Comparison of machine learning data fusion methods applied to aerodynamic modeling of rocket first stage with grid fins
-
摘要: 机器学习数据融合方法可帮助降低飞行器气动数据库建立的成本，加快研制进度，目前已经成为飞行器设计方法领域越来越活跃的研究方向，但其在工程复杂问题方面的应用研究并不充分。将多种常见变可信度数据融合模型应用于运载火箭子级栅格舵落区控制的工程项目，在开展部分工况的风洞试验基础上，结合少量的CFD数值模拟结果，研究相关函数和不同模型预测完整工况气动特性数据的差异性。通过对比加法标度函数修正模型、Co-Kriging模型、分层Kriging模型和多可信度神经网络模型等4种不同的数据融合模型发现：高斯指数相关函数对气动建模问题的适应性更好；Co-Kriging模型对气动数据的内插表现最好；分层Kriging模型对内插的预测精度较高，外插效果不理想；多可信度神经网络模型在外插区域能获得更光滑、合理的预测结果。Abstract: Machine learning data fusion method has attracted significant attention recently in aerodynamic database construction since it makes a trade-off between high prediction accuracy and low fitting cost by fusing samples of different fidelities. But the research on methods for complex engineering project is not sufficient. In this paper, several commonly used variable-fidelity models （VFMs） of data fusion are applied to the control law design in the rocket first stage landing area control project with grid fins. Based on wind tunnel tests of partial test states, combined with CFD simulation results, VFMs successfully predict the whole aerodynamic characteristics of grid fins. Here, our objective is to compare the performances of these four VFM methods （AS-MFS, Co-Kriging, HK, MFNN） and the results show that: Gaussian exponential function is more suitable for aerodynamic modeling problems; Co-Kriging has the best performance in the interpolation of aerodynamic data; HK model has high prediction accuracy for interpolation but has poor performance for extrapolation; MFNN model can obtain smoother and more reasonable results in the extrapolation region.
-
Key words:
- variable-fidelity model /
- aerodynamic modeling /
- data fusion /
- grid fin /
- machine learning
-
图 5 火箭一子级带栅格舵外形跨声速段和超声速段俯仰力矩特性
Figure 5. Pitching moment characteristics of rocket first stage with grid fins in the transonic and supersonic regimes
图 6 栅格舵俯仰力矩系数数据集空间分布情况
Figure 6. Pitching moment data set of rocket first stage with grid fins
图 8 不同超参数下的高斯指数函数变化（p = 2）
Figure 8. Influence of θ on the Gauss correlation function with p = 2
图 9 不同参数p时的高斯指数函数变化（θ = 1）
Figure 9. Influence of index p on the Gauss correlation function with θ = 1
图 10 基于不同相关函数的HK模型对俯仰力矩系数建模结果对比（超参数优化范围受限制）
Figure 10. Comparison of predicted pitching moment coefficients via HK model based on different correlation functions （with optimization boundaries for hyperparameters）
图 11 基于不同相关函数的HK模型对俯仰力矩系数建模结果对比（超参数优化范围不作限制）
Figure 11. Comparison of predicted pitching moment coefficients via HK model based on different correlation functions （with no optimization boundaries for hyperparameters）
图 12 采用两种相关函数的不同变可信度模型对俯仰力矩系数建模的结果对比
Figure 12. Comparison of predicted pitching moment coefficients via different variable-fidelity model based on the two correlation functions
图 13 不同变可信度模型对俯仰力矩系数建模内插结果对比
Figure 13. Comparison of predicted pitching moment coefficients via different VFMs
图 14 不同变可信度模型在马赫数为3.5时俯仰力矩系数预测结果的交叉验证对比
Figure 14. Comparison of cross validation for predicted pitching moment coefficients via different VFMs at Mach 3.5
图 15 不同变可信度模型对俯仰力矩系数建模外插结果对比
Figure 15. Comparison of predicted pitching moment coefficients via different VFMs
表 1 俯仰特性风洞试验情况[2]
Table 1. Fundamental state for wind tunnel experiment on pitching moment characteristics[2]
马赫数 0.4 0.8 0.9 1 1.15 2 2.5 3 3.5 4 5 6 7 车次数 7 7 7 2 7 7 2 2 7 1 0 0 0 
下载: 导出CSV
表 2 不同舵偏角下样本分布情况
Table 2. Data sets for different elevator deflections of grid fins
舵偏角 –20° –10° 0° 10° 总计 训练集样本个数 85 55 85 55 280 测试集样本个数 5 5 15 5 30
下载: 导出CSV
表 3 针对俯仰力矩系数建模不同模型精度指标对比
Table 3. Comparison of different accuracy indicators for pitching moment coefficients via different VFMs
舵偏角 模 型 r2 RRMSE RMAE -20° AS-MFS 0.997148 0.050151 0.080148 Co-Kriging 0.999482 0.024037 0.035985 HK 0.998572 0.040432 0.073526 MFNN 0.949331 0.433717 0.722283 -10° AS-MFS 0.941375 0.328419 0.535310 Co-Kriging 0.953788 0.324708 0.455177 HK 0.938108 0.317452 0.462085 MFNN 0.842811 0.756029 1.124043 0° AS-MFS 0.989935 0.146836 0.245788 Co-Kriging 0.996639 0.068603 0.109666 HK 0.993100 0.104178 0.183757 MFNN 0.985395 0.117386 0.326321 10° AS-MFS 0.988510 0.097516 0.179175 Co-Kriging 0.995607 0.060434 0.101578 HK 0.994743 0.066439 0.101578 MFNN 0.970473 0.175599 0.318173
下载: 导出CSV
-
[1] 杜涛,陈闽慷,李凰立,等. 变精度模型(VCM)的自适应预处理方法研究[J]. 空气动力学学报,2018,36(2):315-319. doi: 10.7638/kqdlxxb-2016.0040DU T,CHEN M K,LI H L,et al. Research on adaptive preconditioning method for variable complexity model[J]. Acta Aerodynamica Sinica,2018,36(2):315-319. doi: 10.7638/kqdlxxb-2016.0040 [2] 杜涛,许晨舟,王国辉,等. 人工智能气动特性预测技术在火箭子级落区控制项目的应用[J]. 宇航学报,2021,42(1):61-73. doi: 10.3873/j.issn.1000-1328.2021.01.007DU T,XU C Z,WANG G H,et al. The application of aerodynamic coefficients prediction technique via artificial intelligence method to rocket first stage landing area control project[J]. Journal of Astronautics,2021,42(1):61-73. doi: 10.3873/j.issn.1000-1328.2021.01.007 [3] 张天姣,钱炜祺,周宇,等. 人工智能与空气动力学结合的初步思考[J]. 航空工程进展,2019,10(1):1-11.ZHANG T J,QIAN W Q,ZHOU Y,et al. Preliminary thoughts on the combination of artificial intelligence and aerodynamics[J]. Advances in Aeronautical Science and Engineering,2019,10(1):1-11. [4] 唐志共,王文正,陈功,等. 气动模型在现代气动试验设计中的应用研究[J]. 空气动力学学报,2017,35(2):172-176. doi: 10.7638/kqdlxxb—2015.0190TANG Z G,WANG W Z,CHEN G,et al. Research on the application of aerodynamic models in modern design of aerodynamic experiments[J]. Acta Aerodynamica Sinica,2017,35(2):172-176. doi: 10.7638/kqdlxxb—2015.0190 [5] SLOTNICK J, KHODADOUST A, ALONSO J, et al. CFD vision 2030 study: A path to revolutionary computational aerosciences[R]. NASA/CR-2014-218178, 2014. [6] 韩忠华,许晨舟,乔建领,等. 基于代理模型的高效全局气动优化设计方法研究进展[J]. 航空学报,2020,41(5):25-65.HAN Z H,XU C Z,QIAO J L,et al. Recent progress of efficient global aerodynamic shape optimization using surrogate-based approach[J]. Acta Aeronautica et Astronautica Sinica,2020,41(5):25-65. [7] 韩忠华. Kriging模型及代理优化算法研究进展[J]. 航空学报,2016,37(11):3197-3225.HAN Z H. Kriging surrogate model and its application to design optimization: a review of recent progress[J]. Acta Aeronautica et Astronautica Sinica,2016,37(11):3197-3225. [8] 周奇,杨扬,宋学官,等. 变可信度近似模型及其在复杂装备优化设计中的应用研究进展[J]. 机械工程学报,2020,56(24):219-245. doi: 10.3901/JME.2020.24.219ZHOU Q,YANG Y,SONG X G,et al. Survey of multi-fidelity surrogate models and their applications in the design and optimization of engineering equipment[J]. Journal of Mechanical Engineering,2020,56(24):219-245. doi: 10.3901/JME.2020.24.219 [9] 何开锋,钱炜祺,汪清,等. 数据融合技术在空气动力学研究中的应用[J]. 空气动力学学报,2014,32(6):777-782. doi: 10.7638/kqdlxxb—2014.0072HE K F,QIAN W Q,WANG Q,et al. Application of data fusion technique in aerodynamics studies[J]. Acta Aerodynamica Sinica,2014,32(6):777-782. doi: 10.7638/kqdlxxb—2014.0072 [10] HAFTKA R T. Combining global and local approximations[J]. AIAA Journal,1991,29(9):1523-1525. doi: 10.2514/3.10768 [11] CHANG K J,HAFTKA R T,GILES G L,et al. Sensitivity-based scaling for approximating structural response[J]. Journal of Aircraft,1993,30(2):283-288. doi: 10.2514/3.48278 [12] ALEXANDROV N M,DENNIS J E,LEWIS R M,et al. A trust-region framework for managing the use of approximation models in optimization[J]. Structural Optimization,1998,15(1):16-23. doi: 10.1007/BF01197433 [13] ALEXANDROV N, NIELSEN E, LEWIS R, et al. First-order model management with variable-fidelity physics applied to multi-element airfoil optimization[C]//Proc of the 8th Symposium on Multidisciplinary Analysis and Optimization. 2000. doi: 10.2514/6.2000-4886 [14] SHU L S,JIANG P,SONG X G,et al. Novel approach for selecting low-fidelity scale factor in multifidelity metamodeling[J]. AIAA Journal,2019,57(12):5320-5330. doi: 10.2514/1.j057989 [15] PARK C,HAFTKA R T,KIM N H. Low-fidelity scale factor improves Bayesian multi-fidelity prediction by reducing bumpiness of discrepancy function[J]. Structural and Multidisciplinary Optimization,2018,58(2):399-414. doi: 10.1007/s00158-018-2031-2 [16] WANG S,LIU Y,ZHOU Q,et al. A multi-fidelity surrogate model based on moving least squares: fusing different fidelity data for engineering design[J]. Structural and Multidisciplinary Optimization,2021,64(6):3637-3652. doi: 10.1007/s00158-021-03044-5 [17] HAN Z H,GÖRTZ S,ZIMMERMANN R. Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function[J]. Aerospace Science and Technology,2013,25(1):177-189. doi: 10.1016/j.ast.2012.01.006 [18] BANDLER J W,BIERNACKI R M,CHEN S H,et al. Space mapping technique for electromagnetic optimization[J]. IEEE Transactions on Microwave Theory and Techniques,1994,42(12):2536-2544. doi: 10.1109/22.339794 [19] ROBINSON T D,ELDRED M S,WILLCOX K E,et al. Surrogate-based optimization using multifidelity models with variable parameterization and corrected space mapping[J]. AIAA Journal,2008,46(11):2814-2822. doi: 10.2514/1.36043 [20] JONSSON E, LEIFSSON L, KOZIEL S. Aerodynamic optimization of wings by space mapping[C]//Proc of the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. 2013. doi: 10.2514/6.2013-780 [21] 何磊,钱炜祺,汪清,等. 机器学习方法在气动特性建模中的应用[J]. 空气动力学学报,2019,37(3):470-479. doi: 10.7638/kqdlxxb—2019.0033HE L,QIAN W Q,WANG Q,et al. Applications of machine learning for aerodynamic characteristics modeling[J]. Acta Aerodynamica Sinica,2019,37(3):470-479. doi: 10.7638/kqdlxxb—2019.0033 [22] KENNEDY M,O'HAGAN A. Predicting the output from a complex computer code when fast approximations are available[J]. Biometrika,2000,87(1):1-13. doi: 10.1093/biomet/87.1.1 [23] QIAN P Z G,WU C F J. Bayesian hierarchical modeling for integrating low-accuracy and high-accuracy experiments[J]. Technometrics,2008,50(2):192-204. doi: 10.1198/004017008000000082 [24] LE GRATIET L,GARNIER J. Recursive co-kriging model for design of computer experiments with multiple levels of fidelity[J]. International Journal for Uncertainty Quantification,2014,4(5):365-386. doi: 10.1615/int.j.uncertaintyquantification.2014006914 [25] XIAO M Y,ZHANG G H,BREITKOPF P,et al. Extended Co-Kriging interpolation method based on multi-fidelity data[J]. Applied Mathematics and Computation,2018,323:120-131. doi: 10.1016/j.amc.2017.10.055 [26] ZAYTSEV A. Reliable surrogate modeling of engineering data with more than two levels of fidelity[C]//Proc of the 2016 7th International Conference on Mechanical and Aerospace Engineering （ICMAE）. 2016: 341-345. doi: 10.1109/ICMAE.2016.7549563 [27] ZHOU Q,WU Y D,GUO Z D,et al. A generalized hierarchical co-Kriging model for multi-fidelity data fusion[J]. Structural and Multidisciplinary Optimization,2020,62(4):1885-1904. doi: 10.1007/s00158-020-02583-7 [28] HAN Z H,GÖRTZ S. Alternative cokriging method for variable-fidelity surrogate modeling[J]. AIAA Journal,2012,50(5):1205-1210. doi: 10.2514/1.J051243 [29] ZIMMERMANN R, HAN Z H. Simplified cross-correlation estimation for multifidelity surrogate cokriging models[J]. Advances and Applications in Mathematical Sciences, 2010. [30] HAN Z H,GÖRTZ S. Hierarchical kriging model for variable-fidelity surrogate modeling[J]. AIAA Journal,2012,50(9):1885-1896. doi: 10.2514/1.J051354 [31] MENG X H,KARNIADAKIS G E. A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems[J]. Journal of Computational Physics,2020,401:109020. doi: 10.1016/j.jcp.2019.109020 [32] MENG X H,BABAEE H,KARNIADAKIS G E. Multi-fidelity Bayesian neural networks: Algorithms and applications[J]. Journal of Computational Physics,2021,438:110361. doi: 10.1016/j.jcp.2021.110361 [33] HE L,QIAN W Q,ZHAO T,et al. Multi-fidelity aerodynamic data fusion with a deep neural network modeling method[J]. Entropy (Basel, Switzerland),2020,22(9):1022. doi: 10.3390/e22091022 [34] ZHANG X S,XIE F F,JI T W,et al. Multi-fidelity deep neural network surrogate model for aerodynamic shape optimization[J]. Computer Methods in Applied Mechanics and Engineering,2021,373:113485. doi: 10.1016/j.cma.2020.113485 [35] SATRIA P P,RIZKI Z L,SHIMOYAMA K. Gaussian process surrogate model with composite kernel learning for engineering design[J]. AIAA Journal,2020,58(4):1864-1880. doi: 10.2514/1.J058807 -
点击查看大图
计量
- 文章访问数: 1571
- HTML全文浏览量: 307
- PDF下载量: 95
- 被引次数: 0
