2023美賽MCM A題M獎獲獎

本文格式為Word版，下載可任意編輯——2023美賽MCMA題M獎獲獎1)RemovingtheKaribaDamandreplacingitwithaseriesoftentotwentysmallerdamsalongtheZambeziriver.

2)ThisnewsystemofdamsshouldhavethesameoverallwatermanagementcapabilitiesastheexistingKaribaDamwhileprovidingthesameorgreaterlevelsofprotectionandwatermanagementoptionsforLakeKaribathatareinplacewiththeexistingdam.

3)Thedecisiontreemodelandtheprobabilitytopicmodelareestablishedtoanalyzetheoptimaldecisionproblemofwaterstorageandflooddischargeintheconditionofdrought,large,mediumandlightrainfall.

III.EvaluationofKaribaDamProjectBasedonComprehensiveBenefitModel

3.1BasicModel

Theannualeconomicbenefitsofthedamaremadeupofanumberofbenefits.Theseincludepowergenerationbenefits,watersupplybenefits,irrigationbenefits,shippingbenefits,thevalueoffloodstorage,culturaltourismvalue,biologicalbenefits,environmentalbenefitsandsoon.Asaresultofthevariousbenefits,especiallythepowergenerationefficiencyischangingyearbyyear.

Theeconomicbenefitmodel,thecomprehensivebenefitmodel,theabsolutereturnmodelafterrestorationandtheinvestmentpaybackperiodmodelareestablishedtooptimizethecostandbenefitofKalibaDamrestorationwork.3.1.1Assumptions

1)Assumingthattheprobabilityofdambreakafterrainfalltoacertainwaterlevelisfixed.

2)Assumethatrainfallisacontinuousvariableandobeysnormaldistribution.3)Assumingthatthedamgroupisaseriesmodel,donotconsidertheparallelandmixed.

4)Itisassumedthatthedesignparameters,siteselectionandconstructionofthedam(damgroup)afterrepair,reconstructionandreconstructionareinaccordancewiththerequirementsofwaterconservancyandhydropowerprojects.Thenumberandlocationofthedamgroupsareinlinewiththerequirementsofwaterconservancyandhydropowerprojects.Therefore,theresearchproblemsare:a)Comparingthecomprehensivebenefitsofthedamsafterrestoration,reconstructionandreconstruction,establishingthemathematicalmodel,andexpoundingthecostsandbenefitsofeachcase;b)Reconstructingthedams(rebuildingtheexistingdams10-20Alittledam),inthecaseofdrought,heavyrain,moderaterainandlightrain,whentheimpoundmentandflooddischargecanensuretheprobabilityofdambreak,theriskdecisionofdamgroupisoptimized.3.1.2TheFoundationofModel

Theannualeconomicbenefitsofthedamaremadeupofanumberofbenefits.Theseincludepowergenerationbenefits,watersupplybenefits,irrigationbenefits,shippingbenefits,thevalueoffloodstorage,culturaltourismvalue,biologicalbenefits,environmentalbenefitsandsoon.Becauseofthevariousbenefits,especiallythepowergenerationbenefitsarechangingyearbyyear,sotheeconomicbenefitsofthedamBisafunctionofrunningtimet,theformulais:

B?Vpower?Vwatersupply?Vshipping?Virrigation?Vstorage?Vtourism?Vbiological?Venvironment

TheannualeconomiclossDisalsoafunctionoftimet,whichincludesgrainproduction,fisheryproduction,organicmatterproduction,soilerosioncontrol,ecologicalrestoration,dammaintenance,reservoirdredging,watertreatment,speciesloss,lossofculturalrelics..Thecalculationformulais:

D?Vfood?Vfish?Vplant?Vsoil?Vmaintenance?Vdredging?Vwaterquality?Vspecies?Vculturalrelics

Ingeneral,thedamisbuiltaftertheinitialoperation,theeconomicbenefitsarefargreaterthantheeconomiclossofD.,Butastherunningtimeincreases,theeconomicbenefitstendtobestable,whilethelossescontinuetoincrease.Accordingtothesizeoftherelationshipbetweenthetwocantakemeasurestoremovethedam,repairmeasures,ornottotakemeasures.Ofcourse,aftertherestorationofthedamintheshorttermtheeconomicbenefitswillbeimproved,butwiththegradualincreaseinlossesandbenefitswiththeflat,thedamwillonceagainfacedemolition.

Generallyspeaking,afterthecompletionofthedamiscompleted,theeconomicefficiencyofratsisfargreaterthantheeconomiclosses.,Butastherunningtimeincreases,theeconomicbenefitstendtobestable,whilethelossescontinuetoincrease.Accordingtothesizeoftherelationshipbetweenthetwocantakemeasurestoremovethedam,repairmeasures,ornottotakemeasures.Ofcourse,aftertherestorationofthedamintheshorttermtheeconomicbenefitswillbeimproved,butwiththegradualincreaseinlossesandbenefitswiththeflat,thedamwillonceagainfacedemolition.

Ingeneral,theabsolutebenefitAafterrepairorreconstructioncanbecalculatedbythefollowingformula：

A????g(t)?f(t)??dt

Where:g(t)fortherepairorreconstructionoftheannualincomefunction;f(t)fortherepairorreconstructionoftheannuallossfunction.

AccordingtothepaybackperiodtocalculatethepaybackperiodT,theformulaisasfollows：

T?LgR?Lg(R?iF1)

Lg(1?i)Where:Ristheaverageannualnetincome;F1isaone-timeinvestmentinrepair;iforthebenchmarkrateofreturn.

Iftheextendedusefullifeofadamislessthanthecostrecoveryperiodafterrestorationorreconstruction,therestorationorreconstructionprogramhasnoeconomicvalue.Onthecontrary,itshowsthattherepairprogramcanachievebettereconomicresults.

Therefore,theinvestmentrecoveryperiodTcanbeusedasanimportantindextoevaluatethechoiceofdamrestorationscheme.

Accordingtotheaboveformula,andusingtheKalibareservoirdatatocalculatetheannualeconomicbenefitsofthedamovertimecurve：

B??0.165t2?630.5t?528374

Similarly,theannuallosscurvecanbeobtained：

D?0.173t2?675.5t?5321213.1.3SolutionandResult

1)Repairing

AccordingtothespecificconditionsofKalibaReservoir,sixrehabilitationmethodsareproposed:oneistorepairtheconcreteofthedambody,whichcanreducethelossofthedam,butitcannoteffectivelyincreasethedamyearlyToreducethelossofthedam,butitcannoteffectivelyincreasetheannualbenefitsofthedam;thirdistoaddthefishtothesurfaceofthedamtoincreasethepressure;Andreducetheecologicallossescausedbythedam,butwillnotsignificantlychangetheeconomicbenefitsofthedam;Fourth,thereservoirdredging,thisapproachcaneffectivelyincreasethedrainage,improvepowergenerationefficiency,butwillnotreducedamlosses;Fiveisthepooloftherepair;sixisthespillwaygaterepair.ThecostoftherestorationprojectfortheKalibahydropowerstationinZambiaisestimatedat$294million.2)Rebuilding

RebuildingtheexistingKaribaDam.3)RemovingandRebuilding

RemovingtheKaribaDamandreplacingitwithaseriesoftentotwentysmallerdamsalongtheZambeziRiver.2)Rebuilding

RebuildingtheexistingKaribaDam.

Therebuiltbudgetincludesdemolitioncostsandnewconstructioncosts.TheconstructioncostoftheKalibaDamisestimatedtobeUS$4.8billion.ThetotalcostofdemolitionandreconstructionisestimatedtobeUS$6billion.Thedesignis100yearsandtherecoveryperiodis65.2years.Theeconomyoftheprogramissignificantlybetter.

202350100500-500incomeoutcome204060801001203)RemovingandRebuilding

RemovingtheKaribaDamandreplacingitwithaseriesoftentotwentysmallerdamsalongtheZambeziRiver.

Therebuiltbudgetincludesdemolitioncostsandnewconstructioncosts.ThecostestimateforthereconstructionoftheKalibaDamis$4.4billion.Itisdesignedfor100yearsandtheinvestmentrecoveryperiodis47.8years.Theeconomyoftheprogramissignificantlybetter.

Insummary,forallthreedifferentfocusofthedamrestorationandreconstructionprogramforcomparison,themostreasonablerepairprogram:theKalibadamremoval,alterationmultipledamssystem,notonlycanextendthedamfor100years,Butalsocangivefullplaytotheeconomicbenefitsofthedam.

100806040200-200incomeoutcome20406080100120

3.1.7StrengthandWeakness

?Strength:Indespiteofthis,themodelhasprovedthattheoptimaloptionof

theKaribaDambasedonelectricity,watersupply,irrigation,shipping,thevalueofbio-productivityandvalueofculturaltourism,biological,

environmental,foodproductionandfisheryproduction,organicproduction,repair,preventionandcontrolofsoilerosion,ecologicalrestoration,damreservoirdredging,watertreatment,speciesdisappear,lossofculturalrelicsandsoon..Moreover,wehavedrawnsomeusefulconclusionsabouthowtochoosethecostsandbenefitsforKaribadam.

?Weakness:Thismodeljustappliestodescribethebenefitof

Karibadam.Assumingthatthedamfortheseriesmodel,whichisnot

consideredinparallelwiththecompositegroup,andthedamgroupdesignregulationofwaterandelectricityisnotlowerthantheoriginaldam.Aswehavestated,thecostofdamprojectisnotaccurate.That’sjustwhatweshoulddointheimprovedmodel.

3.2Conclusion

Theannualeconomicbenefitsofthedamaremadeupofanumberofbenefits.Theseincludepowergenerationbenefits,watersupplybenefits,irrigationbenefits,shippingbenefits,thevalueoffloodstorage,culturaltourismvalue,biologicalbenefits,environmentalbenefitsandsoon.Asaresultofthevariousbenefits,especiallythepowergenerationefficiencyischangingyearbyyear.

Theannualeconomiclossescausedbythedamincludefoodproduction,fisheryproduction,organicmatterproduction,soilerosioncontrol,ecologicalrestoration,dammaintenance,reservoirdredging,watertreatment,speciesloss,lossofculturalrelics.

Accordingtotherelationshipbetweenthesizeofthedamcanbetakentorepair,reconstruction,reconstructionandothermeasures.

Theeconomicbenefitmodel,thecomprehensivebenefitmodel,theabsolutereturnmodelafterrestoration,andtheinvestmentpaybackperiodmodelareestablishedinthisstudy,andtheoptimalcostandbenefitofKalibaDamareselected.

Aftertherestorationofthedamcanextendtheusefullifeof11years,investmentrecoveryperiodof3.2years.

Therebuiltbudgetincludesdemolitioncostsandnewconstructioncosts.TheconstructioncostoftheKalibaDamisestimatedtobeUS$4.8billion.ThetotalcostofdemolitionandreconstructionisestimatedtobeUS$6billion.Thedesignis100yearsandtherecoveryperiodis65.2years.Theeconomyoftheprogramissignificantlybetter.

RemovingtheKaribaDamandreplacingitwithaseriesoftentotwentysmallerdamsalongtheZambeziRiver.

Thebudgetforrebuildingthedamgroupincludesdemolitioncostsandnewconstructioncosts.ThecostestimateforthereconstructionoftheKalibaDamis$4.4billion.Itisdesignedfor100yearsandtheinvestmentrecoveryperiodis47.8years.Theeconomyoftheprogramissignificantlybetter.

Insummary,forallthreedifferentfocusofthedamrestorationandreconstructionprogramforcomparison,themostreasonablerepairprogramis:thedemolitionofthedamtobuildmultipledamssystem,notonlycanextendthelifeofthedam100years,butalsocangivefullplaytotheeconomicbenefitsofthedam.

IV.BasedonGibbssamplingalgorithmofprobability

modelofthetopic（Requirement2）

4.1BasicModel

1)RemovingtheKaribaDamandreplacingitwithaseriesoftentotwentysmallerdamsalongtheZambeziriver.

2)ThisnewsystemofdamsshouldhavethesameoverallwatermanagementcapabilitiesastheexistingKaribaDamwhileprovidingthesameorgreaterlevelsofprotectionandwatermanagementoptionsforLakeKaribathatareinplacewiththeexistingdam.

3)Thisresultsupportthelocationandnumberofthenewdam.

4)EstablishaprobabilitytopicmodelbasedonGibbssamplingalgorithm,andanalyzetheoptimaldecisionproblemofwaterstorageandfloodindrought,large,mediumandlightrainfall.

5)UsingMATLABandSPSSMODELERsoftwaretoestablishAuthorTopicModel,BPnetworkandLS-SVMmodeltoverifytheLDAmodel.

6)UsingMSEandABSmethodtocarryontheerroranalysistotheLDAmodel.4.1.1Terms,DefinitionsandSymbols

Inthecaseofseveraldamsconnectedtoacascadesystem,twodamsareselectedformodelingdiscussion,namely,damAanddamB,andthedecisionofdamBisobviouslyaffectedbyupstreamAdamdecision；HydrologicstationforecastreservoirArainfallandtheprobabilityofrainfallQAisPA，HydrologicstationforecastreservoirBrainfallandtheprobabilityofrainfallQBisPB，thedecisionofQA(QB)fornon-flooddischargeandpre-floodcanbeselected。

A,Breservoirsinthenormalwaterleveltothewarninglevel,warningwaterleveltothehighestwaterlevel,themaximumwaterlevelthantheprobabilityofsafetywere:PA?,PA??,PA???,PB?,PB??,PB???。

Intheactualsituation,duetothecapacityofthereservoirflooddischarge

capacity,emergencyfloodwillbringhighrisk,shouldbeavoided,soherewedonotconsiderthestatusofemergencyflood,soAdamontheBdamismainlyreflectedintheifDamAdam,andAdamfloodingtoreachthedamleadingtothewaterBtobringagreaterrisk.

Inallthecomponentsofthesystem,thefailureofanyoneunitwillaffecttheentiresystem,suchasystemiscalledatandemsystem.Tandemsystemsarethemostcommonandsimplestmodels,asshowninthefollowingfigure.Inthispaper,onlytwodamAanddamBarecalculatedforsimplifiedcalculation.

DAM-ADAM-BDAM-CDAM-EDAM-DFigureDaminseriesdiagram

4.1.2Assumptions

1)Assumingthatthedesignparameters,siteselectionandconstructionofthedam(damgroup)afterrestoration,reconstructionandreconstructionarein

accordancewiththerequirementsofwaterconservancyandhydropowerprojects.Thenumberandlocationofthedamgroupsareinlinewiththerequirementsofwaterconservancyandhydropowerprojects.Therefore,theresearchproblemsare:a)Comparingthecomprehensivebenefitsofthedamsafterrestoration,reconstructionandreconstruction,establishingthemathematicalmodel,andexpoundingthecostsandbenefitsofeachcase;b)Reconstructingthedams(rebuildingtheexistingdams10-20Alittledam),inthecaseofdrought,heavyrain,moderaterainandlightrain,whentheimpoundmentandflooddischargecanensuretheprobabilityofdambreak,theriskdecisionofdamgroupisoptimized.

2)Assumingthattheprobabilityofdambreakafterrainfalltoacertainwaterlevelisfixed.

3)Assumethattherainfallisacontinuousvariable,obeyingthenormaldistribution.

4)Assumingthatthedamgroupisaseriesmodel,donotconsidertheparallelandmixed.

5)Supposetheheadofeachdaminthedamgroupisthesame.

6)Assumingthatthedamgroupisdesignedtoregulatetheamountofwater,generatingcapacityofnotlessthantheoriginaldam.

7)Theriskofflooddischargeinemergenciesishigh,andthisstudydoesnotconsiderthesituationofemergencyflooddischarge.

8)Assumingthattheecologicalrestorationofthewater-leveldrawdownareaafterthedemolitionofthedam,constructionwastetransport,sedimentdepositionareideal.

9)Assumethattheaccuracyofweatherforecastingiscustom.4.1.3TheFoundationofModel

'SGivenasamplecontaining,eachdamhasitsratinginagivencondition,

whichislikelytobeassociatedwiththedamasawhole.Therefore,eachdamcanbe

representedbyavectorofthecorrespondingevaluationvalues，Recordedas

?????g?{g1?,g2,...,gS?1,gS}.Here，{g2s?1,g2s}indicatesthatthedamgroupexceededthe

warninglevelinthesamples（Over-expressed）andlessthanthewarninglevel

's?{1,...,S},ThusS?2S'。Inordertoobtainthesecomplex（Under-expressed）,

integernumberoftimessamplesasfollows,

(?2s?1,i,?2s,i),Wenormalizeadamevaluationvaluein

σ2s-1,i,σ2s,i?c?????|v|?,0,????0,??c?|v|??,s,is,ivs,i?meds

Whichistheexpressionof

vs,idaminthes-thsample，medsrepresentsthe

meanvalueofthewatermassesinthes-thsampleforalldamgroups，Anevaluationvaluegreaterthanorequaltomedsisconsideredtobethedam'ssuper-warningwaterlevelinthes-thsample,otherwiseitislessthanthewarningwaterlevelandcis

acalibrationconstant.

?s,kαzs,tβ?k,nms,tKTsS

FigProbabilityTopicModelRelationofDamGroup

DALADBFloodAALBBFloodBFigProbabilisticTopicModelforSeriesDamGroup

4.1.4AnalysisoftheResult

FigProbabilisticTopicModeling

InordertofacilitatetheanalysisofthestateofthedamBandtheprofitandlossvalue,theactualwaterquantityofthedamBafterprecipitationisshowninthe

followingtable.

TableActualamountofwaterindamBBWater0Vflooddischarge0.4VflooddischargequantityAIncoming0V0.4V0V0.4Vwater0V1.3V1.7V0.9V1.3V0.25V1.55V1.95V1.15V1.55V0.95V2.25V2.65V1.85V2.25VItcanbeseenthatdamAadopts0.25Vflooddischarge,damBtakes0.4Vflooddischargeastheoptimaldecision,theexpectedriskvalueis0.025301V.Therefore,thedamgroupcanresistfloodanddroughtthroughoptimaldecision-making.4.1.5StrengthandWeakness

?Strength:Indespiteofthis,themodelhasprovedthatthenewsystemof

damsshouldhavethesameoverallwatermanagementcapabilitiesastheexistingKaribaDamwhileprovidingthesameorgreaterlevelsof

protectionandwatermanagementoptionsforLakeKaribathatareinplacewiththeexistingdam.

?Weakness:Thismodelaswehavestated,thesameorgreaterlevelsof

protectionandwatermanagementoptionsforLakeKariba.Theparameterofthemodelcanbeoptimized.That’sjustwhatweshoulddointheimprovedmodel.

4.2ImprovedModel

Inthispaper,weusetheGibbsalgorithmtooptimizetheparametersintheprobabilitytopicmodeltoimprovethemodelaccuracy.

Inthispaper,akindoffoldedGibbssamplingmethodisusedtoestimatetheseparameters.TheMonteCarlomethodisusedtosampletheposteriorprobabilityofparameters.

FoldedGibbsSampling

zs,tand

ms,taremarginalizedineachstatesampleby

co-samplingtheimplicitvariablesvariablet,samplesof

?s,kand?k,n.Forthes-thsampleofadamgroup

zs,tand

ms,tcanbeexpressedasaconditionalprobability：

P(zs,t?k|ms,t?n,Z?(s,t),s)?KTCkn?β?Cn'?1T?SKCsk?αKTkn'?Tβ?Cs'?1SSKs'k?Sα

Amongthem，

Z?(s,t)isthecurrentdistributionofthedamgroupwiththe

SKCskexceptionofthesconditiontype。isthenumberoftimesthesamplesisassignedKTCkntothekthdamgroup,excludingthecurrentstate。isexcludedfromthecurrent

state,whethermorethanwarningwaterleveltypenisassignedtothekthdam。Kis

thenumberofimplicitvariablesinthereservoirgroup,andSisthetotalnumberofconditiontypes.

4.2.5AnalysisoftheResult

Improved(maximumprecipitation)NormalprobabilityProbabilityoffailuretotalPre-improvement(maximumprecipitation)NormalprobabilityProbabilityoffailuretotal

7712291,0007652351,00077.10%22.90%76.50%23.50%ConsistencyofmodelresultsbeforeandafterimprovementConsistent85685.60%Inconsistent14414.40%total1,000InordertofacilitatetheanalysisofthestateofthedamBandtheprofitandlossvalue,theactualwaterquantityofthedamBafterprecipitationisshowninthefollowingtable.

TableActualamountofwaterindamBBWaterquantityAIncomingwater0V0.25V0.95V0Vflooddischarge0V0.4V1.3V1.7V1.55V1.95V2.25V2.65V0.4Vflooddischarge0V0.4V0.9V1.3V1.15V1.55V1.85V2.25VItcanbeseenthatafteroptimizationmodelanalysis,damAadopts0.25Vflooddischarge,damBtakes0.4Vfloodastheoptimaldecision,theexpectedriskvalueis0.024591V.Therefore,thedamgroupcanresistfloodanddroughtthroughoptimaldecision-making.

4.3ModelValidation

4.3.1Authortopicmodel

ThispaperappliesATMtotheoptimaldecisionofdamgroup.Themethodalsousesavarietyofinformationsources:waterflow,reservoircapacity,rainfall,warningwaterlevel,totalstoragecapacity,regulatingstoragecapacity.Inthismodel,thedamsystemcorrespondstotheAuthors,thewordsofthedam,thecorrespondingdocumentsofthemeteorologicalconditions,andthetopicsofthewaterstorageanddischargedecision.Thismethodcaneffectivelyobtaintheoptimaldecisionofdamgroup.

Intherainyseason:thereddamthatsuper-warninglevel,theneedforearlydecision-makingflood,greendamthatdidnotexceedthewarninglevel,donotneedflood.Inthedryseason:RedDamsaidthelackofwater,needtoadvancethewater,greendamthatadequatewater,donotneedtoadvancestorage.Eachcirclerepresentsadam,andarrowsindicatetherelationshipbetweenthedamscontrollingwatervolume.

4.3.2BPnetwork

Artificialneuralnetworkisakindofmathematicalmodelofinformationprocessingwhichissimilartothestructureofbrainsynapticconnection.Inengineeringandacademiaalsooftenreferredtodirectlyasneuralnetworkorneuralnetwork.Neuralnetworkisacomputingmodel,whichconsistsofalargenumberofnodesconnectedwitheachother.Eachnoderepresentsaspecificoutputfunction,

calledtheactivationfunction.Theconnectionbetweeneverytwonodesrepresentsaweightedvalueofthesignalpassingthroughtheconnection,calledtheweight,whichisequivalenttothememoryoftheartificialneuralnetwork.Theoutputofthenetworkdependsonhowthenetworkisconnected,theweights,andtheincentivefunctions.Thenetworkitselfisusuallyanaturalalgorithmorfunctionapproximation,itmaybealogicalexpression.

Supposethereares1neuronsinthehiddenlayer,theexcitationfunctionisF1,andthereares2neuronsintheoutputlayer,andthecorrespondingactivationfunctionisF2,whichistheinputdataofthedam.TheoutputisYandthetargetvectorisT.

（1）Thepositivetransferofinformation

①Theoutputoftheneuroninthehiddenlayeris：

y1i?f1(?w1ijxj?b1i),i?1,2,Ls1(4-3)

j?1r②Theoutputofthek-thneuronintheoutputlayeris：

y2k?f2(?w2kiy1i?b2k),k?1,2,Ls2(4-4)

i?1s1③Theerrorfunctionisdefinedas：

1s2E(W,B)??(tk?y2k)2(4-5)

2k?1（2）TheChangeofWeightandtheBackPropagationofError

①Theweightoftheoutputlayerchanges

Theweightchangefromthefirstinputtothefirstoutputis：

?w2ki????E?E?y2k?????(tk?y2k)f2?y1i???kiy1i(4-6)?w2ki?y2k?w2ki(4.18)，?ki?(tk?y2k)f2??ekf2?；ek?tk?y2k。

Similarlyavailable：

?b2k????E?E?y2k??????(tk?y2k)?f2?????ki(4-7)?b2ki?y2k?b2ki②Impliedlayerweightchanges

Fortheweightsfromtheithinputtothejthoutput,thechangeis：

?w1ij???s2?E?E?y2k?y1i??????w1ij?y2k?y1i?w1ij(4-8)

???(tk?y2k)f2??w2kif1??xj????ij?xjk?1?ei?(4-8)，?ij?eif1,??k?1s2kiw2ki

Similarlyavailable：?b1i???ij。

Thiscanbeobtainedfortheoutputofthedamspillway,waterstoragevalue.

4.4ModelErrorAnalysis

Inthispaper,themeansquareerrorandtheabsoluteerrorareusedtoevaluate

thepredictionresults.

4.4.1ABS

Absoluteerror(ABS)isthedifferencebetweentheexactvaluexanditsapproximatevaluex*,denotedase(x*)=x*-x,abbreviatedase*.However,ingeneral,thesizeofe(x*)cannotbeknownaccurately.Theupperboundoftheabsolutevaluecanbeestimatedbymeasuringorcalculating|e(x*)|=|x*-x|≤ε(x*(X*)iscalledtheapproximateabsoluteerrorofthenumberx*limit,referredtoastheerrorlimit,abbreviatedasε*.

?AbsoluteErrorFormula：ABS?yi?yi

Note:whereyiandyirepresenttrueandpredictedvalues

Whenselectingdammonitoringindicatorsfortesting,theerrorisshowninthefollowingtable.

TabModelerrorcomparisonLSSVMATMBPLDAMSE624.4849443.2745160.993450.9441ABS20.857915.283910.92515.7826?Therefore,usin