梯度增强的Kriging模型与Kriging模型在优化设计中的比较研究 -- 西北工业大学学报,2015,33(5):819-826
论文:2015,Vol:33,Issue(5):819-826
引用本文:
刘俊, 宋文萍, 韩忠华, 王乐. 梯度增强的Kriging模型与Kriging模型在优化设计中的比较研究[J]. 西北工业大学学报
Liu Jun, Song Wenping, Han Zhonghua, Wang Le. Comparative Study of GEK (Gradient-Enhanced Kriging) and Kriging When Applied to Design Optimization[J]. Northwestern polytechnical university

梯度增强的Kriging模型与Kriging模型在优化设计中的比较研究
刘俊, 宋文萍, 韩忠华, 王乐
西北工业大学 翼型叶栅空气动力学国家级重点实验室, 陕西 西安 710072
摘要:
在许多工程优化设计问题中,由于需要采用费时的数值模拟方法获得目标函数和约束函数值,出现了优化时间过长、优化难度大的问题。为了提高设计效率,缩短优化设计周期,代理模型方法受到人们的欢迎。近些年来,为了进一步提高设计效率,人们在传统代理模型基础上又发展了一些更高效、预测精度更高的新型代理模型,如变可信度模型、梯度增强的代理模型等。为了研究新型代理模型在优化设计中的优化效率和优化效果,首先结合代理模型、多点加点准则及多种传统优化算法,发展了一套适用于代理模型、梯度增强的代理模型的通用优化算法框架,基于该框架,采用典型的数值算例对当前应用较为广泛的Kriging模型和近些年来发展的梯度增强的Kriging模型进行了对比研究。结果显示,在假定目标函数的梯度与目标函数计算量相同的情况下,采用梯度增强的Kriging模型得到的优化结果在绝大多数情况下都优于采用Kriging模型得到的结果。最后,应用翼型设计算例对两种代理模型进行了对比,其中目标函数的梯度采用与目标函数本身计算量基本一致的Adjoint方法获得;结果显示,梯度增强的Kriging模型表现优于Kriging模型。
关键词:    优化设计    代理模型    Kriging模型    梯度增强的Kriging模型    气动优化设计   
Comparative Study of GEK (Gradient-Enhanced Kriging) and Kriging When Applied to Design Optimization
Liu Jun, Song Wenping, Han Zhonghua, Wang Le
National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China
Abstract:
In many engineering optimization design problems, the objective function (s) as well as the constraint function (s) are really computationally expensive. To reduce the computational time and shorten the design process, surrogate models are often used. In recent years, to further improve the design efficiency, a variety of new surrogate models are developed as extensions from the traditional models and verified to have higher efficiency for prediction, such as the variable-fidelity models and gradient-enhanced models. To investigate the design optimization efficiency when these new surrogate models are used, a universal surrogate-based optimization framework, which combines the surrogate models, multi sample point infill criteria, and multi-type traditional optimization algorithms, is developed first. Then, several typical analytical optimization problems are employed to compare the optimization efficiency when the widely used Kriging and a newly developed GEK are used respectively. The results and their analysis show preliminarily that, for most cases, GEK get better optimal solution with the same computational expense. Finally, an engineering problem, the airfoil inverse design is introduced for comparison; the gradients of the objective functions used to construct the GEK are obtained by the efficient adjoint method. The results and their analysis also show preliminarily that, when using the GEK, not only the efficiency, but also the optimal solution can be improved as compared with the Kriging model.
Key words:    aerodynamic drag    aerodynamics    airfoils    angle of attack    computational efficiency    convergence of numerical methods    design    drag coefficient    efficiency    flowcharting    force cashing    genetic algorithms    inverse problems    Mach number    matrix algebra    maximum likelihood estimation    mean square error    optimization    parameterization    Reynolds number    aerodynamic optimization design    expected improvement    GEK (gradient-enhance Kriging)    infill criteria    Kriging model   
收稿日期: 2015-03-15     修回日期:
DOI:
基金项目: 国家高技术发展计划863项目(2012AA051301)与国家自然科学基金(11272265)资助
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作者简介: 刘俊(1986—),西北工业大学博士研究生,主要从事飞行器的气动优化设计研究。
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