几何不确定性区间分析及鲁棒气动优化设计

doi:10.13700/j.bh.1001-5965.2019.0077

北京航空航天大学学报 ›› 2019, Vol. 45 ›› Issue (11): 2217-2227.doi: 10.13700/j.bh.1001-5965.2019.0077

几何不确定性区间分析及鲁棒气动优化设计

宋鑫^1,2, 郑冠男^1,2, 杨国伟^1,2, 姜倩^1,2

1. 中国科学院力学研究所流固耦合系统力学重点实验室, 北京 100080;
2. 中国科学院大学工程科学学院, 北京 100049

收稿日期:2019-03-04 出版日期:2019-11-20 发布日期:2019-11-30
通讯作者: 郑冠男.E-mail:zhengguannan@imech.ac.cn E-mail:zhengguannan@imech.ac.cn
作者简介:宋鑫女,博士研究生。主要研究方向:气动弹性、优化设计;郑冠男男,博士,高级工程师。主要研究方向:计算流体力学、气动弹性;杨国伟男,博士,研究员,博士生导师。主要研究方向:计算流体力学、气动弹性。
基金资助:
国家自然科学基金（11672303）

Interval analysis for geometric uncertainty and robust aerodynamic optimization design

SONG Xin^1,2, ZHENG Guannan^1,2, YANG Guowei^1,2, JIANG Qian^1,2

1. Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China;
2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2019-03-04 Online:2019-11-20 Published:2019-11-30
Supported by:
National Natural Science Foundation of China (11672303)

摘要/Abstract

摘要： 不确定性因素会导致飞行器偏离预先设计的气动性能，造成气动性能下降甚至产生严重的后果。针对工程中无法给出准确的几何不确定性概率分布以及跨声速条件下非线性气动问题，对几何不确定性的非概率参数化建模进行了研究，并结合Kriging模型及最优化方法建立了快速非线性区间分析方法。采用该方法对对称翼型进行不确定性分析，获得了气动性能参数的定量变化区间。在区间不确定性分析基础上建立了鲁棒优化设计流程。基于区间序关系及区间可能度转换模型将单目标区间不确定性优化问题转化为多目标确定性优化问题，并采用基于Pareto熵的自适应多目标粒子群算法对优化问题进行寻优。考虑几何不确定性以及升力、力矩、面积约束，以阻力性能为目标对超临界翼型进行了鲁棒优化设计。与确定性优化设计结果对比表明，确定性优化设计在不确定性因素的影响下易失效，而鲁棒设计可得到更安全可靠的结果。

关键词: 几何不确定性, 非线性区间分析, 直接操作自由变形(DFFD), 气动优化设计, 鲁棒优化设计, 自适应多目标粒子群算法, Kriging模型

Abstract: Uncertainties will make aircraft deviate from the designed aerodynamic performance, resulting in the decrease in aerodynamic performance and even destruction. Due to the problem that the probability distribution of geometric uncertainty cannot be given in engineering and nonlinear aerodynamic problem in transonic flows, the non-probabilistic parametric modeling of geometric uncertainty is studied, and the fast nonlinear interval analysis method is established in combination with Kriging model and optimization method. The effects of geometric uncertainties on a symmetric airfoil are analyzed using the above method, and the quantitative variation range of aerodynamic performance is obtained. Based on interval uncertainty analysis, a robust optimization design process is established. The single-objective interval uncertainty optimization problem was transformed into deterministic multi-objective optimization problem based on the order relation and possibility degree model of interval number, and the optimization problem was solved by adaptive multi-objective particle swarm optimization which is based on Pareto entropy. The robust optimization design is implemented for the supercritical airfoil with the drag objective as well as lift, moment and area constraints under geometric uncertainties. The results compared with deterministic optimization design show that deterministic design is prone to failure under the influence of uncertainties, while the robust design is more secure and reliable.

Key words: geometric uncertainty, nonlinear interval analysis, directly manipulated free-form deformation (DFFD), aerodynamic optimization design, robust optimization design, adaptive multi-objective particle swarm optimization algorithm, Kriging model

中图分类号:

V211.3

宋鑫, 郑冠男, 杨国伟, 姜倩. 几何不确定性区间分析及鲁棒气动优化设计[J]. 北京航空航天大学学报, 2019, 45(11): 2217-2227.

SONG Xin, ZHENG Guannan, YANG Guowei, JIANG Qian. Interval analysis for geometric uncertainty and robust aerodynamic optimization design[J]. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2019, 45(11): 2217-2227.

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几何不确定性区间分析及鲁棒气动优化设计

Interval analysis for geometric uncertainty and robust aerodynamic optimization design

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