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.     

Safety lifetime analysis method for multi-mode time-dependent structural system

It is important to determine the safety lifetime of Multi-mode Time-Dependent Structural System(MTDSS). However, there is still a lack of corresponding analysis methods.Therefore, this paper establishes MTDSS safety lifetime model firstly, and then proposes a Kriging surrogate model based method to estimate safety lifetime. The first step of proposed method is to construct the Kriging model of MTDSS performance function by using extremum learning function. By identifying possible extremum mode o...     

基于代理模型的运载器头罩外形优化设计

引入Kriging代理模型,选取若干不同头罩外形的运载器,进行气动性能分析,利用运载器气动性能参数作为拟合样本建立代理模型.以具有足够精度的代理模型替代CFD分析,发展了一种基于代理模型的运载器头罩外形优化设计方法.在马赫数为3、飞行攻角为3°、飞行高度为8km条件下,利用该方法对运载器进行最小阻力系数、最大纵向压心系数的单目标优化和综合考虑上述2个目标的多目标优化.结果表明:2个目标存在冲突,为同时兼顾减小阻力和增强纵向稳定性,必须对运载器头罩外形进行多目标优化,得到的外形阻力系数减小了1.95%,纵向压心系数增大了5.93%,采用基于代理模型的优化设计方法能在保证精度条件下有效提高计算效率.      

基于Kriging代理模型的锥柱形膜片屈曲载荷计算

基于Kriging代理模型,建立了一种考虑膜片半径与厚度、锥段高度与角度等典型结构特征的计算屈曲载荷的工程方法,并选取典型样本点对模型进行了数值验证.结果表明:基于Cubic相关函数建立的Kriging代理模型预测未知样本点屈曲载荷误差控制在5%以内,较常用的Gauss相关函数更适合建立锥柱形膜片屈曲载荷的Kriging代理模型;此代理模型能准确计算未知样本点的屈曲载荷,减少了繁杂的有限元建模与计算过程;根据设定的屈曲载荷,代理模型可计算各典型特征的参数值,并可作为锥柱形膜片结构优化设计的约束函数或目标函数.      

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。     

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。     

二维气动问题中Kriging代理模型精度影响因素

以二维跨声速临界翼型的阻力特性为对象,探讨样本点数目、Kriging代理模型参数及其类型等对模型精度的影响.阻力系数采用计算流体力学（CFD）方法得到.模型精度的验证采用交叉验证方法,采用平均误差、最大误差和标准交叉验证残差来衡量Kriging代理模型的精度.研究结果表明:①Kriging代理模型预测气动阻力效果较好.②模型精度随样本点的增多而提高,剔除与样本点响应趋势不相符的“奇异点”后,模型精度显著提高,平均误差减小5%~38%,最大误差减小13%~77%.③核函数类型对模型精度的影响最大,相关参数次之,回归模型的影响最小.采用高斯相关函数、2阶多项式回归模型,以及合适的相关参数值时,Kriging代理模型的精度最高.      

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。