A variable-fidelity method can remarkably improve the efficiency of a design optimization based on a high-fidelity and expensive numerical simulation,with assistance of lower-fidelity and cheaper simulation(s).However...A variable-fidelity method can remarkably improve the efficiency of a design optimization based on a high-fidelity and expensive numerical simulation,with assistance of lower-fidelity and cheaper simulation(s).However,most existing works only incorporate‘‘two"levels of fidelity,and thus efficiency improvement is very limited.In order to reduce the number of high-fidelity simulations as many as possible,there is a strong need to extend it to three or more fidelities.This article proposes a novel variable-fidelity optimization approach with application to aerodynamic design.Its key ingredient is the theory and algorithm of a Multi-level Hierarchical Kriging(MHK),which is referred to as a surrogate model that can incorporate simulation data with arbitrary levels of fidelity.The high-fidelity model is defined as a CFD simulation using a fine grid and the lower-fidelity models are defined as the same CFD model but with coarser grids,which are determined through a grid convergence study.First,sampling shapes are selected for each level of fidelity via technique of Design of Experiments(DoE).Then,CFD simulations are conducted and the output data of varying fidelity is used to build initial MHK models for objective(e.g.C_D)and constraint(e.g.C_L,C_m)functions.Next,new samples are selected through infillsampling criteria and the surrogate models are repetitively updated until a global optimum is found.The proposed method is validated by analytical test cases and applied to aerodynamic shape optimization of a NACA0012 airfoil and an ONERA M6 wing in transonic flows.The results confirm that the proposed method can significantly improve the optimization efficiency and apparently outperforms the existing single-fidelity or two-level-fidelity method.展开更多
翼型及机翼优化设计中,设计变量的个数对优化算法的收敛速度及代理模型的精度有很大的影响。因此,在精确描述翼型的同时,发展较少设计变量的翼型参数化方法对翼型优化设计有着重要的意义。本文基于CST(class function/shape function tr...翼型及机翼优化设计中,设计变量的个数对优化算法的收敛速度及代理模型的精度有很大的影响。因此,在精确描述翼型的同时,发展较少设计变量的翼型参数化方法对翼型优化设计有着重要的意义。本文基于CST(class function/shape function transformation)翼型参数化方法对Kriging模型的预测精度进行研究,并采用改进的粒子群优化算法构建气动优化设计系统。某亚声速机翼单点减阻设计及超临界翼型的稳健性设计表明该系统具有较高的设计质量,方法可靠,有较高的工程应用前景。展开更多
基金sponsored by the National Natural Science Foundation of China(Nos.11772261 and 11972305)Aeronautical Science Foundation of China(No.2016ZA53011)Foundation of National Key Laboratory(No.JCKYS2019607005).
文摘A variable-fidelity method can remarkably improve the efficiency of a design optimization based on a high-fidelity and expensive numerical simulation,with assistance of lower-fidelity and cheaper simulation(s).However,most existing works only incorporate‘‘two"levels of fidelity,and thus efficiency improvement is very limited.In order to reduce the number of high-fidelity simulations as many as possible,there is a strong need to extend it to three or more fidelities.This article proposes a novel variable-fidelity optimization approach with application to aerodynamic design.Its key ingredient is the theory and algorithm of a Multi-level Hierarchical Kriging(MHK),which is referred to as a surrogate model that can incorporate simulation data with arbitrary levels of fidelity.The high-fidelity model is defined as a CFD simulation using a fine grid and the lower-fidelity models are defined as the same CFD model but with coarser grids,which are determined through a grid convergence study.First,sampling shapes are selected for each level of fidelity via technique of Design of Experiments(DoE).Then,CFD simulations are conducted and the output data of varying fidelity is used to build initial MHK models for objective(e.g.C_D)and constraint(e.g.C_L,C_m)functions.Next,new samples are selected through infillsampling criteria and the surrogate models are repetitively updated until a global optimum is found.The proposed method is validated by analytical test cases and applied to aerodynamic shape optimization of a NACA0012 airfoil and an ONERA M6 wing in transonic flows.The results confirm that the proposed method can significantly improve the optimization efficiency and apparently outperforms the existing single-fidelity or two-level-fidelity method.
文摘翼型及机翼优化设计中,设计变量的个数对优化算法的收敛速度及代理模型的精度有很大的影响。因此,在精确描述翼型的同时,发展较少设计变量的翼型参数化方法对翼型优化设计有着重要的意义。本文基于CST(class function/shape function transformation)翼型参数化方法对Kriging模型的预测精度进行研究,并采用改进的粒子群优化算法构建气动优化设计系统。某亚声速机翼单点减阻设计及超临界翼型的稳健性设计表明该系统具有较高的设计质量,方法可靠,有较高的工程应用前景。
