionprocessasadiscreteMarkovdecis ionproblem. Condition-basedmaintenancewasfoundtoleadtosavingsin costoverscheduled maintenance.BeralandSpeckman[ 2 ]observetheadvantageofconditionbased maintenanceusingSHMoverpreventative/scheduledmainte nanceonvariousfactors includinglifecyclecostandweightofairplane.Boller[ 3 ]observedthatusingSHMfor condition-basedmaintenancewouldleadtolowerdowntimea ndinspectioncosts.This dissertationfocusesonquantifyingadvantagesofconditi on-basedmaintenanceover scheduledmaintenancetopreventfatiguefailureinfusela gepanelsofcommercial airplanes. Inpracticalsituations,forcondition-basedmaintenance techniqueisusedtomonitor thecurrentdamagestateofastructure,andrequestmainten anceifthestructurehas 21

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deterioratedconsiderably.Section 1.2.4 describesatechniqueusedtomonitorthe currentdamageofastructure,structuralhealthmonitorin g. 1.2.4StructuralHealthMonitoring Structuralhealthmonitoringisatoolforcondition-based maintenance.This techniqueanalyzesthecurrentdamagestateofastructure. Bolleretal.[ 64 ]provideda backgroundofphysicalandmathematicalmodelsforahugega mutofapplicationsfrom civilinfrastructuretomanagement,onthesubjectofstruc turalhealthmonitoring.Boller andBiemans[ 65 ]presentedvarioustechniquesthatcouldbeusedforstruct uralhealth monitoringpurposesandtheyalsoprovidedmethodstovalid ateastructuralhealth monitoringsystem.Johnsonetal.[ 66 ]denedtherstattemptatbenchmarkproblem forcomparingdifferentstructuralhealthmonitoringtech niques.Theydeneda12DOF shearbuildingmodelasthatbenchmarkproblem. Differenttypesofstructuralhealthmonitoringsystemhav ebeenresearchedin literature.Boller[ 67 ]presenteddifferentmeansofmonitoringandsubsequentli fe managementforagedairplanes.Giurgiutiuetal.[ 68 ]testedE/Mimpedancemethod fornearelddamagedetectionandwavepropagationmethods forfarelddamage detection,onsimplegeometryspecimenswithseededcracks .FriswellandPenny [ 69 ]demonstratedthatforstructuralhealthmonitoringusing lowfrequencyvibration, todetectcracksonbeamstructures.IhnandChang[ 70 ]usedpitchcatchmethod andimagingmethodusingpiezoelectricactuator/sensorto characterizedamage onaluminumplateandstiffenedcompositeplate.Galeaetal .[ 71 ]usedpatchin-situ systemstomonitorthedamageincompositestructures.Sohn etal.[ 72 ]usedstatistical patternrecognitiontechniquetomonitorstructuralcondi tionofaboat.Zhangetal.[ 73 ] detecteddamageawayfromasensorlocationusingTransmitt anceFunctionMonitoring thatusevibrationmeasurementsofpeizoceramicpatchesto detectdamage.Rose [ 74 ]usedultrasonicguidedwavesforstructuralhealthmonito ringpurposes.Theyhave anabilitytoinspecthiddenstructuresunderwater,coatin gs,insulationsandconcrete. 22

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Sekineetal.[ 75 ]usedberBragggraftingtoidentifylocationandshapesof crackin aircraftpanels.Vaniketal.[ 76 ]presentedaBayesianprobabilisticmethodologyfor structuralhealthmonitoring.Theyupdatedthemodelparam etersandprobabilityof damageforeachsubstructureonaregularbasis. Structuralhealthmonitoringtechniquesalsodifferonthe materialusedfor monitoringdamageonastructure.Mufti[ 77 ]usedbrereinforcedpolymersand integratedbreopticsensingtechnologiestomonitorstru ctures,constructedinCanada. Kangetal.[ 78 ]usedcarbonnano-tubepolymermaterialtoformpiezoelect ricstrain sensorforstructuralhealthmonitoringapplications.Bak eretal.[ 79 ]embeddedoptical bresensorsforstructuralhealthmonitoringforadhesive lybondedcompositerepairs toAustralianmilitaryaircraft.BollerandAl[ 80 ]reviewedexistingloadmonitoring systemswithparticularfocusonpiezoelectricsensorsfor monitoringimpactloads.In thisdissertation,anytypeofaforementionedon-boarddia gnosticstechniquecouldbe used.Itisnecessaryforthemtodetectandcharacterizedam ageonfuselagepanelof airplane. Structuralhealthmonitoringisconsideredasanimportant toolformonitoring damageinvariousapplications.KoandNi[ 81 ]exploredtherecentdevelopments instructuralhealthmonitoringandtheirapplicationtola rgescalebridgeprojects. Senkine-Pettitte[ 82 ]notedtheuseofstructuralhealthmonitoringinaccuratel y predictingthelongevityofexistingbridgesandalsodesig ningmoredurable,smarter bridges.BollerandBuderath[ 83 ]advocateduseofstructuralhealthmonitoring techniquestorevolutionizeaircraftmonitoringanddesig nprocess. AnweraerandPeeters[ 84 ]reviewedvariousresearcheffortsspentonproblems ofhealthmonitoringanddamagedetection.Theyfocusedmai nlyonhowreseach effortsmustbedeployedtoaddresstheuserneeds.Inthesam evein,forairplane applications,Beardetal.[ 85 ]presentedalistofissuesthatmustbeaddressedbefore structuralhealthmonitoringsystemscouldbeusedinservi ceofcommercialairplanes 23

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withcompositematerials.Boller[ 86 ]describedhowstructuralhealthmonitoringcould beintegratedintoaircraftdesignprocess,withfocusonac ousto-ultrasonictechnique. BeralandSpeckman[ 87 ]discussedtherequirementsanSHMsystemneedstomeet beforeitisintegratedin-serviceaircraft. Structuralhealthmonitoringtechniquesareprojectedtoh avesomepractical advantagesoverexistingscheduledmaintenance.Derrisoa ndOlson[ 88 ]advocated theuseofstructuralhealthmonitoringasatoolforconditi on-basedmaintenancein improvingmaintenanceandreducinglifecyclecosts.Inthi swork,Section5andSection 6focusonusingstructuralhealthmonitoringtechniquesfo rsavingsinlife-cyclecost andimprovingsafetyovertraditionalscheduledmaintenan ce.TelgkampandSchmidt [ 89 ]discussedthepossibilityofweightsavingsontheairplan e,infuture,usingSHM systems. 1.3ResearchObjective Thisworkcomparestwomaintenancestrategiessettopreven tfatiguefailure infuselagepanelsofairplanes,causedduetoexcessivedam agepropagation.The workfocusesondamagepropagationofcracksonfuselage,ca usedbythepressure differentialbetweenthecabinandatmosphere.Morespeci cally,thisworkquanties theadvantageofcondition-basedmaintenanceoverschedul edmaintenanceonvarious counts.Structuralhealthmonitoringtechniques,withonboardsensorsandactuators, areassumedtobeusedasatoolforcondition-basedmaintena nce.Theobjectiveofthis workisthree-fold. 1)Therstobjectiveistoquantifycostsavingsbysimulati ngdamagepropagation onthefuselagepanel,andmodelingthemaintenanceprocess esforscheduled maintenanceandcondition-basedmaintenanceusingMonteC arlosimulations.The aimistoquantifythesavingsinaveragenumberofmaintenan cetrips,andhence,the savingsinlifecyclecostofairplane,untilitsendoflife. 24

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2)Thesecondobjectiveistotranslatethecostsavingsinto savingsinweightofthe airplane.Decreasingtheweightoftheairplane,reducesth efuelcost,butcausesan increaseinthemaintenancecostoftheairplane,duetofast ercrackgrowth.Thiseffects anincreaseinlifecyclecostforreductioninweightofthea irplane.Theaimtoquantify thesavingsontheweightoftheairplane,soastomaintainth esamelifecycleasthatof scheduledmaintenance. 3)Thethirdobjectiveistosynchronizecondition-basedma intenancewith scheduledmaintenanceschedule.Structuralhealthmonito ringsystemhasalotof un-resolvedissuestofunctionasastand-alonesystemforc ondition-basedmaintenance (CBM).Toexpeditetheuseofstructuralhealthmonitoringf orCBM,structuralhealth monitoringtechniqueisusedtorequestmaintenanceexactl yatthetimeofscheduled maintenance,andalsotoskipthestructuralairframemaint enance(asubsetof scheduledmaintenance),wheneverdeemedunnecessary.The aimistoquantify thesavingsinlifecyclecostobtainedbyskippingunnecess arystructuralairframe maintenance. Theoutlineofthedissertationisasfollows.Damageonairp lanegrowswhenever theairplaneisinoperation.Maintenanceisscheduled,atv arioustimes,duringthelife oftheairplanetorepairdamage.Chapter 2 presentsthemathematicalmodelsusedto modelthedamagegrowthandtheinspectionmodelsforschedu ledandcondition-based maintenanceforA320airplane.Chapter 3 discussesthersttwoobjectives.Chapter 3 quantiesthesavingsinlifecyclecostoverscheduledmain tenance,andtranslating someofthecostsavingsintoweightsavings.Chapter 4 discussessynchronizing condition-basedmaintenancealongwithscheduledmainten ance.Chapter 4 presents thesavingsinlifecyclecostwhenon-boardSHMisusedasato oltoskipunwanted structuralairframemaintenance.Chapter 5 usestheon-boardSHMsystemtopredict thenumberofairplanesinaeet,thatwouldrequirestructu ralairframemaintenanceat thetimeofnextscheduledmaintenance. 25

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CHAPTER2 METHODOLOGY 2.1Introduction Nowadays,airplanestructuresaredesignedwiththeconcep tofdamagetolerance. Indamagetolerancedesign,smalldamageisallowedtoremai nontheairplane,and largedamage,thatotherwiseaffectthesafetyofthestruct ureisrepaired.Maintenance isatoolfordamagetolerance,andisscheduledtomaintaina desiredlevelofsafetyof theairplaneuntilitsendoflife.Inthiswork,maintenance issettopreventfatiguefailure duetoexcessivedamagepropagationinfuselagepanelsofai rplanes. Traditionally,maintenanceisusuallyscheduledatpre-de terminedintervals.Such maintenanceistermedscheduledmaintenance,andthemaint enanceintervalissetto maintainadesiredlevelofsafetyoftheairplane.Alternat ively,damageiscontinuously trackedandmaintenanceisrequestedwhendamagegrowscrit ical.Thistypeof maintenanceistermedcondition-basedmaintenance.Secti on 2.2 delineatesthe differentmaintenanceproceduresusedinthiswork.Themat hematicalmodelstomodel damagepropagationandinspectionaremodeledinSection 2.3 2.2CorrectiveMaintenanceProcedure Correctivemaintenanceprocedureinvolvesscheduling/re questingmaintenance torepair/replaceanydamagethatwouldotherwisethreaten thesafetyofairplane fuselage.Inthiswork,damageonthefuselageismodeledasa through-the-thickness centercrackinaninniteplate.Repeatedpressurizationd uringtake-offandlandingof anairplanecancauseexistingdamageonafuselagepaneltog row.Eachtake-offand landingcausesonecycleofpressurization,andistermedi ghtcycle. Damagegrowthonthefuselagedependsonmanyfactorsinclud ingenvironmental conditions,materialproperties,humanfactorsinvolving pilot,etc.Sincethedamage ismodeledasathrough-the-thicknesscentercrackinanin niteplate,damage/ crackgrowthisaffectedbyparametersofthecrackgrowthmo del.Inthiswork,the 26

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rateofcrackgrowthiscontrolledby,amongotherfactors,t heinitialcracksizedueto manufacturingorpreviousmaintenance,thepressurediffe rentialbetweenthecabinand atmosphere,andthethicknessofthefuselagepanel.Ifleft unattended,thecracksmay growtocausefatiguefailureofthepanel.Indamagetoleran cedesign,thelessfrequent themaintenance,thelowerthedamagesizethresholdforrep airing/replacingpanels,in ordertomaintainadesiredlevelofreliability.Theaction ofrepairing/replacingpanels tomaintainadesiredlevelofsafetyuntilthenextschedule dmaintenanceistermed correctivemaintenance.Thissectionexplainscorrective maintenanceprocedures undertakentopreventfatiguefailureduetoexcessivedama gegrowth. Thesizeofcracksinfuselagepanelsinaeetofairplanesis modeledasarandom variablecharacterizedbyaprobabilitydistributionthat dependsonmanufacturingand theloadinghistoryoftheairplane.Thecorrectivemainten anceprocedurechanges thisdistributionbyrepairinglarge-sizedcracksasillus tratedinFigure 2-1 .Thesolid curverepresentsthedamagesizedistributionoftheairpla neenteringthemaintenance hangar.Themaintenanceprocessisdesignedtorepair/repl acepanelswithcracks largerthanathreshold,a rep.Sincedamagedetectionisnotperfect,maintenance onlypartiallytruncatestheuppertailofthedistribution ,asrepresentedbythedashed curveinFigure 2-1 .Itisnotedthatwhilethereisuncertaintyindamagedetect ion,it isassumedinthisdissertationthatthesizeofthedetected damageisknown,without anyerror/noise.Theareaunderthedashedcurve(grey)repr esentsthefractionof panelsmissedduringmaintenance.Thedamagethatismissed duringmaintenance andhappenstogrowbeyondthefailuredamagesizea failbeforethenextmaintenance affectsthereliabilityoftheairplane.Fasterthecrackgr owthrate,smallerwillbethea repchosen,tomaintainadesiredlevelofreliability.However ,thesmalla repwillincrease costasitrequiresmorereplacementofpanels.Inthiswork, thethreshold,a rep,issetto maintainaspeciclevelofreliabilityandtoreducethelif ecyclecostofanairplane.The 27

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Figure2-1.Theeffectofinspectionandreplacementproces soncracklength distributions numberofmaintenancetripsandthenumberofpanelsrepaire d/replacedinanairplane directlyaffectsitsinspectionandmaintenancecost,andt hus,itslifecyclecost. Inthiswork,twotypesofmaintenanceprocedurearediscuss ed:scheduled maintenanceandcondition-basedmaintenance.Inschedule dmaintenance,as namesuggests,maintenanceisscheduledatspecicinterva ls.Incondition-based maintenance,damageiscontinuouslytrackedandmaintenan ceisrequestedwhenthe damagesizecrossesaparticularthreshold.2.2.1ScheduledMaintenance TheowchartinFigure 2-2 depictsanexampleofscheduledmaintenanceprocess, inwhichmaintenanceisscheduledatspecicpre-determine dintervals(say,everyN pvtightcycles)andcorrectiveactionistakentoensurethesa fetyoftheairplaneuntil thenextscheduledmaintenance.Thedesiredlevelofreliab ilitycanbeachievedby settingathresholdvalue,a rep,forreplacing/repairingpanels.Threeparametersaffect thelifecyclecostofanairplaneundergoingscheduledmain tenance.Thefrequency ofscheduledmaintenancedeterminesthenumberofmaintena ncetripsanairplane undergoesduringitslifetime.Thethicknessofthefuselag epanelisassumedtocontrol 28

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Figure2-2.Exampleofthescheduledmaintenanceprocess thedamagegrowthrate,andthatalongwiththethresholdfor replacement,affectthe numberofpanelsreplaced/repairedinthemaintenancehang artoensuresafetyuntil nextscheduledmaintenance.Maintenancecost,andhence,t helifecyclecostofan airplane,dependsonnumberofmaintenancetripsanairplan eundergoes,andthe numberofpanelsreplacedorrepairedduringthemaintenanc etrips. Sincetheinspectioncostduringscheduledmaintenanceish igh(intheorderof millionsofdollarsperairplane),themaintenanceinterva lN pvtishigh(intheorder of4,000ightcycles).Inordertomaintainahighlevelofre liability,thereplacement threshold,a rep,ischosensuchthattheprobabilityofacrackinthesizeofa repfailing beforenextmaintenancecycleislessthanoneoutoftenmill ions. 2.2.2Condition-basedMaintenanceProcedure Condition-basedmaintenance(CBM)processtracksdamagec ontinuously(or, morepractically,every100ightcycles)andrequestsmain tenancewhenthedamage becomesthreateningtosafety.Inthiswork,condition-bas edmaintenanceisassumed heretobeperformedusingastructuralhealthmonitoring(S HM)technique.SHM useson-boardsensorsandactuatorstoanalyzethepresentd amageconditionof theairplane.Thisprocessiscalledheremaintenanceasses sment.SHM-based maintenanceassessmentcanbeperformedasfrequentlyasev eryight;however, 29

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inthiswork,theassessmentisassumedtobeperformedateve ryN shm(e.g.,100) ightsduetocomputationalconstraintsandslowlygrowing damage.Thisintervalisalso typicaloftheA-checksoftheairplane,i.e.smallmaintena ncetaskcarriedoutovernight attheairlinershubhangars.Itwouldmakesensetocarryout theSHMinspectionatthe A-checkssinceonlythesensorsthemselveswouldhavetobee mbeddedintheairplane butthemonitoringsystemcouldbegroundbased,thusreduci ngyingweight. Figure 2-3 delineatesthecondition-basedmaintenanceprocess.Afte rdamage assessmentviatheon-boardSHMsensors,maintenanceisreq uestedifthemaximum damagesizeinanairplaneexceedsaparticularthreshold(a maint).Thethresholdfor requestingmaintenance(damagesize,a maint)ischosentomaintainadesiredlevel ofreliabilityuntilthenextscheduleddamageassessment( i.e.forthenextN shm=100 cycles).Oncemaintenanceisrequested,allpanelsonthefu selageareinspectedfor damageinthehangarusingtheon-boardSHMequipment,andpa nelswiththreatening damagearerepairedorreplaced.Thethresholdforthreaten ingdamagesizea rep(much lowerthanthresholdforrequestingmaintenance,a maint)issettopreventfrequent maintenanceforthatairplane.Condition-basedmaintenan cebySHMiscontrolled byfourparameters,inthiswork.Thethicknessofthefusela gepanel(t)affectsthe crackgrowthrate.Thepanelthickness(t),alongwiththefr equencyofmaintenance assessment(N shm)andthethresholdforrequestingmaintenance(a maint)affectthe safetyoftheairplane.Thesethreeparametersalsocontrol thenumberofmaintenance tripsandnumberofpanelsrepaired/replacedinanairplane andhence,affectits lifecyclecost.Lowerthethresholdforreplacement/repai r(a rep),lowerthesizeofcracks thatremainsontheairplaneafteramaintenance,andlonger ittakesforthecrack remainingontheairplanetogrowtosizeofa maint,andhence,longerthetimebetween subsequentmaintenance.Hence,thethresholdforreplacem ent/repair(a rep)isset onlytopreventfrequentmaintenanceandhence,affectsonl ythelifecyclecostofthe airplane. 30

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Figure2-3.Flowchartofmaintenanceschedulingandassess mentprocedureforSHM basedinspection Themainadvantageofcondition-basedmaintenanceisthato nlythosepanels thatactuallythreatensafetyarerepaired/replaced.Ther efore,thenumberofpanels repaired/replacedwillbemuchlowerthanthatofscheduled maintenance.Ontheother hand,condition-basedmaintenancehasdisadvantageinsch edulingmaintenanceand eetmanagementbecauseitisdifculttopredictwhenmaint enancewillbeperformed. 2.3ModelingDamageGrowthandInspectionProcess Thefatiguelifecycleoffuselagepanelsisviewedasblocks ofdamagegrowth interspersedwithmaintenance.Themodelthedamagepropag ationandinspectionfor scheduledmaintenanceandconditionbasedmaintenanceise laboratedinthissection. 31

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2.3.1FatigueDamageGrowthduetoFuselagePressurization Cracksordamagerefertoexistingawsonthefuselageofana irplane.Damage causesdifferenttypesoffatiguefailure,dependingonits locationonthefuselage. Cracksemanatingfromboltholesinthefuselagemightinter actwithothercracksinthe areatocausefatiguefailureduetowidespreaddamage(WFD) ormulti-sitedamage (MSD).Crackscanalsoforminthemainportionofthefuselag eandtheygrowlong beforetheycausefatiguefailure(two-baycriterion). Thecrackgrowthcanbemodeledinmyriadwaysdependingonwh etherthecritical siteissubjecttoMSD/WFD,two-baycrackorothertypeoffat iguedamage.Romlayet al.[ 90 ]usedDualBoundaryElementMethodtomodelfatiguecrackgr owthofmultiple cracksites,whileHarrisetal.[ 91 ]usedanalyticalmethodologytopredicttheonsetof WFDinthefuselagestructure.Nilsson[ 92 ]usesDugdalemodelandelasticplastic crackinteractiontomodelcrackgrowthinteractionsbetwe enamajorcrackandmultiple smallcracksinafuselage.Basedonairframefatiguetestso nvariousmilitaryaircraft, Molentetal.[ 93 ]concludedthatasimplecrackgrowthmodeladequatelyrepr esents well,atypicalcrackgrowth.Inthissection,thecrack/dam agerefertoanycrackinthe fuselageandthecrackcanfailduetoanyofaforementionedc riterialikeWSD/MSD, twobaycrack. Inthissection,afuselageismodeledasahollowuniformcyl inder.Damageinthe fuselagepanelofanairplaneismodeledasathrough-the-th icknesscenterstraight crackinaninniteplateintension.Thelifeofanairplanec anbeviewedasconsisting ofdamagepropagationcycles,interspersedwithinspectio nandrepair.Thedamage /crackpropagationcouldbemodeledinmyriadways.Bedenet al.[ 94 ]providedan extensivereviewofcrackgrowthmodels.Mohantyetal.[ 95 ]usedanexponentialmodel tomodelfatiguecrackgrowth.Scarf[ 96 ]advocatedtheuseofsimplemodels,whenthe objectivewassimplytodemonstratemethodology.Inthiswo rk,asimpleParismodelis 32

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consideredtodescribethecrackgrowthbehavior.However, otheradvancedmodelscan alsobeused. Thedamagepropagation,inthissection,ismodeledusingth eParismodel[ 97 ], whichgivestherateofdamagesizegrowthwithnumberofigh tcycles(N)asafunction ofdamagehalfsize(a),pressuredifferential(p),thickne ssofcylindricalfuselage representation(t),fuselageradius(r)andtheParisparam eters,CandminEq. 2–1 as.da dN = C ( K ) m(2–1) wheretherangeofstressintensityfactorisapproximatedi nEq. 2–2 as K = A pr tp a(2–2) Thecoefcient,Ainthestressintensityfactor(SIF)isaco rrectionfactorintendedto compensateformodelingthefuselageasahollowcylinder,l ackofstiffenersinthe modelandforbulgingeffects. ThehalfcracksizeafterNightcyclesofpropagation,a Nisobtainedbysolvingthe differentialequationinEq. 2–1 andgivenbyEq. 2–3 a N = ( a 0 1m=2 + (1m=2)NC( pr tp ) m ) 1 1m=2(2–3) Thecriticalhalfcracksizethatcancausefailureofthepan elisdenedinEq. 2–4 asa cr =K IC pr tp (2–4) whereK ICisthefracturetoughnessinModeI. Itisassumedthatallpanelsarecomposedofaluminumalloy7 075-T651with dimensionsof609.6mm(2') 609.6mm(2') 2.48mm(0.1”).Newmannetal.(Pg113, Fig.3)[ 98 ]showedtheexperimentaldataplotbetweenthedamagegrowt hrateand thestressintensityfactorunderModeIloading.TheParism odelparameters,Candm, areestimatedfromtheinterceptandslope,respectively,o ftheregioncorresponding 33

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tostabledamagegrowth.Astheregionofthestabledamagegr owthcanbebounded byaparallelogram,theestimatesoftheboundsoftheparame ters,Candm,are obtainedfromthegure(Fig.3,Newmannetal.[ 98 ]).However,duetovariabilityin testspecimenandmeasurementenvironment,themeasuredpa rameters,Candm, alsoshowuncertainty.Therefore,theuncertaintyinmodel parametersneedstobe consideredinmodelingdamagegrowth. ForagivenvalueofinterceptC,thereisonlyarangeofslope (m)permissiblein theestimatedparallelogram.Toparameterizethebounds,t heleftandrightedgesof theparallelogramwerediscretizedbyuniformlydistribut edpoints.Eachpointontheleft edgecorrespondstoavalueofC.ForagivenvalueofC,therea reonlycertainpossible valuesoftheslope,m.Figure 2-4 plotsthosepermissiblerangesofslope(m),fora givenvalueofintercept(C).Incalculatingdamagegrowth, therandomcombinationof CandmispopulatedfromtheparallelograminFigure 2-4 .Itcanbeclearlyseenfrom Fig. 2-4 thattheslopeandlog(C)arenegativelycorrelated;thecor relationcoefcientis foundtobeabout-0.8. Figure2-4.PossibleregionofParismodelparameters 34

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2.3.2InspectionModel Kimetal.[ 99 ],Packmanetal.[ 100 ],BerensandHovey[ 101 ],Madsenetal.[ 102 ], MoriandEllingwood[ 103 ],andChungetal.[ 104 ]havemodeledthecrackdetection probabilityasafunctionofcracksize.Coppeetal.[ 105 ]modeledthecrackdetection probabilityasafunctionofcracksizeanditslocationonaf uselagepanel.Inthiswork, theinspectionofpanelsforcrackismodeledusingthePalmb ergequation[ 106 ]given by,P d ( a ) = (2 a=a h ) 1 + (2 a=a h ) (2–5) Theexpressiongivestheprobabilityofdetectingcrackwit hsize2a.InEq. 2–5 ,a his thecracksizecorrespondingto50%probabilityofdetectio n,and istherandomness parameter.Theparametera hrepresentsaveragecapabilityoftheinspectionmethod, while representsthevariabilityintheprocess.Differentvalue softheparameters,a hand ,areconsideredtomodeltheinspectionforscheduledmaint enance,and alsoforSHM-basedmaintenanceassessment.Generally,the inspectiontechniquefor scheduledmaintenanceisverythoroughandwouldeasilydet ectlargecracks.Hence, atruncatedinspectionmodelwithtruncationatcracksize, tentimesa hisconsideredfor scheduledmaintenance.Anycrackpresent,withcracksizeg reaterthanthetruncation limit,willalwaysbedetected,forscheduledmaintenance. Inthisdissertation,probabilityofdetectingacrackisas sociatedwithitslocationon thepanel.Thelocationprobabilityofacrackisproportion altotheeaseofitsdetection. Cracksinthecenterofthepanelareeasiertodetectadhence havealowerlocation probability.Thelocationprobabilityissettobeuniforml ydistributedbetween[0,1] tosimulaterandomnessinlocationofthecrack.Acrackwill bedetectedonlyifits probabilityofdetectionexceedsthelocationprobability 2.4MonteCarloSimulation Thelifecycleoftheairplane(incl.damagegrowthandinspe ction)issimulated usingmontecarlosimulations(MCS).Aeetisassumedtohav e2000airplanes.Each 35

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airplaneisassumedtohave500panels.Eachpanelisassumed tohaveonecrack. Uncertainparametersofthedamagegrowthmodel,initialda magesize,ParisLaw parametersaresampledfromtheirrespectivedistribution sandassignedtoeachpanel. Thedamagesizeoneachpanelaftercertainknowncyclesofpr opagationisobtained fromtheclosedformsolutionofParisLaw(seeEq. 2–3 .Inspectionisperformedat pre-determinedintervals.Inscheduledmaintenance,insp ectionisperformedonall airplanesatthepre-determinedscheduledtimes.Forcondi tion-basedmaintenance,the inspectionissimulatedatthetimeofeverymaintenanceass essmenttodecidewhich airplanesrequiremaintenancepresently.Theinspectionp rocessissimulatedaccording toPalmbergexpression.Detectionofdamageisgovernedbyi tsdetectionprobability. Maintenanceisperformedontheairplanewheneverdeemedne cessary(for CBM),toreplace/repairdamagecriticaltotheairplane'ss afety.Detecteddamageis identiedtobecriticaltothesafetyoftheairplaneifitss izeexceedsthereplacement thresholdatthetimeofmaintenance.Replacementofsuchda mageissimulatedby samplingdamagefromtheinitialcracksizedistributionan dassigningtothepanelin whichadamagewasidentiedtobecriticaltothesafetyofth eairplane.Thedamage sizesonthepanelofeachairplaneisupdatedaftereverymai ntenance.Thedamage propagationandinspectionprocesscontinuesinaloopunti ltheendoflifeofthe airplane. 36

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CHAPTER3 COMPARINGSCHEDULEDMAINTENANCEAND CONDITIONBASEDMAINTENANCE 3.1DamageGrowthParameters Thefatiguelifecycleofashortrangeairplane(like,A320) ismodeledinthis section.Thevaluesoftheparametersfortheshortrangeair planearesettosatisfy certainconstraints(torepresentreality).Theconstrain tsandtheproceduretosetthe parametersaredescribedinAppendix A Theinspectionprocessforscheduledmaintenanceandcondi tionbasedmaintenance ismodeledusingPalmbergexpression,giveninSection 2.3 .Thevaluesofuncertainties andparametersofdamagegrowthmodelandinspectionmodel, fortheshortrange aircraft,A320,aretabulatedinTable 3-1 .Uncertaintyisconsideredintheloading Table3-1.Parametersofdamagegrowthmodelandinspection modelandtheirvalues ParameterTypeValue Initialhalfcracksize(a 0)RandomLN(0.2,35%COV)mm Pressure(p)RandomLN(0.06,0.003)MPaRadiusoffuselage(r)Deterministic1.95mThicknessoffuselagepanel(t)Deterministic2mmParisLawconstant(C)RandomU[log 10(5E-11),log 10(5E-10)] ParisLawexponent(m)RandomU[3,4.3]CorrectionfactorforSIF(A)Deterministic1.255Palmbergparameterforscheduledmaintenance(a hsch) Deterministic0.63mm Palmbergparameterforscheduledmaintenance( sch) Deterministic2.0 PalmbergparameterforSHMbasedinspection(a hshm) Deterministic5mm PalmbergparameterforSHMbasedinspection( shm) Deterministic5.0 conditionandtheParismodelparameters. Sincemodelingofthestructuraldetailsofthefuselageiso utsidethescopeofthis workweuseagenericmodelforthefuselagepanelsandthecor respondingdamage growth.Theparametersofthisgenericmodelaresetsuchast oberepresentative 37

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offuselagefatiguedamageonrealshortrangeaircraft.The panelthickness,initial damagesize,correctionfactorforthestressintensityfac tor,andthedamagereplacement thresholdaretheparametersofourmodelweneedtoset.Thes earedeterminedsuch thatourmodelsatisescertainconstraints(suchasprobab ilitiesoffailureuntilendof lifeandbetweenmaintenancestops)Moredetaileddescript ionoftheconstraintsand theoptimizationprocessestodeterminetheparametersare giveninAppendix A Table 3-2 tabulatescracksizethresholdsfoundtoberepresentative ofrealityin theaforementionedsense.Thesethresholdswerecalculate dusingdirectintegration procedure(seeAppendix C ).Thereare10scheduledmaintenancetripsforan Table3-2.ParametersofCBMprocessesandtheconstraintss ettodeterminethem ParameterTypeConstraint ThresholdforrequestingmaintenanceforCBM(2a maint) 79mmTomaintainPf 108, betweenmaintenanceassessments Replacementthresholdforscheduledmaintenance(2a rep) 12mmTomaintainaPf 108untilnextscheduledmaintenance airplane,andthereplacementthreshold,a repwillensurea107probabilityoffailureuntil endoflifeofanairplane.ForCBM,thethresholdforrequest ingmaintenance,a maintwouldbeensuresafetyuntilthenextmaintenancewhenacrac ksizeequaltoa maintis presentontheairplane.Ifthenumberoftimes,anairplanee ncountersacrackofsizea maintonitislessthan10times,theprobabilityoffailureofapan eluntilendoflifeof airplanewouldbe <107. 3.2ComparisonBetweenMaintenanceProcesses Atypicallifecycleofshortrangeaircraft sfuselage(e.g.fuselageofanA320)is modeledinthissection,withfocusonthefatiguelifeofthe airplaneduetoexcessive crackpropagation.Typicallyforthistypeofairplanes,th erstmaintenanceisafter 20,000ightsandthesubsequentmaintenanceisevery4,000 ightsuntilitsendof lifecycle,whichis60,000ights. 38

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Inthissection,ascheduledmaintenanceprocessofA320air planeiscompared withacondition-basedmaintenanceprocessforthesameair plane.Themaintenance processesarecomparedonthebasisofaveragenumberofmain tenancetripsan airplaneundergoes,theaveragepercentageofpanelsrepla cedperairplane,and theprobabilityoffailureofapanel,untiltheendoflifeof anairplane.Inscheduled maintenance,thenumberofmaintenancetripsdependsonthe pre-determined frequencyofmaintenance(seeFigure 2-2 ,whereasincondition-basedmaintenance, itdependsonthedamagesizeanddamagegrowthparameters.T hereplacement thresholdateachmaintenanceissetat12mm(seeAppendix A )forboththemaintenance processes. ThelifecycleoftheairplaneissimulatedusingMonteCarlo simulations(MCS). Aeetof2,000airplaneswith500panelsperairplaneiscons idered.Eachpanelis assumedtocontainasinglecrack.Theequivalentinitiala wsize(EIFS)anddamage growthparameters(C,m)aresampledfromtheirrespectived istributionsandassigned toeachpanel.Maintenanceprocessesaresimulatedaccordi ngtoPalmbergexpression (Section 2.3.2 ),whichprovidestheprobabilityofdetectingacrackasafu nctionof cracklength.MCSyieldsthenumberofmaintenancetripsand percentageofpanels replacedineachairplane,untilitsendoflife,foraeetof 2000airplanes.Table 3-3 comparesthedifferentmaintenanceprocessesontheaverag enumberofmaintenance tripsandpercentageofpanelsreplacedperairplane.Thenu mberintheparenthesisis thestandarddeviationduetothelimitednumberofMCSsampl esforairplanes. Table3-3.Comparingscheduledandcondition-basedmainte nanceonreliabilityand criteriacontributingtolifecyclecostwithsamereplacem entthreshold(= 12mm)forbothmaintenancestrategies TypeofmaintenanceProbabilityof failureofapaneluntilendoflife Avgno.ofmaintenancetrips/airplane Avg.percentageofpanelsreplaced/airplane Scheduled1E-7106.6(2.5)Condition-based < 1E-72.3(0.7)6.6(2.5) 39

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Itisnotedthatforabetterlevelofreliability,condition -basedmaintenanceleadsto fewernumberofmaintenancetrips.Thisisbecause,CBMtole ratesalargerdamage sizethanscheduledmaintenance(seeTable 3-2 ).Thescheduledmaintenancehas axedscheduledformaintenanceitreplacespanelswithcra cksizeexceedingthe replacementthreshold(=12mm).Condition-basedmaintena ncerequestmaintenance onlywhenthedamageexceedsthethresholdforrequestingma intenance(=79mm). Thepercentageofreplacedpanelsremainsequalbecauseofs amereplacement thresholdsetforbothprocessesHence,CBMcauseslessfreq uentmaintenancetripsas comparedtoscheduledmaintenance,andbyextension,savin gsinmaintenancecost. AcostmodelbasedonliteratureanddetailedinAppendix B isusedinthepresent sectiontofacilitatecomparisonsbetweenthedifferentma intenanceprocesses,onthe basisoftheirmaintenancecost(inclusiveofmaterialandl aborcost).Themaintenance costisanalgebraicsumofairframemaintenanceandenginem aintenancecost.The enginemaintenanceandnon-structuralairframemaintenan ceisalwaysscheduledat thetimeofscheduledmaintenance.Onlystructuralmainten anceisrequestedbyCBM basedonthecurrentdamagestatusoftheairplane. Basedontheempiricalexpressionsandairplaneparameters (Table B-1 ),the airframemaintenancecostis$1,139/ightandtheenginema intenancecostis $258/ights.Theaircraftmakes60,000ightsduringitsli fetime,andundergoes tenscheduledmaintenance.Hence,thecostofonescheduled airframemaintenance (S)is$6.84millionandthecostofonescheduledenginemain tenance(E)is$1.55 million.Scheduledairframemaintenanceisfurtherclassi edintostructuralairframe maintenanceandnon-structuralairframemaintenance.Str ucturalairframemaintenance concernswithpreventingfailureonairframestructures(l ike,fuselage)duetoexcessive crackpropagation.Acostof$1.84millionisassumedforsch eduledstructuralairframe maintenance. 40

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Duringscheduledstructuralairframemaintenance,alotof timeisspentofdetecting cracksontheairplane,andidentifyingthepanelstoberepa ired/replaced.When maintenanceisrequestedbyCBM,theon-boardSHMequipment assessesthecurrent damagestatusoftheairplane,andidentiesthepanelstobe repaired/replaced. Hence,structuralairframemaintenancerequestedbyCBMat thetimeofscheduled maintenancewillcostonlyafractionascomparedtoschedul edmaintenance.The fractionisdenotedask SHM,andarangeof[0.3,0.7]isassumedfork SHM. Anunscheduledmaintenancetrip,requestedbyCBM,ismoree xpensivethan maintenancerequestedbyCBMatthetimeofscheduledmainte nanceduetotwo reasons.Ashorteradvancenoticetheairlinerhasforaccom modatingtheunscheduled maintenanceaswellasduetothefactthatthestructuralair framemaintenanceand theothermaintenance(engine,non-structural)arenotdon eatthesametime.A factor,k unsch( 1)issettodenotethehighercostincurredandarangeof[1.2 ,2]is chosenfork unsch.Factorsk unschandk SHMareindependentofeachotherandthecostof unscheduledairframemaintenance,requestedduetoSHMist heproductofk unsch,k SHMandthecostofonescheduledairframemaintenance(S). Sincebothk unschandk SHMareindependentofeachother,thebestandworstcase costsforeachCBMprocesswouldwhenparametersk unschandk SHMarebothattheir lowerandupperlimitsrespectively.Table 3-4 comparesthebestandworstcasecosts ofdifferentCBMprocesseswiththecostforscheduledmaint enance.Itisnotedthat Table3-4.ComparingthebestandworstcasecostsofCBMwith thecostofscheduled maintenance Maintenancecost(M$) Typek unsch=1.2,k SHM=0.3k unsch=2,k SHM=0.7 Scheduled83.983.9 CBM67(0.4)71.7(0.5) theperformingcondition-basedmaintenanceischeapertha nscheduledmaintenanceto 41

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preventfatiguefailureinfuselagepanelsofairplanes.Th esavingscomefromthefewer maintenancetripscausedduetohigherdamagetolerancebyC BM. CBMsavesin7.7structuralairframemaintenancetripspera irplaneonaverage,per airplanethroughthelifecycleoftheairplane.Basedonthe costmodel,eachstructural airframemaintenancecosts$1.85milliondollarsnettinga totalsavingsof$14.2million dollars.Theeffectofcombinationoffactorsk SHMandk unschonthesavingsisobservedin Table 3-4 3.3WeightSavings Theprevioussectionconcludedthatcondition-basedmaint enanceleadstosavings incostoverscheduledmaintenancewhilemaintainingthesa melevelofsafety.This sectionfocusesontranslatingsomeofthecostsavingsinto weightsavingsofthe airplane. Thefuselageofanairplanehasbeenmodeledasanuniformhol lowcylinder. Theradiusandthelengthofthefuselagesectionisobtained fromSimCAD[ 107 ].The thicknessofthefuselagesectionissetbasedoncertaincon straints(seeAppendix A ). Inthissection,theweightofthefuselageiscontrolledbyc hangingthethicknessof thefuselage.Itisnotedthatitistherepresentativethick nessoftheuniformcylinder fuselagemodelthatischangedtoaccountforchangeinweigh t. 3.3.1MinimumThickness Weightoftheairplaneiscontrolledbyvaryingthethicknes softhefuselage.For thesamepressuredifferentialload,thinnercylinderacce leratesthecrackgrowth. Tomaintainthesamelevelofreliability,extramaintenanc eneedstobescheduled topreventfatiguefailureduetoexcessivecrackgrowth.In addition,thepressure differentialbetweenthecabinandatmospherealsocausesh oopstressonthefuselage cylinder.Thehoopstresscouldcauseyieldingofthefusela gecylinderifthethickness isreducedtoolow.Theminimumoperablethicknessiscomput edusingyielding constraints.Thefuselagecylinderwillfailbyyieldingif thehoopstressexceedsthe 42

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yieldstressofthematerial.Theminimumthicknessrequire dtopreventyieldingisset accordingtoEquation 3–1 .p r t Y)tp r Y(3–1) where,pisthepressuredifferentialbetweenthecabinanda tmosphere,ristheradiusof thefuselagecylinder,tisthethicknessofthefuselagecyl inder, Yistheyieldstressof thefuselagematerial(Al7075-T651) Thedimensionsandmaterialpropertiesoffuselagecylinde r(Al7075-T651)are tabulateinTable 3-5 .Asafetyfactorof1.5isconsideredontheyieldstress,and a Table3-5.Dimensionsandmaterialpropertiesoffuselagec ylinder ParameterValue Radiusoffuselage,r(m)1.95Pressuredifferential,p(MPa)0.08Yieldstress, Y(MPa)503 factorof3isconsideredonthepressureloadtoaccountfors tressconcentrationeffects. Basedontheproperties,stressconstraintsandsafetyfact ors,theminimumthicknessto preventyieldingis1.39mm.Itisnotedthattherealairfram eiscomposedofstiffeners, frames,andvaryingthicknessattheintersectionofwings, tail.Thisminimumthickness of1.39mmisanrepresentativeofequivalentminimumthickn essforauniformhollow cylinderfuselagemodel.3.3.2EffectofVaryingThickness Reducingthefuselagepanelthicknesswillreducetheweigh toftheairplane,and willreducethefuelcosttoytheairplane.But,reducingth efuselagepanelthickness acceleratesthecrackgrowthforthesameloadingcondition .Fastercrackgrowthwill requiremorestructuralairframemaintenancetripsforCBM strategy,tomaintainthe samelevelofreliability,increasingthemaintenancecost 43

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Figure 3-1 plotsthechangeincost(inM$)fromthatofcostatthickness =2mm,for thevariouscontributorsoflifecyclecostasafunctionofc hangeinfuselagethickness, whilemaintainingthesameprobabilityoffailure.Fuelcos tisbasedon$126.1/barrel [ 1 ].AsnotedinFigure 3-1 ,thecostincreaseinmaintenancecostismuchgreater thatthecostsavingsforfuel,forthesamechangeinfuselag ethickness.Decreasing 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 -4 -2 0 2 4 6 8 10 12 14 Thickness (mm)Change in cost until end of life (M$) Manufacturing cost for CBM Fuel cost for CBM Maintenance cost for CBM Figure3-1.Changeincostfromthatofcostatthickness=2mm ,forvariouscontributors forlifecyclecost,forchangeinfuselagethicknesstomain tainsamelevelof probabilityoffailure thefuselagethicknessfrom2mmto1.65mm,decreasesthefue lcostby3M$while maintainingthesameprobabilityoffailureofapaneluntil endoflife.Butthesame thicknessdecreasealsoamountstoa14M$increaseinthemai ntenancecostof theairplane,causinganincreaseinfuel+maintenancecost untiltheendoflifeofan airplane.Figure 3-2 plotsthevariationoffuel+maintenancecostasafunctiono fthe 44

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fuselagepanelthicknessforCBM.InFig 3-2 ,Thesolidhorizontallineonthetop Figure3-2.Comparingvariationoffuel+maintenancecostf orCBMwithfuselage thickness,withfuel+maintenancecostforscheduledmaint enanceat fuselagethickness=2mm,fordifferentcasesofweightincr easedueto onboardSHMequipment representsthefuel+maintenancecostforscheduledmainte nanceatpanelthickness =2mm,untilendoflifeofairplane.Atfuselagepanelthickn essof2mm,thesavings infuel+maintenancecostforCBMoverscheduledmaintenanc eissubstantial.Asthe fuselagepaneldecreases,theweightoftheairplanedecrea ses,butcauseanincrease infuel+maintenancecost.Hence,decreaseinpanelthickne sscauseadecreasein savingsinfuel+maintenanceofCBMoverscheduledmaintena nce. AsnotedinFigure 3-2 ,iftheon-boardSHMequipmentcausesanhigherincrease inweightofthefuselagepanel,lowerthesavingsoffuel+ma intenancecostofCBM overthatofscheduledmaintenance. Theimportantideaofthissectionistotranslatethecostsa vingsofCBMintoweight savingsofthefuselage.BasedonFigure 3-2 ,forthecaseofCBMwith10%weight increase,fuel+maintenancecostequalsthatofscheduledm aintenanceatfuselage panelthicknessof1.68mm.Inotherwords,thecostsavingsa tfuselagepanelthickness 45

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Table3-6.Costandweightsavingsfromtheoriginalfuselag edesign,tothefuel+ maintenancecostofscheduledmaintenance TypeofmaintenanceCostsavingsat fuselagepanelthickness=2mm(M$) Weightsavingstomaintainsamefuel+maintenancecostasscheduledmaintenance(%) Scheduled––CBMwith5%weightincreaseduetoonboardSHMequipment 4.215 CBMwith10%weightincreaseduetoonboardSHMequipment 2.87 of2mmcouldbetranslatedtoweightsavingsof16%tomaintai nthesamecostas scheduledmaintenance. Evenifweassumethatittakes6M$toinstallSHMsystemonthe airplane,the CBMsavesabout2.8M$consideringthe10%fuselagemassincr easeduetothe onboardSHMequipment.Thesavingsinfuel+maintenancecos tcouldbetranslated intopotentialweightsavingsof7%asnotedinTable 3-6 .IftheSHMsystemissetto increasetheairplaneweightby5%,theCBMwouldleadto15%w eightsavingsfrom theoriginalweightoftheairplane,forthesamefuel+maint enancecostasscheduled maintenance. 3.4Summary Condition-basedmaintenancestrategyuseson-boardstruc turalhealthmonitoring (SHM)systemtotrackdamage,andhence,hasatolerancetola rgercracksizethan scheduledmaintenance.Tolerancetolargercracksizecaus esfewermaintenancefor thecommercialairplane,andthereby,savingsinmaintenan cecost,whilemaintaining thesamelevelofreliability.Thepresenceofon-boardSHMs ystemwillincreasethe weightoftheairplane,therebycausinganincreaseinthefu elcostoftheairplane. Condition-basedmaintenanceisfoundtoleadtosavingsint hefuel+maintenancecost 46

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oftheairplaneoverscheduledmaintenance.Thesavingsinf uel+maintenancecostof condition-basedmaintenanceoverscheduledmaintenancei stranslatedtosavingsin weight,whilemaintainingthesamelevelofreliability. 47

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CHAPTER4 SKIPPINGUNWANTEDPREVENTIVEMAINTENANCEUSINGCBM 4.1Introduction Inpractice,condition-basedmaintenancewithSHMhasbeen implementedin militaryandspaceapplications(Gogginetal.[ 108 ]),butisyettobeimplementedin commercialairplanes.FarrarandWorden[ 109 ]andGogginetal.[ 108 ]summarizedthe challengesforSHMsystemstobeincorporatedoncommercial airplanes.Ikegami[ 110 ] observedthecomplexityofusingSHMsystemsoncommerciala irplanes,butpredicts technologytoovercomesuchdifcultyinthenearfuture. Itbecomesquiteevidentthatcondition-basedmaintenance needstoworkin tandemwithscheduledmaintenance,beforeitisacceptedas astand-alonesystem. Fitzwateretal.[ 111 ]combinedSHMwithtraditionalscheduledmaintenanceto minimizelifecyclecostofF-15ghterframestation626bul khead.Inthissection, thecondition-basedmaintenanceisusedtocomplementsche duledmaintenance andenabletoskipmaintenancewhendeemednecessary.Thefu ndamentalidea isthattherewillbemanycasesinwhichnodamageisdetected duringscheduled maintenance.IftheSHMsystemisused,suchunnecessarymai ntenancecanbe skipped. Atthetimeofscheduledmaintenance,theairplaneistakent oahangarand undergoesaseriesofmaintenanceactivities,includingth eairframeandengine maintenance.Structuralairframemaintenanceisasubseto fscheduledmaintenance, andfocusesondetectingandreplacingcracksthatwouldoth erwisethreatenthe safetyoftheairplane.Sincethemaintenancescheduleforc ommercialairplanesis designedforalowprobabilityoffailure(107),thereisapossibilityofnocriticalcracks detectedonanairplaneduringascheduledmaintenance,ear lierinthelifeofthe airplane.But,intrusiveinspectionofallpanelsintheair planeneedtobeperformed,by 48

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non-destructiveinspection(NDI)anddetailedvisualinsp ection(DVI),todeterminethe presence/absenceofcriticalcracks,thatotherwisecause fatiguefailure. Inthischapter,on-boardSHMsystemdeterminesthecurrent damagestatus oftheairplane,atthetimeofscheduledmaintenance.First ly,inspectionbySHM equipmentismuchcheaperoncetheSHMsystemisinplacethan existingtechniques likeNDIorDVI.Secondly,inspectionbySHMcoulddetectwhe nscheduledairframe structuralmaintenanceisunnecessaryduetodamagebeingi fanynon-critical,thus avoidingtime-consuminginspectionprocessesbasedonman ualNDIorDVI.This chapterfocusesonthesavingsinlifecyclecostduetoskipp ingthesemanualstructural inspectionsoftheairframe. 4.2MaintenanceStrategiestoSkipUnnecessaryStructural Airframe Maintenance Inthissection,twomaintenancestrategiestoskipunneces sarystructuralairframe maintenancearediscussed.ThestrategydiscussedinSecti on 4.2.1 ,Sched-SHMisa completelyhypotheticalprocedure.Itisneitherpractica lnoradvocated.Sched-SHM procedureisdiscussedtotheeffecthowinspectionusingSH Mcouldhelpskip unnecessarystructuralairframemaintenance.Ontheother hand,CBM-skipdiscussed inSection 4-2 ismuchmorepracticalinitsexecution,andalsofocusonski pping unnecessarystructuralairframemaintenance.4.2.1Sched-SHM Maintenancescheduleisdesignedsuchthatapanelhasalowp robabilityoffailure ( 107)untilitsendoflife.Thiscausesonlyafractionofairplan estoexperience structuralairframerepairatearlierscheduledmaintenan cetimes.But,inscheduled maintenance,intrusiveinspectionofpanelsneedtobeperf ormedtoascertainthe presence/absenceoflargecracksthataffectthesafetyoft heairplane.InSched-SHM, inspectionofpanelsfordamageisperformedbytheon-board SHMsystem.The 49

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on-boardSHMsystemcanhelpskipstructuralairframemaint enance,ifthereareno life-threateningcracksontheairplaneatthetimeofsched uledmaintenance. ThescheduleforSched-SHMmaintenanceisexactlysameasth atconsideredfor scheduledmaintenance(seeFigure 2-2 ).Theonlydifferenceisthattheinspectionof thefuselagepanelsiscarriedoutbytheon-boardSHMsystem ,beforetheairplane entersthemaintenancehangar.Figure 4-1 depictstheSched-SHMmaintenance process.Ifthemaximumcracksizedetectedintheairplanei slessthanthethreshold,a thskip,theSHMsystemrecommendsskippingthecurrentstructural airframemaintenance. Sincedamageassessmentbyon-boardSHMislessaccuratetha nNDItechniquesused forscheduledmaintenance,SHM-Schedwouldleadtolowerle velofreliabilitythan scheduledmaintenance. Figure4-1.FlowchartoftheSched-SHMmaintenanceprocess 50

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4.2.2ConditionbasedMaintenanceProcedure-skip(CBM-sk ip) UsingSHM,thedamagestatuscanbeevaluated,notjustatthe timeofscheduled maintenance,butasfrequentlyasneeded.Thefrequencyofd amagestatusevaluation (henceforthcalledmaintenanceassessment)isassumedher etocoincidewithA-checks oftheairplane(100ights);i.e.,asmallmaintenancetask carriedoutovernightatthe airliner'shubhangars.ItwouldmakesensetocarryouttheS HM-basedmaintenance assessmentattheA-checkssinceonlythesensorsthemselve swouldhavetobe embeddedintheairplanebutthemonitoringsystemcouldbeg roundbased,thus reducingyingweightandmonitoringsystemcosts. CBM-skiphassameobjectiveasSched-SHMintermsofskippin gunneeded structuralairframemaintenance.However,thefrequentmo nitoringofthedamage statuswouldensurethelevelofreliabilitysameasschedul edmaintenance.Ifacrack missedatthetimeofscheduledmaintenancegrowscriticali nbetweentwoconsecutive scheduledmaintenances,CBM-skiprecommendsstructurala irframemaintenanceto beperformedimmediately.Thiscallsforun-scheduledmain tenance,whichiscostlier. Thethresholdforrequestingunscheduledmaintenance(a maint),issettopreventa crackgrowbeyondcriticalsizebetweenconsecutivemainte nanceassessments. Figure 4-2 plotstheprocedureforCBM-skip.Thedamageassessmentisp erformedat scheduledmaintenancetime,aswellasevery100ights.CBM -skipiscontrolledby threeparameters.Thethresholdforrequestingunschedule dmaintenance(a maint)affects thesafetyoftheairplane.Thisparameter,alongwitha thskipanda rep,controlthenumber ofmaintenancetripsandnumberofpanelsrepaired/replace dinanairplaneandhence, affectitslifecyclecost. 4.3ComparisonBetweenDifferentMaintenanceProcesses Atypicallifecycleofshortrangeaircraft sfuselage(e.g.fuselageofanA320)is modeledinthissection,withfocusonthefatiguelifeofthe airplaneduetoexcessive crackpropagation.Typicallyforthistypeofairplanes,th erstmaintenanceisafter 51

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Figure4-2.Flowchartdepictingmaintenanceschedulingan dassessmentprocedurefor CBM-skip 20,000ightsandthesubsequentmaintenanceisevery4,000 ightsuntilitsendof lifecycle,whichis60,000ights. ThedamagegrowthismodeledbyasimpleParisLawmodel(Sect ion 2.3.1 ). ThevaluesoftheparametersaretabulatedinTable 3-1 .Uncertaintyisconsideredon theloadingconditionandthematerialpropertiesofthefus elagepanel.Someofthe parametersofthedamagegrowthmodelaresettosatisfycert ainconstraintsonthe reliabilityofapanelbetweenmaintenanceassessmentandu ntilendoflifeofairplane. Thedescriptionoftheconstraintsandtheoptimizationpro cessestoxtheparameters aregiveninAppendix A .Constraintsaretomaintainadesiredlevelofsafetyofthe fuselagepanelbetweensubsequentpreventivemaintenance andalsountiltheendof lifeoftheairplane.Thepanelthickness,initialdamagesi zeonthepanel,correction 52

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factorforthestressintensityfactorandthedamagereplac ementthresholdateach preventivemaintenancearetheparameterssettosatisfyth econstraints. Maintenanceassessmentforcondition-basedmaintenancei sperformedeveryN shm=100ights.ThethresholdforrequestingmaintenanceforC BMissetat79mm suchastomaintainaprobabilityoffailureof108betweenmaintenanceassessments (i.e.everyN shm=100cycles).ForCBM-skip,thethresholdforskippingasch eduled preventivemaintenance,a thskipissetat12mm.Thisthresholdissettomaintain aprobabilityoffailureof108untilthenextscheduledpreventivemaintenance.All thresholdsofdamagesize,settomaintainaspeciclevelof reliability,arecalculated usingadirectIntegrationprocedure(Appendix C ). ThelifecycleoftheairplaneissimulatedusingMonteCarlo simulations(MCS) detailedinSection 2.4 .Thedifferenttypesofmaintenancearecomparedonthe basisonthenumberofmaintenancetripsandpercentageofpa nelsreplaced.The replacementthresholdforallmaintenancestrategieshave thesamereplacement threshold(a rep)of12mm.Table 4-1 comparesthedifferentmaintenanceprocesses onthenumberofmaintenancetripsandpercentageofpanelsr eplacedperairplane. Thenumberintheparenthesisisthestandarddeviation.The variantsoftheCBM Table4-1.Comparisonofdifferentmaintenanceprocesseso nthenumberof maintenancetrips,percentageofpanelsreplacedperairpl ane,and probabilityoffatiguefailureofasinglepaneluntiltheen doflife TypeAvgno.of maintenancetrips/airplane Percentageofpanelsreplaced/airplane Avg.no.ofunscheduledmaintenancetrips/airplane Pfofsinglepaneluntilendoflife Scheduled106.6(2.5)–1E-7Sched-SHM3.3(1.0)6.6(2.5)–2.9E-6(2E-6)CBMskip3.3(1.0)6.6(2.5)0.02 < 1E-7 CBM2.3(0.7)6.6(2.5)2.3 < 1E-7 procedure,Sched-SHMandCBM-skip,skipsunwantedstructu ralairframemaintenance, andleadstolownumberofmaintenancetrips/airplane.Thep ercentageofpanels 53

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replacedisconstantforallcases,astheyallhavethesamer eplacementthreshold. Sched-SHMhasahigherprobabilityoffailurebecauseofonboardSHMmissinglarge cracks,criticaltothesafetyoftheairplane,atthetimeof scheduledmaintenance.Rest allmaintenancestrategiesaredesignedforaspecicproba bilityoffailure. Figure 4-3 plotsthefractionofairplanesinaeetthatundergostruct uralairframe maintenanceduringagivenscheduledmaintenance.Thefrac tionofairplanesrequiring structuralairframemaintenanceislowduringearlierlife cycleandincreaseswithlife. Sched-SHMhelpstoskipunneededstructuralairframemaint enance,andtheresultis reectedinTable 4-1 DuetothepoorerdetectioncapabilityofSHM,Sched-SHMcou ldmisscracks criticaltoairplane'ssafety,wheninvokedatthetimeofsc heduledmaintenance,causing ahigherprobabilityoffailurethandesired.However,freq uentdamageassessment inCBMandCBM-skiprecoversthesamelevelofprobabilityof failurewithscheduled maintenance.Inordertomaintain1E-7levelofprobability offailure,CBM-skipcallsfor about0.6%(0.02unscheduledmaintenancetripsoutof3.3ma intenancetrips)ofthe airplanestohaveanun-scheduledmaintenancetripperlife time.Ontheotherhand,all ofthestructuralairframemaintenancerequestedbyCBMare un-scheduled,butitdoes leadtofewerstructuralairframemaintenancetripsperair plane,whilemaintainingthe samelevelofreliability. 4.4CostComparisons TheinformationinTable 4-1 canbeusedtomakedecisionsonthebestmaintenance approachonlywithknowledgeofthecostsassociatedwithea choption.Toillustrate theprocess,acostmodelbasedonliteratureanddetailedin Appendix B isused tofacilitatecomparisonsbetweenthedifferentmaintenan ceprocesses,onthe basisoftheirmaintenancecost(includingmaterialandlab orcost).Inthismodel themaintenancecostisthesumofairframemaintenanceande nginemaintenance cost,wherestructuralmaintenanceisasubsetofairframem aintenance.Theengine 54

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Figure4-3.Fractionofairplanesundergoingstructuralai rframemaintenance(i.e.repair) ateachscheduledmaintenance maintenanceandnon-structuralairframemaintenancearea lwaysperformedatthetime ofscheduledmaintenanceintervals.Onlystructuralmaint enanceisrequestedbyCBM basedonthecurrentdamagestatus. Basedontheempiricalexpressionsandairplaneparameters inTable B-1 in Appendix B ,theairframemaintenancecostis$1,139/ightandtheengi nemaintenance costis$258/ight.Theaircraftmakes60,000ightsduring itslifetime,andundergoes tenscheduledmaintenances.Hence,thecostofoneschedule dairframemaintenance (A)is$6.84millionandthecostofonescheduledenginemain tenance(E)is$1.55 million.Thecostforstructuralairframemaintenance(S)i sassumedtobe$1.8million. Duringscheduledmaintenance,mostofthetimeisspentford etectingcrackson theairplaneandidentifyingthepanelstoberepaired/repl aced.Whenmaintenanceis requestedbyCBM,theon-boardSHMequipmentassessesthecu rrentdamagestatus oftheairplane,andidentiesthepanelstoberepaired/rep laced.Hence,structural airframemaintenancerequestedbyCBMwillcostonlyafract ionascomparedto 55

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scheduledmaintenance.Thefractionisdenotedask SHM,andarangeof[0.3,0.7]is assumedfork SHM. Anun-scheduledmaintenancetrip,requestedbyCBM,ismore expensivethan maintenancerequestedbyCBMatthetimeofscheduledmainte nanceduetoless advancenoticeaswellasduetothefactthatthestructurala irframemaintenanceand theothermaintenance(engine,nonstructural)arenotdone atthesametime.Afactor,k unsch( > 1)issettodenotethehighercostincurredforun-scheduled maintenance,and arangeof[1.2,2]ischosenfork unsch.Factorsk SHMandk unschareindependentofeach otherandthecostofun-scheduledairframemaintenance,re questedduetoCBMisthe productofk unsch,k SHMandthecostofonescheduledstructuralairframemaintenan ce (S).ThetotalmaintenancecostisgivenbytheEq. 4–1 : Maintenancecost= ( E + ( AS )). N p + k SHM S N SA + ( k unsch1). k SHM S N unsch(4–1) whereEisenginemaintenancecost,Aisairframemaintenanc ecost,Sisstructural airframemaintenancecost.Hence,(A-S)isthenon-structu ralairframemaintenance cost.N pisthenumberofscheduledmaintenancetrips,N SAisthenumberoftimes structuralairframemaintenanceisperformedatthetimeof scheduledmaintenance,andN unscisthenumberofun-scheduledstructuralmaintenancetrips requestedbyon-board SHM. Sincebothk unschandk SHMareindependentofeachother,thebestandworstcase costsforeachCBMprocesswouldbewhenparametersk unschandk SHMarebothattheir lowerandupperlimitsrespectively.Table 4-2 comparesthebestandworstcasecosts ofdifferentCBMprocesseswiththecostforscheduledmaint enance.CBMrequests onlythestructuralairframemaintenance.Allothermainte nance(non-structuralairframe, engine)happenatpre-determinedscheduledmaintenanceti mes.Thecostforstructural airframemaintenanceis1.8milliondollars.Savinginabou t6.7maintenancetrips/ airplaneforSched-SHMcausesabout12M$forSched-SHM.the bestcaseandworst 56

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Table4-2.Comparingthebestandworstcasecostsofdiffere ntCBMprocesseswiththe costforscheduledmaintenance Maintenancecost(M$) Typek unsch=1.2,k SHM=0.3k unsch=2,k SHM=0.7 Scheduled83.983.9 SchedSHM66(0.5)69.3(0.6) CBMskip67(0.5)70.1(0.6) CBM67(0.4)71.7(0.5) caseofcostsavingsdependsonthechosenvaluesofparamete rs,k SHMandk unsch.Itis notedthateventheworstcasecostscenariosforCBMleadtos ubstantialsavingsinthe maintenancecostofanairplane. SHMuseson-boardsensorsandactuators,andtheycauseincr easeinweight oftheairplane,andhence,causeanincreaseinfuelcost.An assumptiononthe massoftheon-boardsensorsandactuators,asapercentageo fthefuselagemass, isconsidered.Table 4-3 comparesthefuelcostbetweenpreventivemaintenance andCBM,fordifferentcasesoffuselagemassincreasedueto on-boardsensorsand actuators.BasedonTable 4-3 ,CBMcouldcostabout3.5M$inexcessoverscheduled Table4-3.LifetimeFuelcost(basedon$/gal)forscheduled maintenanceandCBM,for differentcasesoffuselagemassincreaseduetoon-boardse nsorsand actuators.Fuelcostbasedon$126.1/barrel[ 1 ] ScheduledWithSHM(5% fuselagemassincrease) WithSHM(10%fuselagemassincrease WithSHM(20%fuselagemassincrease 210.5M$212.1M$213.8M$217.1M$ maintenancefortheexcessfuel,untilendoflife.But,base donTable 4-2 ,CBMcould leadtoatleast12M$insavingsinmaintenancecostoversche duledmaintenance. BasedonTables 4-2 and 4-3 ,CBMisfoundtoleadtosubstantialsavingsoverthe lifetimeoftheaircraft,consideringmaintenanceandfuel costs.Consideringtheextreme case,”CBM”,withk unsch=2andk SHM=0.7inTable 4-2 ,andSHMwith10%mass increase,inTable 4-3 ,thesavingsforCBMisabout8M$.IfanSHMsystemcanbe 57

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installedonboardtheairplaneforlessthanthisnumbertha nthemaintenancecostcan bereducedbyperformingCBM. Assumingasavingsof5M$forCBMoverscheduledmaintenance foranairplane untilitsendoflife.Now,aA320airplaneundergoesabout56ightseveryday,and hence,takes2000ightsinanyear.Savingsof5M$overtheli feofanairplane(60,000 ights)istranslatedtosavingsof$166,000peryearperair plane.InFiscalYear2011, U.S.Airwaysreportedaprotof$71million,anditreported aprotof$502millionin FY2010[ 112 ].Consideringanetprotof$300millionperyear,andwitha eetof650 airplanes,U.S.Airwaysrecordsanetprotof$400milliond ollarsperairplaneperyear. Hence,useofCBMwillincreasetheprotby40%. 4.5EffectofParametersAffectingCBM-skiponMaintenance Cost ThemaintenancecostforCBM-skipisaffectedbytwoparamet ersa thskipanda rep. Theparametera thskipcontrolsthenumberofunscheduledmaintenancetrips,anda repcontrolsthefrequencyofmaintenance.Thesetwoparameter shaveadirectbearingon themaintenancecost.Thissectionfocusesonndingtheopt imalcombinationofthese parameters. Arangeof[10,40]mmand[0,30]mmwerechosenforparameters2a thskipand2a represpectively.SimulationofCBM-skipmaintenancestrateg ywasperformed onrandomlychosencombinationsintherangeoftheseparame ters.Thenumber ofmaintenancetripsandthepercentageofpanelsreplacedw erecomputedfor eachcombinationoftheparameters,a thskipanda rep.Figure 4-4 plotstheeffectof parameters,a thskipanda repontheno.ofstructuralairframemaintenancetrips,theno. ofunscheduledmaintenancetrips,andthepercentageofpan elsreplaced.Asseenin Fig. 4-4 ,thehigherthevalueofa thskip,themorestructuralairframemaintenancewould beskipped,thanactuallyneededtobedone.Tomaintainades iredlevelofprobabilityof failure,moreunscheduledmaintenancetripsneedtobesche duled.Lowerthevalueofa thskip,fewermaintenancewouldbeskipped,thatactuallyneeded. Thoughloweringthe 58

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Figure4-4.Effectofparameters,a thskipanda repontheno.ofstructuralairframe maintenancetrips,theno.ofunscheduledmaintenancetrip s,andthe percentageofpanelsreplacedforCBM-skipmaintenancestr ategy valueofa thskipdecreasesthenumberofunscheduledmaintenancetrips,thi sleadsto morestructuralmaintenancetripsperairplanethannecess ary. Thereplacementthreshold,a repcontrolsthefrequencyofthemaintenance trips.Lowerreplacementthresholdleadstomorepanelsrep lacedduringagiven maintenance,butitdelaystheonsetofnextmaintenance,ca usingfewermaintenance trips.Butreplacingmorepanelsatagivenmaintenancewill causeanincreaseof maintenancecost.Figure 4-5 plotstheeffectoftheparameters,a thskipanda rep,onthe maintenancecost,forvariouscombinationsofmaintenance costparameters,k SHMandk unsch,andpanelreplacementcost.BasedonFig. 4-5 ,themaintenancecostincreases withincreaseinreplacementthreshold,a rep.Thevariationofcostwithparameter,a thskipdoesn'tfollowadenitevariation.Thereisnoappreciable effectofthepanel replacementcost. Tondtheoptimalcombinationofparameters,aparetofront oftheparameters affectingthemaintenancecost,no.ofmaintenancetripsan dpercentageofpanels 59

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Figure4-5.Theeffectoftheparameters,a thskipanda rep,onthemaintenancecost,asa functionofparameters,k SHMandk unsch,andpanelreplacementcostfor CBM-skipmaintenancestrategy replaced,isconstructedasshowninFigure 4-6 Afactor,k unschof1.2isconsideredto accountforun-scheduledmaintenancetrips.Itisnotedtha ttheresultsdonotchange evenifk unsch=2.AsseeninFigure 4-6 ,theoptimalcombinationof2a repand2a thskipismarkedasastar.Theoptimalvaluesarea rep=20mmanda thskip=10mm. 4.6Summary Twomaintenancestrategies,Sched-SHMandCBM-skiparemod eledinthis chaptertoskipunnecessarystructuralairframemaintenan ceforashortrangeairplane (A320).Thesemaintenancestrategiesarecomparedwithsch eduledmaintenance andcondition-basedmaintenanceonthenumberofstructura lairframemaintenance tripsandairplaneundergoes,andthenumberofpanelsrepai redineachairplane.The maintenancestrategiesarealsocomparedonthebasisonmai ntenancecosts.Itis 60

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Figure4-6.Paretofrontconstructedbasedonparametersaf fectingmaintenancecost concludedthatifon-boardSHMsystemcouldbeinstalledont heairplaneforlessthan8 M$,CBMstrategycouldleadtosavingsonthelifecyclecosto ftheairplane. Twoparameters,thresholdforskippingstructuralairfram emaintenance,a thskipandreplacementthreshold,a repareanalyzedfortheireffectonmaintenancecostfor CBM-skipstrategy.Theoptimalcombinationoftheseparame tersisfoundthatleadsto minimummaintenancecostforCBM-skipstrategy. 61

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CHAPTER5 MAINTENANCEPREDICTION 5.1Introduction Structuralhealthmonitoringhasbeenestablishedasatool totrackdamageas oftenasrequired.InformationobtainedfromtheSHMcouldb eusetopredictfuture scenarios(prognosis)andbebetterpreparedforthefuture .Literatureislledwith techniquesandmethodologiestocomputetheremainingusef ullifeofastructure.Work hasbeendoneinlaboratoryusingmaterialsamplestopredic tremainingusefullife. CrichlowandMcCulloch[ 113 ]comparedandverieddifferentmethodsforfatiguelife predictionsforairframe. Engeletal.[ 114 ]detaildifferentrealissuesinvolvedinpredictionofrem aining usefullife.KellerandRay[ 115 ]observethatresiduallifepredictioncouldbemade possibleforaircraftstructuresbyreal-trackingnon-des tructivetechniqueslikeultrasonic. HoeppnerandKrupp[ 116 ]comparethreedifferentfatiguegrowthmodelsontheir predictionofcomponentlife.Coppeetal.[ 117 ]showthatSHMtechniquescouldbe usedtopredicttheremainingusefullifeofastructure. Asimilarideaofprognosisofremainingusefullifeisusedi nthissectiontopredict thetimeofnextstructuralairframemaintenanceforCBM-sk ipmaintenancestrategy. Predictionofnextairframemaintenanceisdoneforaeetof airplanes.Predicting maintenancewillgiveairplanecompanies,timetopreparef ornecessarycorrective actionduringstructuralairframerepair. Thedamagestatusoftheairplaneisanalyzedasfrequentlya spossibleusing theonboardSHMsystem.TheCBM-skip(Section 4-2 maintenancemethodology isused.Oncedamageisdetected,itscrackgrowthisextrapo lated,assuminga certainvalueofdamagegrowthparameters.Thecrackgrowth wouldbeunder-/overpredictedbasedonthedifferencebetweentheassumedandac tualdamagegrowth 62

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parameters,associatedwiththedetecteddamage.Theoptim umvalueofdamage growthparameterstomakeaproperpredictioniscomputedin thissection. 5.2MaintenancePrediction Inthissection,fatiguelifeofpanelsduetocrackgrowthis modeled,forashort rangeairplane's(A320's)fuselage.Thelifeoftheairplan eismodeledasblocksofcrack propagationinterspersedwithmaintenance.Parismodel(s eeSection 2.3.1 )isusedto representcrackgrowth. ThevaluesoftheParismodelparametersaretabulatedinTab le 3-1 (Section 3.1 ). UncertaintyislimitedtotheloadingconditionandthePari smodelparameters.The panelthickness,initialdamagesize,correctionfactorfo rthestressintensityfactor,and thedamagereplacementthresholdaretheparametersselect edtosatisfythereliability constraints.Moredetaileddescriptionoftheconstraints andtheoptimizationprocesses todeterminetheparametersaregiveninAppendix A ThelifecycleoftheairplaneissimulatedusingMonteCarlo simulations(MCS) describedinSection 2.4 .Assoonasacrackisdetected,crackgrowthforthatcrack ispredicted.TheanalyticalsolutionofParismodelisused tomaketheprediction, consideringadeterministicvalueofmaterialparameters( m,C).Thedeterministicvalue ofmaterialparametersisrandomlychosenfromtheirdistri bution.Giventhedetected sizeofthecrack,structuralairframemaintenance(i.e.ne edforrepair)ispredictedat thetimeofsubsequentscheduledmaintenance,ifthedetect edcrackispredictedto growbeyondthereplacementthreshold,a rep,atthetimeofaforementionedscheduled maintenance.Thispredictionprocessisfollowedforeacha irplaneintheeetatevery maintenanceassessment. Ateachmaintenanceassessment,basedonthedetecteddamag esizes,the fractionofairplanesintheeetthatwouldrequirestructu ralairframemaintenance (repair)atthenextscheduledmaintenanceispredicted.Th ispredictionateach maintenanceassessmentiscomparedwithactualfractionof airplanesundergoing 63

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structuralairframerepairatthetimeofscheduledmainten ance.Theplotofprediction offractionofairplanesrequiringstructuralairframemai ntenanceatthetimeofnext scheduledmaintenance,asafunctionofmaintenanceassess mentistermedthe predictionplot. Thevalueof(m,C)chosenisanimportantparametertomaketh eprediction. Figure 5-1 showsthepredictionplot,consideringtheextremitiesand themeanof(m,C) jointdistribution(seeFig. 2-4 ).Thesolidverticallinesrepresentthetimesofscheduled maintenance.Thetrianglesrepresenttheactualfractiono fairplanesundergoing structuralairframemaintenanceatthetimeofscheduledma intenance.Itisseenthat Figure5-1.Predictionplotconsideringtheextremitiesan dmeanvaluesofjoint distributionof(m,C) thepredictionplotforrighttopvalueof(m,C)distributio n(in(b))initiallyover-predicts (conservative)in-betweenscheduledmaintenances.Predi ctionplotforrighttopvalueof 64

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(m,C)distributionpredictsahigherfractionofairplanes toundergomaintenancethan thefractionofairplanesthatactuallyundergoes.Theover -predictionsubsidesasthe lifeofairplanemovesclosertothenextscheduledmaintena nce.Similarly,thebottom valuesof(m,C)(in(c)and(d))distributioninitiallyunde r-predict(un-conservative) inbetweenscheduledmaintenances.Thisisbecause,therig httopvaluesof(m,C) distributionpredictafastercrackgrowththanexperience d,whilethebottomvaluesof (m,C)distributionpredictaslowercrackgrowththanexper ienced. Itisalsonotedthatconsideringthemeanvalueof(m,C)dist ribution(in(e))still leadstoun-conservativepredictions.Basedonourchoiceo f(m,C)values,wecanend upconservative/un-conservativepredictions. 5.3ChoosingOptimalValueof(m,C) Tondtheoptimalvalueof(m,C),weneedtoaskourselvestwo questions.What istheidealshapeofthepredictionplot,wewouldliketosee ,andwhatvaluesof(m,C) couldgivesuchaplot. Theidealpredictionplotshouldbeabletopredictthefract ionofairplanes undergoingstructuralairframemaintenanceatthesubsequ entscheduledmaintenance, rightafterthepresentscheduledmaintenance.Hence,thei dealpredictionplotwill havehorizontallinesinbetweenscheduledmaintenancesas showninFigure 5-2 .To computetheidealvalueof(m,C),aseriesofvalueswererand omlysampledfromthe uniformdistributionof(m,C)(seeFig. 2-4 ).Thepredictionplotwasconstructedfor eachsampledcombinationof(m,C).Therootmeansquare(rms )ofthedifferencein predictionbetweentheobtainedpredictionplotandidealp redictionplotisminimizedto ndtheoptimalvalueof(m,C).Theoptimalvaluesof(m,C)we reobtainedattheendof eachscheduledmaintenance. Figure 5-3 plotsthepredictionsplots,whenvalueof(m,C)isoptimize dby minimizingthermsvalueofdifferenceinpredictionuntilt henthmaintenance,where n 2 [3,10].Theoptimalvalueforeachcaseisnotedonthelegend ofthesubplot. 65

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Figure5-2.Idealpredictionplot Figure 5-4 plotsallthese8optimalvaluesonthedistributionof(m,C) .Theblueregion Figure5-3.Predictionplotswhen(m,C)wereoptimizedcons ideringrmsofthearea differenceuntilthenthmaintenance representsthefullgamutofdistributionof(m,C)andthegr eenspotsrepresentthe optimalvaluesofdifferentcasesconsideredinFigure 5-3 .Thenumbersontheplot representthen thmaintenanceconsideredtocomputethermserror.Itisnoted thatthe 66

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Figure5-4.Optimalvaluesof(m,C)forcasesconsideredinF igure 5-3 optimalvaluesof(m,C)forthevariouspredictionplotsare concentratedaroundthetop rightcornerofthedistribution,thelocationwiththefast estcrackgrowthrate. Now,theoptimalvaluesof(m,C)obtaineduntiltheendofasc heduledmaintenance areusedtopredictthefractionofairplanesrequiringmain tenanceatthetimeofnext scheduledmaintenance.Figure 5-5 comparessuchapredictionplot.Theerrorin Figure5-5.Predictionplotwhenoptimalvaluesof(m,C)unt ilendofascheduled maintenanceisusedtopredictthemaintenanceforthenexts cheduled maintenance predictioninFigure 5-5 isplottedinFigure 5-6 .Duringprediction,anairplanemay bewronglypredictedtorequiremaintenance(over-predict ed),oranairplanerequiring maintenancemaynotbepredictedtohavemaintenance(under -predicted).Figure 5-6 plotsboththeerrorsThesolidlinerepresentstheidealpre dictionplot.Thedottedline representsthefractionofairplanes,forwhichmaintenanc eispredictedaccurately.The 67

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Figure5-6.Plotoferrorsinthepredictionplot differencebetweenthedottedlineandsolidlinerepresent thefractionofairplane,which requiredmaintenanceandwasn'tpredictedto(under-predi ctionerror) Thedifferencebetweendashedlineandsolidlineintheplot representthe fractionofairplanesforwhich,maintenancewaspredicted ,butdidn'trequireany (over-predictionerror).Itisnotedthattheerrorarehigh attheendofascheduled maintenance,andtheydiedowntozerofairlyquicklybefore thenextscheduled maintenance. 5.4Summary Thischapteramethodologytopredictthefractionofairpla nesinaeetrequiring structuralairframemaintenanceatthetimeofnextschedul edmaintenance,whenthe maintenanceisperformedbasedonCBM-skipstrategy.Thech aptercomputesthe optimalvalueofdamagegrowthparameters,(m,C)tomakeapr operprediction,at theendofeachscheduledmaintenance.Theoptimalvalueof( m,C),computedatthe timeofascheduledmaintenance,isusedtopredictthefract ionofairplanesinaeet requiringstructuralairframemaintenanceatthetimeofne xtscheduledmaintenance. 68

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Theerrorinpredictioniscomputedandisfoundtoreducetod iedowntozeroquickly beforethenextscheduledmaintenance. 69

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CHAPTER6 EFFECTOFDAMAGEQUANTIFICATIONERROROFONBOARD SHMSYSTEM SHMprovideson-boarddiagnosticsoftheexistingdamageon thesystem.There havebeensomeseriousconcernraisedabouttheaccuracyofd amagedetectionand damagequanticationoftheon-boardSHMsystem.Inthiswor k,theSHMsystemthe lossinaccuracyofdamagedetectionismodeledbyhavingale ssaccurateinspection modelforSHMsystemcomparedforthatofinspectionbyNDIor GVI.ThePalmberg parameter,a hismodeledinaccordance.Thischapterfocusesontheeffect ofaccuracy ofdamagequanticationoftheon-boardSHMsystem. 6.1ClassifyingManagementErrorArisingfromDamageQuant icationError Thedamagequanticationerrorcouldleadtothreekindsofm anagementerror. Theseerrorsadverselyaffectthedecisiontorequestmaint enancebytheon-boardSHM system. Error1:Acrackcriticaltothesafetyoftheairplane,isnot detectedbySHMsystem. Inthiswork,error1isexpressedasapercentageoftimesacr ackcriticaltothesafetyof theairplanewasmissed,duetoerrorindamagedetection. Error2:Acrackcriticaltothesafetyoftheairplaneisdete cted,butismeasured tobeNOTcriticalbytheon-boardSHMsystem.Inthiswork,er ror2isexpressedasa percentageoftimesacrackcriticaltothesafetyoftheairp lanewasmissed,duetoerror indamagequantication. Error3:AcrackNOTcriticaltothesafetyoftheairplane,is detectedbutitis measuredtobecriticalbytheon-boardSHMsystem.Inthiswo rk,error3isexpressed asapercentageofpre-maturemaintenancevisits,anairpla neundergoes. Itisnotedthaterrors1and2haveadverseeffectofthesafet yofthesystem. Errors1and2causethemaintenanceNOTtoberequestedwhent hereisaneedfor one.Error3isofconservativenaturewhereinthemaintenan cewouldberequested 70

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earlierthanwhenitisactuallydesired.Theeffectofdamag equanticationerroronthe managementerrorwouldbeanalyzedinthefollowingsection s. 6.1.1Condition-basedMaintenance Inthissection,theeffectofdetectionerrorisanalyzedfo racondition-based maintenancestrategy(seeSection 2.2.2 ).Thesimulationofmaintenanceprocedure isdoneaccordingtoMonteCarlosimulationsasdescribedin Section 2.4 .The maintenanceassessmentisdoneevery100cycles.Thereplac ementthresholdand thethresholdforrequestingmaintenancearesetbasedonTa ble 3-2 6.1.2ConstantRatiobetweenDetectedandActualCrackSize Thissectionfocusesondamagequanticationerrorofon-bo ardSHMsystem whenaconstantratioismaintainedbetweenactualanddetec tedcracksizes.Such errorwouldoccuriftheon-boardSHMsystemconsistentlyov er-/under-predictsa cracksize,dependingonthelocationofthecrackwithrespe cttotheSHMsystem.The effectofdamagequanticationerrorisanalyzedbyaddinga noisetothecracksize. Thenoiseisameasureofthedamagequanticationerroraris ingfromthedistance betweenthecrackandtheon-boardSHMsystem.Whenacrackis rstdetected,its detectedcracksizewouldbesampledfromanormaldistribut ionwithmeanasitsactual cracksize,andthewithaconstantknowncoefcientofvaria tion(COV).Everytime thecrackisdetectedhenceforth,aconstantratiobetweend etectedandactualcrack sizeismaintained.Forinstance,letusassumetheactualcr acksizeis10mm,when itrstdetected.Duetonoiseindamagequantication,thec racksizewasquantied as8mm.Everytimehenceforth,thecrackisdetected,thesam eratiobetweenactual anddetectedcracksizeswouldbemaintained.Iftheactualc racksizegrowsto50mm, thecrackwouldbedetectedofsize40mm.Table 6-1 tabulatestheeffectofthreshold forrequestingmaintenanceonthenumberofmaintenancetri ps,percentageofpanels replaced,andtheprobabilityoffailureofapaneluntilthe endoflifeofanairplanewhen theerrorindamagequanticationofon-boardSHMis10%.Iti snotedthattheCBM 71

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Table6-1.Effectofthresholdforrequestingmaintenanceo nthenumberofmaintenance trips,percentageofpanelsreplaced,andtheprobabilityo ffailureofapanel untiltheendoflifeofaA320airplane,withalifeof60,000 ightcycles CaseAvg.no.of maintenancetrips/airplane Percentageofpanelsreplaced/airplane Pfofapaneluntilendoflife(60,000ights)ofairplane(A320) SHMwith0%errorPerfectdetection 2.3(0.7)6.6(2.5) < 1E-7 SHMwith10%COVerror,2a maint= 79.8mm 2.3(0.7)6.6(2.3)6.7E-4 SHMwith10%COVerror,2a maint= 70mm 2.5(0.8)6.8(2.2)9E-5 SHMwith10%COVerror,2a maint= 60mm 2.5(0.8)6.8(2.3) < 1E-6 strategyisdesignedforaprobabilityoffailureof1E-7.Du etotheerrorinmeasurement, somecriticalcracksaremissedandtheprobabilityoffailu reincreasesto6E-4.Itisalso notedthatthereisn'tanappreciableeffectofthenoiseind amagemeasurementonthe numberofmaintenancetripsandthepercentageofpanelsrep lacedintheairplane. Fig. 6-1 illustrateswhyprobabilityoffailureincreasesduetodam agequantication error,andalsoexplainsthedenitionofError2.Figure 6-1 plotsanillustrationofcrack growthofanactualanddetectedcrack.Thecrackwasrstdet ectedwhentheactual cracksizewas10mm.Duetodamagequanticationerror,thec rackwasdetectedas 8mm.Thepositionofmaintenanceassessmentintervalsisno tedasblackdottedlines intherightsideoftheplot.Thelocationofmaintenanceass essmentintervalsisnot plottedinearliersegmentsforclaritypurposes.Letusass ume2a maintis 80mmas shownin(a)inFigure 6-1 .Thesystemfailswhenthecrackgrowsun-detectedbeyond 95mm.Whentheactualcracksizeis80mm,thedetectedcracks izeismeasuredat 68mm.Structuralairframemaintenanceisnotrequestedast hedetectedcracksizeis lessthan2a maint.Bythetimethedetectedcracksizegrowsbeyond80mm,theac tual 72

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Figure6-1.Explainingtheeffectofdamagequanticatione rror crackhascrossed95mmandhence,thesystemfails.Theinacc uracyofthedamage quanticationsystemhascontributedtothefailureofthea irplane. Consideranothercasewhen2a maintisreducedto70mmasshownin(b)in Figure 6-1 .Whentheactualcracksizeis70mm,thedetectedcracksizei s56mm. Hence,maintenancewillnotberequestedwhenitshouldbe.W henthedetectedcrack sizereaches70mm,theactualcracksizeis90mm,andthesyst emhasn'tfailedyet. Hence,reducing2a maintimprovesthereliabilityofthesystem. Structuralairframemaintenancewasrequested5maintenan ceassessments aftertheactualcracksizecrossed2a maint(=70mm).So,in4ofthosemaintenance assessments,structuralairframemaintenancewasNOTrequ estedeventhoughtthere wasalargedamageonthesystem.Fromthetimetheactualcrac ksizecrossed70mm, 73

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therewere4maintenanceassessmentwhereinthecorrectman agementdecisionwasn't taken(requestingstructuralairframemaintenance).So,e rror2inthiscasewouldbe4/ 5=80%. Thisillustrationisforasinglecrack.Table 6-2 tabulatestheerrorsforaeetof2000 airplanesand500panelsperairplane.Thesimulationofcon dition-basedmaintenance strategy(seeSection 2.2.2 isperformedforashortrangeairplanelikeA320.Table 6-2 tabulatesthedifferentmanagementerrorresultingfromda magequantication errorforvariouscombinationsofthresholdforrequesting maintenance,a maintand theCOVofdamagequantication(DQ)error.InTable 6-2 ,themanagementerror Table6-2.Managementerrorresultingfromdamagequantic ationerrorforvarious combinationsofthresholdforrequestingmaintenance,a maintandtheCOVof damagequantication(DQ)errorwhenaconstantratioismai ntained betweenthedetectedandactualcracksizes CaseCriticalcrack missedduetoerrorindetection(%oftimes) Criticalcrackmissedduetoerrorindamagequantication(%oftimes) Pre-maturemaintenancevisits(%) Pf DQCOV=10%,2a maint=79.8mm 040.426.66.7E-4 DQCOV=10%,2a maint=70mm 046.132.19E-5 DQCOV=10%,2a maint=60mm 051.033.3 < 1E-6 DQCOV=5%,2a maint= 79.8mm 024.718.91.9E-4 DQCOV=5%,2a maint= 70mm 024.923.4 < 1E-6 DQCOV=5%,2a maint= 60mm 025.225.8 < 1E-6 74

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isquantiedasthepercentageofincorrectdecisionsthath appenedduetodamage detectionquanticationerror.Asthea maintdecreases,thedistancebetweena maintanda critincreases,andhence,therepresentsmoreopportunitiesto detectacrackcriticalto thesafetyoftheairplane.Thepresenceofmoreopportuniti esincreasethepercentage ofmanagementerrors,buthelpdecreasetheprobabilityoff ailure,asdescribedby Figure 6-1 Also,ahigherCOVofDQerrorleadstomorethenoiseindamage quantication, andhence,greaterpercentageofmanagementerrors.Itisno tedthatError3isof conservativenature,andcausesapre-maturerequestforma intenance. 6.1.3ConstantDifferencebetweenDetectedandActualCrac kSize Thissectionfocusesondamagequanticationerrorofon-bo ardSHMsystem whenaconstantdifferenceismaintainedbetweenactualand detectedcracksizes. Thisisacaseofbiasinthedamagequanticationbyon-board SHMsystem.Theeffect ofdamagequanticationerrorisanalyzedbyaddinganoiset othecracksize.The noisequantiestheamountofbiasinvolvedwithdamagequan tication,foracrack. Whenacrackisrstdetected,itsdetectedcracksizewouldb esampledfromanormal distributionwithmeanasitsactualcracksize,andthewith aconstantknowncoefcient ofvariation(COV).Everytimethecrackisdetectedhencefo rth,aconstantdifference betweendetectedandactualcracksizeismaintained.Forin stance,letusassumethe actualcracksizeis10mm,whenitrstdetected.Duetonoise indamagequantication, thecracksizewasquantiedas9mm.Everytimehenceforth,t hecrackisdetected, thesamedifferencebetweenactualanddetectedcracksizes wouldbemaintained.If theactualcracksizegrowsto50mm,thecrackwouldbedetect edofsize49mm.Table 6-3 tabulatesthedifferentmanagementerrorresultingfromda magequantication errorforvariouscombinationsofthresholdforrequesting maintenance,a maintandthe COVofdamagequantication(DQ)error.AsnotedinTable 6-3 ,theerrorscaused bymaintainingaconstantdifferencebetweentheactualand detectedcracksizesis 75

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Table6-3.Managementerrorresultingfromdamagequantic ationerrorforvarious combinationsofthresholdforrequestingmaintenance,a maintandtheCOVof damagequantication(DQ)errorwhenaconstantdifference ismaintained betweenthedetectedandactualcracksizes CaseCriticalcrack missedduetoerrorindetection(%oftimes) Criticalcrackmissedduetoerrorindamagequantication(%oftimes) Pre-maturemaintenancevisits(%) Pf DQCOV=10%,2a maint=79.8mm 05.33.7 < 1E-6 DQCOV=10%,2a maint=70mm 05.64.4 < 1E-6 DQCOV=10%,2a maint=60mm 07.45.2 < 1E-6 DQCOV=5%,2a maint= 79.8mm 03.11.9 < 1E-6 DQCOV=5%,2a maint= 70mm 03.01.9 < 1E-6 DQCOV=5%,2a maint= 60mm 02.82.3 < 1E-6 muchsmallerthanthatcausedbymaintainingaconstantrati obetweentheactualand detectedcracksizes.Thisisbecausethereislittlediffer encebetweentheactualand detectedcrackgrowthpathincaseofconstantdifferencebe tweenactualanddetected cracksizes. 6.2CounteringDamageQuanticationError Thedamagequanticationerrorcanhaveadverseeffectsont heprobabilityof failureofapanelandmanagementdecisionsasnotedinTable s 6-2 and 6-3 .The damagequanticationerrorcouldbecounteredbyalwayscon sideringaconservative approachindamagequantication.Thedetectedcracksizec ouldbeassumedtobeof 76

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a10%largersizethanquantiedbytheon-boardSHMsystem.C onsideringalarger detectedcrackisameansofincorporatingapositivebiason thecracksizequantiedby on-boardSHMsystem.Alargerdetectedcrackwillreduceerr or2,i.e.theerrorcaused bycriticalcrackmissedbydamagequantication,butwillc auseanincreaseinerror3, i.e.thenumberofpre-maturemaintenancevisits.Buterror 3isofconservativenature andmaycauseaslightincreaseinthenumberofmaintenancet rips,anairplanegoes to. Theeffectofconsideringalargerdetectedsizeisconsider edforCBMstrategy withaconstantratiobetweenthedetectedandactualcracks izes.Thethresholdfor requestingmaintenance,2a maintissetat70mm,andtheCOVofdamagequantication errorissetat10%.Table 6-4 comparesthemanagementerrorsarisingconsideringthe detectedcracksizetobelargerthanthecracksizequantie dbyon-boardSHMsystem. AsnotedinTable 6-4 ,greaterthevalueofdetectedcracksizeascomparedtothat Table6-4.Managementerrorresultingfromconsideringdet ectedcracksize(aDet)tobe ofavaluegreaterthanthatquantied(aQuant)byon-boardS HMsystem, whenthresholdforrequestingmaintenance,a maint=70mmandtheCOVof damagequantication(DQ)error=10%whenaconstantratioi smaintained betweenthedetectedandactualcracksizes CaseCriticalcrack missedduetoerrorindetection(%oftimes) Criticalcrackmissedduetoerrorindamagequantication(%oftimes) Pre-maturemaintenancevisits(%) Pf aDet=aQuant046.132.19E-5aDEt=1.05 aQuant037.053.52E-5 aDEt=1.1 aQuant034.169.8 < 1E-6 quantiedbyon-boardSHMsystem,lowerpercentageofcriti calcracksmisseddueto damagequantication,butcauseahigherpercentageofprematurevisits.Theincrease inmaintenancevisitscausedduetoincreaseinpre-maturev isitswasnotfoundtobe signicant. 77

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6.3Summary Theeffectofdamagequanticationerroroftheon-boardSHM systemon managementerrorsisanalyzedinthischapterforCBMstrate gy.Themanagement errorsincludenotrequestingmaintenancewhenacriticalc rackwaspresent,or requestingmaintenancepre-maturely,becauseoferrorinq uanticationofcrack size.Thequantiedcracksizeismodeledashavingeitherac onstantratiooraconstant differencewiththeactualcracksize.Theeffectofthenois eindamagequantication andthresholdforrequestingmaintenanceonthemanagement errorarediscussed, forvariouscasesofdamagequanticationerror(constantd ifferenceandconstant ratio).Consideringthedetectedcracksizetobeofagreate rcrackthanquantiedby theon-boardSHMsystemwasfoundtoreducetheprobabilityo ffailureandcause conservativemanagementdecisions. 78

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CHAPTER7 CONCLUSIONS Thisworkrstcomparescondition-basedmaintenancestrat egywithscheduled maintenance,settopreventfatiguefailureduetoexcessiv ecrackpropagationinthe fuselagepanelsofcommercialairplanes.Condition-based maintenancestrategyuses on-boardstructuralhealthmonitoring(SHM)systemtotrac kdamage,andhence,has atolerancetolargercracksizethanscheduledmaintenance .Tolerancetolargercrack sizecausesfewermaintenanceforthecommercialairplane, andthereby,savingsin maintenancecost,whilemaintainingthesamelevelofrelia bility.Thesavingsincostof condition-basedmaintenanceoverscheduledmaintenancei stranslatedtosavingsin weight,whilemaintainingthesamelevelofreliability. Inspectionbyon-boardSHMsystemischeaperthantheintrus iveinspection performedbynon-destructiveinspectionduringscheduled maintenance.Condition-based maintenancestrategies,Sched-SHMandCBM-skipusinginsp ectionbyon-board SHMismodeledtoskipunnecessarystructuralairframemain tenanceatthetime ofscheduledmaintenance.Thesemaintenancestrategieswe refoundtoleadto savingsinlifecyclecostoverscheduledmaintenance.Theo ptimumcombinationoftwo parametersaffectingCBM-skip,thresholdforskippingstr ucturalairframemaintenance andreplacementthreshold,isfoundbyminimizingthemaint enancecost. ForCBM-skipmaintenancestrategy,amethodologyisdevelo pedispredictthe fractionofairplanesinaeetthatwouldrequirestructura lairframemaintenanceatthe timeofnextscheduledmaintenance.Theoptimalvaluesofda magegrowthparameters, (m,C)tomakeaproperisdeterminedatthetimeofeachschedu ledmaintenance. Theoptimalvaluesofdamagegrowthparameterscomputeddur ingascheduled maintenancewereusedtopredictthefractionofairplanesi naeetrequiringstructural airframemaintenanceatthetimeofsubsequentscheduledma intenance.Theerror 79

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inthepredictionisfoundtoreducedtozerowellbeforethes ubsequentscheduled maintenance. Theremightanerrorinvolvedinthedamagequanticationby theon-boardSHM system.Theerrorindamagequanticationcouldcausemanag ementerrorsthatmight resultinhigherprobabilityoffailureofapanelthandesir ed.Theeffectofdamage quanticationerroroftheon-boardSHMsystemonmanagemen terrorsisanalyzed forCBMstrategy.Themanagementerrorsincludenotrequest ingmaintenancewhen acriticalcrackwaspresent,orrequestingmaintenancepre -maturely,becauseof errorinquanticationofcracksize.Thequantiedcracksi zeismodeledashaving eitheraconstantratiooraconstantdifferencewiththeact ualcracksize.Theeffectof thenoiseindamagequanticationandthresholdforrequest ingmaintenanceonthe managementerrorarediscussed,forvariouscasesofdamage quanticationerror (constantdifferenceandconstantratio).Consideringthe detectedcracksizetobeof agreatercrackthanquantiedbytheon-boardSHMsystemwas foundtoreducethe probabilityoffailureandcauseconservativemanagementd ecisions. Theon-boardSHMsystemcouldinspecttheairplaneandtrack damageonthe airplane,asfrequentlyasneeded.Continuoustrackingoft hedamagecouldidentify thoseairplanesthathasafastercrackgrowthandwouldrequ iremorestructural airframemaintenancethantherestoftheeet.Amethodolog y,modiedHierarchical samplingisdevelopedtoidentifysuchanomaliesinaeetof airplanes. 80

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APPENDIXA IDENTIFYINGPARAMETERSFORPARISLAW Inthiswork,damage/crackreferstodamageinanylocationo fthefuselage, andthecrackgrowthismodeledusingasimpleParisLawmodel .Sincethepractical fuselagestructureisdifferentfromtheidealizedParismo del,theparametersoftheParis Lawareadjustedtosatisfycertainconstraints,inorderto mirrorrealisticcircumstances. FollowingaretheparametersoftheParisLawthatneedtobes et. Thicknessofthefuselagepanel,t Correctionfactorforthestressintensityfactor,A Replacementthresholdforthepreventivemaintenance,a reppvt Initialdamagesizedistribution Theconstraintsthathelpmirrorrealityare: Probabilityoffailureofapaneluntilendoflife,forpreve ntivemaintenance=107 Probabilityoffailureofapanelbetweensuccessivepreven tivemaintenance=108 Thesensitivityofinspectionintervaltofuselagepanelth ickness,forpreventive maintenancemustmatchreality. Inspectionintervalisthetimetaken(inightcycles)fora crackofsize,2a reppvt,to growcriticalwithaprobabilityoffailureof108.Theprobabilityoffailureiscalculated bythedirectintegrationprocedure(Appendix C ).Aplotforthevariationofinspection intervalasafunctionofpanelthicknessforvariousstring erlengthsisobtainedfrom theliterature[ 118 ].TheparametersoftheParisLawneedtobeadjustedtomaint aina similarsensitivityofinspectionintervaltopanelthickn esstomirrorreality. Theparametersaffectingtheinspectionintervalarevarie dindividuallytondthe optimumsetofparameters.Figure A-1 comparesthesensitivityofinspectioninterval topanelthicknessfortheoptimizedsetofparametersandre ality.Theoptimizedsetof parametersthatsatisfyaforementionedconstraintsisnot edinthecaptionTheoptimal 81

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FigureA-1.Comparingthesensitivityofinspectioninterv alforoptimalsetofparameters andthetrendobservedinreality parametersthatsatisfyaforementionedconstraintsareSI Fcorrectionfactor,A=1.255, replacementthreshold(2a rep)=12mm,andfuselagepanelthickness,t=2mm. ThedistributionofEIFSisassumedtolognormalwith35%coe fcientofvariation. Themeanoftheinitialdamagesizedistributionissettomai ntainaprobabilityoffailure atthetimeofrstmaintenance,whichis20,000ights.Dire ctintegrationprocedureis usedtocomputetheprobabilityoffailureforagivensetofp arameters.Theoptimized meanofEIFSisfoundtobe0.2mm 82

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APPENDIXB COSTMODELFORSHORTRANGEAIRPLANE(A320) InordertoestimatethecostefciencyoftheSHMsystems,it isnecessaryto discussaboutthecostmodelrst.Trip-costofanairplanei ncludes,amongothers,fuel cost,airframemaintenancecostandenginemaintenancecos t.Thesecostelementsare givenintermsofempiricalexpressioninKundu[ 119 ].FuelcostisgiveninEq. B–1 as Fuelcharges=blockfuel fuelcost blocktime (B–1) TheairframelaborcostisgiveninEq. B–2 as 0.09W airframe + 6.7350 W airframe + 75 0.8 + 0.68( t0.25 ) t R(B–2) whereW airframeisthemaximumemptyweight(MEW)oftheairplanelesstheeng ine weight,intons,Risthelaborratein$/hour,andtisthebloc ktimeofairplaneperight. TheairframematerialcostisgiveninEq. B–3 by 4.2 + 2.2( t0.25 ) t C airframeR(B–3) whereC airframeisthepriceofairplanelessengineprice,inmillionsofdol lars.The airframemaintenancecostperightisgivenasthesumofair framelaborandairframe materialcost.EnginelaborcostisgiveninEq. B–4 by0.21RC 1C 3(1 + T ) 0.4(B–4) where,Tisthesealevelstaticthrust,intons,C 1 = 1.270.2BPR 0.2,whereBPRisthe bypassratiooftheengine,C 3 = 0.032n c + K,wheren cisthenumberofcompressor stages,K=0.50foroneshaft,0.57fortwoshaftsand0.64for 3shafts.Enginematerial costisgiveninEq. B–5 as2.56( 1 + T ) 0.8C 1C 2C 3(B–5) 83

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where,C 2 = 0.4( OAPR=20 ) 1.3 + 0.4,whereOAPRistheoverallpressureratioofthe engine. Theenginemaintenancecost(labor+material)peright,is giveninEq. B–6 byN e enginelaborcost+materialcostt + 1.3 t0.25 (B–6) Parametersaffectingthecostmodelareobtainedfromaircr aftpreliminarydesign software(SimCAD)[ 107 ]andenginespecications[ 120 ].Parametersaffectingthe costmodelaretabulatedinTable B-1 .Fuelcostiscalculatedonthebasisof$126.1/ TableB-1.Airplaneparametersaffectingcost ParameterValue MWE(tons)51.6 Enginewt(tons)13.0 Laborrate($/hr)63 blocktime(hr)1.1W airframe(tons)38.6 Cost airframe(M$)83 Sealevelstaticthrust(tons)24.6 Enginebypassratio(BPR)6 No.ofcompressorstages(n c)9 K0.57 Overallpressureratio(OAPR)31.3 No.ofengines(N e)2 Blockfuel(kg)3604.3 Fuelcost($/kg)0.9 barrelofjetfuel[ 1 ].Abarrelhouses42gallonsofjetfuelandthedensityofjet fuelis6.8 lb/gallon 84

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APPENDIXC DIRECTINTEGRATIONPROCEDURE Thedirectintegrationprocedureisamethodusedtocompute theprobabilityofan outputvariablewithrandominputvariables.Inthiswork,t hedirectintegrationprocess isusedtocomputetheprobabilityofhavingaspecicdamage size.Thedamagesize distributionisafunctionofinitialdamagesize,pressure differential,andParismodel parameters(m,C),whichareallrandomasgivenbyEq. C–1 f N ( a ) = h ( a 0 f ( p ), J ( C m ) )(C–1) wherea 0,f N ( a ),f ( p )representtheinitialdamagesize,theprobabilitydensity functionsofdamagesizeafterNcyclesandpressurediffere ntial,respectively.J ( C m )isthejointprobabilitydensityoftheParismodelparamete rs(m,C).Theprobabilityof damagesizebeinglessthana NafterNcyclesistheintegrationofthejointprobability densityofinputparametersovertheregionthatresultsina damagesizebeinglessthan orequaltoa N;thatisgivenbyEq. C–2 Pr ( a
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m).Theregioningreyresultsinadamagesize(a N)40mm.Thepoints1and2that denethegreyregionarecomputedrstusingtheanalytical expressionofParismodel andtheareaofthepolygoniscomputedfrombasicgeometry. FigureC-1.Regionsof(C,m)forN=50,000anda 0=1mm Iftheinitialdamagesizeisdistributed,thentheintegran disevaluatedatdifferent valuesintherangeoftheinitialdamagesize,andthetrapez oidalruleisusedto computetheprobabilityatthedesireddamagesize. 86

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APPENDIXD IDENTIFYINGANOMALIESINAFLEETOFAIRPLANES D.1Introduction Structuralhealthmonitoringtechniques,onceinstalledo ntheairplanes,willhelp trackthedamageonairplanecontinuously.Thecontinuoust rackingenablesprediction ofonsetofnextstructuralairframemaintenance,asdiscus sedinChapter 5 .Inaddition, trackingdamagecontinuouslyimprovesourknowledgeofthe crackgrowthencountered bytheairplane.Theknowledgeofcrackgrowthbyeachairpla neinaeetcouldbe utilizedtodetectairplanesthathaveadeviantcrackgrowt hbehaviorthantherest oftheeet.Thischapterfocusesmethodologytoidentifyth eairplanesthatrequires moremaintenancethantherestoftheeet.Identicationof suchairplanes,earlyinits lifecycle,wouldprovidetheairplanecompanies,tomakene cessarycorrectiveaction, like,retiringtheairplaneearly,sellingtheairplaneoff ,orbebetterpreparednancially. Anairplanepassesthroughstringentinspectionsbeforeit isclearedtoy.The deviatorybehaviorforanairplanecouldarisefromfactors like,thematerialusedfor airplane,environmentalconditionstheplaneisownin,hu manfactors(like,pilot). Thesefactorscouldcausevaryingrateofcrackgrowthonthe airplane.Inautomobile industry,theautomobilesthatrequiremorefrequentmaint enancethanthenominalones arecalled'lemons'.Inthischapter,thesameterminologyh asbeenusedtoqualifythe anomaliesinaeetofairplanesthatrequiremorefrequentm aintenancethantherestof theeet. D.2Methodology Aeetof200airplanesareinspectedbasedonCBMmethodolog ydiscussed inSection 2.2.2 .Themaintenanceassessmentisdoneevery100ights,andth e simulationoflifecycleoftheairplaneisdoneaccordingto montecarlosimulation processdetailedinSection 2.4 87

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Duringeachmaintenanceassessment,theon-boardSHMdevic ewillprovide informationonwhetheracrackisdetectedornotatagivenlo cation,andifdetected, thecracksizeatthatgivenlocation.Itisassumedthatther eisnoerrorindamage quantication,oncethecrackisdetected. Cumulativeno.ofcracksdetectedinpanels(CDP)isthepara meterdenedto classifytheairplanesintonominalanddeviant.Itisthecu mulativecountofnumber ofcracksdetectedintheairplanewitheachmaintenanceass essment.Thelogicfor choosingsuchparameterisasfollows.Airplaneswithfaste rcrackgrowthwarrant frequentmaintenance.Fastercrackgrowthcauseslargecra ckstoformonanairplane thantherestoftheeet.Largercrackshavehigherprobabil ityofdetection.Hence, airplaneswithfastercrackgrowthwillhavemorecracksdet ectedonit,thantherestof eet. 'Lemon'airplaneswillhaveahigherCDPvaluethantheresto ftheeet.This sectionfocusesonclassifyinganairplaneasalemonornomi nal,basedonitsCDP value.Duringeachmaintenanceassessment,basedontheCDP valueforeach airplane,twoclustersofairplanesareformed,alemonclus terandanominaleet cluster.Whileformingacluster,itisimperativetondwhe thertheCDPvaluesof airplanesoneachclusteraresignicantlydifferentfrome achother,orifitissimplyan abberation.Thisdistinctionismadethroughclusteringte chniques. Therearemanyclusteringtechniquesavailableinliteratu re.PatchaandPark [ 121 ]presentsanoverviewofanomalydetectiontechniquescurr entlypracticed. WuandZhang[ 122 ]performedanomalydetectionandclusteringtechniquesus ing factoranalysisfornetworkintuitionproblem.Wang[ 123 ]usekernel-basedclustering techniquestoidentifyoutliersforanautomobileapplicat ion.Ramos[ 124 ]used hierarchicalclusteringtechniquestoanalyzevariabilit yinrainfalldistributionpattern. Srivastava[ 125 ]discoveredrecurringanomaliesinaerospaceproblemusin ghigh 88

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dimensionalclusteringtechniques.AmodiedversionofHi erarchicalclusteringisused inthissection. InHierarchicalclustering,rstthepointsarearrangedas leavesofatree.All pointsarethenmergedintotheirownclusters.Whenthereis morethanonecluster, theclosestpairofclustersismergedtogether.Todetermin ethedistancebetweenthe clusters,theyusesinglelink,averagelinkorcompletelin kasdescribedinFigure D-1 InHierarchicalclustering,averagelinkisameanstojoinc lusters.AverageLinkis FigureD-1.ExplainingHierarchicalclusteringanddiffer entwaystocomputedistance betweenclusters usedasameansofdistinguishingbetweenclustersofCDPval uesinthissection.Two clustersofCDPvalueswouldbeseparatedfromeachotherbya break-offCDPvalue. Thebreak-offCDPvalueiscomputedsuchthatdistancebetwe enthemeanofclusters oneithersideofthebreakoffCDPvalueismaximum. Duringeachmaintenanceassessment,basedonthecurrentCD Pvalueofeach airplaneontheeet,abreak-offCDPvalueiscomputed.Airp laneswithCDPvalues greaterthanthebreak-offCDPvalue,willbeclassiedasle mons.Theaccuracyofsuch classicationisinvestigatedinthischapter. 89

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D.3ErrorQuantication Lemonsarerstcreatedinaeetofairplanessuchthattheyh aveahigherrateof crackgrowththannominalairplanes.Duringsimulationofa irplanelifecycle,anairplane isclassiedasalemonornominal,usingHierarchicalclust ering,basedonitsCDP valueatagivenmaintenanceassessment.Thedifferenttype soferrorthatcreepsup wheneveraclassicationissuchmade,isquantiedinthiss ection. Nullhypothesis:H 0:AirplaneisanominalairplaneAlternatehypothesis:H a: AirplaneisalemonTypeIerror( ):Rejectinganullhypothesiswhenitisactuallytrue. i.e.tocallanominalairplaneasalemon.TypeIIerror( ):Acceptinganullhypothesis whenitisafalse.i.e.tofailtodetectalemonwhenitisone. Theimmediatehistoryofanairplaneisconsideredbeforecl assifyingitasalemon. 4differentcasesofclassifyingalemonbasedonimmediateh istoryisconsidered. Anairplaneisclassiedaslemonifithasbeenclassiedasa lemonCase1:Atthat maintenanceassessmentCase2:inatleast10%ofits”immedi ate”pastmaintenance assessmentsCase3:inatleast25%ofits”immediate”pastma intenanceassessments Case4:inatleast75%ofits”immediate”pastmaintenanceas sessmentsThelast1000 cycles(10maintenanceassessments)isconsideredastheim mediatepast. D.4ModelingLemon Airplaneswithdeviantbehaviorthantherestoftheeet(le monairplane),are rstmodeledindifferentways.Thehighercrackgrowthrate forlemonsismodeledby increasingtheinitialcracksizeorthepressuredifferent ialactingoflemonairplanes.Itis notedhere,thattheincreaseininitialcracksizeortheinc reaseinpressuredifferentialis simplyamodelingaspect,andnotnecessarilyrepresentthe actualcase.Inreality,the fastercrackgrowthcouldbeattributedtodifferentmateri alofairplaneorenvironmental conditions. Thelifecycleoftheairplaneissimulatedandtheairplanes areclassiedas lemonornominalairplaneateachmaintenanceassessment.T heerrorinvolvedin 90

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wronglyclassifyinganominalairplaneoralemoniscompute dateachmaintenance assessment.Thevariationoftheerrorinclassicationwit hmaintenanceassessmentis plottedtondtheeffectivenessoftheclusteringtechniqu e. D.4.1ModelingLemonbyInitialCrackSize Lemonsarecreatedwithhigherinitialcracksizethanthere stoftheeet.In practice,thestringentnormsoninspection,beforetheair planeentersservice,wouldn't allowsuchdisparityininitialcracksizebetweenairplane s.Thehigherinitialawsize issimplytosimulatethefastercrackgrowthinlemons.Then ominaleetofairplanes haveainitialcracksize,distributedasLN(0.2,0.07)mm.I nthissection,thelemons aremodeledtodifferinthemeanoftheinitialcracksizesit uation.Threecasesof0.5 mmmean,0.4mmmeanand0.3mmmeanareconsideredforthelemo ns.Allother parametersremainconstantbetweennominalandlemonairpl anes. Aeetof200airplanesisconsidered.Eachairplanehas500p anels.10%of the200airplanesaremodeledlemons.Maintenanceassessme ntisperformedevery 100cycles.CDPvalueiscomputedforeachairplaneduringth osemaintenance assessments.BasedontheCDPvalueoftheeet,hierarchica lclusteringisused toclassifyeachairplaneasnominal/lemon.Figure D-2 plotsthevariationofTypeI andIIerrorswithmaintenanceassessments,forvariouscas esofimmediatehistory consideredtoclassifyalemonAsnotedinFigure D-2 ,whenthereisasignicant differencebetweenthecrackgrowthofnominalairplaneand lemonairplane,theerrorin classifyingthemaccuratelydiesdowntozeroataround10,0 00ightcycles,wellbefore thetimeofrstmaintenance.Airplanecompaniescouldbeab letomakeadecisionon thelemonairplane,veryearlyinitslifecycle. Ifthelemonandnominalairplanearenotsignicantlydiffe rent,therewillbesome errorremainingintheirclusteringoflemonandnominalair plane.Itisnotedthatthere isnoappreciableeffectofconsideringtheimmediatehisto ryinclassifyingalemon, 91

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FigureD-2.VariationofTypeIandIIerrorswithmaintenanc eassessments,forvarious casesofimmediatehistoryconsideredtoclassifyalemon concludingthatonceanairplaneisclassiedasalemon,itw asalwaysclassieda lemon.D.4.2ModelingLemonbyPressureDifferential Inthissection,thelemonsaremodeledbybeingactedonadif ferentpressure differentialthannominalairplanes.Nominalairplanesar eactedonapressure differential,withadistributionofLN(0.06,0.003)MPa.T helemonsaremodeled withahighermeanpressuredifferential.Twocasesofpress uredifferential,0.07 MPameanand0.08MPamean,wereconsideredforthelemons.Fi gure D-3 plots thevariationofTypeIandIIerrorswithmaintenanceassess ments,forvariouscases ofimmediatehistoryconsideredtoclassifyalemonAsseeni nFigure D-3 ,amean pressuredifferentialof0.08MPaforlemonscreatesasigni cantdifferencebetweenthe nominalandlemonairplanes,andtheallerrorsforthiscase vanishesataround30,000 ightcycles,i.e.aroundthehalfthelifeoftheairplane.F orlesssignicantdifference, thereremainsanerrorinclassifyingtheairplaneasnomina lorlemon.Itisnotedthat thereisnoappreciabledifferencebetweenconsideringimm ediatehistory.Itreiterates thatonceanairplanewasclassiedasalemon,italwayswas. 92

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FigureD-3.VariationofTypeIandIIerrorswithmaintenanc eassessments,forvarious casesofimmediatehistoryconsideredtoclassifyalemonba sedon differenceinpressuredifferential D.5Summary Continuoustrackingofdamagebyon-boardSHMsystemcouldh elpidentifythe airplanesthathavefastercrackgrowththantherestofthe eet,andhence,require morestructuralairframemaintenancevisitsthantheresto ftheeet.Amodied Hierarchicalclusteringmethodisusedtoidentifysuchano maliesinaeetofairplanes, usingcumulativenumberofdetectedpanelsasthemeasureto clustertheanomalies fromnominalones.Theanomaliesaremodeleddifferentfrom thenominaleetbased ontheirinitialcracksizeandpressuredifferential.Them odiedHierarchicalclustering identiestheanomalieswhenthereissignicantdifferenc ebetweentheanomaliesand therestoftheeetofairplanes. 93

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REFERENCES [1] “Iata,”11Feb2012. [2] B.BeralandH.Speckman,“Structuralhealthmonitoring(sh m)foraircraft structures:Achallengeforsystemdevelopersandaircraft manufacturers,”in StructuralHealthMonitoring ,F.-K.Chang,Ed.DEStechPublications,2003. [3] C.Boller,“Nextgenerationstructuralhealthmonitoringa nditsintegrationinto aircraftdesign,” InternationalJournalofSystemsScience ,vol.31,no.11,pp. 1333–1349,2000. [4] J.E.Mcbreaty,“Fatigueandfailsafeairframedesign,”Tec h.Rep.,SAE,1956. [5] K.Amer,“Anewphilosophyofstructuralreliability,fails afeversussafelife,”in AHS,AnnualForum,44th ,June1988,pp.3–16. [6] D.Broek,“Conceptsinfail-safedesignofaircraftstructu res,”Tech.Rep.,Defense metalsinformationcenter,1971. [7] F.QueslatiandS.Sankar,“Performanceofafail-safeactiv esuspensionwith limitedstatefeedbackforimprovedridequalityandreduce dpavementloadingin heavyvehicles,”in InternationalTruckandBusMeetingandExposition ,Nov1992. [8] D.G.BreeseandF.Gordaninejad,“Semi-active,fail-safem agneto-rhelogicaluid dampersformountainbicycles,” InternationalJournalofVehicleDesign ,vol.33, no.1,pp.128–138,2003. [9] P.Sun,J.Arora,andE.HaugJr,“Fail-safeoptimaldesignof structures,” EngineeringOptimization ,vol.2,pp.43–53,1976. [10] F.Moses,“Reliabilitybasedstructuraldesign,” StructuralDivision ,vol.96,no.2, pp.221–244,1970. [11] D.Broek,“Conceptsoffracturecontrolanddamagetoleranc eanalysis,”in ASM International ,1996,pp.410–419. [12] J.L.Rudd,“Airforcedamagetolerancedesignphilosophy,” in DamageTolerance ofMetallicStructures:AnalysisMethodsandApplications ,J.ChangandJ.Rudd, Eds.,ASTMSTP842,pp.134–141.AmericanSocietyforTestin gandMaterials, 1984. [13] N.C.Lind,“Ameasureofvulnerabilityanddamagetolerance ,” Reliability EngineeringandSystemSafety ,vol.48,no.1,pp.1–6,1995. [14] M.R.Artley,“Probabilisitcdamagetolerancemethodforme tallicaerospace structure,”Tech.Rep.,WrightResearchandDevelopmentCe nter,1989. 94

PAGE 95

[15] R.Lazzeri,“Acomparisonbetweensafe-life,damagetolera nceandprobabilisitic approachestoaircraftstructurefatiguedesign,” AerotecnicaMissileSpazio ,vol. 81,no.2,pp.53–64,2002. [16] M.AlamandC.Jenkins,“Damagetoleranceinnaturallycompl iantstructures,” InternationalJournalofDamageMechanics ,vol.14,no.4,2005. [17] D.Broek,“Failsafedesignprocedures,”Tech.Rep.,NATOAd visoryGroupfor AerospaceRD,1974. [18] P.M.Toor,“Areviewofsomedamagetolerancedesignapproac hesforaircraft structures,” EngineeringFractureMechanics ,vol.5,no.4,pp.837–876,1973. [19] T.Swift,“Developmentofthefail-safedesignfeaturesoft hedc-10,”in Damage ToleranceinAircraftStructures ,ASTMSTP486,pp.164–214.AmericanSociety forTestingandMaterials,1971. [20] M.J.GravesandP.A.Lagace,“Damagetoleranceofcomposite cylinders,” CompositeStructures ,vol.4,no.1,pp.75–91,1985. [21] S.G.Russell,W.Lin,H.-P.Kan,andR.B.Deo,“Damagetolera nceandfail-safety ofcompositesandwichpanels,”Tech.Rep.,SAETechnicalPa per,1994. [22] K.T.OBrien,“Towardsadamagetolerancephilosophyforcom positematerials andstructures,”in CompositeMaterials:TestingandDesign ,S.P.Garbo,Ed., vol.9of ASTMSTP1059 ,pp.7–33.AmericanSocietyforTestingandMaterials, 1990. [23] B.Hayman,“Approachestodamageassessmentanddamagetole rancefor frpsandwichstructures,” SandwichStructuresandMaterials ,vol.9,no.6,pp. 571–596,2007. [24] L.LazzeriandU.Mariani,“Applicationofdamagetolerance principlesto thedesignofhelicopters,” InternationalJournalofFatigue ,vol.31,no.6,pp. 1039–1045,2009. [25] U.Zerbst,K.Madler,andH.Hintze,“Fracturemechanicsinr ailwayapplicationsanoverview,” EngineeringFractureMechanics ,vol.72,no.2,pp.163–194,2005. [26] F.Mistree,T.Lyon,andJ.Shupe,“Designofdamagetolerant offshorestructures,” in Oceans82 ,Sep1982,pp.1201–1206. [27] C.C.Chamis,“Damagetoleranceandreliabilityofturbinee nginecomponents,”in RTOAVTWorkshop ,Oct1998. [28] X.ZhangandY.Li,“Damagetoleranceandfailsafetyofwelde daircraftwing panels,” AIAAJournal ,vol.43,no.7,pp.1613–1623,2005. 95

PAGE 96

[29] N.SalgadoandM.Aliabadi,“Anobjectorientedsystemforda magetolerance designofstiffenedpanels,” EngineeringAnalysiswithBoundaryElements ,vol.23, no.1,pp.21–34,1999. [30] M.Alibdai,P.Wen,andN.Salgado,“Boundaryelementanalys isfordamage toleranceassessmentofaircraftpanels,” InternationalJournalofComputer ApplicationsinTechnology ,vol.15,no.4,pp.147–156,2002. [31] R.G.EastinandJ.B.Mowery,“30yearsofdamagetolerance-h avewegotit right?,”in ICAF2009,BridgingtheGapbetweenTheoryandOperationalP ractice M.Bos,Ed.Springer,2009. [32] Y.SherifandM.Smith,“Optimalmaintenancemodelsforsyst emssubjectto failure-areview,” NavalResearchLogistics ,vol.28,no.1,pp.47–74,1981. [33] H.Wang,“Asurveyofmaintenancepoliciesofdeteriorating systems,” European JournalofOperationalResearch ,vol.139,no.3,pp.469–489,2002. [34] R.Bea,“Marinestructuralintegrityprograms,” MarineStructures ,vol.7,no.1,pp. 51–76,1994. [35] A.StyuartandK.Lin,“Maintenanceplanningforaircraftda magetolerance compositestructuresbasedonriskassessment,”in 48thSMDMConference 2007. [36] G.W.Breen,“Aircraftscheduledstructuralmaintenancepr ograms:Current philosophiesandmethodsinunitedstatesandtheirapplica bilitytoroyalaustralian airforce,”M.S.thesis,AirForceInstituteofTechnology, 1988. [37] S.-H.Baek,S.-S.Cho,H.-S.Kim,andW.-S.Joo,“Reliabilit ydesignofpreventive maintenanceschedulingforcumulativefatiguedamage,” MechanicalScienceand Technology ,vol.23,no.5,pp.1225–1233,2009. [38] S.Manning,J.Yang,F.Pretzer,andJ.Marler,“Reliability centeredmaintenance formetallicairframesbasedonstochasticcrackgrowthapp roach,”in Advancesin FatigueLifetimePredictiveTechniques ,M.MitchellandR.Landgraf,Eds.,ASTM STP1122,pp.422–434.AmericanSocietyforTestingandMate rials,1992. [39] S.leYang,D.M.Frangopol,andL.C.Neves,“Optimummaintne nacestrategy fordeterioratingbridgestructuresbasedonlifetimefunc tions,” Engineering Structures ,vol.28,no.2,pp.196–206,2006. [40] S.OkeandO.Charles-Owaba,“Anapproachforevaluatingpre ventive maintenanceschedulingcost,” InternationalJournalofQualityandReliability Management ,vol.23,no.7,pp.847–879,2006. [41] C.JingandW.Huawei,“Optimalmaintenanceofaircraftstru cturebasedon imperfectinspection,” NanjingUniversityofAeronauticsandAstronautics ,vol.4, 2009. 96

PAGE 97

[42] A.Brot,“Evalluatingstrategiesforminimizingfatiguefa iluresinmetallic structures,”in USAFAircraftStructuralIntegrityProgramConference ,Dec 2004. [43] N.M.OkashaandD.M.Fangopol,“Lifetime-orientedmulti-o bjectiveoptimization ofstructuralmaintenanceconsideringsystemreliability ,redundancyandlife-cycle costusingga,” StructuralSafety ,vol.31,no.6,pp.460–474,2009. [44] A.Akdeniz,“Aeroplanestructuralmaintenanceandcorrosi onprevention,” Aircraft EngineeringandAerospaceTechnology ,vol.68,no.3,pp.3–7,1996. [45] A.Ahmadi,P.Soderholm,andU.Kumar,“Anoverviewoftrends inaircraft maintenanceprogramdevelopment:past,presentandfuture ,”in EuropeanSafety andReliabilityConference ,2007,pp.2067–2076. [46] D.Hagemaier,“Inspectionofagingaircraft-amanufacture r'sperspective,”in InternationalConferenceonAgingAircraftandStructural Airworthiness ,Nov 1991,p.231. [47] U.G.Goranson,“Fatigueissuesinaircraftmaintenanceand repairs,” International JournalofFatigue ,vol.19,no.93,pp.3–21,1997. [48] R.SinghandC.Koenke,“Simulationframeworkforriskasses smentofdamage tolerantstructures,” ComputersandStructures ,vol.77,no.1,pp.101–115,2000. [49] N.Nechval,K.Nechval,M.Purgailis,andV.Strelchonok,“P lanninginspectionsin thecaseofdamagetoleranceapproachtoserviceoffatigued aircraftstructures,” InternationalJournalofPerformabilityEngineering ,vol.7,no.3,pp.279–290, 2011. [50] A.A.KaleandR.T.Haftka,“Trade-offofweightandinspecti oncostin reliability-basedstructuraloptimization,” JournalofAircraft ,vol.45,no.1,pp. 77–85,2008. [51] D.L.SimpsonandC.L.Brooks,“Tailoringthestructuralint egrityprocesstomeet thechallengesofagingaircraft,” InternationalJournalofFatigue ,vol.21,no.1,pp. 1–14,1999. [52] Y.-T.Tsai,K.-S.Wang,andL.-C.Tsai,“Astudyofavailabil ity-centeredpreventive maintenanceformulti-componentsystems,” ReliabilityEngineeringandSystem Safety ,vol.84,no.3,pp.261–270,2004. [53] F.M.Grimslev,J.W.Lincoln,andM.L.Zeigler,“Usafstrate gyforagingaircraft structuresresearchanddevelopment,”in RTOAVTSpecialists'Meeting ,Oct 2001. [54] A.Starr,“Astructuredapproachtotheselectionofconditi on-basedmaintenance,” in 5thInternationalConferenceonFACTORY2000 .TheTechnologyExploitation Process,1997. 97

PAGE 98

[55] A.K.Jardine,D.Lin,andD.Banjevic,“Areviewonmachinery diagnosticsand prognosticsimplementingcondition-basedmaintenance,” MechanicalSystems andSignalProcessing ,vol.20,no.7,pp.1483–1510,2006. [56] L.Dieulle,C.Berenguer,A.Grall,andM.Roussignol,“Sequ entialcondition-based maintenanceschedulingforadeterioratingsystem,” EuropeanJournalof OperationalResearch ,vol.150,no.2,pp.451–461,2003. [57] M.Marseguerra,E.Zio,andL.Podollini,“Condition-base dmaintenance optimizationbymeansofgeneticalgorithmsandmontecarlo simulation,” ReliabilityEngineeringandSystemSafety ,vol.77,no.2,pp.151–165,2002. [58] D.ChenandK.S.Trivedi,“Optimizationforcondition-base dmaintenancewith semi-markovdecisionprocess,” ReliabilityEngineeringandSystemSafety ,vol. 90,no.1,pp.25–29,2005. [59] A.Ghasemi,S.Yacout,andM.Ouali,“Optimalconditionbase dmaintenancewith imperfectinformationandtheproportionalhazardsmodel, ” InternationalJournal ofProductionResearch ,vol.45,no.4,pp.989–1012,2007. [60] B.Castanier,A.Grall,andC.Barenguer,“Acondition-base dmaintenancepolicy withnon-periodicinspectionsforatwo-unitseriessystem ,” ReliabilityEngineering andSystemSafety ,vol.87,no.1,pp.109–120,2005. [61] D.ChenandK.S.Trivedi,“Closed-formanalyticalresultsf orcondition-based maintenance,” ReliabilityEngineeringandSystemSafety ,vol.76,no.1,pp. 43–61,2002. [62] A.Grall,C.Berenguer,andL.Dieulle,“Aconditionbasedma intenancepolicyfor stochasticallydeterioratingsytems,” ReliabilityEngineeringandSystemSafety vol.76,no.2,pp.167–180,2002. [63] J.A.Hontelez,H.H.Burger,andD.J.Wijnmalen,“Optimumco ndition-based maintenancepoliciesfordeterioratingsystemswithparti alinformation,” Reliability EngineeringandSystemSafety ,vol.51,no.3,pp.267–274,1996. [64] C.Boller,F.Chang,andY.Fujino, Encyclopediaofstructuralhealthmonitoring Vol.1 ,WileyandSons,2009. [65] C.BollerandC.Biemans,“Structuralhealthmonitoringina ircraft-stateoftheart, perspectivesandbenets,”Tech.Rep.,TechnomicPublishi ngCoInc,1997. [66] E.Johnson,H.Lam,L.Katafygiotis,andJ.Beck,“Abenchmar kproblemfor structuralhealthmonitoringanddamagedetection,”in 3rdinternationalworkshop onStructuralcontrol ,2001. [67] C.Boller,“Waysandoptionsforaircraftstructuralhealth management,” Smart MaterialsandStructures ,vol.10,no.3,pp.432,2001. 98

PAGE 99

[68] V.Giurgiutiu,A.Zagrai,andJ.J.Bao,“Piezoelectricwafe rembeddedactive sensorsforagingaircraftstructuralhealthmonitoring,” StructuralHealthMonitoring ,vol.1,no.1,pp.41–61,2002. [69] M.FriswellandJ.Penny,“Crackmodelingforstructuralhea lthmonitoring,” StructuralHealthMonitoring ,vol.1,no.2,pp.139–148,2002. [70] J.-B.IhnandF.-K.Chang,“Pitch-catchactivesensingmeth odsinstructuralhealth monitoringforaircraftstructures,” StructuralHealthMonitoring ,vol.7,no.1,pp. 5–19,2008. [71] S.C.Galea,I.G.Powlesland,S.D.Moss,M.J.Konak,S.P.van derVelden,A.A. Baker,andB.Stade,Eds., Developmentofstructuralhealthmonitoringsystems forcompositeboundedrepairsonaircraftstructures ,vol.246of SPIE4327 ,2001. [72] H.Sohn,C.R.Farrar,andN.F.Hunter,“Structuralhealthmo nitoringusing statisticalpatternrecognitiontechniques,” DynamicSystemsMeasurementand Control ,vol.123,no.4,pp.706–711,2001. [73] H.Zhang,M.Schulz,A.Naser,F.Ferguson,andP.Pai,“Struc turalhealth monitoringusingtransmittancefunctions,” MechanicalSystemsandSignal Processing ,vol.13,no.5,pp.765–787,1999. [74] J.L.Rose,“Ultrasonicguidedwavesinstructuralhealthmo nitoring,” Key EngineeringMaterials ,vol.270,pp.14–21,2004. [75] H.Sekine,S.-E.Fujimoto,T.Okabe,N.Takeda,andT.Yokobo ri,“Structuralhealth monitoringofcrackedaircraftpanelsrepairedwithbonded patchesusingber bragggratingsensors,” AppliedCompositeMaterials ,vol.13,no.2,pp.87–98, 2006. [76] M.Vanik,J.Beck,andS.Au,“Bayesianprobabilisticapproa chtostructuralhealth monitoring,” EngineeringMechanics ,pp.738–745,2000. [77] A.A.Mufti,“Structuralhealthmonitoringofinnovativeca nadiancivilengineering structures,” StructuralHealthMonitoring ,vol.1,no.1,pp.89–103,2002. [78] I.Kang,M.J.Schulz,J.H.Kim,V.Shanov,andD.Shi,“Acarbo nnanotubestrain sensorforstructuralhealthmonitoring,” SmartMaterialsandStructures ,vol.15, no.3,pp.737–748,2006. [79] W.Baker,I.McKenzie,andR.Jones,“Developmentoflifeext ensionstrategiesfor australianmilitaryaircraft,usingstructuralhealthmon itoringofcompositerepairs andjoints,” CompositeStructures ,vol.66,no.1,pp.133–143,2004. [80] C.BollerandE.Al,“Fundamentalsofdamagemonitoring,”in SmartStructures andMaterials:ImplicationsforMilitaryAircraftofNewGe neration ,1996. 99

PAGE 100

[81] J.KoandY.Ni,“Technologydevelopmentsinstructuralheal thmonitoringoflarge scalebridges,” EngineeringStructures ,vol.27,no.12,pp.1715–1725,2005. [82] C.Sekine-Pettite,“Structuralhealthmonitoring,” Bridges ,vol.8,no.2,pp.36–38, 2005. [83] C.BollerandM.Buderath,“Fatigueinaerostructures-wher estructuralhealth monitoringcancontributetoacomplexsubject,” PhilosophicalTransactionsofThe RoyalSocietyA ,vol.365,no.1851,pp.561–587,2007. [84] H.vanderAueraerandB.Peeters,“Internationalresearchp rojectsonstructural healthmonitoring:Anoverview,” StructuralHealthMonitoring ,vol.2,no.4,pp. 341–358,2003. [85] S.J.Beard,A.Kumar,X.Qing,H.Chan,C.Zhang,andT.K.Ooi, “Practical issuesinreal-worldimplementationofstructuralhealthm onitoringsystems,”Tech. Rep.,AccelentTechnologiesInc,2005. [86] C.Boller,“Nextgenerationstructuralhealthmonitoringa nditsintegrationinto aircraftdesign,” InternationalJournalofSystemsScience ,vol.31,no.11,pp. 1333–1349,2000. [87] B.BeralandH.Speckman,“Structuralhealthmonitoringfor aircraftstructures:A challengeforsystemdevelopersandaircraftmanufacturer s,”in StructuralHealth Monitoring ,F.-K.Chang,Ed.,pp.12–29.DEStechPublications,2003. [88] M.DerrisoandS.Olson,“Thefutureofstructuralhealthmon itoringforairvehicle applications,”in StructuralHealthMonitoring ,F.-K.Chang,Ed.,pp.17–25. DEStechPublications,2005. [89] J.TelgkampandH.-J.Schmidt,“Benetsbytheapplicationo fstructuralhealth monitoringsystemsonciviltransportaircraft,”in StructuralHealthMonitoring F.-K.Chang,Ed.,pp.285–292.DEStechPublications,2003. [90] F.Romlay,H.Ouyang,A.Arifn,andN.Mohamed,“Modelingof fatiguecrack propagationusingdualboundaryelementmethodandgaussia nmontecarlo method,” EngineeringAnalysiswithBoundaryElements ,vol.34,no.3,pp. 297–305,2010. [91] C.E.Harris,J.C.NewmanJr,R.S.Piascik,andJ.H.StarnesJ r,“Analytical methodologyforpredictingthewidespreadfatiguedamagei nfuselagestructure,” in ProceedingsofFAA-NASASymposiumontheContinuedAirwort hinessof AircraftStructures ,C.A.BigelowandW.J.Hughes,Eds.,pp.63–88.National TechnicalInformationService,1996. 100

PAGE 101

[92] K.-F.Nilsson,“Elasto-plasticmodelsforinteractionbet weenmajorcrackand multiplesmalllcracks,”in ProceedingsofFAA-NASASymposiumontheContinuedAirworthinessofAircraftStructures ,C.A.BigelowandW.J.Hughes,Eds., pp.197–224.NationalTechnicalInformationService,1996 [93] L.MolentandS.A.Barter,“Acomparisonofcrackgrowthbeha viorinseveral full-scaleairframefatiguetests,” InternationalJournalofFatigue ,vol.29,no.6,pp. 1090–1099,2007. [94] S.Beden,S.Abdullah,andA.Arifn,“Reviewoffatiguecrac kpropagationmodels formetalliccomponents,” EuropeanJournalofScienticResearch ,vol.28,pp. 364–397,2009. [95] J.Mohanty,B.Verma,andP.Ray,“Predictionoffatiguecrac kgrowthandresidual lifeusinganexponentialmodel:Partii(mode-ioverloadin ducedretardation),” InternationalJournalofFatigue ,vol.31,no.3,pp.425–432,2009. [96] P.A.Scarf,“Ontheapplicationofmathematicalmodelsinma intenance,” EuropeanJournalofOperationalResearch ,vol.99,no.3,pp.493–506,1997. [97] P.ParisandF.Erdogan,“Acriticalanalysisofcrackpropag ationlaws,” Journalof BasicEngineering ,vol.85,no.4,pp.528–534,1963. [98] J.NewmanJr,E.Phillips,andM.Swain,“Fatiguelifepredic tionmethodology usingsmallcracktheory,” InternationalJournalofFatigue ,vol.21,no.2,pp. 109–119,1999. [99] S.KimandD.M.Frangopol,“Optimuminspectionplanningfor minimizingfatigue damagedetectiondelayofshiphullstructures,” InternationalJournalofFatigue vol.33,no.3,pp.448–459,2011. [100] P.Packman,H.Pearson,J.Owens,andG.Young,“Denitionof fatiguecracks throughnon-destructivetesting,” JournalofMaterials ,vol.4,pp.666–700,1969. [101] A.P.BerensandP.W.Hovey,“Evaluationofndereliabilityc haracterization,”Tech. Rep.,AirForceWrightAeronauticalLaboratory,1981. [102] H.Madsen,R.Torhaug,andE.Cramer,“Probabilitybasedcos tbenetanalysis offatigue,designandmaintenance,”in MarineStructuralInspection,Maintenance andMonitoringSymposium ,1991,pp.1–12. [103] Y.MoriandB.Ellingwood,“Maintainingreliabilityofconc retestructuresi:Roleof inspection/repair,” StructuralEngineering ,vol.120,no.3,pp.824–845,1994. [104] H.-Y.Chung,L.Manuel,andK.Frank,“Optimalinspectionsc hedulingofsteel bridgesusingnon-destructivetestingtechniques,” BridgeEngineering ,vol.11,no. 3,pp.305–319,2006. 101

PAGE 102

[105] A.Coppe,R.T.Haftka,N.H.Kim,andP.Ramu,“Optimizationo fdistribution parametersforestimatingprobabilityofcrackdetection, ” JournalofAircraft ,vol. 46,no.6,pp.2090–2097,2009. [106] B.Palmberg,A.Blom,andS.Eggwertz,“Probabilisticdamag etoleranceanalysis ofaircraftstructures,” ProbabilisticFractureMechanicsandReliability ,vol.10,pp. 275–291,1987. [107] L.Jaeger,C.Gogu,S.Segonds,andC.Bes,“Multidisciplina ryoptimizationunder uncertaintyforpreliminaryaircraftsizing,”in SAE2011AerotechCongress ,Oct 2011. [108] P.Goggin,J.Huang,E.White,andE.Haugse,“Challengesfor shmtransition tofutureaerospacesystems,”in StructuralHealthMonitoring ,F.-K.Chang,Ed. DEStechPublications,2003. [109] C.R.FarrarandK.Worden,“Anintroductiontostructuralhe althmonitoring,” PhilosophicalTransactionsofTheRoyalSocietyA ,vol.365,pp.303–315,2007. [110] R.Ikegami,“Structuralhealthmonitoring:Assessmentofa ircraftcustomerneeds,” in StructuralHealthMonitoring ,F.-K.Chang,Ed.DEStechPublications,2003. [111] L.M.Fitzwater,C.L.Davis,T.Torng,andJ.Poblete,“Cost/ benetanalysis forintegrationofnon-deterministicanalysisandinsitum onitoringforstructural integrity,”Tech.Rep.,USAFCBM+initiativeAFLMAReport, 2003. [112] U.A.G.Inc.,“Form10-k,”Tech.Rep.,UnitedStatesSecurit iesandExchange Commission,2011. [113] W.CrichlowandA.McCulloch,“Anengineeringevaluationof methodsforthe predictionoffatiguelifeinairframestructures,”Tech.R ep.,FlightDynamics Laboratory,1962. [114] S.Engel,B.Gilmartin,K.Bongort,andA.Hess,“Prognostic s,therealissues involvedwithpredictingliferemaining,”in AerospaceConferenceProceedings IEEE,2000. [115] E.KellerandA.Ray,“Real-timenondestuctiveevaluationo fairframestructuresfor healthmonitoringandresiduallifeprediction,”in DigitalAvionicsSystems .DASC, 2001. [116] D.HoeppnerandW.Krupp,“Predictionofcomponentlifebyap plicationoffatigue crackgrowthknowledge,” EngineeringFractureMechanics ,vol.6,no.1,pp. 47–62,1974. [117] A.Coppe,R.Haftka,andN.-H.Kim,“Uncertaintyidenticat ionofdamagegrowth parametersusingnon-linearregression,” AIAA ,vol.49,no.12,pp.2818–2821, 2011. 102

PAGE 103

[118] J.M.Gaillardon,H.-J.Schmidt,andB.Brandecker,“Ageing airplanerepair assessmentprogramforairbusa300,”in InternationalConferenceonAgeing AircraftandStructuralAirworthiness ,Nov1991,p.283. [119] A.K.Kundu, AircraftDesign ,CambridgeUniversityPress,2010. [120] “Cfminternational,makersofcfm56family,”11Feb2012. [121] A.PatchaandJ.-M.Park,“Anoverviewofanomalydetectiont echniques:Existing solutionsandlatesttechnologicaltrends,” ComputerNetworks ,vol.51,no.12,pp. 3448–3470,2007. [122] N.WuandJ.Zhang,“Factor-analysisbasedanomalydetectio nandclustering,” DecisionSupportSystem ,vol.42,no.1,pp.375–389,2006. [123] C.-H.Wang,“Outlieridenticationandmarketsegmentatio nusingkernel-based clusteringtechniques,” ExpertSystemswithApplications ,vol.36,no.2,pp. 3744–3750,2009. [124] M.Ramos,“Divisiveandhierarchicalclusteringtechnique stoanalysevariability ofrainfalldistributionpatternsinamediterraneanregio n,” AtmosphericResearch vol.57,no.2,pp.123–138,2001. [125] A.Srivastava,“Enablingthediscoveryofrecurringanomal iesinaerospace problemusinghigh-dimensionalclusteringtechniques,”i n AerospaceConference Proceedings .IEEE,2006. 103

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BIOGRAPHICALSKETCH SriramPattabhiramanwasborninTiruchirappalli,India,i n1985.Hecompletedhis Bachelors(B.Tech)inMechanicalEngineeringattheNation alInstituteofTechnology, Tiruchirappalli(NIT-T)in2007.HemovedtoUnitedStatesi nAugust2007tojointhe MultidisciplinaryOptimizationGroupintheDepartmentof MechanicalandAerospace EngineeringattheUniversityofFlorida.Heenrolledintot hedirect-PhDprogram,and graduatedwithaPhDinMay2012,workingwithProf.NamHoKim andProf.RaphaelT. Haftka 104