Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids

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 infill-sampling 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.     

锥导乘波体气动代理建模方法研究

传统的气动计算方法计算繁琐、计算效率低,不适应于乘波体多学科设计优化,通过建立气动代理模型可以很好地解决气动计算精度和效率的矛盾.利用面元法进行气动估算,采集了锥导乘波体在设计点、非设计点的气动特性作为训练数据,构建了Kriging和LS-SVM代理模型,对比了两种模型对此高维问题的代理效果.结果表明,Kriging代理模型能更准确地表达锥导乘波体的气动特性,应用代理模型进行优化等工作的计算效率与传统气动计算方法相比有显著的提高.     

粒子群优化的Kriging近似模型及其在可靠性分析中的应用

将粒子群优化(PSO)算法引入Kriging建模过程,依靠PSO算法的群体搜索能力克服了模式搜索法单点序列搜索方式的局限性以及严重依赖于初猜解的缺点,保证了在任意初始条件下都能获取极大似然意义下的最优相关参数,从而有效确保了Kriging预测结果的最优无偏性.涡轮盘低循环疲劳可靠性分析实例表明,粒子群优化的Kriging(PSO-Kriging)近似模型对危险点周向应变变程的预测精度相对神经网络有数量级上的优势(最大误差由5.94%降低到0.09%),可不牺牲精度地代替有限元程序进行Monte Carlo模拟;同时PSO-Kriging建模与预测的总时间不及一次有限元分析的1/10.由于预测精度高(其最优无偏性由PSO算法保证)且计算开销不大,提出的PSO-Kriging对于实际工程结构的可靠性分析有一定应用价值.      

基于改进的动态Kriging模型的结构可靠度算法

对于复杂航空航天机械产品,极限状态方程往往表现出隐式、高度非线性的特点,而且通常需要调用有限元分析,从而耗费大量时间。将混合粒子群-模拟退火（PSOSA）算法应用到Kriging模型中相关参数的寻优过程,提高了预测精度。同时结合动态更新机制,逐渐加入样本点,尽可能减少函数的调用次数,从而提高了计算效率,并将该算法应用到结构可靠性分析中。通过案例分析,和传统蒙特卡罗模拟方法、响应面等经典方法进行对比,所提算法与蒙特卡罗模拟方法计算结果更加接近,计算时间大大缩短,效率和精度都明显改进。      

耦合梯度与分级Kriging模型的高效气动优化方法

Kriging代理模型中引入梯度信息能够提高模型的预测精度,但常规耦合梯度的方法都有不足之处。本文结合分级Kriging模型,提出了一种变可信度分级Kriging模型耦合梯度（GEHK）信息的新方法。首先利用梯度信息,选取扰动步长得到初始样本点附近的派生点,以派生点拟合出能够预测目标函数趋势的低精度Kriging模型。然后以初始样本点修正该模型得到高精度的Kriging模型。翼型减阻优化设计算例表明,与常规耦合梯度的Kriging模型相比,基于分级Kriging的梯度耦合方法对于扰动步长引入的误差不敏感,明显提高了模型预测精度,优化效率因此提升并使得目标函数值下降得更加迅速。相比Euler解作为低精度数据的常规分级Kriging模型,由梯度信息得到的派生点为模型提供了更准确的全局趋势预测,取得了更好的优化结果。本文方法成功应用于翼型多点减阻优化问题,说明该方法对复杂设计问题有很好的适应性。基于分级Kriging模型的耦合梯度方法克服了常规方法的缺点,提高了模型全局拟合精度,是一种优化效率更高的Kriging方法。     

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.     

基于Kriging模型的浮空器氦气昼夜温差最优化

分析浮空器氦气昼夜温差时通常将整个囊体蒙皮涂层设置为同一种材料,分析材料的吸收率与发射率对氦气昼夜温差的影响。为进一步减小氦气昼夜温差,提出了将囊体分为迎光面和背光面,迎光面采用吸收率低的材料,背光面采用发射率高的材料。建立了囊体热力学模型,采用Kriging模型对囊体不同部位的材料特性进行优化,其基本思想是将囊体划分为48个部分,采用拉丁超立方体方法进行抽样,进行热力学分析得到样本的响应,以此建立Kriging近似模型。经过该方法优化后发现,氦气的昼夜温差减小到28.6 K,比传统的分析减少7.7%。      

基于正交法和Kriging模型的液体火箭发动机液膜冷却优化

通过FLUENT对火箭发动机推力室中跨临界甲烷液膜冷却稳态流场进行数值传热计算。根据正交法设计试验,得到不同膜孔孔径、轴向夹角、径向夹角和孔型四个影响因素共同作用下的冷却效果,选出最优的膜孔几何参数组合.在采用最优膜孔几何参数组合的条件下,基于最优拉丁超立方抽样建立Kriging模型,利用遗传算法得到多目标条件下最优的跨临界液膜质量流量、冷却环带的分配比和位置。结果表明,正交法和Kriging模型可以解决液体火箭发动机液膜冷却优化高设计成本和数值噪声问题。正交试验设计考虑的因素中,影响冷却效率和不均匀度的最大的因素依次为孔型、孔径、径向夹角和轴向夹角。最优的几何参数组合为孔径0.003mm,轴向夹角45°,径向夹角15°,孔型为扩散型。建立的Kriging模型能准确反映液膜质量流量、液膜分配比和冷却环带位置与目标函数的关系。最终得到的优化方案平均冷却效率提高4.9%,不均匀度减少0.025,比冲损失增加0.37%,总目标函数提高184%。优化后涡对的不对称性使得冷却剂展向分布更加均匀,同时反向涡对衰减更快,增强了液膜的附壁性,从而提高冷却效果。     

涡轮叶片的气动-热-结构多学科设计优化研究

涡轮叶片设计是典型的多学科问题,在保证结果精度的同时必须重视计算效率.通过控制样本的数量和质量,近似模型能够在保证一定精度的前提下,简化多学科优化过程中的数据管理,并提高优化效率.通过分析涡轮转子叶片的气动-热-结构三个学科的设计过程和数据传递关系,充分利用各学科现有的分析工具,建立了涡轮叶片的气动-热-结构多学科优化设计框架.对某涡轮转子叶片分别使用Kriging近似模型和精确分析方法进行优化对比,可以看出两者的结果误差约为1.86%,而效率提高了将近46%,表明采用近似方法的优化结果在工程上是可用的,而且在计算效率更占优势.      

飞机多学科设计优化中的近似方法分析

首先介绍了近似方法中的二次响应面方法、径向基神经网络方法、Kriging方法和增强的径向基函数方法。结合测试函数和某机翼模型为例,分别用这四种方法构造测试函数和某机翼结构和气动学科的近似模型,并总结这四种方法的特点和在对各种模型近似中的适用性。结果表明,Kriging方法和增强的径向基函数方法的近似是非常精确和稳健的。