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Missing Aircraft Type Comparison - Cumulative Success Probability747 CrashCessna 172 CrashPage31of35
10.90.80.7Probability0.60.50.40.30.20.102468Search Day101214161820Figure28:ComparisonofSearchforSmallandLargeMissingAircraft.
Thisplotshowsapotentiallysurprisingresultofourmodel:itismorelikelythatasearchwillresultinthe?ndingofasmallaircraft,suchasaCessna172,thanalargeaircraft,suchasaBoeing747.Thoughthee?ectivenessparameterfortheBoeingsearchislargerthanthatoftheCessnasearch,thesearchareafortheCessnaismuchsmallerthanthesearchareafortheBoeing,duetothelowercruisingaltitudeandlowerlifttodragratio.Thisshowsthatwhilethee?ectivenessparameterdoesin?uencetheprobabilityofsuccessofasearch,theinitialconditionsofthesearcharealsoimportantwhenconsideringtheoverallprobabilityofsuccess.Itisalsoimportanttonotethatthevaluesforthee?ectivenessparametersusedinthesesimulationswereentirelyhypothetical.Tomodelthismoreaccurately,abetterestimateofthee?ectivenessparameterwouldbeneeded.
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4
4.1
FinalRemarks
StrengthsandWeaknesses
Ourmodelisaprobabilisticapproachtodesignatinglikelylocationsforadownedaircraftaswellasanattempttooptimizesearchpatternsandsearchregionsinlightofphysicalcon-straints.Thismodelwaspurposefullydesignedwiththeintentionofbeingeasilycustomiz-ableandapplicabletoavarietyofscenarios.Thisintentionaluseofmodularprogrammingandgeneralizationleadstoasetofstrengthsandweaknessoftheoverallmodel.Strengths:
?Theinitialprobabilitydistributioncanbeeasilyvariedbasedonthepropertiesofthemissingaircraft.
?Di?erenttypes,numbers,ande?ectivenessofsearchaircraftcanbeeasilyconsidered.?Di?erenttypesofmissingaircraftcanbeeasilyconsidered.
?Theglobaloptimumsearchlocationandsize/shapeisfoundforthesquareandrect-angularsearchmodels.
?Ourmodelcanbepracticallyimplementedinthe?eld.Byvaryingtheinitialparam-etersbasedonthespeci?ccase,optimalsearchpathscanbedetermined.Weaknesses:
?Theoptimizationfortherectangleiscomputationallyintensive.?Theoctagonalsectorsearchmethodisnotgloballyoptimized.
?Themodelreliesonmanyassumptions.Inordertomodelarealworldscenario,theseassumptionswouldneedtoberemovedandincorporatedintothemodel.
?Wedonotconsiderthecost-e?ectivenessofthesearch.Weonlymodelan“all-out”searche?ort.
4.2FutureModelDevelopment
Asdiscussedintheprevioussection,manyoftheissuesarisingfromsuchageneralizedsimulationisthatthemoreuniquefactorsofthescenarioareoverlooked.Also,manyoftheassumptionsofthemodelarenotrealistic.Inthefuture,wewouldfurtherdevelopthemodelinthefollowingways:
?Furtherexploretheoptimizationofsearchingwithmanydi?erentplanesanddi?erentpatternssimultaneously.
?Determinemorerealisticvaluesforcertainsearchparameters,suchasthee?ectivenessparameter.
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?Consideraprobability-of-successtocostratiosothatthesearchcanbe?nanciallylimitedwhenitisappropriate.
?Considertheplane/debrissinkingandunderwatersearche?orts.?Accountforweatherandoceancurrents.
?Reworktheoptimizationalgorithmssothattheyaremorecomputationallye?cient.?Considermultiplesearchandrescuestaginglocations,aswellasmid-airrefuelingforthesearchaircraft.
4.3Conclusions
Wemodeledthedisappearanceofanaircraftoverwaterbydividingtheproblemintoparts:theinitialprobabilitymodelandthesearchmodels.Todeveloptheinitialprobabilitymodel,weconsideredthetypeofaircraftthatdisappearedandthelikelihoodofdi?erentcrashtra-jectories.Wedevelopedfourseparatemodelsforaircraftsearchpatternsbasedoncommonlyusedsearchtechniques.WethenusedBayesianSearchTheorytocalculateandoptimizetheprobabilityofasuccessfulsearchforeachofthedi?erentsearchpaths,updatingourproba-bilitydistributioncontinuallyasareasweresearchedandnoaircraftwasfound.Finally,wetestedvariationsofourmodels,includingcombinationsofsearchpatterns,multiplesearchaircraft,moree?ectivesearchaircraft,anddi?erenttypesoffailuresthatwouldcauseloss-of-signal.Overall,ourmodelshowedthattooptimizethesearch,squareandrectangularparallel-sweepsearchpatternsshouldbeusedbecausetheymoste?cientlycoveranareaandleavetheun-searchedareasreadytobesearchedbysimilarpatternsonfuturedays.
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References
[1]“AirFrance447-FinalReport.”(n.d.):n.pag.BEA,July2012.Web.8Feb.2015.[2]‘’MissingMalaysiaPlane:WhatWeKnow.”BBCNews.BBC,30Jan.2015.Web.02
Feb.2015.[3]Anderson,JohnDavid.IntroductiontoFlight.NewYork:McGraw-Hill,1985.Print.[4]“747Family.”Boeing:747FunFacts.Boeing,n.d.Web.08Feb.2015.
[5]Pike,John.“Boeing747.”Military.GlobalSecurity,7July2011.Web.9Feb.2015.[6]Ross,SheldonM.AFirstCourseinProbability.NewYork:Macmillan,1976.Print.[7]“WorkingoutaPartoftheBayesianSearchTheoryEquation.”Weblogpost.Math
Crumbs.N.p.,25Dec.2012.Web.9Feb.2015.[8]Stone,LawrenceD.TheoryofOptimalSearch.NewYork:Academic,1975.Print.[9]Lenk,Peter.“BayesianInferenceandMarkovChainMonteCarlo.”UniversityofMichi-gan,1Nov.2001.Web.9Feb.2015.[10]“C-130Hercules.”U.S.AirForce,1Sept.2013.Web.8Feb.2015.
[11]“TheTheoryofSearch:ASimpli?edExplanation.”Soza&Company,Ltd.Web.8Feb.
2015.[12]“VisualSearchPatterns.”WashingtonStateDepartmentofTransportation.13Jan.
1997.Web.8Feb.2015.[13]“BellBoeingV-22Osprey-History,SpecsandPictures-MilitaryAircraft.”BellBoeing
V-22Osprey.29Jan.2015.Web.8Feb.2015.[14]“Cessna172.”Cessna.us.CessnaAirplanesRSS,n.d.Web.08Feb.2015.
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ConvergentIndustries,L.L.C.*LettertoCommercialAirlines2/9/15
Towhomitmayconcern:
FollowingtheeventsofMH370andothercommercialaircraftdisappearances,wewouldliketopresentaplantoallairlinesforfutureopen-wateraircraftsearches.Weunderstandtheurgencythataccompaniesatragedyofthismagnitudetoyourorganiza-tion,aswellasthedesiretobefullypreparedforanysuchemergency.Tothisend,wehavedevelopedafar-reachingmodeltoaccommo-dateandsupplementanyoperationconcern-ingthelossofanaircraftatsea.
Wepresentageneric,?exiblemathemat-icalmodelthatwillaccountforthevariouspossiblesearchandrescuescenariosthatmaybeencounteredwithinyoursphereofopera-tions.Asyourcompanyspansasigni?cantportionoftheglobe,thismodelisspeci?callydesignedtoaccommodatethemyriadofpos-sibleincidentsthatmayoccur.Thebreadthofourmodelincorporatesavarietyofthesepossibleincidents,rangingfromafullandim-mediatepowerlosstoasustainedglideofthea?ectedaircraft.Ourmodelbeginswiththeproductionofamapoflikelylocationsforthedownedair-craft.Thismapisconstructedthroughtheuseofspeci?cationsthatyouwouldbefullyquali?edtoprovide,suchasthemakeoftheplane,standardcruisingaltitudes,and?ightpathoftheplaneatpointoflastcontact.Withthisinformationastrongpredictionofaircraftlocationwillbeproducedtobeginthesearche?ort.
Furthermore,asthesearchprogresses,thismodelwillcontinuouslyupdateprobableplanelocationswiththegatheringofinfor-mationanddatafromthesearch.Thedy-namicmodelallowsforyoursearche?ortstobefullyoptimized,bothwithrespecttotimeandavailableresources.
Additionally,thesearchpathsusedbyyourpilotsinthesearche?ortwillbecom-monlyusedpatternsthataremostlikelyfa-miliartopersonnelalready.Thesestandardpatternsincludetheparallelsweepmethods,spiralsquaremethod,andoctagonalsectorsearch.Afurtherbene?tofourmodelisthatthesimpleconversionofcoordinatesfromthesimulationscanbeeasilytranslatedto?ightpathsandgeographiccoordinatesfortheuseofyourpilots.
Wehopethatthismodelissu?cientinmeetingyourneedsinanyfurthersearchandrescueendeavors.
*
Thiscompanyispurelyaworkof?ction.
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