美赛C题论文.pdf

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