The initial stage of missile design usually requires quick and rough evaluation of missile aerodynamic performance. To improve the low calculation accuracy of traditional engineering estimation software and reduce the high calculation cost of CFD method, we propose a scheme based on the Gaussian Process Regression (GPR) surrogate model to quickly and accurately predict the aerodynamic performance of typical missiles. The prediction results of the GPR model are analyzed, taking the missile shape parameters and angle of attack as the input and the lift coefficient, drag coefficient and moment coefficient as the output. First of all, compared with the prediction accuracy of other commonly used surrogate models, the prediction errors of the GPR model for the three coefficients are only 0.24%, 0.36% and 0.36%, respectively, lower than those of other surrogate models. Secondly, considering the problem that the kernel function selection of the GPR model depends heavily on artificial prior knowledge, we embed an automatic kernel construction algorithm which can automatically learn the kernel function from data without prior knowledge into the GPR framework. Compared with the traditional GPR model, the prediction errors of the GPR model incorporating the algorithm for the three coefficients are reduced to 0.10%, 0.22% and 0.17%, respectively. Finally, an application example of rapid prediction of missile aerodynamic performance is conducted, and the results show that the prediction scheme of the missile aerodynamic performance based on the GPR model is effective and can meet the requirements of fast and accurate aerodynamic performance prediction in the initial stage of missile design.
[1] 陈卫东, 唐小平, 曾奎, 等. 基于工程和数值方法的导弹气动特性计算[J]. 航空计算技术, 2012, 42(3):1-5. CHEN W D, TANG X P, ZENG K, et al. Calculation of missile aerodynamic characteristics based on engineering and numerical methods[J]. Aeronautical Computing Technique, 2012, 42(3):1-5(in Chinese).
[2] ROSEMA C, DOYLE J, AUMAN L, et al. Missile datcom user's manual-2011 revision[R]. Army Aviation and Missile Research Development Eng Ctr Redstone Arsenal Al System Simulation and Development Directorate, 2011.
[3] ROSEMA C C. A comparison of predictive methodologies for missile configurations with strakes[C]//33rd AIAA Applied Aerodynamics Conference. Reston:AIAA, 2015.
[4] LEVIN D, SIGAL A. Wind tunnel tests of a missile having elliptic cross sectioned body[C]//AIAA Atmospheric Flight Mechanics Conference and Exhibit. Reston:AIAA, 2002.
[5] ABNEY E, MCDANIEL M. High angle of attack aerodynamic predictions using missile datcom[C]//23rd AIAA Applied Aerodynamics Conference. Reston:AIAA, 2005.
[6] COIRIER W J, STUTTS J, ROSEMA C C. Development of a transonic fin aerodynamic database for incorporation into missile datcom[C]//32nd AIAA Applied Aerodynamics Conference. Reston:AIAA, 2014.
[7] DESPIRITO J. CFD aerodynamic characterization of 155-mm projectile at high angles-of-attack[C]//35th AIAA Applied Aerodynamics Conference. Reston:AIAA, 2017.
[8] 陈海昕, 邓凯文, 李润泽. 机器学习技术在气动优化中的应用[J]. 航空学报, 2019, 40(1):522480. CHEN H X, DENG K W, LI R Z. Utilization of machine learning technology in aerodynamic optimization[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1):522480(in Chinese).
[9] 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综述方法研究进展[J]. 航空学报, 2020, 41(5):623344. 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):623344(in Chinese).
[10] AHEMD M Y. Surrogates for the aerodynamic coefficients of supersonic airfoils[C]//53rd AIAA Aerospace Sciences Meeting. Reston:AIAA, 2015.
[11] 彭博, 聂蓉梅, 陈海东. 基于支持向量机的火箭气动学科代理模型构建方法[J]. 导弹与航天运载技术, 2013(4):33-37. PENG B, NIE R M, CHEN H D. Surrogate model construction for rocket aerodynamic discipline based on support vector machine[J]. Missiles and Space Vehicles, 2013(4):33-37(in Chinese).
[12] CARPENTER M, HARTFIELD R, BURKHALETR J. A comprehensive approach to cataloging missile aerodynamic performance using surrogate modeling techniques and statistical learning[C]//29th AIAA Applied Aerodynamics Conference. Reston:AIAA, 2011.
[13] RITZ S G, HARTFIELD R J, DANLEN J A, et al. Rapid calculation of missile aerodynamic coefficients using artificial neural networks[C]//2015 IEEE Aerospace Conference, 2015:1-19.
[14] HAN Z H, GORTZ S. Hierarchical kriging model for variable-fidelity surrogate modeling[J]. AIAA Journal, 2012, 50(9):1885-1896.
[15] 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(in Chinese).
[16] ÇETINER A E, YSGIZ B, GUZEL G, et al. CFD based response surface modeling with an application in missile aerodynamics[C]//34th AIAA Applied Aerodynamics Conference. Reston:AIAA, 2016.
[17] WILLIAMS C K I, RASMUSSEN C E. Gaussian processes for machine learning[M]. Cambridge:MIT Press, 2006.
[18] ZHANG Y, SUNG W J, MAVRIS D N. Application of convolutional neural network to predict airfoil lift coefficient[C]//2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston:AIAA, 2018.
[19] YILMAZ E, GERMAN B. A convolutional neural network approach to training predictors for airfoil performance[C]//18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Reston:AIAA, 2017.
[20] 韩忠华, 张瑜, 许晨舟, 等. 基于代理模型的大型民机机翼气动优化设计[J]. 航空学报, 2019,40(1):522398. HAN Z H, ZHANG Y, XU C Z, et al. Aerodynamic optimization design of large civil aircraft wings using surrogate-based model[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1):522398(in Chinese).
[21] 韩少强, 宋文萍, 韩忠华, 等. 基于梯度增强型Kriging模型的气动反设计方法[J]. 航空学报, 2017, 38(7):120817. HAN S Q, SONG W P, HAN Z H, et al. Aerodynamic inverse design method based on gradient-enhanced Kriging model[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(7):120817(in Chinese).
[22] LIU Z J, LIU X J, LYU H Q. A new hybrid aerodynamic optimization framework based on differential evolution and invasive weed optimization[J]. Chinese Journal of Aeronautics, 2018, 31(7):1437-1448.
[23] LE N D, ZIDEK J V. Statistical analysis of environmental space-time processes[M]. Springer Science & Business Media, 2006.
[24] DUVENAUD D, LLOYD J R, GROSSE R, et al. Structure discovery in nonparametric regression through compositional kernel search[DB/OL]. arXiv preprint:1302.4922, 2013.
[25] REGGENTE M, PETERS J, THEUNIS J, et al. Prediction of ultrafine particle number concentrations in urban environments by means of Gaussian process regression based on measurements of oxides of nitrogen[J]. Environmental Modelling & Software, 2014, 61:135-150.
[26] RICHARDSON R R, OSBORNE M A, HOWEY D A, et al. Gaussian process regression for forecasting battery state of health[J]. Journal of Power Sources, 2017,357:209-219.
[27] TOLBA H, DKHILI N, NOU J, et al. GHI forecasting using Gaussian process regression[C]. 2019.
[28] 高赫, 刘学军, 郭晋, 等. 基于高斯过程回归的连续式风洞马赫数控制[J]. 空气动力学学报, 2019, 37(3):480-487. GAO H, LIU X J, GUO J, et al. Mach number control of continuous wind tunnel based on Gaussian process regression[J]. Acta Aerodynamica Sinica, 2019, 37(3):480-487(in Chinese).
[29] HU J, WANG J. Short-term wind speed prediction using empirical wavelet transform and Gaussian process regression[J]. Energy, 2015, 93:1456-1466.
[30] DUVENAUD D. Automatic model construction with Gaussian processes[D]. Cambridge:University of Cambridge, 2014:1-47.
[31] MICCHELLI C A, XU Y, ZHANG H. Universal kernels[J]. Journal of Machine Learning Research, 2006, 7:2651-2667.
[32] DUVENAUD D K, NICKISCH H, RASMUSSEN C E. Additive gaussian processes[C]//Advances in Neural Information Processing Systems, 2011:226-234.
[33] SCHWARZ G. Estimating the dimension of a model[J]. The Annals of Statistics, 1978, 6(2):461-464.
[34] RASMUSSEN C E, NICKISCH H. The gpml toolbox version 4.0[R]. 2016.
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