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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (3): 632-642    DOI: 10.3785/j.issn.1008-973X.2023.03.022
    
Integrated aerodynamic optimization of wing/nacelle based on Gaussian process regression
Ting-wei JI(),Shao-chang MO,Fang-fang XIE*(),Xin-shuai ZHANG,Yi-yang JIANG,Yao ZHENG
School of Aeronautics and Astronautics, Zhengjiang University, Hangzhou 310027, China
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Abstract  

A new optimization design method based on Gaussian process regression (GPR) model was proposed to resolve the high-dimensional nonlinear optimization problem of integrated aerodynamic design of wing/nacelle. The geometric parametric modeling of the airfoils in the integrated configuration of wing/nacelle was realized by the class and shape transformation (CST) method. The deformation of the integrated configuration of wing/nacelle was achieved by controlling the wing shape parameters, the nacelle shape parameters and the nacelle installation parameters. The parametric modeling process included 50 design parameters in total. The GPR model was used to construct a surrogate model between the design parameters and the aerodynamics performance of the integrated wing/nacelle geometry. Bayesian optimization (BO) algorithm was used to realize the self-update of the surrogate model and the acquisition of the optimal aerodynamic shape. Results showed that the drag coefficient of the integrated configuration was reduced by 10.95% after the optimization. The flow field analysis shows that the optimization of the wing shape and the nacelle shape improves the surface flow field structure, and the optimization of the nacelle’s installation position reduces the aerodynamic interference between wing and nacelle.

Key words： wing/nacelle      aerodynamic optimization design      parametric modeling      Gaussian process regression (GPR)      Bayesian optimization (BO)     
Received: 09 October 2022      Published: 31 March 2023
CLC:  V 221.3  
Corresponding Authors: Fang-fang XIE     E-mail: zjjtw@zju.edu.cn;fangfang_xie@zju.edu.cn
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Ting-wei JI
Shao-chang MO
Fang-fang XIE
Xin-shuai ZHANG
Yi-yang JIANG
Yao ZHENG
Cite this article:

Ting-wei JI,Shao-chang MO,Fang-fang XIE,Xin-shuai ZHANG,Yi-yang JIANG,Yao ZHENG. Integrated aerodynamic optimization of wing/nacelle based on Gaussian process regression. Journal of ZheJiang University (Engineering Science), 2023, 57(3): 632-642.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.03.022     OR     https://www.zjujournals.com/eng/Y2023/V57/I3/632


基于高斯过程回归的机翼/短舱一体化气动优化

为了解决机翼/短舱一体化气动设计的高维非线性优化问题，基于高斯过程回归（GPR）模型提出新型优化设计方法. 采用类别形状函数变换（CST）方法对机翼/短舱一体化构型中的翼型进行几何参数化建模；通过控制机翼形状参数、短舱形状参数和短舱安装参数实现机翼/短舱构型变形，该参数化建模过程共计包含50个设计参数. 通过GPR模型构建机翼/短舱设计参数与气动性能之间的代理模型，并采用贝叶斯优化（BO）算法实现代理模型的自更新和最优气动外形的获取. 结果表明：优化后一体化构型的阻力系数下降了10.95%，通过流场分析发现机翼外形和短舱外形的优化改善了表面流场结构，短舱安装位置的优化减弱了机翼和短舱间的气动干扰.


关键词： 机翼/短舱,  气动优化设计,  参数化建模,  高斯过程回归（GPR）,  贝叶斯优化（BO） 
参数 数值
参考面积S/m2 0.072 7
平均气动弦长c/m 0.141 2
展长b/m 0.585 7
短舱前伸量X/mm 15.0
短舱下沉量Z/mm 7.5
Tab.1 Parameters of initial geometry of wing-body-nacelle-pylon
Fig.1 Comparison between parameterized RAE2822 airfoil and RAE2822 airfoil
Fig.2 Geometry of DLR-F4 wing
Fig.3 Geometric parameters of nacelle profile
Fig.4 Geometry of non-axisymmetric nacelle
Fig.5 Nacelle boundary
Fig.6 Mesh of DLR-F4 geometry
Fig.7 Wing pressure coefficient distribution of DLR-F4 geometry
Fig.8 Pressure coefficient distribution of NAL-AERO-02-01 geometry
Fig.9 Design space of DLR-F4 wing sections
参数 初始值 参数设计范围
$ {r_{{\text{if}}}} $ $ {r_{{\text{if,0}}}} $ (0.5 $ {r_{{\text{if,0}}}} $, 1.5 $ {r_{{\text{if,0}}}} $)
$ {r_{{\text{max}}}} $ $ {r_{{\text{hl}}}}+\Delta {r_{{\text{up}}}} $ ( $ {r_{{\text{hl}}}} $+0.89 $ \Delta {r_{{\text{up}}}} $, $ {r_{{\text{hl}}}} $+1.44 $ \Delta {r_{{\text{up}}}} $)
$ {f_{{\text{max}}}} $/% 32.5 (25, 40)
$\;{\beta _{ {\text{nac} } } }$/(°) ?12.89 (?25, ?11)
$ {r_{{\text{hi}}}} $ $ {r_{{\text{hi,0}}}} $ ( ${r_{ {\text{hi,0} } } } - \Delta {r_{ {\text{do} } } }$, ${r_{ {\text{hi,0} } } }$)
$ {f_{\text{i}}} $/% 39 (29, 49)
${\;\beta _{ {\text{int} } } }$/(°) 1 (0, 10)
X/mm 15 (0, 30)
Z/mm 7.5 (0, 15)
Tab.2 Design scope of intuitive parameters of nacelle profile and installation position of nacelle
Fig.10 Optimization framework of machine learning architecture based on Gaussian process regression
Fig.11 Convergence histories of optimizing wing-body-nacelle-pylon configuration
构型 Cd
机翼 机身 短舱 挂架
初始构型 209.1 100.2 55.7 4.0
优化构型 196.6 91.8 34.5 5.7
Tab.3 Change in drag coefficient of each component before and after optimization
构型 $ {d_{{\text{s1}}}} $ $ {d_{{\text{s2}}}} $ $ S $ $ {C_{\text{l}}} $ $ {C_{\text{d}}} $ $ {C_{{\text{d,p}}}} $ $ {C_{{\text{d,f}}}} $
初始构型 0.150 640 0.121 876 0.072 700 0.492 397 0.036 898 0.022 295 0.014 434
优化构型 0.154 776 0.124 436 0.077 607 0.492 451
(+0.01%) 		0.032 859
(?10.95%) 		0.018 898
(?15.24%) 		0.013 961
(?3.28%)
Tab.4 Comparison of aerodynamic performance and structural parameters of wing-body-nacelle-pylon configuration before and after optimization
Fig.12 Comparison of profiles of nacelle before and after optimization
Fig.13 Comparison of airfoil sections before and after optimization
Fig.14 Comparison of pressure coefficient of upper wing surface
Fig.15 Comparison of pressure coefficient of wing before and after optimization
Fig.16 Mach number distribution at 37.1% span station of wing
Fig.17 Comparison of pressure coefficient of nacelle at different section
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