【作者】 张瑜；

【导师】 韩忠华；

【作者基本信息】 西北工业大学 ， 空气动力学， 2021， 博士

【摘要】 稳健气动优化设计方法能够在优化过程中考虑飞行状态或加工误差等不确定性因素的影响,对提升飞行器在工作状态下气动性能的鲁棒性具有重要意义。但是稳健优化由于需要对每个候选外形采用计算流体力学(CFD)分析进行不确定性量化,即使采用代理模型代替费时的CFD分析程序,其计算量仍然过大,难以满足实际工程快速、稳健的设计需要。针对该问题,本文首先对多可信度代理模型和优化加点方法展开研究,发展了高效的气动优化设计方法,然后对基于多可信度代理模型的不确定性量化方法展开研究,给出了误差估计和收敛性分析,最后提出了一种高效的稳健气动优化设计新方法,并应用于自然层流翼型和跨声速机翼稳健设计,为开展满足实际工程稳健性需要的飞行器气动外形设计提供了理论与算法基础。本文主要开展了以下几方面研究:(1)发展了一种设计空间自适应的代理优化方法,解决了设计空间过大导致全局优化困难的问题。在优化过程中,根据当前最优样本点位置不断移动和调整设计空间,从而求解初始解远离最优解的优化问题。NACA0012翼型跨声速减阻优化算例和宽体客机机翼多点减阻优化设计算例结果表明,所提出的方法能够有效求解翼型/机翼单目标、多目标的气动优化设计问题;(2)提出了一种多可信度改善期望(EI)优化加点准则,显著提高了气动优化设计的效率。在优化过程中自适应判断新增样本点的可信度层和位置,充分利用低可信度的样本信息辅助寻优,使优化收敛于高可信度优化目标的最优解,大大提高了基于高可信度CFD的全局气动优化设计的效率。采用RAE2822翼型跨声速减阻优化设计和M6机翼无黏减阻优化设计算例,通过与单可信度优化和采用EI加点准则的多可信度优化方法对比,验证了本文提出的多可信度优化新方法的高效性;(3)提出了一种基于多可信度代理模型的RANS-LES优化方法,显著提高了高可信度数值模拟优化问题的优化效率。该方法采用Spa RTA机器学习方法,利用高可信度大涡模拟(LES)数据建立数据驱动湍流模型,改善低可信度雷诺平均Navier-Stokes(RANS)分析的精度,并在优化过程中利用新增高可信度LES样本数据更新湍流模型,增强了高、低可信度函数的相关性,从而显著提高了RANS-LES变可信度代理模型的精度,减少了优化所需的高可信度LES样本点数。周期山优化算例表明仅需2个高可信度LES样本点,就能获得优化问题的最优解;(4)开展了基于多可信度代理模型的高效不确定性量化方法的误差估计和计算量收敛性理论分析。推导了在给定不确定性量化精度要求下,使计算量最小的多可信度层样本点理论最优抽样个数。与蒙特卡洛、多层蒙特卡洛和基于单可信度代理模型的不确定性量化方法进行了对比。结果表明,在相同的不确定性量化精度要求下,多可信度代理模型方法的计算量最小,且随着精度要求的提高,计算量增长速度最缓。采用地下水渗透率不确定的达西流问题和几何不确定的翼型气动性能量化问题,对本文提出的理论分析结果进行了验证;(5)提出了一种结合多可信度不确定性量化方法和多可信度EI优化加点准则的高效稳健气动优化设计新方法。充分利用多可信度数据辅助代理模型进行预测,显著减少了不确定性量化和优化所需的高可信度CFD分析次数,大大提高了稳健气动优化的效率。对于高可信度CFD分析十分费时的优化问题,进一步发展了递进式多轮多可信度稳健优化策略,能够快速获得工程实用的稳健设计。通过考虑工况不确定性的RAE2822翼型减阻稳健优化设计算例对所提出的方法进行了验证,优化效率明显高于单可信度方法;(6)应用所发展的高效稳健气动优化设计新方法,开展了自然层流翼型和跨声速机翼稳健气动优化设计研究。分别开展了仅考虑T-S(Tollmien-Schlichting)波扰动诱导的转捩放大因子(NT S)tr不确定性和同时考虑(NT S)tr和升力系数不确定性的自然层流翼型高升力稳健气动优化设计,以及同时考虑工况和几何不确定性的跨声速机翼减阻优化设计。结果表明,采用本文发展的高效不确定性量化和稳健气动优化设计方法,能够快速获得稳健的设计结果。与确定优化的结果对比,稳健优化设计外形的气动性能更加鲁棒,在不确定性因素扰动下能够维持较优的气动性能。更多还原

【Abstract】 Robust design optimization(RDO),which can take the uncertainties in manufacturing,op-erating conditions et al.into consideration,is of great significance in improving the robustness of aerodynamic performance of an aircraft.However,as the uncertainty of each of the de-signs generated during the optimization has to be quantified using computational fluid dynam-ics(CFD),RDO is very time-consuming.Even though surrogate models can be used to take place of CFD simulations,it is still unaffordable for engineering application.To address this problem,in this thesis,first,we studied the multi-fidelity surrogate model and infill-sampling criterion,and then developed an efficient aerodynamic design optimization method; second,rigorous convergence and computational cost analyses are provided for multi-fidelity surrogate model based uncerntainty quantification method; finally,an efficient RDO method is proposed and applied to the designs of natural-laminar-flow airfoil and transonic-flow wing.The studies can provide support for the theory and algorithms of the robust design of modern aircrafts.(1)An adaptive design space technique is developed for surrogate-based aerodynamic shape optimization.This method can automatically adjust the design space during an optimiza-tion for guiding the design to the optimum,while all the sample points are adopted to train the surrogate models.As a result,for global optimization using the surrogate-based opti-mization(SBO),the design space is avoided to be too large to generate odd designs and lead to failure.The proposed method is applied to drag minimizations of a NACA0012 airfoil in inviscid flow and a supercritical wing of a large-civil aircraft at multiple design points,which shows that the proposed method is feasible and effective for single/multi-objective aerodynamic shape optimization problems,with good capability of constraint handling and global optimization;(2)A multi-fidelity EI(MFEI)criterion is proposed for efficient aerodynamic design optimiza-tion.A correction based multi-fidelity surrogate model(via additive-bridge function)and a multi-fidelity hierarchical Kriging model are studied and implemented.Then,through maximizing the MFEI function,both the sample location and fidelity level of next nu-merical evaluation can be determined,which is used to update the multi-fidelity surrogate models,and in turn drives the optimization converging to the global optimum of the high-fidelity function.The proposed multi-fidelity optimization method is demonstrated by two engineering problems,including aerodynamic shape optimizations of a RAE 2822 airfoil in transonic viscous flow and a ONERA M6 wing in transonic inviscid flow.The repeating tests show that the proposed method can remarkably improve the optimization efficiency and compares favorably to the existing methods;(3)An efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation(LES)and enhanced Reynolds-averaged Navier-Stokes(RANS)as the high- and low-fidelity analyses is proposed.Machine-learning techniques,specif-ically sparse regression to obtain corrections of the turbulence anisotropy tensor and the production of turbulence kinetic energy are used to derive a custom-tailored RANS closure model.As the correlation between LES and enhanced RANS are dramatically strength-ened,the accuracy of bi-fidelity surrogate model is remarkably improved.Our method therefore offers a promising path towards LES-quality optimization with only a handful of LES samples.A proof-of-concept shape optimization of the well-known periodic-hill case is presented,which shows that our method can converge to the LES-optimum with only two LES samples;(4)Rigorous convergence and computational cost analyses are provided for a multi-fidelity surrogate based uncertainty quantification(UQ).By minimizing the total cost,optimal numbers of sampling points on each grid level are determined.Numerical tests demon-strate the theoretical results for Darcy flow with random conductivity coefficients,and RANS flow over an airfoil with geometric uncertainties.The efficiency and accuracy of this method are compared with standard- and multi-level Monte Carlo.All the test cases show that using the proposed multi-fidelity method can significantly reduce the cost of CFD based UQ;(5)Based on the multi-fidelity UQ method and MFEI criterion,an efficient robust aerody-namic design optimization method is proposed.For optimization problem with plenty of design and uncertain variables,the multi-fidelity surrogate model based UQ and optimiza-tion method can significantly improve the efficiency; For problem using expensive high-fidelity CFD analysis,a progressive multi-round multi-fidelity strategy are developed to further save the cost.Robust design of transonic airfoil under operational uncertainties is adopted to verify the proposed methods.The comparison with single-fidelity optimization proves the effectiveness and efficiency of the proposed method;(6)The proposed efficient method is applied to the designs of natural-laminar-flow airfoil and transonic-flow wing.The cases include drag optimizations of a NLF airfoil consider-ing the uncertainty in Tollmien-Schlichting transition critical N factor with or without the uncertainty in lift coefficient,and a transonic wing under the operational and geometric uncertainties.The results show that the proposed method can optimize the configuration within affordable computational budget.Compared with the deterministic optimum,the robust configurations are significantly less sensitive to input variation.更多还原