Adaptive optimization methodology based on Kriging modeling and a trust region method

Surrogate-Based Optimization (SBO) is becoming increasingly popular since it can remarkably reduce the computational cost for design optimizations based on high-fidelity and expensive numerical analyses. However, for complicated optimization problems with a large design space, many design variables, and strong nonlinearity, SBO converges slowly and shows imperfection in local exploitation. This paper proposes a trust region method within the framework of an SBO process based on the Kriging model. In each refinement cycle, new samples are selected by a certain design of experiment method within a variable design space, which is sequentially updated by the trust region method. A multi-dimensional trust-region radius is proposed to improve the adaptability of the developed methodology. Further, the scale factor and the limit factor of the trust region are studied to evaluate their effects on the optimization process. Thereafter, different SBO methods using error-based exploration, prediction-based exploitation, refinement based on the expected improvement function, a hybrid refinement strategy, and the developed trust-region-based refinement are utilized in four analytical tests. Further, the developed optimization methodology is employed in the drag minimization of an RAE2822 airfoil. Results indicate that it has better robustness and local exploitation capability in comparison with those of other SBO methods.     

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.     

基于Kriging模型的翼型气动性能优化设计

将基于Kriging模型的近似技术引入气动优化设计。通过计算两个测试函数的全局极值以及翼型几何形状的重构,比较了基于Kriging模型的优化方法与传统的梯度类优化方法、标准遗传算法的特点。结果表明基于近似模型的优化方法不仅全局性良好,而且有效节约了计算资源。用此方法进行了翼型的气动优化设计,目标函数为来流马赫数为0.7、攻角为3°时升阻比最大。设计结果表明,与参考翼型相比,优化翼型升阻比提高了81%,而翼型截面积减少不到1%,优化效果非常明显。     

基于Kriging形函数的线性时变结构模态参数辨识

近年来,对航空航天飞行器随时间变化的动力学特性研究需求越来越迫切。仅输出参数化时域的时变时间序列模型以其结构简约、精度高且跟踪能力强而成为研究热点,尤其是泛函向量时变自回归(FS-VTAR)模型已经得到了广泛应用。然而传统的FS-VTAR模型在保证其辨识优势的同时却需要针对不同时变结构选择合适的基函数形式及较高的基函数阶数,该过程相当复杂且耗时。本文借鉴无网格法中移动最小二乘(MLS)法构造形函数的思想,提出一种基于Kriging形函数的线性时变结构模态参数辨识方法。该方法首先引入自适应于辨识信号的Kriging形函数;再把时变系数在形函数上线性展开,利用最小二乘(LS)法得到形函数的展开系数;最后把时变模型特征方程转换为广义特征值问题提取出模态参数。利用时变刚度系统非平稳振动信号验证该方法,结果表明:基于Kriging形函数的FS-VTAR模型相比于传统的FS-VTAR模型能有效地避免基函数形式的选择和较高的基函数阶数,且精度相当;相比于移动最小二乘法能有效地解决其数值条件问题且具有更高的模态参数辨识精度。     

代理模型选样准则研究

致力于针对确定问题,利用其在已知空间中的样本信息指导该问题其他空间中的样本选择.基于Kriging模型和拉丁超立方设计选样方法,以某数学函数为例,首先研究了设计空间大小对样本选择的影响,然后具体分析了样本分布特性对代理模型预测误差的影响.引入了样本平均疏密度、样本稀疏度、样本紧凑度等概念衡量样本特性,依据不同空间中各参数与代理模型预测精度的关系提出了样本稀疏度准则,并以不同维数的数学函数和翼型气动力分析模型验证了准则的准确性和实用性.     

Double-stage Metamodel and Its Application in Aerodynamic Design Optimization

Constructing metamodel with global high-fidelity in design space is significant in engineering design. In this paper, a double-stage metamodel (DSM) which integrates advantages of both interpolation metamodel and regression metamodel is constructed. It takes regression model as the first stage to fit overall distribution of the original model, and then interpolation model of regression model approximation error is used as the second stage to improve accuracy. Under the same conditions and with the same samples, DSM expresses higher fidelity and represents physical characteristics of original model better. Besides, in order to validate DSM characteristics, three examples including Ackley function, airfoil aerodynamic analysis and wing aerody-namic analysis are investigated. In the end, airfoil and wing aerodynamic design optimizations using genetic algorithm are presented to verify the engineering applicability of DSM.     

基于 Kriging模型机翼平面外形气动优化设计

使用基于Kriging模型的优化设计方法,进行了非常规布局机翼的平面外形多目标优化设计。利用CFD技术进行机翼升力系数和阻力系数的气动计算,通过拉丁超立方试验设计生成样本点,建立了Kriging代理模型,结合多目标遗传算法对机翼平面外形进行多点多目标优化设计,最终得到了Pareto最优解集。根据设计需求,从Pa-ret0前沿选取一个非劣解作为优化结果。结果表明：陆ging模型与cFD计算误差很小,可信度高;在不问设计状态下,机翼气动性能都得到了提高,表明优化设计方法具有可行性和高效性。     

矩独立重要性分析的Kriging代理模型方法

结构重要性分析是结构不确定性分析的重要研究内容之一。作为一种矩独立的重要性测度指标,基于失效概率的重要性测度能够有效地反映输入变量的不确定性对结构失效概率的影响。然而,相比于其他形式的重要性测度,对基于失效概率的矩独立重要性测度进行高效准确的求解仍然存在一定的困难。基于此,结合Kriging代理模型提出了一种高效的矩独立重要性分析的新方法。所提方法首先通过较少的实验设计样本构建能够充分近似真实输入输出响应函数的Kriging代理模型,进而通过数值模拟策略对所构建的Kriging模型进行分析,最终求解得到各个输入变量基于失效概率矩独立重要性测度的主效应和总效应,给出各个输入变量对于失效概率的影响程度排序。相比于现有方法,所提方法由于引入Kriging代理模型极大地降低了对响应函数的计算次数,同时保证了重要性分析的计算精度。两个工程应用实例结果表明了所提方法在计算效率和计算精度方面的优势,体现了所提方法良好的适用性。     

基于Kriging模型的风洞应变天平静态校准方法

本文提出了一种基于Kriging代理模型的风洞应变天平静态校准方法。采用拉丁超立方设计的试验设计（DOE）方法选取校准加载点,以六分量组合加载技术为支撑,采用一阶回归基函数和EXP关联函数对校准数据构建Kriging模型,以电压信号增量和其他条件变量为自变量,通过Kriging模型对天平所受载荷进行预测。校准结果表明,与传统的OFAT（One Factor at A Time）校准方法相比,该方法具有相同的准度,加载点数量极大减少。将该方法应用于某矢量喷管推力测量天平的校准工作中,以通气流量和天平电压信号增量作为自变量,较好预测了喷管产生的推力,解决了传统校准方法难以克服的通气影响问题。     

基于Kriging模型的结构耐撞性优化

提出了基于Kriging模型的耐撞性优化方法。首先就Kriging模型的构造方法及其精度评估问题进行了讨论;然后,以薄壁管为研究对象,采用瞬态非线性有限元分析程序作为计算核心,以薄壁圆管的直径和壁厚为优化变量,以最大撞击载荷为目标函数,薄壁管的最大压缩量等作为约束函数,构造了基于Kriging模型的全局近似函数来逼近真实的优化目标函数与约束函数;随后,提出了提高全局近似函数精度的Kriging模型更新方法,改进了优化设计分析流程;最后,在所构造的全局近似函数的基础上,采用遗传算法进行优化分析。算例分析结果表明,该方法构造的最大撞击载荷与最大压缩量的全局近似函数在最优解处与真实解非常吻合,说明了Kriging模型的有效性。