一種基于Kriging模型的天線高維全局優化算法Title:AnAntennaHigh-DimensionalGlobalOptimizationAlgorithmbasedonKrigingModelAbstract:Thispaperpresentsaninnovativeapproachforoptimizingtheperformanceofantennasusingahigh-dimensionalglobaloptimizationalgorithmbasedonKrigingmodel.Antennadesignisacomplextaskthatrequiresbalancingmultipledesignparameterstoachieveoptimalperformance.TheproposedalgorithmtakesadvantageoftheKrigingmodeltomodeltheantenna'sresponsesurfaceandefficientlyexplorethedesignspacetoobtainthebestsetofparametervalues.Theeffectivenessofthealgorithmisdemonstratedthroughextensiveexperimentationandcomparisonwithexistingoptimizationmethods.1.IntroductionAntennadesignplaysacrucialroleinmodernwirelesscommunicationsystems.Theperformanceofantennasishighlydependentonseveraldesignparameters,suchasheight,width,andmaterialsused.Theoptimizationoftheseparametersisachallengingtaskduetothelargeparameterspaceandcomplexinteractionsbetweenparameters.Traditionaloptimizationalgorithmsareoftencomputationallyexpensiveandunabletoefficientlyexploretheentiredesignspace.Therefore,thereisaneedforanefficientandaccurateoptimizationalgorithmthatcanhandlehigh-dimensionaldesignproblems.ThispaperpresentsanovelapproachtoaddressthischallengeusingtheKrigingmodel.2.Background2.1AntennaDesignOptimizationAntennadesignoptimizationinvolvesfindingthebestsetofdesignparametersthatcanmaximizetheperformancemetricsofinterest,suchasgain,radiationpattern,orimpedancematching.Variousoptimizationalgorithms,suchasgeneticalgorithms,particleswarmoptimization,andsimulatedannealing,havebeenappliedtosolveantennadesignproblems.However,thesealgorithmshavelimitationswhendealingwithhigh-dimensionalproblemsduetotheirslowconvergencerateandtheneedforalargenumberoffunctionevaluations.2.2KrigingModelTheKrigingmodel,alsoknownasGaussianprocessregression,isastatisticalinterpolationtechniquewidelyusedinsurrogatemodeling.Itprovidesamathematicalframeworkformodelingtheresponsesurfaceofafunctionbasedonasetofobserveddatapoints.TheKrigingmodelincorporatesbothadeterministiccomponentandaspatiallycorrelatedrandomcomponent,makingiteffectiveformodelingcomplexandirregularresponsesurfaces.3.MethodologyTheproposedalgorithmconsistsofthefollowingsteps:3.1InitializationIntheinitializationphase,aLatinHypercubeSampling(LHS)designisusedtogenerateaninitialsetofsamplepointsintheparameterspace.Thesamplepointsareselectedtoprovidegoodcoverageofthedesignspace.3.2ResponseSurfaceModelingBasedontheinitialsamplepoints,theKrigingmodelisconstructedtoapproximatetheunderlyingresponsesurface.TheKrigingmodelestimatesthevaluesoftheresponsefunctionatanyunobservedpointbasedontheobserveddatapoints,providingasurrogatemodelthatcanbeusedtoevaluatetheobjectivefunctionefficiently.3.3OptimizationUsingtheconstructedKrigingmodel,anoptimizationalgorithm,suchastheSequentialGaussianOptimization(SGO),isemployedtoiterativelysearchfortheglobaloptimum.Eachiterationinvolvesselectinganewsamplepointbasedonanacquisitionfunctionthatbalancesexplorationandexploitation.TheacquisitionfunctionquantifiestheuncertaintyoftheKrigingmodelandguidesthesearchtowardsregionswithhighpotentialforimprovement.3.4ValidationandRefinementOncetheoptimizationprocessconverges,theobtainedsolutionisvalidatedusingamoreaccurateevaluationoftheobjectivefunction.Ifnecessary,theKrigingmodelcanberefinedbyincorporatingthevalidateddataintothemodel,improvingitsaccuracyforfutureoptimizationruns.4.ExperimentalResultsToevaluatetheproposedalgorithm,severalantennadesignproblemswithdifferentdimensionsandcomplexitylevelsareconsidered.Theresultsobtainedusingtheproposedalgorithmarecomparedwithotherstate-of-the-artoptimizationmethods,suchasgeneticalgorithmsandparticleswarmoptimization.Thecomparisonisbasedonperformancemetrics,suchassearchefficiency,convergencespeed,andsolutionquality.5.ConclusionThispaperpresentsahigh-dimensionalglobaloptimizationalgorithmforantennadesignbasedontheKrigingmodel.Theproposedalgorithmdemonstratesexcellentperformanceintermsofsearchefficiency,convergencespeed,andsolutionquality.Itofferssignificant