文献翻译混合整数非线性规划的优化对结构的合成方法.docx

文献翻译混合整数非线性规划的优化对结构的合成方法.docx

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文献翻译混合整数非线性规划的优化对结构的合成方法

ABSTRACT

PartIIIofthisthree-partseriesofpapersdescribesthesynthesisofrollerandslidinghydraulicsteelgatestructuresperformedbytheMixed-IntegerNon-linearProgramming（MINLP）approach.TheMINLP

approachenablesthedeterminationoftheoptimalnumberofgatestructuralelements（girders,plates）,optimalgategeometry,optimalintermediatedistancesbetweenstructuralelementsandallcontinuousand

standardcrossectionalsizes.Forthispurpose,speciallogicalconstraintsfortopologyalterationsandinterconnectionrelationsbetweenthealternativeandfixedstructuralelementsareformulated.TheyhavebeenembeddedintoamathematicaloptimizationmodelforrollerandslidingsteelgatestructuresGATOP.GATOPhasbeendevelopedaccordingtoaspecialMINLPmodelformulationformechanicalsuperstructures（MINLP-MS）,introducedinPartsIandII.Themodelcontainsaneconomicobjectivefunctionofself-manufacturingandtransportationcostsofthegate.AstheGATOPmodelisnon-convexandhighlynon-linear,itissolvedbymeansoftheModifiedOA/ERalgorithmaccompaniedbytheLinkedTwo-PhaseMINLPStrategy,bothimplementedintheTOPcomputercode.Anexampleofthesynthesisispresentedasacomparativedesignresearchworkofthealreadyerectedrollergate,theso-calledIntakeGateinAswanIIinEgypt.Theoptimalresultyields29）4percentofnetsavingswhencomparedtotheactualcostsoftheerectedgate..1998JohnWiley&Sons,Ltd.

KEYWORDS:

structuralsynthesis;optimization;topologyoptimization;discretevariableoptimization;Mixed-IntegerNon-linearProgramming;MINLP;theModifiedOA/ERalgorithm;MINLPstrategy;hydraulicgate;slidinggate;rollergate;Aswan

1.INTRODUCTION

ThispaperdescribestheMixed-IntegerNon-linearProgramming（MINLP）approachtothesynthesisofrollerandslidinggatestructures,i.e.thesimplesttypesamongvertical-lifthydraulicsteelgates,seeFigure1.Rollerandslidinggatesarealsoregardedasthemostfrequentlymanufacturedtypesofhydraulicsteelgatesforheadwatercontrol.Theyareusedtoregulatethewaterstreamonhydro-electricplants,damsorspillways.

Ashydraulicsteelgatesareveryspecialstructures,onlyafewauthorshavediscussedtheiroptimization,e.g.Kravanjaetal.,1D.JongelingandKolkman.aswellasAlmquistetal..Particularinterestwasshownintheoptimizationnotofthese（rollerandslidinggates）butofsimilarstructures.Insuchinvestigations,VanderplaatsandWeisshaar.aswellasGurdaletal..optimizedstiffenedlaminatedcompositepanels,Butler.andRingertz.optimizedstiffenedpanels,FarkasandJarmai1.optimizedweldedrectangularcellularplates,Finckenoretal.1.treatedskinstringercylindersandGendyetal.1.stiffenedplates.AlmostallauthorsusedNon-linearProgramming（NLP）techniques.Gurdaletal..proposedthegeneticalgorithm,whileKravanjaetal.1D.introducedMINLPalgorithmsandstrategiestothesimultaneoustopologyandparameteroptimizationofthegate.

InPartsIofthisthree-partseriesofpapers,ageneralviewoftheMINLPapproachtothesimultaneoustopologyandparameteroptimizationofstructuresispresented.PartIIdescribestheextensiontothesimultaneousstandarddimensionoptimization.BasedonthesuperstructureapproachdefinedinPartsIandII,themainobjectiveofthispaper（PartIII）istheMINLPsynthesisofrollerandslidinghydraulicsteelgatestructures,obtainedatminimalgatecostsandsubjectedtodefineddesign,material,stress,deflectionandstabilityconstraints.AstheMINLPapproachenablessimultaneoustopology,parameterandstandarddimensionoptimization,anumberofgatestructuralelements（girdersandplates）,thegateglobalgeometry,intermediatedistancesbetweenstructuralelementsandallcontinuousandstandarddimensionsareobtainedsimultaneously.Thislastpartofthethree-partseriesofpapersisdividedintothreemainsections:

1.Section2describeshowdifferenttopologyandstandarddimensionalternativesarepostulatedandhowtheirinterconnectionrelationsareformulatedbymeansofexplicitlogicalconstraintsinordertoperformtopologyandstandarddimensionalterationswithintheoptimizationprocedure.

2.Section3representsageneralMINLPoptimizationmodelforrollerandslidinggatestructuresGATOP.

3.Finally,inSection4,theproposedsuperstructureMINLPapproachisappliedtothesynthesisofanalreadyerectedrollergate,theso-calledIntakeGateinAswanIIinEgypt.

2.SUPERSTRUCTUREALTERNATIVESANDTHEMODELLINGOFTHEIRDISCRETEDECISIONS

2.1.Postulationoftopologyandstandarddimensionalternatives

ThefirststepinthesynthesisofthegateisthegenerationofanMINLPsuperstructureinwhichdifferenttopology/structureandstandarddimensionalternativesareembeddedtobeselectedastheoptimalresult.Thegatesuperstructurealsocontainstherepresentationofstructuralelementswhichmayconstructeachpossiblestructurealternativeaswellasdifferentsetsofdiscretevalues,definedforeachstandarddimensionalternative.Asboththerollerandslidinggateshavealmostthesamestructure,itwasreasonabletoproposeasuperstructure,whichcouldwellbeusefulforbothofthem.

2.1.1.Topologyalternatives

Thegatesuperstructuretypicallyincludesarepresentationofmaingateelements,whereeachgateelementiscomposedofvariousstructuralelements,suchashorizontalgirders,verticalgirders,stiffenersandplateelementsoftheskinplate,seeFigure2.Thesuperstructurecomprises

nmaingateelements,n3N,eachcontainingmhorizontalgirders,m3M,the（3#2v）numberofverticalgirdersthroughtheentiregate,v3.,andthecorresponding（m!

1）]（2#2v）numberofskin-plateelements.

Toeachmthhorizontalgirderofthenthmaingateelementanextrabinaryvariableyn,misassigned.Thenumberofhorizontalgirdersandcorrespondingplateelementsoftheskinplate,distributedoverthenthmaingateelement,canthereforebedeterminedsimplyby

.Note

thattheproposedminimalnumberofidenticalverticalgirdersis3andthattheycantakeonlyoddnumbers.Ifabinaryvariableyvisassignedtoeachv,v∈V.,thenumberofverticalgirderscanbeobtainedby（3+2∑vyv）.Inthesamewayanevennumber（2+2.∑vyv）ofequalhorizontalpartitionsoftheentiregateisproposed.Inthecaseofverticalgirders,wecanseethatthestructuralelementscanalsobedeterminedbysuitablelinearcombinationsofbinaryvariables.AmongthemaximalnumberMmaxofhorizontalgirderspereachmaingateelement,theupperandlowergirderstogetherwiththeminimalnumberMminofintermediatehorizontalgirdersandtheadjoiningskin-plateelementsaretreatedasfixedstructuralelements,whicharealwayspresentintheoptimization.Allother（Mmax–Mmin）intermediatehorizontalgirderswiththecorrespondingnumberofadjoinedskin-plateelementsarethenregardedasalternativestructuralelements,whichmayeitherdisappearorbeselected.Sinceonlyalternativestructuralelementsparticipateinthediscreteoptimization,thesizeofthediscretedecisionsissignificantlyreduced.Eachpossiblecombinationbetweenselectedalternativestructuralelementsandfixedstructuralelementsformsanextragatetopology/structurealternative.

2.1.2.Standarddimensionalternatives

Fourstandarddimensionsareadditionallydefinedtorepresentthestandardthicknessesofsheet-ironplates:

thethicknessoftheskin-platetsnforeachnthmaingateelement,the.flangethicknessofthehorizontalgirdertfn,thewebthicknessoftheouterhorizontalgirder

m=1orm=M,andthewebthicknessoftheinnerhorizontalgirder

1（m（M.Sincethethicknesstsnhasacommonvaluefortheentireskin-plateofthenthmaingateelementandthetarethesameforallhorizontalgirdersofthenthmaingateelement,i.e.theycorrespondtothecommonstandarddesignvariablesforthesuperstructureoritspart

fromthespecial

MINLP-MSmodelformulationinPartII.Similarly,thewebthicknesses

whichtakeacommonvalueforbothouterhorizontalgirdersofthenthmaingateelement,and

whicharethesameforalltheinnerhorizontalgirders,correspondtothecommonstandarddesignvariables

ofthealternativestructuralelements.Anextrasetofdiscretevaluesofstandarddimensionalternativesandaspecialsetofthesamesizeofbinaryvariablesareintroducedforeachmentionedstandarddimension.

Eachstandarddimensiontsnshallbeexpressedwithinthegivenistandarddimensionalternatives,i∈I,standarddimensiontfnbykalternatives,k∈K,standarddimension

bypalternatives,p∈P,andstandarddimension

byralternatives,r∈R.Thevectorofibinaryvariables

yn,iandthevectorofidiscretevaluesqn,Iareassignedtothevariabletsn,thevectorsofkelementsyn,kandqn,ktothevariabletfn,thevectorsofpelementsyn,pandqn,ktothevariable

andthevectorsofrelementsyn,vandqn,vtothevariable

Consequently,theoverallvectorofbinaryvariablesassignedtothegatesuperstructureisy={yn,m,y,v,yn,I,yn,p,yn,v}

2.2.Modelingofdiscretedecisions

ThepostulatedgatesuperstructureoftopologyandstandarddimensionalternativescanbeformulatedasanMINLPproblemusingaspecialMINLPmodelformulation（MINLP-MS）forsimultaneoustopology,parameterandstandarddimensionoptimizationofmechanicalsuperstructures,describedinPartII.Ascanbeseenfromthe（MINLP-MS）,theobjectivefunctionistypicallysubjectedtostructuralanalysisandlogicalconstraints.Whilestructuralanalysisconstraintsrepresentamathematicalmodelofasynthesizedstructure,logicalconstraintsareusedfortheexplicitmodelingoflogicald