DOC

GENETIC

By Chris Collins,2014-07-23 14:59
11 views 0
GENETICGENETI

    GENETIC

Availableonlineatwww.sciencedirect.corn

    ;二言ScienceDirect

    ;JournalofHydrodynamics

    ;2008,20(4):477484

    ;477

    ;www.sciencedirect.corn/

    ;science/journ~/10016058

    ;GENETICPROGRAMMINGTOPREDICTSl(I.JUMPBUCKETSPILL-

    ;WAYSCOUR

    ;AZAMATHULLAH.MD.,GHANIA.AB.,ZAKARIAN.A.,LAIS.H.,CHANGC.K.,L

    EOWC.S.,

    ;ABUHASANZ.

    ;RiverEngineeringandUrbanDrainageResearchCentre,UniversitySainsMalaysia,EngineeringCampus,14300

    ;NibongTebal,PulauPinang,Malaysia,Email:redacazamath@eng.usm.my

    ;(ReceivedNovember2,2007,RevisedApril8,2008)

    ;Abstract:ResearchersinthepasthadnoticedthatapplicationofArtificialNeuralNetworks(ANN)inplaceofconventional

    ;statisticsonthebasisofdataminingtechniquespredictsmoreaccurateresultsinhydraulicpredictions.Mostlytheseworks

    ;pertainedtoapplicationsofANN.Recently,anothertoolofsoftcomputing,namely,GeneticProgramming(GP)hascaughtthe

    ;attentionofresearchersincivilengineeringcomputing.ThisarticleexaminestheusefulnessoftheGPbasedapproachtopredictthe

    ;relativeScourdepthdownstreamofacommontypeofski-jumpbucketspillway.Acmalfieldmeasurementswereusedtodevelopthe

    ;GPmode1.TheGPbasedestimationswerefoundtobeequallyandmoreaccuratethantheANNbasedones,especially,whenthe

    ;underlyingcauseeffectrelationshipbecamemoreuncertaintomode1.

    ;Keywords:GeneticProgramming(GP),neuralnetworks,spillwayscour,ski-jumpbucket ;1.IntrOductiOn

    ;Thedisposaloffloodwaterexceedingthereservoir

    ;capacityisnormallyachievedthroughprovisionof

    ;spillwaysinthebodyofadam.Therearemanytypes

    ;ofspillways,outofwhichtheski-jumpbuckettypeis

    ;morecommonlyused(Fig.1).Theenergydissipation

    ;insuchaspillwayisintheforlTlofaietofwater

    ;leavingawayfromthebucketlipintotheair,andthen,

    ;fallingintotheplungepoolformedatthepointof

    ;impactonthetailwater.Theietimpactistransmitted ;throughcracksandfissuresoftherockintheformof ;hydrodynamicpressurefluctuations,whichmightgive ;risetohydrauliciackingactionandwhichmight ;furthergetintensifiedbecauseofairlocking.This ;causestherockmasstobreakintosmallpiecesthat ;getsweptawayatthedownstreamoftheriver ;resultinginlargeamountofscouring.Thescouringor ;erosioncontinuesuptothepointwherethelmpmgmg ;ietisnomoreabletoexertbreakingpressureonthe ;Biography:AZAMATHULLAH.MD.(1972),Male,Ph.

    ;D.,SeniorLecturer

    ;rockorwherethesecondarycurrents

    ;,

    ;producedare

    ;lessstrongtoremovetherockblocks.Theprocess ;ofscouringalsocontinuestillanequilibriumscour ;depthisreached,whichcorrespondstoasituation ;wheretheincreasedwaterdepthintheScourhole ;resultsinexertionofbedshearstressthatis ;insucienttocausefurtherbederosionortoa ;conditionwheretherateofbederosionisbalancedby ;therateofdepositionofmaterialbroughtbackintothe ;scourholebytheeddyflow.

    ;Therearevarioushydraulic,morphologic,and ;geotechnicalfactorsgoverningthedepthofscour,ds, ;namely,(referringtoFig.1)dischargeintensityq, ;heightoffallH1,bucketradiusR,bucketlipangle,

    ;typeofrock,degreeofrockhomogeneity,time,and ;modeofoperationofspillway.Overaperiodof ;severaldecadesmanyinvestigatorsinthepasthave ;givenempiricalformulaeonthebasisoflaboratoryas ;wellasprototypeobservationsinordertopredictthe ;SCOurdepthdownstreamoftheski~umpbucket ;spillway.Thefollowingformulaearepopularto ;predictspillwayscourdepth:

    ;

    ;

    ;478

    ;Fig.1Theski-jumpbucketspillwayscour[ ;Veroneseformula:(recommendedbythe

    ;USBR[2)

    ;_2.11(g,o?5

    ;Min,sformula[]:

;=1.5gn.’

    ;(2)

    ;(3)

    ;Theaboveformulaeareveryconvenienttouse ;buthaveamajordrawback,thatis.theyinvolve ;idealization,approximation,andaveragingofwidely ;varyingprototypeconditions.Asaresult,the ;predictedscourdepthscanbeconsiderablydifferent ;thantheiractualvalues.Apartfromthecomplexityof ;thephenomenoninvolved,thiscouldalsobebecause ;ofthelimitationoftheanalyticaltoolusedbymostof ;theearlierinvestigators.namely.thestatistical ;regression.

    ;TheuseofasoftcomputingtoollikeArtificial ;NeuralNetworks(ANN)inplaceoftheregressionfor ;theproblemunderconsiderationmetwithlarge ;successasshowninAzamathullaeta1.’andLeeet

    .Recently.Singheta1.appliedgenetic ;a1.

    ;programmingforestimationoftheLongshore ;SedimentTransportRate(LSTR).Moredetailscanbe ;foundinSingheta1..Thisismotivatedthepresent

    ;work.inwhichthescourproblemistackledwiththe ;helpofanothersoftcomputingtool,namely,the ;GeneticProgrammingfGP1andhence,itisextremely ;flexibleindatamining.Inthecurrentstudy,theGPis ;usedtopredicttherelativedepthofscourwhenthe ;ski-jumpbucketspillwayisinvolved.Thescourdepth ;wouldbeusefulindesigningtheplungepoo1. ;2.Geneticprogramming

    ;TheconceptOfGPisborrowedfromtheprocess ;ofevolutionoccurringinnature,wherethespecies ;surviveaccordingtotheprincipleof”survivalofthe

    ;fittest”.GP.abranchoftheGeneticAlgorithm(GA)

    ;

    ;.isamethodforlearningthemost”fit”computer

    ;programsbymeansofartificialevolution[ioj.Inother ;words,itsbehaviorformsametaphoroftheprocesses ;ofevolutioninnature.GP,similartoGA,initializesa ;populationthatcompoundstherandommembers ;knownaschromosomes(individua1).Afterward, ;fitnessofeachchromosomeisevaluatedwithrespect ;toatargetvalue.TheprincipleofDarwiniannatural ;selectionisusedtoselectandreproduce’’fitter’’

    ;programs.ThemaindifferencebetweenGPandGAis

    ;therepresentationofthechromosomesandfmal ;solution.AGAcreatesequallengthstringsof ;numbers(chromosomes)intheformofbinaryorreal, ;whichrepresentthesolution.However,GPcreates ;equalorunequallengthcomputerprograms(Fig.2)(a ;symbolicexpressionthatconsistsofvariables ;(termina1)andseveralmathematicaloperators(Fig.3, ;(function))intheLISPlanguageorothercomputer ;languagesasthesolution.

    ;Fig.2Aparsetreeoftheexpression(+a(/bc)) ;Therefore,unlikeGA,inGPthereisnoneedto ;definetheformoftheobjectivefunctionapriori.In ;fact,itistheGPthatdeterminesnotonlythe ;coefficientsandparametersoftheobjectivefunction ;w

    ;

    ;butalso,andmoreimportantly,theformofthe ;objectivefunctionitself.Thisisoneoftheadvantages ;ofGPascomparedtoGA.AlthoughresearchonGP ;techniquesdatesbacktothe1960sand1970s,GP ;emergedasadistinctdisciplinell1.

    ;Fig.3Anillustrationofamutationoperationforgenetic ;programming

    ;TheapplicationsofGPtosolveproblemsin ;hydraulicengineeringareveryfew.Thereare, ;however,somestudiesdealingwiththesolutionof ;generalcivilengineeringproblemswithGP.Unlike ;theANNtheseworkshavebeenmaderecently. ;typically,abouteightyearsagoandfurther,theyare ;restrictedtorelativelyfewerareasandinclude ;optimizationanddesigningoftrussandother ;structures[12lrainfa11runoffmodelingL.modeling

    ;ofwastewatertreatmentplantsLJ.ultimateshear ;strengthofreinforcedconcretedeepbeams.

    ;estimationofconcretestrengthL….predictionof

    ;stabilityofslopes/J,andevaluationofresistanceto ;flowbyvegetation.

    ;3.GPmodelingofski-jumpbucketscour

    ;AGPsoftware.GPLABinconiunctionwith

    ;subroutinescodedinMatlabwereusedinthisstudy. ;Frompreviousexperience.groupedvariables

    ;producedgoodresults.Theparameters,namely, ;Froudenumber,q/(gHl1”,andtherelativescour

    ;depth.ds//41.wereselectedasinputterminalandthe

;outputterminal,respectively.

    ;Tofindeoptimumformulation.fivefunctions. ;namely,plus,minus,product,division,andpower ;wereused.Alargenumberofgenerationswere ;neededtofindaformulawithminimumerror.First, ;themaximumdepthofthetreeandthelengthofe

    ;branchwereassigned.Withtheseconstants.alarge ;numberofgenerationswererequiredtominimizethe ;error.Theseconstantswerechangedandtheprogram ;wasexecutedtosearchforaformulawithminimum ;errorandasshortaspossibleinlength.Theoptimum ;GPstructurehadthefollowingcharacteristics: ;fl1SelectionMethod:Selectionisdonebythe ;Lexictourmethod.Inthismethod,similartothe ;tournamentapproach,arandomnumberofindividuals ;aretakenfromthepopulationandthebestfitischosen ;Themaindifferenceisthatiftwoindividualsare ;479

    ;equallyfit,theshortestonetreewithfewernodesis ;chosenasthebest.

    ;f21Operations:Theoperationsthatwereusedin ;thisstudywerecrossoverandmutation.Thevwere ;selectedbyadoptingarulewithaminimum ;probabit,,Of0.1.

    ;f31FimessFunction:Thesumofabsolute

    ;differencesbetweentheobtainedandexpected ;gravimetricwatercontentforallsetsofdatainthe ;databasewasusedasameasureforfimess. ;f41Populationsize:300members.

    ;f51Maximumdepthoftreerepresentation ;allowedduringgenerations:5.

    ;f61Totalgenerations:4000.

    ;Themajorityofpreviousresearchworkonscour ;predictionswerebasedonhydraulicmodelstudies….

    ;Whilehydraulicmodelstudieshaveadvantageslike ;repeatability,theyhavehelpedmoreinexploringthe ;scourmechanismthaninobtainingmoreaccuracyin ;thedepthestimation.Scaleeffects.inabilitVtO ;correctlymodelcertainfieldconditionslikebed ;morphologyandlossofflowenergyinaeration,and ;failuretoconsideravarietyofcausativefactors ;simultaneouslyaresomeofthedeficienciesassociated ;withthemodelmeasurements.Itwas,thus,decidedto ;calibratetheneuralnetworksLandGPwiththehelp

    ;ofrealisticfieldconditionsonlyalthoughitis ;recognizedthatprototypemeasurementsmightalso ;sufferfrominstrumentaluncertaintiesand ;inaccuracies.andlackofavailabilityofdataonall ;causativeparameters.

    ;Fig.4Observedscourdepthsagainstvaryingvaluesofgand ;HI

    ;4.GPmodeldevelopmentandvalidation

    ;Amajorityofearlierworksonscourpredictions ;usedthehydraulicmodelstudies,andthepublications ;reportingsuchobservationsindicatedthatonlythree ;typesofinformation,namelyscourdepthbelowtail ;waterlevelds,dischargeintensityq,andheaddrop ;areuniformlyreportedinallreferencesandthatthe ;

    ;480

    ;Table1Observationsoftheprototype5

    ;

    ;48l

    ;Validationset.

    ;

    ;482

    ;informationonotherfactorsaffectingthescourwas ;notcommonlyavailableacrossthem.Althoughthere ;aremanyfactorsthataffecttheSCOurdepth,onlysome ;ofthemareofprimaryimportance.Inaddition ;consideringthatmanytraditionalpredictionformulae, ;includingthosebecauseofVeroneseL”J.Damleet

    ;a1.,Wu,andMartins,arebasedonlyonqandH1. ;A

    ;neuralnetworkwith2inputnodesandoneoutput ;nodeonlywasdevelopedinAzamathullaL….Intota1.

    ;therewere91inDutoutputpairsformedfromthe

    ;publisheddatareportedinDamleeta1.LZ~l,Wu. ;_Manins[,sen[:Spun-[25,wang2,Akhmedov[,

    ;Khatsurl.a[28.

    ;andYildizandOzcek[29,30.Tablel

    ;presentsthecompiledmeasurements.Theyare ;graphicallyshowninFig.4whichshowstheordinates ;oftheobservedscourdepthsagainstthevarying ;valuesofqandH.Presenceofawidescatterand ;absenceoffixedorregularandsimplerelationships ;betweentheseinputoutputvariablescanbenoted.

    ;whichiustifiesapplicationoftheGPfortheprediction

;problemunderconsideration.

    ;Fromthe91datasetsusedinthisstudy,70data ;sets(approximatelyseventyfivepercentofthese ;patterns)chosenrandomlyfillthebesttraining ;performancewasseenwereusedfortraining,whereas ;remainingoneswereusedfortestingorvalidatingGP ;mode1.

    ;5.Analysisandresults

    ;Thescourpredictioninthepresentstudyhasbeen ;madeonthebasisoffielddatareportedearlierin ;Azmathulla[.

    ;

    ;Thepastpublicationsuniformlyreportinput ;valuesof(referringtoFig.1)dischargeintensityq, ;heightoffa11H1,andSCOurdepthbelowtailwater ;level,although,apartfromthese,thetypeofrock, ;degreeofrockhomogeneity,time,andmodeof ;operationofspillwayalsoinfluencethescourprocess. ;TheGPmodelwas,therefore.developedwiththe ;formersetofvaluesasinput(Froudenumber)inorder ;topredicttherelativescourdepth.UnliketheANN ;andANFISmodelsreportedearlierJ.incaseofthese. ;GPbasedforecastswerefoundtobenecessaryto ;predicttheSCOurdepth.ThisaDpearstobeconsistent ;withthefactthat.intheend,theGPgivesaprogram ;(orasetofmathematicalalgorithm)foronlyone ;outputparameterunlikeamatrixofconnection ;weightsandbiaslikeanANNthatmaDstheentire ;inputvectorwiththeoutputvector.

    ;Figure5showstheoutcomeintheformofscatter ;plotforthetestingsetofdata,notinvolvedintraining ;theGP.Foruseinpractice,thepredictionsaregiven ;intermsofSCOurdepth,andanexcellentprediction ;madebytheGPcanbeseen.Thisisquantitatively ;reflectedintheerrorstatisticsoftheCorrelation ;Coecient(CC),theroot.mean.squareerror,RMSE, ;andtheaverageabsoluteerror(deviation)..These ;values,respectively,were0.977,0.861,and0.177for ;theSCOurdepthfTable21.Azamathullaeta1.Lohad ;presentedavarietyofalternativeANNmodelsoffeed ;forwardandcascadecorrelationtypesintheirwork.A ;lookintoallOftheirscatterplotanderrorstatistics ;revealedthatthepredictionaccuraciesofthepresent ;GPmodelsaregenerallycomparabletothevarious

    ;ANNmodels.Additionally.alltheGPmodelshave ;theabsoluteerrorsfmuchlowerthantheANN ;modelsalthoughtheCCandRMSEarerelatively ;somewhatlowerandhigher,respectively.For ;englneenngapplications,theaveragepercentage ;errorsreflectedinthestatistic..couldbemore ;attractive.indicatingbetteracceptabilityoftheGP. ;However,theresultsseemtobenotascertainin ;highvaluepredictionsasreflectedinsomewhatlower ;RMSEandCC.whicharethemeasuressensitiveto ;errorsatlargerobservations.Itisalsopossiblethatthe ;flexibilityinthedataminingapproachesincorporated ;(ANN,GP1mighthavereachedasaturationlevelfor ;thegivensamplesizeandhence,verylargevariations ;intheaccuracylevelsbyeithermethodmightnotbe ;possibletoachieve.However,itisfeltthatingeneral ;that.intheanalysesinvolvinglargersamplesizes,the ;GPcanbeexpectedtobefairlyrelativelybetterthall ;theANNsincetheGPcanhaveverylargedegreesof ;freedomandhence,moreflexibilityinmodelingand ;further,itisnotgovernedbymanyandfixed ;mathematicalfunctions(1ikesigmoidalfunctionand ;variouslearningalgorithms)unliketheANN.This ;aspectneedstobefurtherexploredbyapplyingthe ;GPmethodtosolvemanyothertypesofproblems, ;likethespatialandtemporalmappingaDartfromthe ;presentcauseeffecttype.Thecurrentworkmight

    ;inspiresuchapplicationsinfuture.

    ;Observedrelativescourdepth/m

    ;Fig.5ObservedversuspredictedrelativescourdepthsbyGP ;Itistobenotedthatthepreviousstudy[had

    ;alreadyreportedsuperiorperformanceoftheANN ;modelsthanthetraditionalstatisticalregression ;schemes.Consideringthehigherlevelsofaccuracy ;attainedbyadoptionofsofttoolslikeANNandGP, ;姜长8q%8?焉一aIpal3Ipa

    ;

    ;thesamecanbeadvocatedforregularuseinfuture ;althoughtheregressionisveryeasytoapply.With ;advancesincomputerhardwareandsoftware,the ;applicationofsofttoolsshouldnotposeproblemsin ;evenroutineapplications.

    ;Table2Networkyieldedandtruerelativescourdepths ;F.MeIh

;.dCCRMSE

    ;Av.abs.

    ;deviation,

    ;5GP0.9770.86l0.177

    ;6.Conclusions

    ;Accuratepredictionsofthescourdepthatthebase ;ofski~umpbucketspillwayareessentialforthe ;stabilitywithregardtothedam.Thisarticlehas ;proposedanalternativeapproachOfGPinthe ;estimationofrelativescourdepthusingfielddata.The ;comparisonsbetweenthepresentGPmodelwith ;previousworksofAzamathullaeta1._oJ.alsofound ;mattheGPmodelhasgoodabilityofforecastingthe ;scourdepth.

    ;Inscourestimation.thereareseveralinfluencing ;parameters,suchasthehead,dischargeintensity,and ;mediandiameterofbedmaterial,classifiedasrock ;quality,rockmassratingbyusingGPmodelis ;underway.

    ;Acknowled~ement

    ;Theauthorswishtoexpresstheirsincere ;gratitudetoUniversitySainsMalaysiaforfundinga ;shorttermgrant(304.PREDAC.60352621toconduct ;mison.goingresearch.TheauthorsthankstoPro~ ;DeoM.C..1iTBombayforhishelpinthismanuscript ;preparationbyprovidingusefulliterature. ;References

    ;[2]

    ;[3]

    ;[4]

    ;[5]

    ;MAS0NP.J.,ARUMUGAMK.Freeetscourbelow ;damsandski:jumpbuckets[J].JournalofHydraulic ;Engineering.,ASCE,l985,lll(2):220235.

    ;UNITEDSTATESBUREAU0FRECLAMAT10N.

    ;Designofsmalldams[M].1987.

    ;WU?

Report this document

For any questions or suggestions please email
cust-service@docsford.com