ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Aerodynamic inverse design method based on gradient-enhanced Kriging model
Received date: 2016-09-26
Revised date: 2016-10-17
Online published: 2016-11-24
Supported by
National Natural Science Foundation of China (11272265)
Up to date, the surrogate-based optimization methods using Kriging model are widely used in the aerodynamic optimization design. However, the huge time costs seriously restrict the in-depth development of Kriging model when it comes to cases with dimension course (more than 30 design variables). Inverse design problems of airfoils and wings are formulated as optimization problems. Surrogate-based optimization using gradient-enhanced Kriging (GEK) model is adopted to conduct aerodynamic inverse design of 18, 36 and 108 variables, and gradient is solved via the efficient adjoint method. It is worth mentioning that the dimension of aerodynamic inverse design using surrogate-based optimization is successfully expanded to more than 100 by constructing GEK model in part of the design space. Besides, the influence of gradient accuracy on surrogate-based optimization using GEK model is studied. The results show that the effect of optimization is improved with more accurate gradients. BFGS (Broyden, Fletcher, Goldfarb and Shanno) and surrogate-based optimizations using GEK and Kriging models are compared through aerodynamic inverse design of different dimensions. The results show that surrogate-based optimization using GEK model has significantly higher efficiency, and the advantage of efficiency is more obvious with higher dimension of design. At the same time, surrogate-based optimization using GEK model has better optimization effect and less number of calls of analysis programs than the BFGS method.
HAN Shaoqiang , SONG Wenping , HAN Zhonghua , WANG Le . Aerodynamic inverse design method based on gradient-enhanced Kriging model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017 , 38(7) : 120817 -120817 . DOI: 10.7527/S1000-6893.2016.0299
[1] 韩忠华. Kriging模型及代理优化算法研究新进展[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).
[2] HAN Z H. SurroOpt: A generic surrogate-based optimization code for aerodynamic and multidisciplinary design[C]//30th Congress of the International Council of the Aeronautical Aciences, 2016.
[3] 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).
[4] 许瑞飞, 宋文萍, 韩忠华. 改进Kriging模型在翼型气动优化设计中的应用研究[J]. 西北工业大学学报, 2010, 28(4): 503-510. XU R F, SONG W P, HAN Z H. Application of improved Kriging-model-based optimization method in airfoil aerodynamic design[J]. Journal of Northwestern Polytechnical University, 2010, 28(4): 503-510 (in Chinese).
[5] 白俊强, 王波, 孙智伟, 等. 基于松散式代理模型管理框架的亚音速机翼优化设计方法研究[J]. 西北工业大学学报, 2011, 29(4): 515-519. BAI J Q, WANG B, SUN Z W, et al. Developing optimization design of subsonic wing with losse type of agent model[J]. Journal of Northwestern Polytechnical University, 2011, 29(4): 515-519 (in Chinese).
[6] 张科施, 韩忠华, 李为吉, 等. 基于近似技术的高亚声速运输机机翼气动/结构优化设计[J]. 航空学报, 2006, 27(5): 810-815. ZHANG K S, HAN Z H, LI W J, et al. Multidisciplinary aerodynamic/structural design optimization for high subsonic transport wing using approximation technique[J]. Acta Aeronautica et Astronautica Sinica, 2006, 27(5): 810-815 (in Chinese).
[7] 姚拴宝, 郭迪龙, 孙振旭, 等. 基于Kriging代理模型的高速列车头型多目标优化设计[J]. 中国科学:技术科学, 2013, 43(2): 186-200. YAO S B, GUO D L, SUN Z X, et al. Multi-objective optimization of the streamlined head of high-speed trains based on the Kriging model[J]. Scientia Sinica: Techchnologica, 2013, 43(2): 186-200 (in Chinese).
[8] LIU J, SONG W P, HAN Z H, et al. Efficient aerodynamic shape optimization of transonic wings using a parallel infilling strategy and surrogate models[J]. Structural & Multidisciplinary Optimization, 2016: 1-19.
[9] KIM H J, RHO O H. Aerodynamic design of transonic wings using the target pressure optimization approach[J]. Journal of Aircraft, 1998, 35(5): 671-677.
[10] 赵国庆, 招启军. 基于目标压力分布的旋翼先进气动外形反设计分析方法[J]. 航空学报, 2014, 35(3): 744-755. ZHAO G Q, ZHAO Q J. Inverse design analysis method on rotor with advanced aerodynamic configuration based upon target pressure distribution[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(3): 744-755 (in Chinese).
[11] TOAL D J J, BRESSLOFF N W, KEANE A J. Kriging hyperparameter tuning strategies[J]. AIAA Journal, 2008, 46(5): 1240-1252.
[12] TOAL D J J, BRESSLOFF N W, KEANE A J, et al. The development of a hybridized particle swarm for kriging hyperparameter tuning[J]. Engineering Optimization, 2011, 43(6): 675-699.
[13] 刘俊, 宋文萍, 韩忠华, 等. Kriging模型在翼型反设计中的应用研究[J]. 空气动力学学报, 2014, 32(4): 518-526. LIU J, SONG W P, HAN Z H, et al. Kriging-based airfoil inverse design[J]. Acta Aerodynamica Sinica, 2014, 32(4): 518-526 (in Chinese).
[14] SHAN S. Survey of modeling and optimization strategies for high-dimensional design problems[J]. Chemical Engineering Science, 2015, 141(2): 184-194.
[15] JAMESON A, REUTHER J. Control theory based airfoil design using the Euler equations[C]//5th Symposium on Multidisciplinary Analysis and Optimization. Reston: AIAA, 1994.
[16] JAMESON A. Aerodynamic design via control theory[J]. Journal of Scientific Computing, 1988, 3(3): 233-260.
[17] JAMESON A. Optimum aerodynamic design using CFD and control theory: AIAA-1995-1729[R]. Reston: AIAA, 1995.
[18] LIU W Y, BATILL S M. Gradient-enhanced response surface approximations using kriging models[C]//9th AIAA/ISSMO Symposium and Exhibit on Multidisciplinary Analysis and Optimization. Reston: AIAA, 2002.
[19] 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.
[20] LAURENCEAU J, SAGAUT P. Building efficient response surfaces of aerodynamic functions with kriging and cokriging[J]. AIAA Journal, 2008, 46(2): 498-507.
[21] LAURENCEAU J, MEAUX M, MONTAGNAC M, et al. Comparison of gradient-based and gradient-enhanced response-surface-based optimizers[J]. AIAA Journal, 2010, 48(5): 981-994.
[22] 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.
[23] HAN Z H, SONG C X, ZHANG Y. A new formulation of gradient-enhanced surrogate model and application to aerodynamic design[C]//34th AIAA Applied Aerodynamics Conference. Reston: AIAA, 2016.
[24] 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 C, YANG X D, SONG W P. Efficient aerodynamic optimization method using hierarchical Kriging combined with gradient[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(7): 2144-2155 (in Chinese).
[25] CHUNG H S, ALONSO J J. Design of a low-boom supersonic business jet using cokriging approximation models: AIAA-2002-5598[R]. Reston: AIAA, 2002.
[26] XUAN Y, XIANG J H, ZHANG W H, et al. Gradient-based Kriging approximate model and its application research to optimization design[J]. Science in China Series E: Technological Sciences, 2009, 52(4): 1117-1124.
[27] 刘俊, 宋文萍, 韩忠华,等. 梯度增强的Kriging模型与Kriging模型在优化设计中的比较研究[J]. 西北工业大学学报, 2015, 33(5): 819-826. LIU J, SONG W P, HAN Z H, et al. Comparative study of GEK (Gradient-Enhanced Kriging) and Kriging when applied to design optimization[J]. Journal of Northwestern Polytechnical University, 2015, 33(5): 819-826 (in Chinese).
[28] KULFAN B M. Universal parametric geometry representation method[J]. Journal of Aircraft, 2008, 45(1): 142-158.
[29] GIUNTA A A, WOJTKIEWICZ S F, ELDRED M S. Overview of modern design of experiments methods for computational simulations[C]//Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit. Reston: AIAA, 2003.
[30] METROPOLIS N, ULAM S. The Monte Carlo method[J]. Journal of the American Statistical Association, 1949, 44(247): 335-341.
[31] HOYLE N, BRESSLOFF N W, KEANE A J. Design optimization of a two-dimensional subsonic engine air intake[J]. AIAA Journal, 2006, 44(11): 2672-2681.
[32] HAN Z H, ZHANG K S, SONG W P, et al. Optimization of active flow control over an airfoil using a surrogate-management framework[J]. Journal of Aircraft, 2010, 47(2): 603-612.
[33] HAN Z H, ZHANG K S, LIU J, et al. Surrogate-based aerodynamic shape optimization with application to wind turbine airfoils: AIAA-2013-1108[R]. Reston: AIAA, 2013.
[34] LIU J, HAN Z H, SONG W P. Comparison of infill sampling criteria in Kriging-based aerodynamic optimization[C]//28th International Congress of the Aeronautical Sciences, 2012.
/
| 〈 |
|
〉 |
CJA