多学科设计优化代理模型技术的研究应用

南京航空航天大学硕士学位论文-1-摘要代理模型是多学科设计优化中一种包含试验设计和近似方法等多项内容的建模方法，它通过在系统中用数学模型来替代原有分析模块的方式，实现了分析模块与MDO计算框架的集成，使复杂系统的多学科设计优化变的切实可行。本文系统分析了多学科设计优化方法中代理模型的构造过程，比较了几种相关的试验设计方法和数学近似方法。通过对比分析，我们认为要构造代理模型就必须引入能够大大减少试验次数的试验设计方法和能够解决高维非线性问题的近似方法。为此本文中分别介绍了正交试验，均匀试验以及中心复合试验等几种试验设计方法，以及多项式响应面，Kriging，和径向基函数等几种数学近似方法。并且通过构造描述机翼展向升力分布的代理模型，对上述几种方法作了对比分析。算例的结果表明，试验设计方法的选取与要解决问题的规模直接相关。同时计算结果还显示，Kriging模型和径向基函数模型作为两种通用模型，可以很好的解决一般的高维非线性代理模型的构造问题；另外，从算例问题的物理本质出发所构造的广义多项式响应面模型也能够满足精度要求。关键词：多学科设计优化代理模型试验设计近似方法多项式响应面模型Kriging模型径向基函数模型多学科设计优化代理模型技术的研究应用-2-AbstractSurrogatemodelisanimportantcomponentofMultidisciplineDesignOptimization(MDO).Asurrogatemodeliscreatedwithexperimentdesignmethodsandapproximationapproaches,anditcanbeeasilyintegratedintoaMDOFramework.ThisarticledescribesthedevelopmentprocessofsurrogatemodelsandintroducessomeexperimentdesignmethodsandapproximationapproachesthatcanbeusedforaMDOsurrogatemodel,theyareFullFactorialExperimentDesign,OrthogonalExperimentDesign,UniformExperimentDesign,Central-CompositeExperimentDesign,andPolynomialResponseSurfacemethod,Krigingmethod,RadialBasisFunctionmethodandArtificialNeuralNetwork.Attheendofthisarticle,asurrogatemodeliscreatedtodescribetheliftdistributionofawing.ResultshowsthatKrigingmethodandRBFmethodaretwousefulapproximationapproaches,especiallyforhighdimensionproblem.Inaddition,thisarticlecreatedageneralizedpolynomialresponsesurfacemodel,andresultshowsthatitcanbealsousedtodescribetheliftdistribution.Keywords:MultidisciplineDesignOptimization,Surrogatemodel,DesignofExperiment,Approximationapproaches,PolynomialResponseSurfacemethod,Krigingmethod,RadialBasisFunctionmethod南京航空航天大学硕士学位论文-3-目录一.绪论....................................................................................................................................................51.1多学科设计优化的兴起.................................................................................................................51.2代理模型的出现.............................................................................................................................61.3本文的研究内容.............................................................................................................................7参考文献...............................................................................................................................................7二.代理模型技术..................................................................................................................................102.1试验设计方法..............................................................................................................................102.1.1全析因试验设计....................................................................................................................102.1.2正交试验设计........................................................................................................................112.1.3均匀试验设计........................................................................................................................122.1.4中心复合试验设计................................................................................................................132.2近似方法.......................................................................................................................................142.2.1多项式响应面模型................................................................................................................152.2.2.Kriging模型...........................................................................................................................162.2.3径向基函数模型....................................................................................................................182.2.4人工神经网络模型................................................................................................................202.3小结..............................................................................................................................................22参考文献.............................................................................................................................................23三.机翼多学科设计优化问题中的气动建模.......................................................................................263.1问题的由来..................................................................................................................................263.2机翼外形的建模...........................................................................................................................273.2.1机翼的展向弯曲变形............................................................................................................283.3.2机翼的扭转变形....................................................................................................................283.2.3机翼弯扭组合变形................................................................................................................293.3CFD软件MGAERO......................................................................................................................