美赛MCM A题M奖获奖论文.docx

美赛MCM A题M奖获奖论文.docx

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2017

MathematicalContestinModeling（MCM/ICM）SummarySheet

TheKaribaDamontheZambeziRiverisoneofthelargerdamsinAfrica.Itsconstructionwascontroversial,anda2015reportbytheInstituteofRiskManagementofSouthAfricaincludedawarningthatthedamisindireneedofmaintenance.AnumberofoptionsareavailabletotheZambeziRiverAuthority（ZRA）thatmightaddressthesituation.

Itisassumedthatthedesignparameters,siteselectionandconstructionofthedam（damgroup）afterrepair,reconstructionandreconstructionareinaccordancewiththerequirementsofwaterconservancyandhydropowerprojects.Thenumberandlocationofthedamgroupsareinlinewiththerequirementsofwaterconservancyandhydropowerprojects.Therefore,theresearchproblemsare:

a）Comparingthecomprehensivebenefitsofthedamsafterrestoration,reconstructionandreconstruction,establishingthemathematicalmodel,andexpoundingthecostsandbenefitsofeachcase;b）Reconstructingthedams（rebuildingtheexistingdams10-20Alittledam）,inthedrought,heavyrain,moderaterain,lightrain,whenthewaterstorage,flooddischargetoensuretheprobabilityofdambreakthesmallest,thatis,damgroupriskdecisionoptimization.

Forthefirstproblem,thispaperchoosestheoptimalcostandbenefitplanforKalibaDamrestorationworkbyestablishingtheeconomicbenefitmodel,theeconomiclossmodel,thecomprehensivebenefitmodel,theabsolutereturnmodelafterrestorationandtheinvestmentpaybackperiodmodel.

Thecost-effectivenessofthethreeprogramswasevaluatedindetailaccordingtotheresultsofthemathematicalmodel.Option1,therestorationofthedamcanextendtheusefullifeof11years.Whiletheone-timecostofaccesstotheinvestmentrecoveryperiodof3.2years.Option2,100yearsafterthedesignofthereconstruction,theinvestmentrecoveryperiodof65.2years.Option3,afterrebuildingforthedamgroup,designedtouse100years,theinvestmentrecoveryperiodof47.8years.Threeprogramshavebetterbenefits,ofwhichthebestoverallbenefitsofthethreeprograms.

Fortheproblem1,thispaperusestheRlanguagesoftwaretodrawtheheatmaptovalidatetheconclusion.UsingtheMatlabsoftwaretobuildtheMSEmodel,theerroranalysisoftheaboveresultsisfurtherprovedtobethebest.

Forthesecondproblem,weuseMATLABandSPSSMODELERsoftwaretoestablishAuthorTopicModel,BPnetworkandLS-SVMmodeltovalidatetheLDAmodel,anduseMSEandABSmethodtoanalyzetheerrorofLDAmodel.TheresultsshowthattheLDAmodelisaccurateandreliable,andtheerrorissmall.Itfurther

showsthatthemathematicalmodelestablishedinthispaperhasacertaingeneralizationability.

Keywords:

Thezambeziriver ；Karibadam;Waterconservancy;reconstruction

I.Introduction

InordertoindicatemanagingtheZambeziriver,thefollowingbackgroundisworthmentioning.

1.1ZambeziRiver

TheZambezi（alsospelledZambezeandZambesi）isthefourth-longestriverinAfrica,thelongesteast-flowingriverinAfricaandthelargestflowingintotheIndianOceanfromAfrica.Theareaofitsbasinis1,390,000squarekilometres（540,000sqmi）,[1][2]slightlylessthanhalfthatoftheNile.The2,574-kilometre-longriver（1,599mi）risesinZambiaandflowsthrougheasternAngola,alongtheeasternborderofNamibiaandthenorthernborderofBotswana,thenalongtheborderbetweenZambiaandZimbabwetoMozambique,whereitcrossesthecountrytoemptyintotheIndianOcean.

FromVictoriatotheFallsfortheupperreachesofVictoriaFalls,1287kmlong;fromVictoriaFallstotheterritoryofMozambiqueKabulaBassareservoirforthemiddle,869kmlong;CabraBassaisthefollowingdownstream,579kmlong.

Zambeziaverageslopeof0.4‰,runoffof223.2billioncubicmeters,secondonlytotheCongoRiver,rankedsecondinAfrica.

1.2KaribaDamConstruction

ThedoublecurvatureconcretearchdamwasdesignedbyCoyneetBellierandconstructedbetween1955and1959byImpresitofItaly[2]atacostof$135,000,000forthefirststagewithonlytheKaribaSouthpowercavern.FinalconstructionandtheadditionoftheKaribaNorthPowercavernbyMitchellConstruction[3]wasnotcompleteduntil1977duetolargelypoliticalproblemsforatotalcostof$480,000,000.Duringconstruction,86menlosttheirlives.[2][4]

ThegrasslandinthefloodplainsaroundtheZambeziRiverreliesonannualfloodsandseasonalrainfall,whilerainfallintheregionisricherthanintheverydrywest.FloodsandvegetationexpansionduringtherainyseasonislimitedinthenorthoftheZambeziRiver,indicatinganincreaseinthenorthernmarginofthe