耦合梯度与分级Kriging模型的高效气动优化方法

doi:10.7527/S1000-6893.2015.0260

流体力学与飞行力学

本期目录 | 过刊浏览 | 高级检索

前一篇 | 后一篇

耦合梯度与分级Kriging模型的高效气动优化方法

宋超, 杨旭东, 宋文萍

西北工业大学翼型叶栅国家重点实验室, 西安 710072

收稿日期:2015-07-21 修回日期:2015-09-20 出版日期:2016-07-15 发布日期:2015-09-25
通讯作者: 杨旭东男, 副教授, 硕士生导师。主要研究方向:计算流体力学、设计空气动力学。Tel.:029-88494621E-mail:xdyang@nwpu.edu.cn;Tel.:029-88494621,E-mail:xdyang@nwpu.edu.cn E-mail:xdyang@nwpu.edu.cn
作者简介:宋超男, 博士研究生。主要研究方向:计算流体力学、流动控制及飞行器气动设计。Tel.:029-88491419 E-mail:songxiaochao90@163.com;
基金资助:
国家自然科学基金（11272263)；中央高校基本科研业务费专项资金（310201401JCQ01017)

Efficient aerodynamic optimization method using hierarchical Kriging model combined with gradient

SONG Chao, YANG Xudong, SONG Wenping

National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China

Received:2015-07-21 Revised:2015-09-20 Online:2016-07-15 Published:2015-09-25
Supported by:
National Natural Science Foundation of China (11272263); the Fundamental Research Funds for the Central Universities (310201401JCQ01017)

摘要/Abstract

摘要：

Kriging代理模型中引入梯度信息能够提高模型的预测精度，但常规耦合梯度的方法都有不足之处。本文结合分级Kriging模型，提出了一种变可信度分级Kriging模型耦合梯度（GEHK）信息的新方法。首先利用梯度信息，选取扰动步长得到初始样本点附近的派生点，以派生点拟合出能够预测目标函数趋势的低精度Kriging模型。然后以初始样本点修正该模型得到高精度的Kriging模型。翼型减阻优化设计算例表明，与常规耦合梯度的Kriging模型相比，基于分级Kriging的梯度耦合方法对于扰动步长引入的误差不敏感，明显提高了模型预测精度，优化效率因此提升并使得目标函数值下降得更加迅速。相比Euler解作为低精度数据的常规分级Kriging模型，由梯度信息得到的派生点为模型提供了更准确的全局趋势预测，取得了更好的优化结果。本文方法成功应用于翼型多点减阻优化问题，说明该方法对复杂设计问题有很好的适应性。基于分级Kriging模型的耦合梯度方法克服了常规方法的缺点，提高了模型全局拟合精度，是一种优化效率更高的Kriging方法。

关键词: 翼型, 分级Kriging模型, 耦合梯度, 气动优化, 减阻

Abstract:

It is well-known that the accuracy of Kriging model can be improved when the gradients of objective function are involved in the model. But ordinary methods have some defects. A new method combining gradients with hierarchical Kriging (Gradient Enhanced Hierarchical Kriging, GEHK) model is developed in this paper. New samples are derived by Taylor approximation using gradients and selected steps. Then a low-fidelity Kriging model is built using derived samples. Finally, a high-fidelity model is obtained by adjusting the low-fidelity Kriging with initial samples. Optimization cases of airfoils have proved that the gradient-based GEHK is not sensitive to derived steps and the accuracy of prediction is enhanced. Taking this advantage, GEHK is more efficient than indirect Kriging and performs better in aerodynamic optimization and gets a better result. Compared with standard hierarchical Kriging model, using Euler solutions as low-fidelity data, derived samples provide a better global prediction for building Kriging model and thus GEHK obtains better results. GEHK model has been successfully used in a multipoint drag reduction case, which indicates its ability in complicated design cases. The new method has overcome limitations of traditional gradient-based Kriging model and the prediction accuracy of the model can be improved globally. The optimization is more efficient employing the proposed model.

Key words: airfoil, hierarchical Kriging model, combining gradient, aerodynamics optimization, drag reduction

中图分类号:

V211.4

宋超, 杨旭东, 宋文萍. 耦合梯度与分级Kriging模型的高效气动优化方法[J]. 航空学报, 2016, 37(7): 2144-2155.

SONG Chao, YANG Xudong, SONG Wenping. Efficient aerodynamic optimization method using hierarchical Kriging model combined with gradient[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(7): 2144-2155.

参考文献

[1] KHURI A I, MUKHOPAHYAY S. Response surface methodology[J]. Wiley Interdisciplinary Reviews Computational Statistics, 2011, 2(2):128-149.
[2] AHN J, KIM H J, LEE D H, et al. Response surface method for airfoil design in transonic flow[J]. Journal of Aircraft, 2012, 38(2):231-238.
[3] 白俊强, 王丹, 何小龙, 等. 改进的RBF神经网络在翼梢小翼优化设计中的应用[J]. 航空学报, 2014, 35(7):1865-1873. BAI J Q, WANG D, HE X L, et al. Application of an improved RBF neural network on aircraft winglet optimization design[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(7):1865-1873(in Chinese).
[4] 蒙文巩, 马东立, 楚亮. 基于神经网络响应面的机翼气动稳健性优化设计[J]. 航空学报, 2010, 31(6):1134-1140. MENG W G, MA D L, CHU L. Wing aerodynamic robustness optimization based on neural network response surface[J]. Acta Aeronautica et Astronautica Sinica, 2010, 31(6):1134-1140(in Chinese).
[5] MCDONALD D B, GRANTHAM W J, TABOR W L, et al. Global and local optimization using radial basis function response surface models[J]. Applied Mathematical Modelling, 2007, 31(10):2095-2110.
[6] WANG J G, LIU G R. On the optimal shape parameters of radial basis functions used for 2-D meshless methods[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 91(23):2611-2630.
[7] 王晓锋, 席光. 基于Kriging模型的翼型气动性能优化设计[J]. 航空学报, 2005, 26(5):545-549. WANG X F, XI G. Aerodynamic optimization design for airfoil based on Kriging model[J]. Acta Aeronautica et Astronautica Sinica, 2005, 26(5):545-549(in Chinese).
[8] JEONG S, MURAYAMA M, YAMAMOTO K. Efficient optimization design method using Kriging model[J]. Journal of Aircraft, 2005, 42(2):413-420.
[9] 孙智伟, 白俊强, 高正红, 等. 现代超临界翼型设计及其风洞试验[J]. 航空学报, 2015, 36(3):804-818. SUN Z W, BAI J Q, GAO Z H, et al. Design and wind tunnel test investigation of the modern supercritical airfoil[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(3):804-818(in Chinese).
[10] TOAL D J J, BRESSLOFF N W, KEANE A J. Kriging hyperparameter tuning strategies[J]. AIAA Journal, 2008, 46(5):1240-1252.
[11] ZHANG Y, LEITHEAD W E. Exploiting Hessian matrix and trust-region algorithm in hyperparameters estimation of Gaussian process[J]. Applied Mathematics and Computation, 2005, 171(2):1264-1281.
[12] CHUNG H S, ALONSO J J. Using gradients to construct coKriging approximation models for high-dimensional design optimization problems:AIAA-2002-0317[R]. Reston:AIAA, 2002.
[13] LAURENCEAU J, SAGAUT P. Building efficient response surfaces of aerodynamic functions with kriging and coKriging[J]. AIAA Journal, 2008, 46(2):498-507.
[14] KENNEDY M C, O'HAGAN A. Predicting the output from a complex computer code when fast approximations are available[J]. Biometrika, 2000, 87(1):1-13.
[15] HAN Z H, GÖRTZ S. Hierarchical Kriging model for variable-fidelity surrogate modeling[J]. AIAA Journal, 2012, 50(9):1885-1896.
[16] LIU W, BATILL S M. Gradient-enhanced response surface approximations using Kriging models:AIAA-2002-5456[R]. Reston:AIAA, 2002.
[17] FORRESTER A I J, KEANE A J. Recent advances in surrogate-based optimization[J]. Progress in Aerospace Sciences, 2009, 45(1):50-79.
[18] JAMESON A, MARTINELLI L, PIERCE N A. Optimum aerodynamic design using the Navier-Stokes equations[J]. Theoretical and Computational Fluid Dynamics, 1998, 10(1-4):213-237.
[19] COOK P, MCDONALD M, FIRMIN M. Aerofoil RAE2822 pressure distributions, and boundary layer and wake measurements:AGARD 138[R]. Paris:AGARD, 1979.
[20] PALACIOS F, COLONNO M R, ARANAKE A C, et al. Stanford University unstructured (SU2):An open-source integrated computational environment for multi-physics simulation and design:AIAA-2013-0287[R]. Reston:AIAA, 2013.
[21] 张扬, 白俊强, 朱军, 等. 改进Hicks-Henne型函数法在翼型参数化中的应用[J]. 飞行力学, 2011, 29(5):35-38. ZHANG Y, BAI J Q, ZHU J, et al. Application of improved Hicks-Henne shape function to airfoil parameterization[J]. Flight Dynamics, 2011, 29(5):35-38(in Chinese).
[J]

E-mail：hkxb@buaa.edu.cn

关于我们

期刊社服务

专业学科

封面文章

友情链接

主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

耦合梯度与分级Kriging模型的高效气动优化方法

Efficient aerodynamic optimization method using hierarchical Kriging model combined with gradient

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	王海峰, 刘坤澎, 江泓鑫, 杜晨曦. 螺旋桨多设计点气动优化方法和变桨距角策略[J]. 航空学报, 2024, 45(9): 528831-528831.
[2]	柳家齐, 陈荣钱, 楼锦华, 韩旭, 吴昊, 尤延铖. 基于深度学习的高速直升机旋翼翼型气动优化设计[J]. 航空学报, 2024, 45(9): 529828-529828.
[3]	王雪鹤, 柴春硕, 邢世龙, 樊枫, 黄水林. 共轴高速直升机反流区翼型设计及减阻机理[J]. 航空学报, 2024, 45(9): 529960-529960.
[4]	孙蓬勃, 周洲, 李旭, 王科雷. 目标气动特性下动力翼参数影响分析与优化[J]. 航空学报, 2024, 45(6): 629368-629368.
[5]	李广佳, 王红波, 张凯, 仪志胜. 临近空间太阳能无人机增升减阻技术综述[J]. 航空学报, 2024, 45(5): 529644-529644.
[6]	余婧, 蒋安林, 刘亮, 吴晓军, 桂业伟, 刘深深. 基于PCA降维的气动外形参数化方法[J]. 航空学报, 2024, 45(10): 129125-129125.
[7]	高世琦, 丁博, 解旭祯, 李铮, 陈林, 钱首元, 焦子涵, 白光辉. 等离子体激励在高速流动中的减阻机制[J]. 航空学报, 2023, 44(S2): 729373-729373.
[8]	农历, 盛子帅, 冼军, 张怀宝. 基于高精度算法的结冰翼型分离流动数值模拟[J]. 航空学报, 2023, 44(S2): 729291-729291.
[9]	许岭松, 吴渊, 朱东宇, 张付昆, 刘昱. FL⁃61结冰风洞翼型俯仰振荡机构研制[J]. 航空学报, 2023, 44(S2): 729296-729296.
[10]	曾繁宇, 邱云龙, 曹占伟, 张伦, 陈伟芳. 超声速湍流边界层阵列式微吹气流动控制与减阻特性[J]. 航空学报, 2023, 44(S2): 729396-729396.
[11]	马高杰, 安刚, 史佑民, 康宁, 孙军帅. 民用飞机高升力系统先进技术及发展[J]. 航空学报, 2023, 44(S1): 727516-727516.
[12]	陈艺夫, 马宇航, 蓝庆生, 孙卫平, 史亚云, 杨体浩, 白俊强. 基于多项式混沌法的翼型不确定性分析及梯度优化设计[J]. 航空学报, 2023, 44(8): 127446-127446.
[13]	赵欢, 高正红, 夏露. 基于新型多可信度代理模型的多目标优化方法[J]. 航空学报, 2023, 44(6): 126962-126962.
[14]	赵欢, 高正红, 夏露. 基于新型高维代理模型的气动外形设计方法[J]. 航空学报, 2023, 44(5): 126924-126924.
[15]	韩荣, 刘伟, 杨小亮. 高超声速飞行器自适应减阻盘动态减阻机理[J]. 航空学报, 2023, 44(4): 126633-126633.