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Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (11): 2314-2324    DOI: 10.3785/j.issn.1008-973X.2023.11.019
    
Multi-fidelity aerodynamic modeling method of aerospace vehicles based on Gaussian process regression
Ting-wei JI(),Xu ZHA,Fang-fang XIE*(),Yu-si WU,Xin-shuai ZHANG,Yi-yang JIANG,Chang-ping DU,Yao ZHENG
School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China
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Abstract  

A multi-fidelity aerodynamic modeling method of aerospace vehicles with shape configuration independent was proposed based on Gaussian process regression model, in order to satisfy the demand of full speed domain and large airspace of aerospace vehicle in the preliminary design stage. The traditional engineering estimation method and computational fluid dynamics (CFD) numerical simulation method were treated as the data sources of low-fidelity and high-fidelity aerodynamic characteristics, respectively. Specifically, a fast estimation model for aerodynamics of aerospace vehicles was established by using the panel method in the enigineering estimation method. Then, high-fidelity aerodynamic performance of aerospace vehicles was achieved based on the three-dimensional compressible Euler equations in the CFD numerical simulation. Moreover, the developed multi-fidelity aerodynamic modeling method was validated by the dual-parameter problems of FTB. The prediction accuracy and stability of the developed multi-fidelity aerodynamic model were better than that of the single-fidelity surrogate model with the same number of high-fidelity data points through comparison and analysis. Meanwhile, the relative error of prediction was less than 1%. The multi-fidelity aerodynamic model was used as the source of aerodynamic data for the reentry problem of the aerospace vehicle, and the influence of single fidelity and multi-fidelity modeling methods on the simulation of re-entry trajectory was compared and analyzed. Results show that the proposed multi-fidelity aerodynamic model can fast provide a high accurate aerodynamic data required from trajectory simulation.



Key wordsaerospace vehicle      aerodynamic performance analysis      multi-fidelity      numerical simulation      Gaussian process regression     
Received: 16 August 2022      Published: 11 December 2023
CLC:  V 411.8  
Fund:  国家自然科学基金资助项目(92271107);浙江省自然科学基金资助项目(LY21A020010);中央高校基本科研业务费资助项目(226-2022-00155)
Corresponding Authors: Fang-fang XIE     E-mail: zjjtw@zju.edu.cn;fangfang_xie@zju.edu.cn
Cite this article:

Ting-wei JI,Xu ZHA,Fang-fang XIE,Yu-si WU,Xin-shuai ZHANG,Yi-yang JIANG,Chang-ping DU,Yao ZHENG. Multi-fidelity aerodynamic modeling method of aerospace vehicles based on Gaussian process regression. Journal of ZheJiang University (Engineering Science), 2023, 57(11): 2314-2324.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.11.019     OR     https://www.zjujournals.com/eng/Y2023/V57/I11/2314


基于高斯过程回归的空天飞行器多精度气动建模方法

为了满足空天飞行器在初步设计阶段宽速域、大空域模型的需求,将传统工程估算方法和计算流体动力学(CFD)数值模拟方法分别作为低精度和高精度气动数据来源,基于高斯过程回归模型提出独立于构型的空天飞行器气动性能多精度气动建模方法. 在工程估算方法中,以面元法为基础,建立空天飞行器气动力快速估算模型. 在CFD数值模拟中通过求解三维可压缩Euler方程实现空天飞行器气动高精度计算. 将所提出的多精度气动建模方法应用于FTB外形的双参数气动建模问题中,通过对比分析,发现所提出的多精度气动模型的预测精度、稳定性均优于用同等数量高精度样本构建的单精度代理模型的,预测的相对误差小于1%. 将多精度气动模型作为该空天飞行器再入问题气动数据来源,对比分析单、多精度建模方法对再入轨迹仿真的影响,发现所提出的空天飞行器多精度气动建模方法能够更加快速、准确地给出轨迹仿真所需的气动数据.


关键词: 空天飞行器,  气动性能分析,  多精度,  数值模拟,  高斯过程回归 
Fig.1 Basic process of fast predicting method
Fig.2 Calculation fidelity versus cost distribution for high fidelity and low fidelity model
Fig.3 Density model of atmosphere between 0 and 70 km
Fig.4 Three views of FTB model
Fig.5 Comparison of calculation results of lift and drag coefficients
气动系数 $ {\bar \varepsilon _{{\rm{en}}}} $ $ {\bar \varepsilon _{{\rm{CFD}}}} $ $ \eta $/%
Cl 0.02763 0.02222 3.53
Cd 0.01203 0.00411 9.56
Tab.1 Comparison of average errors of solving aerodynamic coefficients by two methods
方法 Ns CPU配置 NC t
CFD数值模拟 1997434 Intel(R) Xeon(R) Platinum 8175M CPU @ 2.50 GHz 45 1.79 h
基于工程估算的
快速预测方法
5912 Intel(R) Core(TM)
i5-8400 CPU @ 2.80 GHz
1 0.58 s
Tab.2 Comparison of calculation cost of solving aerodynamic coefficients by two method
Fig.6 Process of multi-fidelity aerodynamic modeling
Fig.7 Correlation between high-fidelity samples and multi-fidelity predicted values for lift coefficient under different numbers of high-fidelity samples
Fig.8 Error cloud figure of multi-fidelity model for lift coefficient
Fig.9 Correlation between data of test set and multi-fidelity predicted values for lift coefficient under different numbers of high-fidelity samples
N ${ {\rm{lg } } }\left( { { {\bar \varepsilon }^2} } \right)$
单精度GPR 多精度GPR
4 ?1.286 ?3.097
9 ?2.325 ?4.281
18 ?2.149 ?4.245
35 ?5.623 ?6.082
42 ?5.733 ?6.083
Tab.3 Mean of squared error for multi-fidelity model of lift coefficient
N ${\lg}\;\left( {{\sigma _{{{\bar \varepsilon }^2}}}} \right)$
单精度GPR 多精度GPR
4 ?2.337 ?6.225
9 ?4.407 ?8.059
18 ?4.011 ?7.966
35 ?10.956 ?11.515
42 ?11.146 ?11.367
Tab.4 Variance of squared error for multi-fidelity model of lift coefficient
Fig.10 Cloud figure of multi-fidelity modeling results for lift and drag coefficients
Fig.11 Process of reentry trajectory simulation
Fig.12 Curve of reentry characteristic and comparison of errors based on single-fidelity and multi-fidelity aerodynamic models
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