无参数自适应罚函数的高效代理模型优化设计方法  

Efficient surrogate-based aerodynamic optimization with parameter-free adaptive penalty function

作　　者：张伟[1] 高正红[1,2] 王超 夏露[1,2] ZHANG Wei;GAO Zhenghong;WANG Chao;XIA Lu(School of Aeronautics,Northwestern Polytechnical University,Xi’an 710072,China;State Key Laboratory of Airfoil and Cascade Aerodynamics,Northwestern Polytechnical University,Xi’an 710072,China;Beijing Institute of Electronic System Engineer,Beijing 100854,China)

机构地区：[1]西北工业大学航空学院,西安710072 [2]西北工业大学翼型、叶栅空气动力学国家级重点实验室,西安710072 [3]北京电子工程总体研究所,北京100854

出　　处：《北京航空航天大学学报》2024年第4期1262-1272,共11页Journal of Beijing University of Aeronautics and Astronautics

基　　金：翼型、叶栅空气动力学国家级重点实验室基金(614220121020128)。

摘　　要：在飞行器气动外形优化设计中,复杂约束条件导致设计空间可行域呈现不连续的特征,且理想解大多靠近约束边界,传统高效代理模型方法难以适用。研究了参考点对优化设计的影响,提出了一种考虑约束的参考点选择机制;对于最优解靠近边界的问题,罚函数法更加有效,但惩罚因子的设置对于罚函数方法影响很大,不合适的惩罚因子反而会损害优化效率,分析了优化过程中罚函数方法对惩罚因子的要求,提出了一种无参数自适应罚函数的代理模优化设计方法,引入基于样本分析的惩罚项,结合归一化目标值和约束值,在优化过程中动态调整惩罚因子,使优化能够尽可能地聚焦于可行域内,迅速收敛到最优解,实现样本的高效配置。通过带约束的函数算例和翼型优化算例证实,所提方法可以大幅提高飞行器气动外形优化设计效率。Complex constraints must be addressed in the aerodynamic optimizations.Distinct constraints not only influence the optimization outcomes but also significantly influence the optimization method's efficacy.This paper investigates the impact of reference points on optimization design results using the constrained efficient global optimization method(EGO)and suggests a mechanism for selecting reference points that takes constraints into account.Afterwards,for the problem of constraint processing,the constrained expected improvement(EI)method and the penalty function method are compared and found that the penalty function method can find a feasible solution that satisfies the constraints more quickly.However,in this process,the penalty factor has a great influence on the optimization efficiency,and inappropriate penalty factors will damage the optimization efficiency.Drawing on the aforementioned evaluation,this study suggests a constrained EGO technique utilizing an adaptive penalty function that is free of parameters.By normalizing the target value and the constraint value,the feasible solution with the smallest target value or the infeasible solution closest to the feasible region is selected as the reference point.The penalty factor is adaptively adjusted,so that the algorithm can search for the ideal solution sufficiently.This approach can significantly increase the optimization efficiency,as shown by the constrained test functions and airfoil design challenges.

关 键 词：优化设计 代理模型 参考点 气动设计 自适应罚函数 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]