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
在飞行器的气动外形优化设计中,参数化方法和优化算法具有十分重要的作用,对优化的计算时间设计空间的数学特性有着深刻的影响.类别形状函数(class and shape transformation,CST)方法是一种简洁高效的参数化方法,但对于复杂曲面很难使...在飞行器的气动外形优化设计中,参数化方法和优化算法具有十分重要的作用,对优化的计算时间设计空间的数学特性有着深刻的影响.类别形状函数(class and shape transformation,CST)方法是一种简洁高效的参数化方法,但对于复杂曲面很难使用统一的CST方法进行拟合.文章首先介绍了CST方法的三维实现,分析了其数学性质,提出了分块CST参数化方法,保留CST方法的特性,实现了分块曲面之间的光滑连接.针对气动外形优化设计的复杂情况,需要根据具体的飞行任务提出设计目标,并处理不同目标的矛盾问题.其次采用Pareto策略自动寻找最优方案集,并基于分块CST参数化方法遗传算法和气动力快速计算方法,对类乘波翼身组合飞行器进行了优化设计,并改变原有问题的设定条件优化得到了全新外形.研究结果表明分块CST方法参数少,精度高,Pareto策略处理多目标准确有效,是气动外形优化设计中非常有用的工具.展开更多
This paper presents a novel optimization technique for an efficient multi-fidelity model building approach to reduce computational costs for handling aerodynamic shape optimization based on high-fidelity simulation mo...This paper presents a novel optimization technique for an efficient multi-fidelity model building approach to reduce computational costs for handling aerodynamic shape optimization based on high-fidelity simulation models. The wing aerodynamic shape optimization problem is solved by dividing optimization into three steps—modeling 3D（high-fidelity） and 2D（lowfidelity） models, building global meta-models from prominent instead of all variables, and determining robust optimizing shape associated with tuning local meta-models. The adaptive robust design optimization aims to modify the shape optimization process. The sufficient infilling strategy—known as adaptive uniform infilling strategy—determines search space dimensions based on the last optimization results or initial point. Following this, 3D model simulations are used to tune local meta-models. Finally, the global optimization gradient-based method—Adaptive Filter Sequential Quadratic Programing（AFSQP） is utilized to search the neighborhood for a probable optimum point. The effectiveness of the proposed method is investigated by applying it, along with conventional optimization approach-based meta-models, to a Blended Wing Body（BWB） Unmanned Aerial Vehicle（UAV）. The drag coefficient is defined as the objective function, which is subjected to minimum lift coefficient bounds and stability constraints. The simulation results indicate improvement in meta-model accuracy and reduction in computational time of the method introduced in this paper.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.
文摘在飞行器的气动外形优化设计中,参数化方法和优化算法具有十分重要的作用,对优化的计算时间设计空间的数学特性有着深刻的影响.类别形状函数(class and shape transformation,CST)方法是一种简洁高效的参数化方法,但对于复杂曲面很难使用统一的CST方法进行拟合.文章首先介绍了CST方法的三维实现,分析了其数学性质,提出了分块CST参数化方法,保留CST方法的特性,实现了分块曲面之间的光滑连接.针对气动外形优化设计的复杂情况,需要根据具体的飞行任务提出设计目标,并处理不同目标的矛盾问题.其次采用Pareto策略自动寻找最优方案集,并基于分块CST参数化方法遗传算法和气动力快速计算方法,对类乘波翼身组合飞行器进行了优化设计,并改变原有问题的设定条件优化得到了全新外形.研究结果表明分块CST方法参数少,精度高,Pareto策略处理多目标准确有效,是气动外形优化设计中非常有用的工具.
文摘This paper presents a novel optimization technique for an efficient multi-fidelity model building approach to reduce computational costs for handling aerodynamic shape optimization based on high-fidelity simulation models. The wing aerodynamic shape optimization problem is solved by dividing optimization into three steps—modeling 3D（high-fidelity） and 2D（lowfidelity） models, building global meta-models from prominent instead of all variables, and determining robust optimizing shape associated with tuning local meta-models. The adaptive robust design optimization aims to modify the shape optimization process. The sufficient infilling strategy—known as adaptive uniform infilling strategy—determines search space dimensions based on the last optimization results or initial point. Following this, 3D model simulations are used to tune local meta-models. Finally, the global optimization gradient-based method—Adaptive Filter Sequential Quadratic Programing（AFSQP） is utilized to search the neighborhood for a probable optimum point. The effectiveness of the proposed method is investigated by applying it, along with conventional optimization approach-based meta-models, to a Blended Wing Body（BWB） Unmanned Aerial Vehicle（UAV）. The drag coefficient is defined as the objective function, which is subjected to minimum lift coefficient bounds and stability constraints. The simulation results indicate improvement in meta-model accuracy and reduction in computational time of the method introduced in this paper.
