美国大学生数学建模竞赛优秀论文.docx

美国大学生数学建模竞赛优秀论文.docx

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美国大学生数学建模竞赛优秀论文

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Summary

Thearticleisaimedtoresearchthepotentialimpactofthemarinegarbagedebrisonmarineecosystemandhumanbeings，andhowwecandealwiththesubstantialproblemscausedbytheaggregationofmarinewastes.

Intaskone，wegiveadefinitionofthepotentiallong-termandshort-termimpactofmarineplasticgarbage.Regardthetoxinconcentrationeffectcausedbymarinegarbageaslong-termimpactandtotrackandmonitorit.Weetablishthecompositeindicatormodelondensityofplastictoxin，andthecontentoftoxinabsorbedbyplasticfragmentintheoceantoexpresstheimpactofmarinegarbageonecosystem.TakeJapanseaasexampletoexamineourmodel.

Inasktwo,wedesigneanalgorithm,usingthedensityvalueofmarineplasticofeachyearindiscretemeasurepointgivenbyreference，andweplotplasticdensityofthewholeareainvarieslocations.Basedonthechangesinmarineplasticdensityindifferentyears，wedeterminegenerallythatthecenteroftheplasticvortexisEast—West140°W—150°W,South—North30°N—40°N.Accordingtoouralgorithm,wecanmonitoraseaareareasonablyonlybyregularobservationofpartofthespecifiedmeasuringpoint

Intaskthree，weclassifytheplasticintothreetypes，whichissurfacelayerplastic，deeplayerplasticandinterlayerbetweenthetwo.Thenweanalysisthethedegradationmechanismofplasticineachlayer.Finally，wegetthereasonwhythoseplasticfragmentscometoasimilarsize.

Intaskfour，weclassifythesourceofthemarineplasticintothreetypes，thelandaccountingfor80%，fishinggearsaccountingfor10%，boatingaccountingfor10%，andestimatetheoptimizationmodelaccordingtotheduel-targetprincipleofemissionsreductionandmanagement.Finally,wearriveatamorereasonableoptimizationstrategy.

Intaskfive，wefirstanalyzethemechanismoftheformationofthePacificoceantrashvortex，andthusconcludethatthemarinegarbageswirlwillalsoemergeinsouthPacific，southAtlanticandtheIndiaocean.AccordingtotheConcentrationofdiffusiontheory,weestablishthedifferentialpredictionmodelofthefuturemarinegarbagedensity，andpredictthedensityofthegarbageinsouthAtlanticocean.Thenwegetthestabledensityineightmeasuringpoint.

Intasksix,wegettheresultsbythedataoftheannualnationalconsumptionofpolypropyleneplasticpackagingandthedatafittingmethod,andpredicttheenvironmentalbenefitgeneratedbytheprohibitionofpolypropylenetake-awayfoodpackaginginthenextdecade.Bymeansofthismodelandourprediction，eachnationwillreducereleasing1.31milliontonsofplasticgarbageinnextdecade.

Finally,wesubmitareporttoexpedictionleader，summarizeourworkandmakesomefeasiblesuggestionstothepolicy-makers.

Task1:

Definition:

●Potentialshort-termeffectsoftheplastic:

thehazardeffectswillbeshownintheshortterm.

●Potentiallong-termeffectsoftheplastic:

thepotentialeffects,ofwhichhazardsaregreat,willappearafteralongtime.

Theshort-andlong-termeffectsoftheplasticontheoceanenvironment:

Inourdefinition,theshort-termandlong-termeffectsoftheplasticontheoceanenvironmentareasfollows.

Short-termeffects:

1）Theplasticiseatenbymarineanimalsorbirds.

2）Animalsarewrappedbyplastics,suchasfishingnets,whichhurtorevenkillthem.

3）Deadenthewayofthepassingvessels.

Long-termeffects:

1）Enrichmentoftoxinsthroughthefoodchain:

thewasteplasticintheoceanhasnonaturaldegradationintheshort-term,whichwillfirstbebrokendownintotinyfragmentsthroughtheroleoflight,waves,micro-organisms,whilethemolecularstructurehasnotchanged.These"plasticsands",easytobeeatenbyplankton,fishandother,areSeeminglyverysimilartomarinelife’sfood,

causingtheenrichmentanddeliveryoftoxins.

2）Acceleratethegreenhouseeffect:

afteralong-termaccumulationandpollutionofplastics,thewaterbecameturbid,whichwillseriouslyaffectthemarineplants（suchasphytoplanktonandalgae）inphotosynthesis.Alargenumberofplankton’sdeathswouldalsolowertheabilityoftheoceantoabsorbcarbondioxide,intensifyingthegreenhouseeffecttosomeextent.

Tomonitortheimpactofplasticrubbishonthemarineecosystem:

Accordingtotherelevantliterature,weknowthatplasticresinpelletsaccumulatetoxicchemicals,suchasPCBs、DDE,andnonylphenols,andmayserveasatransportmediumandsoureoftoxinstomarineorganismsthatingestthem

.Asitisdifficultfortheplasticgarbageintheoceantocompletedegradationintheshortterm,theplasticresinpelletsinthewaterwillincreaseovertimeandthusabsorbmoretoxins,resultingintheenrichmentoftoxinsandcausingseriousimpactonthemarineecosystem.

Therefore,wetrackthemonitoringoftheconcentrationofPCBs,DDE,andnonylphenolscontainingintheplasticresinpelletsintheseawater,asanindicatortocomparetheextentofpollutionindifferentregionsofthesea,thusreflectingtheimpactofplasticrubbishonecosystem.

Toestablishpollutionindexevaluationmodel:

Forpurposesofcomparison,weunifytheconcentrationindexesofPCBs,DDE,andnonylphenolsinacomprehensiveindex.

Preparations:

1）DataStandardization

2）Determinationoftheindexweight

BecauseJapanhasdoneresearchesonthecontentsofPCBs,DDE,andnonylphenolsintheplasticresinpellets,weillustratethesurveyconductedinJapanesewatersbytheUniversityofTokyobetween1997and1998.

✧TostandardizetheconcentrationindexesofPCBs,DDE,andnonylphenols.WeassumeKasaiSessidePark,KeihinCanal,KugenumaBeach,ShiodaBeachinthesurveyarethefirst,second,third,fourthregion;PCBs,DDE,andnonylphenolsarethefirst,second,thirdindicators.

Thentoestablishthestandardizedmodel:

（

）

where

isthemaximumofthemeasurementofjindicatorinthefourregions.

istheminimumofthemeasurementofjindicatorinthefourregions.

isthemeasurementofjindicatoriniregion.

isthestandardizedvalueofjindicatoriniregion.

Accordingtotheliterature[2],JapaneseobservationaldataisshowninTable1.

Table1.PCBs,DDE,and,nonylphenolsContentsinMarinePolypropylenePlasticResinPellets

PCBs（

）

DDE（

）

nonylphenols（

）

KasaiSessidePark

97.3

2.0

16

KeihinCanal

117

3.1

8.9

KugenumaBeach

43.5

1.6

12

ShiodaBeach

3.97

0.16

0.13

Table1Usingtheestablishedstandardizedmodeltostandardize,wehaveTable2.

Table2.

PCBs（

）

DDE（

）

nonylphenols（

）

KasaiSessidePark

0.826

0.626

1

KeihinCanal

1

1

0.553

KugenumaBeach

0.350

0.490

0.748

ShiodaBeach

0

0

0

InTable2，thethreeindicatorsofShiodaBeachareaareall0,becausethecontentsofPCBs,DDE,andnonylphenolsinPolypropylenePlasticResinPelletsinthisareaaretheleast,while0onlyrelativelyrepresentsthesmallest.Similarly,1indicatesthatinsomeareathevalueofaindicatoristhelargest.

✧TodeterminetheindexweightofPCBs,DDE,andnonylphenols

WeuseAnalyticHierarchyProcess（AHP）todeterminetheweightofthethreeindicatorsinthegeneralpollutionindicator.AHPisaneffectivemethodwhichtransformssemi-qualitativeandsemi-quantitativeproblemsintoquantitativecalculation.Itusesideasofanalysisandsynthesisindecision-making,ideallysuitedformulti-indexcomprehensiveevaluation.

Hierarchyareshowninfigure1.

Fig.1Hierarchyofindexfactors

Thenwedeterminetheweightofeachconcentrationindicatorinthegenerallpollutionindicator,andtheprocessaredescribedasfollows:

Toanalyzetheroleofeachconcentrationindicator,wehaveestablishedamatrixPtostudytherelativeproportion.

Where

representstherelativeimportanceoftheconcentrationindicators

and

.Usuallyweuse1，2，…，9andtheirreciprocalstorepresentdifferentimportance.Thegreaterthenumberis,themoreimportantitis.Similarly,therelativeimportanceof

and

is

（

）.

SupposethemaximumeigenvalueofPis

thentheconsistencyindexis

Theaverageconsistencyindexis

thentheconsistencyratiois

ForthematrixPof

if

theconsistencyisthougttobebetter,ofwhicheigenvectorcanbeusedastheweightvector.

WegetthecomparisonmatrixaccodingtotheharmfullevelsofPCBs,DDE,andnonylphenolsandtherequirmentsof

EPAonthemaximumconcentrationofthethreetoxinsinseawaterasfollows:

WegetthemaximumeigenvalueofPbyMATLABcalculation

andthecorrespondingeigenvectorofitis

Coincidenceindicatoris

Forthematrixof

theaveragecoincidenceindicatoris

thenthecoincidenceratiois

Therefore,wedeterminethedegreeofinconsistencyformatrixPwithinthepermissiblerange.

Withtheeigenvectorsof

asweightsvector,wegetthefinalweightvectorbynormalization

.

DefiningtheoveralltargetofpollutionfortheNo

oceanis

amongotherthingsthestandardizedvalueofthreeindicatorsfortheNo

oceanis

andtheweightvectoris

Thenweformthemodelfortheoveralltargetofmarinepollutionassessment

（

）

Bythemodelabove,weobtainedtheValueofthetotalpollutionindexforfourregionsinJapaneseoceaninTable3

Table3.

Ocean

Valueofthetotalpollutionindex

KasaiSessidePark

0.8138

KeihinCanal

0.9268

KugenumaBeach

0.4437

ShiodaBeach

0