美赛MCM A题M奖获奖论文.docx
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美赛MCM A题M奖获奖论文.docx
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TeamControlNumber
66666
ProblemChosen
A
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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
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