美赛C题论文.pdf
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美赛C题论文.pdf
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ForofficeuseonlyT1_T2_T3_T4_TeamControlNumber21165ProblemChosenCForofficeuseonlyF1_F2_F3_F4_2013MathematicalContestinModeling(MCM)SummarySheet(Attachacopyofthispagetoyoursolutionpaper.)Typeasummaryofyourresultsonthispage.Donotincludethenameofyourschool,advisor,orteammembersonthispage.AbstractInthispaper,webuildamodeltomeasuretheearthshealthintheaspectofairquality.WechooseAirQualityIndex(AQI)asthebasisofhealthmeasure,whileusingaweightedaverageasthefinalexpression.Ourmodeltakestheformofdual-layernetwork.Amongthetwolayers,thelocalnetworkisimplementedusingneuralnetworkoptimizedbyParticleSwarmOptimization(PSO)algorithm,whiletheglobalnetworklinksthenodeswithfeedbacklinksdefinedbycertainpropagationfunction.Themodeltakestheoutputfromtheformeryearastheinputofthefollowingyear,thusestablishinganautonomoussystembyitself.Wethenmoveontoverifythemodel.Firstwetestthemodelsfundamentalnetworkpropertyfromtheperspectiveoffit,criticalnodes,andmissingrelationships.Ascasestudies,weappliedourmodeltospecificnationsonatimespanof1985-2008,namelyJapan,India,andHungaryinhopetodemonstratethatourmodelisabletogeneratepredictionandwarningsofstatechanges,andprovideinformationfordecision-makers.Ourmodelhasshownacompletenessoffunctionalityandimpressiveflexibilityinthesetests.Furthermore,wehavebeenabletoseethatthepredictiontestofourmodelcoincidesfairlywellwiththefact.Keywords:
global,neuralnetwork,AirQualityIndex,autonomousTeam#21165Page1of18LinkOurBreath:
ALinkedNeuralNetworkApproachtoAGlobalEnvironmentModelContent1Introduction.21.1Background.21.2AnOverviewofAirQuality.21.2.1AirQuality:
AReflectionofEarthsHealth.21.2.2PrimaryInfluenceFactors.31.3AirQualityIndex(AQI).31.4Assumptions.41.5Notations.42Model.42.1GenericMethodology.42.2BasicModel.72.2.1InputandOutputofLocalNetwork.72.2.2GlobalNetworkAspect.72.3AdvancedModel.72.3.1InputandOutputofLocalNetwork.72.3.2GlobalNetworkAspect.73Verification.83.1Overview.83.2Fitverification.93.3Identifyingcriticalnodes.103.4Sensitivitytoarelationshipchange.103.5CaseStudy.124Conclusion.154.1StrengthandWeakness.154.2Extension.15References.17OtherReferences.17ListofFiguresFigure1:
World3ComputerModelScenario2:
MoreAbundantNonrenewableResources3.2Figure2(a)(b)TheIncreasingratesofchangeinhumanactivity(c)GlobalscalechangesintheEarthsystemasaresultofthedramaticincreaseinhumanactivity:
atmosphericN2Oconcentration2.3Figure3Thebasicframework.5Figure4Theresultofstepwiseforecast:
Belgium.9Figure5Identifyingthecriticalnodes.10Figure6(a)(b)Sensitivitytoarelationshipchange:
removingornotremovingChina.11Figure7(a)(b)Thechangeofworldpollutiondistribution.12Figure8CaseStudyusinganautonomousforecast:
Japan.13Figure9CaseStudyusinganautonomousforecast:
India.14Figure10CaseStudyusinganautonomousforecast:
Hungary.14ListofTablesTable1.3Table2.4Table3.7Team#21165Page2of181Introduction1.11BackgroundThegrowingstressonEarthsenvironmentandbiologicalsystemareextremelyapparentnow.15outof24oftheecosystemservicesexaminedduringtheUN-basedMillenniumEcosystemAssessmentarebeingdegradedorusedunsustainably,includingfreshwater,capturefisheries,airandwaterpurificationandtheregulationofregionalandlocalclimate,naturalhazards,andpests1.HumanactivityisthemainreasoncausingthesignificantchangesofecosystemswhichharmEarthhealthalot.Thelargelygrowingdemandofnaturalsourceoverthepast50yearschangedecosystemsmorerapidlyandextensivelythaninanycomparableperiodoftimeinhumanhistory.1Moreover,excessiveemissionofthewasteandpollutantleadstodramaticenvironmentalchangesaswell.Manyglobalscalechangesinecosystemsaredisplayedasexponentialgrowthinthepasthalfcentury.Theycanbelargeinmagnitudeanddifficultorimpossibletoreverseonceathresholdiscrossed.Asmanyofthetrendsappearedinthepastcenturyhavecontinued,itislikelythatthedegradationofecosystemservicescouldgrowworseinthiscentury.Inthisway,globalecosystemmaybeapproachingaplanetary-scaletippingpoint.ThereforeapredictionofpotentialstatechangeofEarthshealthisneeded.2Figure1:
World3ComputerModelScenario2:
MoreAbundantNonrenewableResources3Figure1postulatesthatadvancesinresourceextractiontechnologiesarecapableofpostponingtheonsetofincreasingextractioncosts3.Undersuchpostulation,thetippingpointwilloccurinaround2050.1.2AnOverviewofAirQuality1.2.1AirQuality:
AReflectionofEarthsHealthAirqualityregulationisoneofthatfifteenecosystemserviceswhicharebeingdegradedandusedunsustainably.HumanneedtopaymuchattentiononairqualityfornotonlyitcanreflecttheconditionoftheEarthenvironmentbutalsodirectlyaffectthehealthofmanycreatures.Moreover,itcannotbeneglectedthatatmosphereactivityhelpsthepollutantdispersionaswell.Inmostcases,climatechangesandairqualityarecombinedandmanyrecentstudiesprefertopaymoreattentiononthegreenhouseeffect.However,bothGreatLondonSmogin1952andNorthChinahazein2013showthatheavyairpollutionandparticlepollutionhavelethalpotential.Team#21165Page3of181.2.2PrimaryInfluenceFactorsPopulationexplosionandrapideconomicgrowthBetween1800and2000,thehumanpopulationgrewfromaboutonebilliontosixbillion,whileenergyusegrewbyabout40-foldandeconomicproductionby50-fold4.Inaddition,theconsumptionofpetroleumgrewbyafactorof3.5since1960.Thenumberofmotorvehiclesrosefromonly40millionattheendofWWIItoabout700millionby1996,andcontinuestorisesteadily2.Despitesuchrapidgrowthinpopulationandeconomy,suchagrowthhasalsoleftasignificantimprintontheenvironment,whichisshowninthefiguresbelow.(a)(b)(c)Figure2(a)(b)TheIncreasingratesofchangeinhumanactivity(c)GlobalscalechangesintheEarthsystemasaresultofthedramaticincreaseinhumanactivity:
atmosphericN2Oconcentration2ForestcoverageForestcoverageisanotablefactortoairquality.Ontheonehand,gaseousandparticlepollutantscanbedry-depositedbytreesthroughamechanismnameddrydeposition,thusimprovingairquality6.Ontheotherhand,manygaseousandparticlepollutants,actingindividuallyorincombination,affectsforestsparticularly7.1.3AirQualityIndex(AQI)AirQualityIndex(AQI),developedbyEnvironmentProtectionAgency(EPA)ofUnitedStates,isaimingathelpingpeopleknowwhatlocalairqualitymeanstotheirhealth.ThisindexiscalculatedbysomemajorairpollutantswhichareregulatedbytheCleanAirAct,suchasparticlepollutionandsulfurdioxide,etc.Table18showsthesixcategoriesofAQIandtheirmeanings,eachofthecategoriesisassignedbyaspecificcolor.Table1Team#21165Page4of181.4AssumptionsThehealthmeasureofearthsatmospherecanbeassessedbyAirQualityIndex(AQI)WechooseAQIastheearthhealthmeasuretoassociatetheenvironmentalandbiologicalsystems,moredetailsofAQIcanbefoundinthebackgroundpartofthepaper.Thefollowingthreeassumptionsonlyconstrainthebasicmodel.Whileconsideringtheairflow,theimpactoftopographyisignored.Oneyearistakenastheminimaltimeunitinthemodel.WechoosethenationsaroundtheworldastheGlobalNodes.Thecoordinatesofthenodesarerepresentedbythecapitalslongitudeandlatitudepositions.Theassumptionsaboveareduetothelimitationofthedatawehave.Infact,themoredatawecollect,themoreaccurateresultthatthemodelwillcatch.1.5NotationsTable2SymbolMeaningfthefeedbackfunctionofanodecomingfromanothernodeintheglobalnetworkgtheinfluencedegreefunctionofanodederivedfromfeedbackfunctiondpopulationdensityofanationrforestcoveragerateofanationpproportionofsecondarysectoroftheeconomyinGDPinanationFthesumoffeedbackstoanodecomingfromothernodesinthewholenetworkqAQIvalueofanationSlandareaofnationldistancebetweeneverytwonations2ModelInordertofulfilltherequirementsofInternationalCoalitionofModelers(ICM),thegoalofourteamseemstobeveryclear.ThecontentofourpaperisaimingatbuildingadynamicglobalairqualitynetworkmodeltoshowthehealthconditionofPlanetEarthbyidentifyinglocalelementsofthisconditionandappropriatelyconnectingthemtotrackrelationshipandattributeeffect.ThemodelwebuildneedstoincludethehumanelementandhasthefunctionofpredictingEarthshealthfuturestatesbyaspecifichealthmeasure.2.1GenericMethodologyWemodelthedynamicglobalairqualitynetworkasacombinationoflocalandglobalnetworkswithinterlinkedarchitecture,whichhashighsimilaritywithInternet.Figure3showsthebasicframeworkvisually.Theleftpartshowthewholeframeworkofglobalnetworkwhiletherightpartdisplaysthedetailsofasinglelocalnetwork.Tomakethemethodologymoreunderstandably,wedefinedsevenconceptsbelow.Team#21165Page5of18i+1i+2.GlobalLink(i,i+1)GlobalLink(i,i+2)GlobalLink(i,.)GlobalLink(i+1,i+2)LocalTypeOutputLocalViewLocalNetworknLocalNetworkNode.Inputs12n.iGlobalNodesLocalNodesGlobalTypeOutputFigure3ThebasicframeworkLocalNetwork:
NeuralnetworkHavingconsideredthefactthatthedataavailablemightbeverylimited,wedecidetouseneuralnetworkaslocalpartofthewholesystem.Unlikethetraditionalmathematicalmethodssuchasregressionortimeseriesprediction,neuralnetworkisfamousforitsuniq
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