Variable-fidelity optimization with design space reduction

Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity (LF) model provides physics-based approximation of the high-fidelity (HF) model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.     

基于代理模型的气动外形优化

探讨了一种将CAD软件、CFD商用软件与代理模型相结合的飞机气动外形优化方法。重点介绍建立气动分析代理模型的过程,这一过程包括确定设计变量及其取值范围、生成试验设计点、建立参数化几何模型、CFD数值计算、提取气动特性和构造代理模型。通过一个简单的机翼气动外形优化算例验证了这种方法的可行性和有效性。     

基于神经网络的翼型优化设计方法研究

针对气动外形优化设计中,气动特性计算可信度要求与巨大计算量之间的矛盾,采用一种基于神经网络构建适用于气动外形优化设计的气动特性计算模型的计算方法.同时,以神经网络近似模型来代替原有的流场数值计算气动分析程序,结合基于遗传算法建立的气动外形优化搜索方法,建立了一种新的翼型优化设计方法.实际翼型优化设计算例表明该方法有效减少了计算量,提高了工作效率,可以获得具有高可信度的设计结果.     

基于代理模型的高效全局气动优化设计方法研究进展

基于高可信度计算流体力学的数值优化设计方法，在提高飞行器气动与综合性能方面正发挥着越来越重要的作用。基于代理模型的优化算法（SBO），由于能够实现高效全局优化，逐渐成为了气动优化设计领域的研究热点之一。近20年来，代理优化算法研究已取得了长足进步，多种先进的新型代理模型被提出，优化理论和算法也不断完善和发展。以飞行器精细化气动优化设计为背景，综述了基于代理模型的高效全局气动优化设计方法研究进展。首先，介绍了基于变可信度代理模型的气动优化设计方法、结合代理模型和伴随方法的气动优化设计方法以及基于非生物进化的并行气动优化设计方法的研究现状和最新进展。然后，针对飞行器气动优化设计学科领域的前沿问题，介绍了基于代理模型的多目标气动优化设计方法、混合反设计/优化设计方法、稳健气动优化设计方法的研究进展，以及基于代理模型的多学科优化设计方法的研究进展。文献综述表明，代理优化算法在设计效率、全局性以及鲁棒性等方面性能优良，已经发展到可以解决100维（100个设计变量）以内的气动优化设计问题，具有良好的工程应用前景。最后，探讨了基于代理模型的高效全局气动优化设计在理论、方法及飞行器设计应用方面所面临的问题和挑战，给出了未来研究方向的建议。     

Application of a PCA-DBN-based surrogate model to robust aerodynamic design optimization

An efficient method employing a Principal Component Analysis (PCA)-Deep Belief Network (DBN)-based surrogate model is developed for robust aerodynamic design optimization in this study. In order to reduce the number of design variables for aerodynamic optimizations, the PCA technique is implemented to the geometric parameters obtained by parameterization method. For the purpose of predicting aerodynamic parameters, the DBN model is established with the reduced design variables as input and the aerodynamic parameters as output, and it is trained using the k-step contrastive divergence algorithm. The established PCA-DBN-based surrogate model is validated through predicting lift-to-drag ratios of a set of airfoils, and the results indicate that the PCA-DBN-based surrogate model is reliable and obtains more accurate predictions than three other surrogate models. Then the efficient optimization method is established by embedding the PCA-DBN-based surrogate model into an improved Particle Swarm Optimization (PSO) framework, and applied to the robust aerodynamic design optimizations of Natural Laminar Flow (NLF) airfoil and transonic wing. The optimization results indicate that the PCA-DBN-based surrogate model works very well as a prediction model in the robust optimization processes of both NLF airfoil and transonic wing. By employing the PCA-DBN-based surrogate model, the developed efficient method improves the optimization efficiency obviously.     

某型倾转旋翼机的旋翼桨叶气动优化设计

倾转旋翼机的旋翼气动外形设计需要对其直升机模式和固定翼模式下的不同要求进行综合考虑。通过基于Kriging模型的多目标遗传算法建立一套适用于倾转旋翼桨叶气动外形优化设计方法,采用拉丁超立方抽样试验设计方法得到样本点,并建立Kriging模型替代费时的流动数值模拟。以最大化旋翼地面悬停拉力和高空巡航效率为目标,以地面悬停功率不增和巡航拉力不减为约束条件,进行倾转旋翼桨叶平面形状优化设计,并经过非定常数值模拟和风洞试验验证。结果表明:数值模拟结果和风洞试验结果吻合良好,优化结果满足设计指标。     

基于自适应代理模型的气动优化方法

气动优化设计中,为了减少优化系统的计算周期,提高搜索效率,引入结构简单、计算量较小的代理模型,而运用有效的插值和选样方法(自适应选样)可以大大减少建立代理模型的时间。因此本文提出了一种基于自适应代理模型的气动优化方法。首先对自适应代理模型进行研究,建立了 Kriging 自适应代理模型和支持向量回归自适应代理模型,这两种自适应代理模型在相同样本点情况下比一般代理模型拥有更高的预测能力,然后将这其应用到翼型优化设计中,取得了良好的优化效果,从而表明这两种自适应代理模型不仅简单实用,而且明显提高了气动分析的计算效率。     

吸气式空空导弹外形多学科一体化优化设计

针对采用整体式固冲发动机的吸气式空空导弹外形气动与推进耦合的推阻匹配设计难题,引入多学科优化设计方法提出了一种综合考虑气动/推进/质量/弹道的导弹外形多学科一体化优化设计技术。其中,气动性能预测采用代理模型技术,主要基于外形参数化建模、非结构网格技术和流场精细数值计算来自动构建气动数据库,据此建立了包含外形几何信息的气动预测代理模型,并对其预测精度进行了验证;推进性能预测采用推进求解模型,该模型根据固冲发动机理论建立,精度满足工程要求。对所建立的学科预测模型完成一体化集成后,以质点弹道仿真评估的战技指标为优化目标,对一款吸气式空空导弹进气道和翼面外形进行了优化设计,取得了推阻匹配的优化外形,优化后导弹动力射程提高10%。所提出的一体化优化设计技术,有助于吸气式空空导弹外形气动与推进耦合推阻匹配设计和提高导弹动力射程。     

Optimization of aerodynamic efficiency for twist morphing MAV wing

Twist morphing(TM) is a practical control technique in micro air vehicle(MAV) flight.However, TM wing has a lower aerodynamic efficiency(CL/CD) compared to membrane and rigid wing. This is due to massive drag penalty created on TM wing, which had overwhelmed the successive increase in its lift generation. Therefore, further CL/CDmaxoptimization on TM wing is needed to obtain the optimal condition for the morphing wing configuration. In this paper, two-way fluid–structure interaction(FSI) simulation and wind tunnel testing method are used to solve and study the basic wing aerodynamic performance over(non-optimal) TM, membrane and rigid wings. Then,a multifidelity data metamodel based design optimization(MBDO) process is adopted based on the Ansys-DesignXplorer frameworks. In the adaptive MBDO process, Kriging metamodel is used to construct the final multifidelity CL/CDresponses by utilizing 23 multi-fidelity sample points from the FSI simulation and experimental data. The optimization results show that the optimal TM wing configuration is able to produce better CL/CDmaxmagnitude by at least 2% than the non-optimal TM wings. The flow structure formation reveals that low TV strength on the optimal TM wing induces low CDgeneration which in turn improves its overall CL/CDmaxperformance.     

A study of morphing aircraft on morphing rules along trajectory

Morphing aircraft can meet requirements of multi-mission during the whole flight due to changing the aerodynamic shape, so it is necessary to study its morphing rules along the trajectory. However, trajectory planning considering morphing variables requires a huge number of expensive CFD computations due to the morphing in view of aerodynamic performance. Under the given missions and trajectory, to alleviate computational cost and improve trajectory-planning efficiency for morphing aircraft, an offline optimization method is proposed based on Multi-Fidelity Kriging (MFK) modeling. The angle of attack, Mach number, sweep angle and axial position of the morphing wing are defined as variables for generating training data for building the MFK models, in which many inviscid aerodynamic solutions are used as low-fidelity data, while the less high-fidelity data are obtained by solving viscous flow. Then the built MFK models of the lift, drag and pressure centre at the different angles of attack and Mach numbers are used to predict the aerodynamic performance of the morphing aircraft, which keeps the optimal sweep angle and axial position of the wing during trajectory planning. Hence, the morphing rules can be correspondingly acquired along the trajectory, as well as keep the aircraft with the best aerodynamic performance during the whole task. The trajectory planning of a morphing aircraft was performed with the optimal aerodynamic performance based on the MFK models, built by only using 240 low-fidelity data and 110 high-fidelity data. The results indicate that a complex trajectory can take advantage of morphing rules in keeping good aerodynamic performance, and the proposed method is more efficient than trajectory optimization by reducing 86% of the computing time.     

Kriging模型及代理优化算法研究进展

代理模型方法由于能显著提高工程优化设计问题的效率,在航空航天及其他领域得到了广泛重视,并逐渐发展成为一类优化算法,本文称其为代理优化（SBO）算法。在现有的代理模型方法中,如多项式响应面、径向基函数、神经网络、支持向量回归、多变量插值/回归、多项式混沌展开等,源于地质统计学的Kriging模型具有代表性,是一种非常具有应用潜力的代理模型方法。以飞行器设计领域的优化问题为背景,介绍了Kriging代理模型及应用于优化设计的理论和算法的最新研究进展。首先,概述了Kriging模型的基本理论和算法,并讨论了影响Kriging模型鲁棒性和效率的几个关键性问题。其次,回顾了Kriging模型理论和算法研究的3个最新研究进展,包括梯度增强型Kriging、CoKriging和分层Kriging模型。而后,分析提炼了基于Kriging模型的代理优化算法的优化机制和优化框架,给出了“优化加点准则”和“子优化”的概念,并介绍了目前常用的几种优化加点准则及其相应子优化问题的求解与约束处理;同时,还介绍了最新提出的局部EI加点准则以及代理优化的终止条件。最后,介绍了代理优化在标准测试函数算例验证、飞行器气动与多学科优化设计典型算例确认方面的研究进展,并对当前存在的一些关键科学问题以及未来研究方向进行了讨论。     

悬停状态直升机桨叶扭转分布的优化数值计算

建立了一套基于高精度计算流体力学(CFD)技术和代理模型优化算法的旋翼气动外形设计方法。在该方法中,旋翼流场气动性能的计算采用了基于Navier-Stokes/Euler方程的CFD方法,并根据流场特点、精度和效率的要求采用Baldwin-Lomax(B-L)湍流模型,通量计算采用Roe-MUSCL格式进行。为提高网格生成质量和便于流场控制方程的求解,将流场分成两个区域,即围绕旋翼的黏性区和无黏的背景网格区。其中,桨叶网格使用了基于二维翼型网格的参数化方法生成,数值计算结果表明该方法有效地提高了网格生成质量及效率。在参考旋翼流场及桨叶细节流动分析的基础上给出设计变量及范围,有效减小了优化问题的规模;为满足优化和机理分析的需要,将基于置换遗传算法优化的拉丁超立方(PermGA LHS)方法和径向基函数(RBF)的代理模型优化方法引入到桨叶外形的优化设计中。首先以Helishape 7A旋翼为算例,检验了数值模拟方法的准确性。然后,应用所建立的优化方法针对旋翼负扭转分布进行了优化计算,结果表明优化后的旋翼悬停气动性能比优化前有了明显提高。     

Research on multi-fidelity aerodynamic optimization methods

 Constructing high approximation accuracy surrogate model with lower computational cost has great engineering significance. In this paper, using co-Kriging method, an efficient multifidelity surrogate model is constructed based on two independent high and low fidelity samples. Co-Kriging method can use a greater quantity of low-fidelity information to enhance the accuracy of a surrogate of the high-fidelity model by modeling the correlation between high and low fidelity model, thus computational cost of building surrogate model can be greatly reduced. A wing-body problem is taken as an example to compare characteristics of co-Kriging multi-fidelity (CKMF) model with traditional Kriging based multi-fidelity (KMF) model. A sampling convergence of the CKMF model and the KMF model is conducted, and an appropriate sampling design is selected through the sampling convergence analysis. The results indicate that CKMF model has higher approximation accuracy with the same high-fidelity samples, and converges at less high-fidelity samples. A wing-body drag reduction optimization design using genetic algorithm is implemented. Satisfying design results are obtained, which validate the feasibility of CKMF model in engineering design.     

Aerodynamic performance enhancement for flapping airfoils by co-flow jet

Introducing active flow control into the design of flapping wing is an effective way to enhance its aerodynamic performance. In this paper, a novel active flow control technology called Co-Flow Jet (CFJ) is applied to flapping airfoils. The effect of CFJ on aerodynamic performance of flapping airfoils at low Reynolds number is numerically investigated using Unsteady Reynolds Averaged Navier-Stokes (URANS) simulation with Spalart-Allmaras (SA) turbulence model. Numerical methods are validated by a NACA6415-based CFJ airfoil case and a S809 pitching airfoil case. Then NACA6415 baseline airfoil and NACA6415-based CFJ airfoil with jet-off and jet-on are simulated in flapping motion, with Reynolds number 70,000 and reduced frequency 0.2. As a result, CFJ airfoils with jet-on generally have better lift and thrust characteristics than baseline airfoils and jet-off airfoil when C_μ is greater than 0.04, which results from the CFJ effect of reducing flow separation by injecting high-energy fluid into boundary layer. Besides, typical kinematic and geometric parameters, including the reduced frequency and the positions of the suction and injection slot, are systematically studied to figure out their influence on aerodynamic performance of the CFJ airfoil. And a variable C_μ jet control strategy is proposed to further improve effective propulsive efficiency. Compared with using constant C_μ, an increase of effective propulsive efficiency by 22.6% has been achieved by using prescribed variable C_μ for NACA6415-based CFJ airfoil at frequency 0.2. This study may provide some guidance to performance enhancement for Flapping wing Micro Air Vehicles (FMAV).     

一种高效的CFD/CSD耦合飞行器多学科优化设计方法

建立了一种基于CFD/CSD (computational fluid dynamics/computational structure dynamics)耦合的多学科优化设计方法.该方法采用结构有限元方程进行结构特性分析,同时采用数值求解N-S方程方法获得气动载荷,保证了设计结果的可信性,并采用基于代理模型的优化设计方法解决了采用高精度模型后计算量太大的问题.采用RBF(径向基函数)插值方法进行流固耦合界面数据插值,保证了传递过程中的能量守恒.利用建立的优化设计方法对一典型的翼身组合体进行了气动和结构优化设计,算例表明在满足约束条件的前提下优化后阻力和质量分别减小了5.0%和4.2%,证明了该方法的有效性.      

基于伴随理论的大型客机气动优化设计研究进展

大型民用客机的气动设计具有巡航马赫数高、部件间流动干扰复杂、外形精细化修形难度大等特点,完全依靠人工试凑法进行气动设计工作量巨大。基于高可信度数值模拟的优化设计技术可以对该类问题进行自动寻优设计,给设计师提供有力参考,因此在大型民用客机气动设计中发挥着越来越显著的作用。首先,以大型民用客机为背景,总结了民机气动设计中的关键科学问题,指出了梯度优化设计方法在民用客机不同优化设计问题中的适用性,并进一步对梯度求解中的伴随方法理论进行了详细介绍。然后,分析了基于伴随理论的气动优化设计方法以及气动结构多学科优化设计方法在民用客机设计中的研究进展,其中气动优化设计方面着重突出了复杂全机多部件气动外形优化设计方法以及飞机/发动机一体化优化设计方法。最后,对基于伴随理论的气动优化设计方法在大型民机中的应用进展进行了提炼,对未来发展趋势进行了展望与建议。     

Robust design of NLF airfoils

 A robust optimization design approach of natural laminar airfoils is developed in this paper. First, the non-uniform rational B-splines (NURBS) free form deformation method based on NURBS basis function is introduced to the airfoil parameterization. Second, aerodynamic characteristics are evaluated by solving Navier-Stokes equations, and the γ-Re_θt transition model coupling with shear-stress transport (SST) turbulent model is introduced to simulate boundary layer transition. A numerical simulation of transition flow around NLF0416 airfoil is conducted to test the code. The comparison between numerical simulation results and wind tunnel test data approves the validity and applicability of the present transition model. Third, the optimization system is set up, which uses the separated particle swarm optimization (SPSO) as search algorithm and combines the Kriging models as surrogate model during optimization. The system is applied to carry out robust design about the uncertainty of lift coefficient and Mach number for NASA NLF-0115 airfoil. The data of optimized airfoil aerodynamic characteristics indicates that the optimized airfoil can maintain laminar flow stably in an uncertain range and has a wider range of low drag.     

An efficient aerodynamic shape optimization of blended wing body UAV using multi-fidelity models

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.     

低压涡轮的气动-声学三维数值优化: 倾斜导叶策略

 低压涡轮既是飞机进场着陆时发动机的重要声源,也是发动机中对效率要求很高的部件之一,为了实现低压涡轮低噪声的设计目标必须同时兼顾气动性能指标。研究给出了高效低噪声低压涡轮气动-声学三维优化的思路,即首先通过计算流体力学(CFD)定常计算评估三维设计变化对气动性能的影响;然后利用非定常CFD方法与三平面压力模态匹配(TPP)方法的结合来评估其降噪的效果与非定常气动影响;最后确定最佳的设计方案。以GE-E³(Energy Efficient Engine)低压涡轮末级为算例,数值模拟了导叶倾斜作为低压涡轮降噪措施的潜力。计算结果表明,正倾斜导叶角度小于19°时单级涡轮气动性能较直列叶栅要好,效率最大提高了0.3%。对单音噪声级的评估指出,正倾斜由于改变了导叶的尾迹特征,涡轮级噪声水平是增大的,因此不能作为有效的降噪策略。数值研究的结果表明CFD方法能够同时反映出叶片三维设计的细节变化对气动和噪声级的影响,可以作为三维气动-声学优化的手段。     

高效粒子群算法研究及飞翼无人机气动隐身优化设计

针对飞翼布局无人机气动隐身多目标优化设计问题,以无人机翼面为设计对象,开展气动、隐身多目标优化设计研究。采用FFD方法实现飞翼布局的参数化表达;分别采用基于雷诺平均N-S方程的计算流体力学方法(CFD)及大面元物理光学法(LEPO)配合一致性几何绕射理论(UTD)计算边缘绕射场的RCS分析方法计算飞翼布局无人机的气动、隐身性能;选择结合基于动态超体积期望改善(EHVI)加点的动态Kriging代理模型与ASMOPSO算法的高效多目标粒子群算法对飞翼布局无人机进行综合寻优设计研究。在较少的调用真实目标函数的情况下,获得了比较优秀的Pareto前沿,通过对所选解的分析比较可知优化后的飞翼布局无人机在气动及隐身方面均优于原始构型。