美赛C题论文_精品文档.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:
AReflectionofEarthsHealthAirqualityregulationisoneofthatfifteenecosystemserviceswhic