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1、TeamControlNumberForofficeuseonlyT1T2T3T433842ProblemChosenForofficeuseonlyFlF2F3F42015MathematicalContestinModeling(MCM)SummarySheetSearchingforalostairplane:genericmodelandexamplesAbstractAlthoughairplanescanberegardedasthesafesttransport,passengershavelittlechancetosurviveifaccidents
2、occur.Oncecrashed,itisdifficulttofindtheaccuratelocation,especiallyonopenwater.Andaneffectivesearchstrategyisnecessarytosavesearchtimeandexpense.Inthispaper,wedevelopagenericmodeltosearchforalostairplane,whichconsistsofthreephases:theglobalsearchareadecision,searchareadivision,localarea
3、search.Intheglobalsearchareadecisionphase,thefallingtrajectoryisdividedintotwostages:thefallingtrajectoryintheairandfallingtrajectoryinthewater.Forfallingtrajectoryintheair,gravity,airfrictionandliftaretakenintoaccountintheforcediagramandthusthefallingtrajectoryintheaircanbedecided.Fort
4、hefallingtrajectoryinthewater,thebuoyancy,gravityandwaterfrictionareconsideredwhichdeterminesthefallingtrajectoryinthewate匚What'smore,theaccuratetimeoftheaccident,thepossiblechangesinflightdirectionandotheruncertaintiesarealsoconsideredsoastogetasearcharea.Inthesecondphase,theBayesianst
5、atisticisappliedwhichhasbeenusedtosearchforlostboatsandairplanessuccessfully.BasedontheBayesianstatistic,Bayesiansearchtheoryisputforward.Wefirstdecidethepriordistributionaccordingtotheknowninformation,thenconstructthesearchorderinwhichtheareawithhigherprobabilityissearchedatfirst,andfi
6、nallyupdatetheposteriordistributiontopreservethepossibilityoffindingthemissingobjects.Inthethirdphase,thesearchandrescueaircraftsseekforthecrashedairplanewithinadeterminedsmallsearcharea.Inordertoreducesearchtimeandimprovesearchefficiency,wechoosethesearchpathwithfewerturns.Thecooperati
7、onamongseveralsameaircraftsanddifferentaircraftsisalsoevaluatedtogetthebestcombinationoftheaircrafts.Withtheproposedmethod,thesearchtimecanbereducedforacertainsearchareawhilepreservingthehighpossibilityoffindingthelostairplane.Insummary,wedevelopathree-stagegenericmodel,whichis
