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This paper presents a gradient-based response surface (GBRS) model and its applications to the aerodynamic design optimization. Since the widely used polynomial response surface model is continuous and differentiable, the gradients of the original response can be involved in constructing the quadratic polynomial response surface model. For the quadratic GBRS model, the number of the required samples depends linearly, instead of quadratically on the number of design parameters. Firstly, the samples are determined through the modified design of experiment with shortened sampling time to construct the GBRS model. Then function experiments are performed to evaluate the accuracy of GBRS model and its effectiveness in searching for the global minimum. Finally the gradients for constructing the GBRS model are calculated by the adjoint method and then an inverse design and an optimization design for improving the efficiency of a cascade are performed based on the GBRS model and the complex method. Results demonstrate that the optimization method based on the GBRS model is feasible and effective for obtaining the global optimum with high optimization efficiency; and the aerodynamic performance of the cascade can be significantly improved.
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Keywords:
- aerodynamic design optimization /
- response surface model /
- adjoint method /
- complex method
[1] Zhang Y F 2012 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese) [张宇飞 2012 博士学位论文 (北京: 清华大学)]
[2] Box G E P, Wilson K B 1951 J. R. Stat. Soc. B 13 1
[3] Yu H L, Wang Y Q, Chen H L, Cun H Y 2012 Journal of Xi’an Jiaotong University 46 80 (in Chinese) [于海莲, 王永泉, 陈花玲, 寸花英 2012 西安交通大学学报 46 80]
[4] Xie G F, He X H, Tong J J, Zheng Y H 2007 Acta Phys. Sin. 56 3193 (in Chinese) [谢国锋, 何旭洪, 童节娟, 郑艳华 2007 物理学报 56 3193]
[5] Samad A, Kim K Y, Goel T 2008 J. Propul. Power 24 301
[6] Bonaiuti D, Zangeneh M 2009 J. Turbomach. 131 021014
[7] Naylor E M J, Duenas C O, Miller R J, Hodson H P 2010 J. Turbomach. 132 011011
[8] Jameson A 1988 J. Sci. Comput. 3 233
[9] Luo J, Xiong J, Liu F, McBean I 2011 J. Turbomach. 133 011026
[10] Luo J, Xiong J, Liu F, McBean I 2010 Proceedings of the ASME Turbo Expo Glasgow, UK, June 14-18, 2010 p547
[11] Luo J, Liu F, McBean I 2011 Proceedings of the ASME Turbo Expo Vancouver, Canada, June 6-10, 2011 p1335
[12] Gao Y Y, He F, Shen M 2012 Acta Phys. Sin. 61 200206 (in Chinese) [高莹莹, 何枫, 沈孟育 2012 物理学报 61 200206]
[13] Vavalle A, Qin N 2007 J. Aircraft 44 365
[14] Box M J 1965 Comput. J. 8 42
[15] Hicks R M, Henne P A 1978 J. Aircraft 15 407
[16] Yang S, Wu H Y, Liu F, Tsai H M 2003 AIAA Paper 2003 1068
[17] Denton J D 1993 J. Turbomch. 115 621
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[1] Zhang Y F 2012 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese) [张宇飞 2012 博士学位论文 (北京: 清华大学)]
[2] Box G E P, Wilson K B 1951 J. R. Stat. Soc. B 13 1
[3] Yu H L, Wang Y Q, Chen H L, Cun H Y 2012 Journal of Xi’an Jiaotong University 46 80 (in Chinese) [于海莲, 王永泉, 陈花玲, 寸花英 2012 西安交通大学学报 46 80]
[4] Xie G F, He X H, Tong J J, Zheng Y H 2007 Acta Phys. Sin. 56 3193 (in Chinese) [谢国锋, 何旭洪, 童节娟, 郑艳华 2007 物理学报 56 3193]
[5] Samad A, Kim K Y, Goel T 2008 J. Propul. Power 24 301
[6] Bonaiuti D, Zangeneh M 2009 J. Turbomach. 131 021014
[7] Naylor E M J, Duenas C O, Miller R J, Hodson H P 2010 J. Turbomach. 132 011011
[8] Jameson A 1988 J. Sci. Comput. 3 233
[9] Luo J, Xiong J, Liu F, McBean I 2011 J. Turbomach. 133 011026
[10] Luo J, Xiong J, Liu F, McBean I 2010 Proceedings of the ASME Turbo Expo Glasgow, UK, June 14-18, 2010 p547
[11] Luo J, Liu F, McBean I 2011 Proceedings of the ASME Turbo Expo Vancouver, Canada, June 6-10, 2011 p1335
[12] Gao Y Y, He F, Shen M 2012 Acta Phys. Sin. 61 200206 (in Chinese) [高莹莹, 何枫, 沈孟育 2012 物理学报 61 200206]
[13] Vavalle A, Qin N 2007 J. Aircraft 44 365
[14] Box M J 1965 Comput. J. 8 42
[15] Hicks R M, Henne P A 1978 J. Aircraft 15 407
[16] Yang S, Wu H Y, Liu F, Tsai H M 2003 AIAA Paper 2003 1068
[17] Denton J D 1993 J. Turbomch. 115 621
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