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1、MCM2015SummarySheetfTeam35565FofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber35565ProblemChosenBFofficeuseonlyF1________________F2________________F3________________F
2、4________________SummaryThelostMH370urgesustobuildauniversalsearchplantoassistsearcherstolocatethelostplaneefficientlyoptimizethearrangementofsearchplans.Fthelocationofthesearchareawedivideditintotwostagesrespectivelytol
3、ocatethesplashpointthewreckage’ssunkpoint.Inthefirststageweconsiderthetypesofcrashedaircraftitsmotiondifferentpositionoutofcontact.WealsoconsidertheEarth’srotationotherfacts.Takingalltheseintoaccountweestablishamodeltolo
4、catethesplashpoint.ThenweapplythismodeltoMH370.wecangetthesplashpointintheopenwateris6.813N103.49Ethefallingtimeis52.4s.Inthesecondstageconsideringresistancesofthewreckageindifferentshapesitsdistributionaffectedbyoceancu
5、rrentsweestablishawreckagesunkpointmodeltocalculatethehizontaldisplacementtheangledeviationaffectedbytheoceancurrents.Theresultis1517m0.11respectively.NextweextractasatellitemapofsubmarinetopographyuseMATLABtodepictseabe
6、dtopographymapdeterminingthesettlementofthewreckagebyusingdichotomyalgithmunderdifferentterrains.FinallywebuildaBayesianmodelcalculatetheweightofcrespondingareasendingaircraftstoobtainnewevidencerefreshsuspectedwreckagea
7、rea.Ftheassignmentofthesearchplaneswedivideitintotwostagesrespectivelytodeterminethenumberoftheaircrafttheassignmentschemeofthesearchaircraft.Inthefirststageweconsiderthesearchabilityofeachplaneotherfacts.thenweestablish
8、globaloptimizationmodel.NextweuseDinkelbachalgithmtothebestnsearchaircraftsfromallsearchaircrafts.Inthesecondstagewedividetheassignmentintotwocaseswhethertherearesearchaircraftsinthetargetarea.Ifthereisnosearchaircraftwe
9、takethesearchareaasanarbitrarypolygonestablishthesubdivisionmodel.Consideringthesearchingabilityofeachplanewedividensmallpolygonsinto2nsubpolygonsbyusingNonconvexDividealgithmwhichassignsspecificanchpointstothese2nsubpol
10、ygonsrespectively.Ifthereexistsearchaircraftswedividethesearchareaintoseveralpolygonswiththesearchaircraftsbeingattheboundaryofthesmallpolygons.Toimprovesearchefficiencyweintroduce”maximizetheminimumanglestrategy”tomaxim
11、izerightanglesubdivisionsothatwecanreducetheturningtimesofsearchaircraft.Whenwechangedthespeedofthecrashedplaneabout36msthelatitudeofthesplashpointchangesabout1.Whenawrecklingat5.888moutfromtheinitialzoneitwilldivcefroms
12、uspectedsearchingareawhichmeansourmodelsarefairlyrobusttothechangesinparameters.Ourmodelisabletoefficientlydealwithexistingdatamodifysomeparametersbasingthepracticalsituation.Themodelhasbetterversatilitystability.Theweak
13、nessofourmodelisneglectofhumanfactsthesearchtimeotheruncontrollablefactsthatcouldleadtodeviationcomparedtopracticaldata.Therefewemakesomeindepthdiscussionsaboutthemodelmodifyingassumptionsestablishmentabovetooptimizeourm
14、odel.Team#35565Page3of53Contents1Introduction.............................................................................................................................................51.1RestatementoftheProblem…………………
15、…………………….................................….51.2LiteratureReview……………………………………………………………………..…...…...62AssumptionsJustifications..............................................................................................
16、.....73Notations………………………………………………………………………………………………….74ModelOverview……………...............................................................................................................105ModelingFLocatingtheLostPlane...
17、...............................................................................105.1ModelingFLocatingtheSplashPoint………………………………….115.1.1TypesofPlanes………………………………………………...…115.1.2PreparationoftheModel—EarthRotation……………….
18、..….....125.1.3Modeling……………………………………………………….....135.1.4SolutionofTheModel…………………………………………....145.2ModelingFLocatingWreckage………………………………………...155.2.1AssumptionsoftheModel………………………………………..165.2.2PreparationoftheModel……………
19、…………………………….165.2.3Modeling…………………………………………………………..215.2.4SolutionoftheModel……………………………………………..255.3VerificationoftheModel……………………………………..……………265.3.1VerificationoftheSplashPoint……………………………….…..265.3.2Verificationofthebi
20、narysearchalgithm………………………..276ModelingFOptimizationofSearchPlan……………………………...……296.1TheGlobalOptimizationModel…………………………………………...296.1.1PreparationoftheModel…………………………………………..296.1.2Modeling……………………………………………………….….316.1
21、.3SolutionoftheModel……………………………………..……….316.2TheAreaPartitionAlgithm……………………….…………….…………..……...……336.2.1PreparationoftheModel……………………….………………….336.2.2Modeling………………………………………………………..…346.2.3SolutionoftheModel…………………………………
22、…….…….356.2.4ImprovementoftheModel……………………………..…………367SensitivityAnalysis……………………………………………………………..388FurtherDiscussions……………………………………………………………..399StrengthsWeaknesses………………………………………………..…….419.1Strengths……………………………………………
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