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。     

基于梯度增强型Kriging模型的气动反设计方法

基于Kriging模型的代理优化算法目前在气动优化设计中得到了广泛应用。但在高维(设计变量大于30个)气动优化中,计算量过大的问题对其进一步发展产生了严重制约。将翼型和机翼气动反设计问题转化为优化问题,采用Adjoint方法进行快速梯度求解,利用基于梯度增强型Kriging(GEK)模型的代理优化算法分别开展了18、36和108个设计变量的气动反设计。首先,通过采用在设计空间局部建立GEK模型的方法成功地将基于代理优化算法的气动反设计问题的维度拓展到了100维以上。其次,研究了梯度计算精度对基于GEK模型的反设计的影响,发现梯度精度越高,反设计的最终效果越好,同时效率相当。最后,通过不同维度的气动反设计算例,比较了改进拟牛顿法(BFGS)、基于GEK模型和Kriging模型的代理气动反设计方法,结果表明基于GEK模型的代理优化算法的效率大幅度高于基于Kriging模型的代理优化算法,并且维度越高,效率优势越明显;同时,基于GEK模型的代理优化算法在优化效果及分析程序调用次数上相比于BFGS方法也略有优势。     

基于代理模型全局优化的自适应参数化方法

对于翼型气动隐身设计问题,设计变量的配置对设计结果影响很大,而简单地增加设计变量不能保证得到理想的结果。提出一种适用于代理模型全局优化的自适应参数化方法：利用全局敏感性分析方法——基本效应法,得到设计空间关于目标函数的敏感区域信息,并以此为根据增加设计变量;利用节点插入算法将低维样本在高维空间内进行重构,避免了重新取样的工作量。相对于传统固定设计空间维度方法,自适应参数化方法在设计空间的敏感区域扩展维度,能够更加精准地描述外形并反映目标的变化趋势。通过飞翼布局翼型的气动隐身优化算例,证实自适应参数化方法可以大幅提高优化设计质量和效率。     

Recent advances in surrogate-based optimization

The evaluation of aerospace designs is synonymous with the use of long running and computationally intensive simulations. This fuels the desire to harness the efficiency of surrogate-based methods in aerospace design optimization. Recent advances in surrogate-based design methodology bring the promise of efficient global optimization closer to reality. We review the present state of the art of constructing surrogate models and their use in optimization strategies. We make extensive use of pictorial examples and, since no method is truly universal, give guidance as to each method's strengths and weaknesses.     

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。     

基于POD-BPNN的热启动策略及其在气动代理优化中的应用

传统气动优化设计需要大量CFD 分析,而代理优化（SBO）方法能够有效降低CFD 分析次数,但该方法并没有改变单个CFD 分析时间。提出一种基于本征正交分解-反向传播神经网络（POD-BPNN）模型的热启动策略,并应用于气动代理优化。使用POD-BPNN 模型对SBO 中的初始样本建立从几何设计变量到流场数据的预测模型...     

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.     

一种计及静气动弹性变形影响的跨声速机翼气动优化设计方法研究

耦合流场控制方程和结构静平衡方程求解得到大展弦比跨声速弹性机翼气动性能,分析研究了结构静弹性变形对气动载荷的影响.在此基础上以机翼典型剖面外形和机翼型架外形为设计变量进行了基于控制理论的跨声速弹性机翼气动优化设计方法研究,实现了在真实飞行条件下考虑静气动弹性变形影响的大展弦比跨声速弹性机翼一体化优化设计.优化设计算例结果表明所发展的方法是成功的,优化得到的弹性机翼在满足升力系数约束条件下提高了升阻比.     

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.     

通用飞行器气动优化设计数字化集成平台——DIPasda

未来航空工业的发展，需要解决多学科综合设计的关键问题，为新型高性能飞行器的设计提供有力的设计方法和设计工具。DIPasda作为复杂外形设计的通用飞行器多学科优化设计平台，研制目的主要是提供一套新型通用、鲁棒、高效的优化设计架构，应用于通用飞行器工业设计环境，改善传统设计耗时低效的状况，提高新型飞行器设计的效率和精度。DIPasda平台系统包含了优化设计过程中所需用到的各类方法，主要包括数值优化算法、几何模型参数化方法、代理模型方法、高精度的学科分析工具等。通过详细介绍平台的系统架构、主要的功能模块、伴随优化设计和多目标优化设计流程，展现了DIPasda平台系统架构设计的灵活性和功能模块的完备性。最后通过优化算例展示了系统的综合优化设计能力。     

基于代理模型的高效全局低音爆优化设计方法

研究发展高效实用的低音爆优化设计方法,对于新一代低音爆超声速客机的研制具有重要的理论意义和应用价值。目前国内外发展的低音爆优化方法主要包括遗传算法（GA）和基于Adjoint的梯度优化。遗传算法虽然具有较强的全局优化能力,但其优化效率较低,无法很好满足实际应用的需要;而梯度优化虽然优化效率高,但易陷入局部最优。将最新发展的代理优化算法与音爆预测方法相结合,发展了一种具有全局优化能力的高效低音爆优化设计方法。首先,概述了所采用的线性音爆预测方法,并用NASA超声速圆锥体模型进行验证,表明其计算效率高、预测精度可满足飞行器初步设计的需要。其次,对所采用的代理优化（SBO）方法进行了概述,包括试验设计、代理模型建模、优化加点准则和收敛标准等。再次,运用所发展的方法开展了NASA多段圆锥体模型的低音爆优化设计算例研究,并与遗传算法和梯度优化的结果进行了比较,表明其优化效率比遗传算法提高了2个量级以上,且优化结果优于梯度方法。最后,将所发展的方法应用于AIAA音爆预测大会提供的翼身组合体外形（69°后掠三角翼）的低音爆优化设计,将远场音爆N型波峰值减少了27.4%,表明所发展的方法在复杂外形低音爆优化设计中具有很好的应用潜力。     

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.     

Multi-disciplinary design optimization with variable complexity modeling for a stratosphere airship

This paper proposes a hybrid architecture based on Multi-disciplinary Design Optimization(MDO) with the Variable Complexity Modeling(VCM) method, to solve the problem of general design optimization for a stratosphere airship. Firstly, MDO based on the Concurrent SubSpace Optimization(CSSO) strategy is improved for handling the subsystem coupling problem in stratosphere airship design which contains aerodynamics, structure, and energy. Secondly, the VCM method based on the surrogate model is presented for reducing the computational complexity in high-fidelity modeling without loss of accuracy. Moreover, the global-to-local optimization strategy is added to the architecture to enhance the process. Finally, the result gives a prominent stratosphere airship general solution that validates the feasibility and efficiency of the optimization architecture. Besides, a sensitivity analysis is conducted to outline the critical impact upon stratosphere airship design.     

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。     

Aerodynamic/Stealthy/Structural Multidisciplinary Design Optimization of Unmanned Combat Air Vehicle

An optimization strategy is proposed to deal with the aerodynamic/stealthy/structural multidisciplinary design optimization (MDO) issue of unmanned combat air vehicle (UCAV). In applying the strategy, the MDO process is divided into two levels, i.e. system level optimization and subsystem level optimization. The system level optimization is to achieve optimized system objective (or multi-objective) through the adjustment of global external configuration design variables. The subsystem level optimization consists of the aerodynamic/stealthy integrated design and the structural optimization. The aerodynamic/stealthy integrated design aims at achieving the minimum aerodynamic drag coefficient under the constraint of stealthy requirement through the adjustment of local external configuration design variables. The structural optimization is to minimize the structural weight by adjusting the dimensions of structural components. A flowchart to implement this strategy is presented. The MDO for a flying-wing configuration of UCAV is employed to illustrate the detailed process of the optimization. The results indicate that the overall process of the surrogate-based two-level optimization strategy can be implemented automatically, and quite reasonable results are obtained.     

Multi-infill strategy for kriging models used in variable fidelity optimization

In this paper, a computationally efficient optimization method for aerodynamic design has been developed. The low-fidelity model and the multi-infill strategy are utilized in this approach. Low-fidelity data is employed to provide a good global trend for model prediction, and multiple sample points chosen by different infill criteria in each updating cycle are used to enhance the exploitation and exploration ability of the optimization approach. Take the advantages of low-fidelity model and the multi-infill strategy, and no initial sample for the high-fidelity model is needed. This approach is applied to an airfoil design case and a high-dimensional wing design case. It saves a large number of high-fidelity function evaluations for initial model construction. What’s more, faster reduction of an aerodynamic function is achieved, when compared to ordinary kriging using the multi-infill strategy and variable-fidelity model using single infill criterion. The results indicate that the developed approach has a promising application to efficient aerodynamic design when high-fidelity analyses are involved.     

A high-fidelity design methodology using LES-based simulation and POD-based emulation: A case study of swirl injectors

Engineering design is undergoing a paradigm shift from design for performance to design for affordability, operability, and durability, seeking multi-objective optimization. To facilitate this transformation, significantly extended design freedom and knowledge must be available in the early design stages. This paper presents a high-fidelity framework for design and optimization of the liquid swirl injectors that are widely used in aerospace propulsion and power-generation systems. The framework assembles a set of techniques, including Design Of Experiment (DOE), high-fidelity Large Eddy Simulations (LES), machine learning, Proper Orthogonal Decomposition (POD)-based Kriging surrogate modeling (emulation), inverse problem optimization, and uncertainty quantification. LES-based simulations can reveal detailed spatiotemporal evolution of flow structures and flame dynamics in a high-fidelity manner, and identify important injector design parameters according to their effects on propellant mixing, flame stabilization, and thermal protection. For a given a space of design parameters, DOE determines the number of design points to perform LES-based simulations. POD-based emulations, trained by the LES database, can effectively explore the design space and deduce an optimal group of design parameters in a turn-around time that is reduced by three orders of magnitude. The accuracy of the emulated results is validated, and the uncertainty of prediction is quantified. The proposed design methodology is expected to profoundly extend the knowledge base and reduce the cost for initial design stages.     

A novel surrogate modeling strategy of the mechanical properties of 3D braided composites

In this paper, a surrogate-based modeling methodology is developed and presented to predict the elastic properties of three dimensional (3D) four-directional braided composites. Using this approach, the prediction process becomes feasible with only a limited number of training points. The surrogate models constructed using Finite Element (FE) method and Diffuse Approximation, reduce the computational time and cost for preparing experimental samples. In the FE model, multiscale method is applied to couple the computations of elastic properties at microscale and mesoscale. Subsequently, a parametric study is performed to analyze the effects of the three design parameters on the elastic properties. Satisfactory results are obtained via the surrogate-based modeling predictions, which are compared with the experimental measurements. Moreover, the predictions obtained from surrogate models concur well with the FE predictions. This study orients a new direction for predicting the mechanical properties based on surrogate models which can effectively reduce the sample preparation cost and computational efforts.     

基于代理模型的大型民机机翼气动优化设计

先进的气动优化设计思想与方法，对于提升大型民机气动与综合性能具有至关重要的意义。探讨了大型民机超临界机翼气动优化设计的基本准则和要点，并结合代理优化算法，提出了一种面向工程应用的多轮次高效全局气动优化设计方法。首先，通过一系列解析函数/翼型/机翼优化测试算例进行了验证。其次，将所提出的方法与人工修型相结合，开展了针对宽体客机超临界机翼的两轮气动优化设计，使其气动性能得到显著改善。最后，采用不同的雷诺平均Navier-Stokes（RANS）方程求解器对安装优化机翼的全机巡航构型进行了典型状态的气动性能综合评估。研究结果表明，所提出的代理优化算法具有很高的优化效率、较强的约束处理和全局优化能力；将所发展的基于代理模型的多轮次气动优化设计方法与人工修型相结合，能够获得满足设计要求的气动外形，验证了该方法在大型民机超临界机翼气动设计中的有效性和工程实用性。