Survivability Assessment Method of Spacecraft at the Threat of Space Debris.doc

Survivability Assessment Method of Spacecraft at the Threat of Space DebrisJournalofSystemsScienceandInformation2006,Vo1.4,No.2,PP.203-213PublishedbyResearchInformationLtd(RIL),UKSurvivabilityAssessmentMethodofSpacecraftattheThreatofSpaceDebrisYangPei,BifengSong,QingHanCollegeofAeronautics,NorthwesternPolytechnicalUniversity,Xian710072,China(ReceivedNovember30,2004)Abstract:Thethreatofspacedebronspacecrafthasincreasedourattentiontothesurvivabilityenhancementdesignofspacecraft.Thispaperstudiesthesurvivabilityassessmentmethod,whichhasmainlytwoparts,namelysusceptibilityassessmentandvul-nerabilityassessment.Ouremphasisfocusesonhowtoassessthevulnerabilityofspacecrafttospacedebris.Thebasicvulnerabilityassessmentprocessincludes:(1)theanalysesofthethreatenvironmentofspacedebris;(2)theprocessofidentificationofcriticalcompo-nentsofspacecraft,inwhichaDMECA(damagemode,effects,andcriticalityanalysis)isintroducedandanexpesystemisproposedtogetthedamageratioofeachcomponent;(3)thespacecraftgeometricaldescriptionmethod,inwhich"shotlinescanningmethod"isdescribedtocalculatetheprojected/overlappingareaofcomponentsanddeterminethemasking/shieldingrelationshipamongcomponents;(4)thecalculationofspacecraftkillprobabilityandvulnerablearea.Atlast,theauthorsconcludethattheproposedassess-mentmethodissystemicandfeasible,anditca31giveaquantitativeassessmentresultofsurvivability/vulnerabilityinthespacecraftconceptualdesign.Thetheorycontainedinthispaperisusefultodevelopcomputerizedtoolforspacecraftsurvivabilityanalysis.Keywords:spacecraft;survivability;vulnerability;spacedebris;probability1.IntroductionEveryspacecraftinorbitissubjectedtoseveraltypesofenvironmentalhazardssuchasneu.tralatmosphere,thermal,plasma,meteoroids,orbitaldebris,solaractivity,ionizingradiation,andSOonI-3.Meteoroidsarecreatedfromthebreakupofasteroidsandcomets.OrbitalThisprojectissupportedbyNationalNaturalScienceFoundationofChina(10372082);theAerospaceScienceFoundation(02B53008);andtheDoctorateFoundationofNorthwesternPolytechnicalUniversity(CX200301)204JournalofSystemsScienceandInformationVo1.4No.2debrisisaby-productofmansactivitiesinspace,andconsistsofobjectsranginginsizefromapieceofpaintthathasflakedoffofarocketoraspacecrafttofragmentsofanexplodedrocketupperstagetoanentirederelictspacecraft.ManmadeorbitaldebrisparticlesinlOWearthorbitincreaseatarateofupto5%peryear引.Addedtothenaturallyoccurringme-teoroidenvironment,thisparticulateenvironmenthasbecomeaformidablespacecraftdesignchallenge.Inordertoaccomplishmissionandsurvivethespacedebrisenvironment,spacecraftmusthavetheabilitytowithstandthehypervelocityimpact.So,Survivabilitybecomesanimportantconcernofspacecraftdesign.Despiteseveralsurvivabilityassessmentmethodhasbeenproposed4-6,anacceptedmethodofanalysishasnotbeendeveloped7.Theaircraftcommunityhasexpendedagreatamountofeffortoverthelastyearstodevelopacoordinatedsurvivabilitymethodology.Reference7hasintroducedanotionalconceptofhowtoadaptawell-developedaircraftsurvivabilityanalysismethodforuseonspacecraft.Thispaperpro-posesasystematicsurvivabilityassessmentmethodandmayberegardedastheextensionofthemethodologyinreference7.2.SpacecraftSurvivabilityAssessmentForspacedebristhreat,spacecraftsurvivabilityisdefinedhereasthecapabilityofaspacecrafttoavoidbeinghitbydebrisorwithstandthedebrisenvironmentwithoutsufferinganabortiveimpairmentofitsabilitytoaccomplishitsdesignatedmission.SurvivabilityCanbemeasuredbytheprobabilityofsurvivabilityPs.Survivabilityiscomposedoftwofocusareas:1)suscep-tibility;2)vulnerability.SusceptibilityreferstotheinabilityofaspacecrafttoavoidbeinghitbyspacedebrisandCanbeexpressedastheprobabilityofhitPH.VulnerabilityreferstotheinabilityofaspacecrafttowithstandthedamageafterbeinghitbyspacedebrisandCanbeexpressedastheconditionalprobabilityofkillgivenahitr/日.TheprobabilityofkillofthespacecraftPK(thespacecraftSkillability)istheproductoftheprobabilityofhit(thespace-craftSsusceptibility)PHandtheconditionalprobabilityofkillgivenahit(thespacecraftSvulnerability,PKfH.ThusS,91,PK=PHPK/H(1)TheprobabilityPsisthecomplementofPK.Hence,Ps=1一(2)3.SusceptibilityAssessmentThepurposeofspacecraftsusceptibilityassessmentistodeterminetheprobabilityPHthatspacecraftwillcollidewithspacedebris.First,PHdependsonthespacedebrisenvironmentsincludingthesize,mass,spatialdensityandthree-dimensionalvelocitydistributionofdebris.PeiY.eta1.SurvivabilityAssessmentMethodofSpacecraftattheThrt.205Second,isrelatedtothephysicalcharacteristicsandorbitofspacecraft.ThemostobviousfactisthatPHisproportionaltothesectionalareaandorbitaldurationofspacecraft.Atthesametime.PHisrelatedtosomeorbitalparameterssuchasorbitalobliquity,semi-longaxes,eccentricity,andSOon.SpaceDebrisMitigationHand-bookcompiledbyESAgivesthesatelliteprobabilityofhitbyspacedebrisasfollows.Assumingthemovementofdebrisfollowsarandomprobabilitydistribution,accordingtogaskinematicstheoryandthePoissondistribution,PHisexpressedas101PH=1一exp(一.AcDDAt)(3)where,istherelativevelocityofsatellitetospacedebris;AcDistheaveragesatellitecollisionsectionalarea(m2);Distheaveragedebrisspatialdensityinsatelliteorbit(particles/m);Atisthedurationofsatelliteindebrisenvironments.Aftercalculation,reference【11JpointsoutthaltnOmatterwhateverorbitthesatelliteis,thesatelliteprobabilityofhitbydebrislargerthan1amisverysmall,thatmeansonlyahitOCCurSinseveralmillionyearsorevenseveral10millionyears;butthesatelliteprobabilityofhitbydebrislargerthan0.1cm.mostofwhicharesubmillimeterdebris.iSapparentlyincreased.VulnerabilityAssessmentMethodVulnerabilityistheimportantindexofspacecraftsurvivabilitydesign.Themorevulnerableaspacecraftis,themorelikelyitwillbekilledwhenhitbyspacedebris.Figure1showstheflowchartofspacecraftvulnerabilityanalysis.Fig.1VulnerabilityanalysisflowchartFig.2Basicstepsofcriticalcomponentsidentification4.1.ThreatCharacteristicAnalysisTheeffectsofspacedebrisonspacecraftdependonthesize,maSS,velocityandimpacting206JournalofSystemsScienceandInformationVl01.4No.2obliquity.Spacedebriscouldbedividedintothreediametercategories.(1)Diameterlessthan0.01cm.Thiskindofdebriscouldproducecraterorcontaminantsonthespacecraftsurfaces.Thedebrisislargeinamountandcouldresultinobviouscumulativedamageinspacecraftafterlongtimecollisionwithspacecraft.(2)Diameterbetween0.01cmand1am.Thiskindofdebriscouldcausesignificantlycumulativedamageinspacecraftandtheamountofdamageitdoesdependsonthedamage-worthinessandprotectionmethodsofspacecraft.(3)Diameterlargerthanlcm:Thiskindofdebriscouldproducecatastrophicdamageinspacecraft.Atpresent,protectionmethodsusedinspacecraftonlywithstandthedamageproducedbydebriswithdiameterlessthan0.01cmandmasslessthan1.46g.Debrisobjectslargerthanlcmmustbeavoidedbypropulsivemaneuvers.4.2.CriticalComponentsIdentificationMethodFigure2showstheprocessofidentificationofthecriticalcomponents.(1)Selectingthespacecraftkillleve1.Identificationofthecriticalcomponentsisrelatedtotheselectionofthekillleve1.AccordingtoMILSTD一882D31.therearefoursuggestedcategoriesofmishapseverity(wechoosethemasthekilllevelsofspacecraft).CategoryI:catastrophic;categoryII:critical;categoryIII:marginal;categoryIV:negligible.(2)Determiningtheflightandmissionessentialfunctions.Flightessentialfunctionsarethosesystemandsubsystemflmctionsrequiredtoenableaspacecrafttosustaincontrolledflight.Missionessentialfunctionsarethosesystemandsubsystemfunctionsrequiredtoenableaspacecrafttoperformitsdesignatedmission.Theanalysisfortheessentialfunctionsshouldconsidereachphaseofthemission.Forexample,atypicalmissionforaspacecraftcouldincludesuchphasesasbefore-launching,propelling,orbitaloperating,returning,andlanding.(3)Determiningthesystemandsubsystemfunctionsthatcontributetotheessentialfunctions.Theabilityofthespacecrafttoflyandtoconductitsmissiondependsuponthecontinuedoperationofthosesystemsthatprovideorcontributetotheflightandmissionessentialfunc-tions.Ageneralexaminationofeachsystemandsubsystemonthespacecraftmustbeconductedtodetermineitsspecificcontributiontotheessentialfunctionsidentifiedintheprecedingpro-cessforeachphaseofthemission.Thebasicsystemsofspacecraftincludesuchsystemsasstructure,energy,movementcontrol,heatcontrol,tracking,remoteorbiting,remotecontrol,programmingcontrol,andsoon.(4)Conductingadamagemodeandeffectsanalysis(DMEA).ThroughaccomplishingaDMEA,wecanknowtherelationshipofdamagemodesofeverycomponent/subsystemandtheessentialfunctions.TheitemsinDMEAworksheetaresomewhatliketheitemsinFMEA141(Failuremodeandeffectsanalysis)worksheet(seeFigure3).ThemaindifferenceliesinthedamagemodeinDMEAandthefailuremode,whichisoftenidentifiedinreliabilityanalysis,inFMEA.Failurereferstothemalfunctionofproduct/componentinthenormalenvironment.ButdamageinsurvivabilityreferstothekillofthecomponentwhenthethreatspacedebrishitsPeiY.eta1.SurvivabilityAssessmentMethodofSpacecraftattheThreat207spacecraft.Spacedebrisposestheobvioushazardofpenetratingspacecraftsurfaces,producingdamagetoexternalandinternalequipment,decompressingpressurizedvolumes,andgeneratingplasmapulsesthatCancausearcingandburnoutofelectricalandelectroniccomponents.ig.3ItemsinDMEAworksheet(5)Performingdamagemode,effects,andcriticalityanalysisfDMECA).CriticalityAnalysis(CA)referstotheestimationofeverydamagemodeofcomponentSOastoevaluatethedamageeffectsonspacecraft.ThecombinationoftheDMEAandCAisthedamagemode,effects,andcriticalityanalysis(DMECA).DMECACanbequalitativeand/orquantitative.Whenthedamagerateandconfigurationdataofcomponentisunknown,qualitativemethodCanbeused;otherwise,criticalitynumberCanbecalculatedandthusquantitativemethodCanbeadopted.1)QualitativemethodWesuggestthefollowingfivelevelsofdamageprobabilityofoccurrencereferringtothefivelevelsoffailureprobabilityofoccurrenceinFMECAM】:levelA(Frequent),levelB(Probable),levelC(Occasiona1),levelD(Remote),andlevelE(Improbable).2)QuantitativemethodsThepurposeofquantitativeDMECAofcomponentistocalculatethecriticalitynumberCrgivenaparticularkillleve1.ThecriticalitynumberCforacomponentisthenumberofdamagesexpectedforagiventimeduetothecomponentSdamagemodesunderaparticularkillleve1.isgivenbytheexpression】:n=0.岛?tj=1where,nisthenumberofdamagemodesunderthesainekillleve1.isthecomponentdamageratio.(4)JournofSyStemsScienceandInformationV_01.4N0.2ble1ThevaluesDamageeffectActualloSSProbablelossPossiblelossNoeffectfvalues1.00.11.00.00.10.0isdamagemoderatioortheprobability,expressedasadecimalfraction,thatthecomponentwillbekilledintheidentifiedmodej.8jistheconditionalprobabilityofmissionlossgiventhatthedamagemodejhasoccurred.ThesuggestedvaluecanbefoundinTable1.isthedurationofapplicablemissionphaseusuallyexpressinhoursornumberofoperatingcycles.(6)Drawingthecriticalitymatrix.Thecriticalitymatrixprovidesameansofidentifyingandcomparingeachdamagemodetoallotherdamagemodeswithrespecttokilllevels.Theresultingmatrixdisplayshowsthedistributionofcriticalityofcomponentdamagemodesandprovidesatoolforassigningcorrectiveactionpriorities.Thematrixisconstructedbyinsert-ingdamagemodeidentificationnumbersinma-trixlocationsrepresentingthekilllevelinthehorizontalaxisandeithertheprobabilityofOC-currencelevelorthecriticalitynumber()forthecomponentSdamagemodesintheverticalaxis.AsshowninFigure4.thefurtheralongIncre,amgCriticalityBI./I/Fig.4Exampleofcriticalitymatrixthediagonallinefromtheoriginthedamagemodeisprojected,thegreaterthecriticalityandthemoreurgenttheneedforimplementingcorrectiveaction?TheexampleinFigure4showsthattheprojectionlengthOBislongerthantheprojectionlengthOA,80thecriticalityofdamagemodeBismorecritica1thanthecriticalityofdamagemodeA.4.3?GettingtheDamageRatioofEachComponentTheequation(4)iscalculatedassumingthatInfact,thedamageratioofeachcomponentthedamageratioofeachcomponentisknownfirst.isdependentonthelivefiretestofcomponentsorthegatheringofdamagedata.Sincethevulnerabilitytestisveryexpensiveandthedamagedataislimited,thedamageratioofeachcomponentisverydifficulttoget.Weintr0duceanexpertsystemusingtherelevancematrixevaluatedmethodstosolvetheproblemofgettingthedamageratioofeachcomponent.Invitingsomeexpertstofillintheexpertanalysistable,whichconsidersmanyfactorssuchasthecomponentssizes,shieldingandcomplexitythataffectthedamageratio,wecangettherelativevalueofdamageratioofeachcomponent.LetAI,A2-.?,Ambemcomponentsofspacecraft;,.,%bethe扎ftorswhic王laffectsthedamageratioofeachcomponent;,.,betheweightofeverytorwhichBCDE_I9毒,Ioo矗.IJlIoo(v言每oJPeiY.eta1.SurvivabilityAssessmentMethodofSpacecraftattheThreat209canbedeterminedinreference15;Ykobetheevaluatedvalueofcomponentiwhithrespecttofactorxjinthekthexperttable;J)塘betheevaluatedvalueofcomponentiwhichcanbecalculatedinTable2.Table2ThekthexperttableA1ii121Dlk=W1Vk11+W2Vk12+Vk1A221222J2D2W1Vk21+Vk22+Vk2礼:A竹1m1m2JmnD竹1k=厂1Vk竹11+厂2Vk2+竹1canbedeterminedusingthefollowingrule.Giventhefactor,wecanrankthecomponentbasedon1-10scaleaccordingtothedamageratiovalues.Thecomponentwiththemaximumdamageratiovaluecanberanked10;thecomponentwiththeminimumdamageratiovaluecanberanked1.Basedonexpertanalysistable,damageratiovalue入肌ofcomponentAiisexpressedas入m=D=iqwhere,J)i=Dik,Dmax=max(Di),qisthenumberofexperttable=1(5)4.4.SpacecraftGeometricDescriptionThemasking/shieldingrelationshipamongcomponentsofspacecraftexistsinthepossiblethreataspectsofspacedebris.Forthepurposeofprotection,itisnecessarytoprovidethegeometricdescriptionforvulnerabilityassessment,namelycalculatingtheprojectedareas/overlappingareasofcomponentsanddeterminingthemaskingorpartialmaskingrelationshipamongcomponents.Basedonfiniteelementsmodelofspacecraft,Figure5showsthegeometricdescriptionflowchartofanalgorithmcalledshotlinescanningmethod【,引.Thepreparationoftheorig-inalmodelofthealgorithmisbuiltinsomefiniteelementsoftwaresuchasMSC/PATRANorNASTRAN.Thealgorithmsuperimposesaplanargridwithchangeablegridcellsizeovereachcomponentandgeneratesashotlineineachgridcel1.Thecoordinatesofintersectionpointofshotlineandeachquadrilateralfiniteelementintheoverlappingareaarerecordedtodeterminethemasking/shieldingforcomponents.Throughscanningthecomponentssurfacesfromshotline1toshotlineN,thenumberofgridcellsonthecomponentiscountedandmultipliedbythegridcellareatodetermineitspresentedareaandoverlappingarea.210JournalofSystemsScienceandInformationVo1.4No.2lBuildingthefiniteelementm.del1上rlConstmclingprojected咄蛐柚dgDeletingDacw删sIInacetotprotrumngpolynlron一厂SupdmrposinggridonspacecraftandproducingNshotliness=lJ:一一n0一Intrsect/oncalculationofshotlineandquadriIaIfinitedement,cumulatingthepresented/over?