基于梯度响应面模型的优化设计

罗佳奇; 刘锋

doi:10.7498/aps.62.190201

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基于梯度响应面模型的优化设计

罗佳奇 , 刘锋

基于梯度响应面模型的优化设计

罗佳奇, 刘锋

物理学报. 2013, 62(19): 190201.

doi: 10.7498/aps.62.190201.

摘要

本文主要研究一种梯度响应面模型及其在气动优化设计中的应用. 目前应用广泛的多项式响应面模型是连续可导的, 采用梯度信息构造完全二阶多项式响应面模型, 所需样本数与设计参数个数呈线性关系. 首先通过改进实验设计方法, 快速生成满足精度要求的样本并确定梯度响应面模型. 随后通过函数实验验证梯度响应面模型的精度, 及该模型在多极值函数最值搜索中的有效性. 最后由伴随方法快速求解气动优化设计目标函数的梯度信息, 并开展基于梯度响应面模型和复合形法的叶片压力反设计和效率优化设计. 结果表明: 基于梯度响应面模型的优化方法在全局最优及提高优化效率两方面均有出色表现, 基于该优化方法的气动优化设计能够显著改善叶片的气动性能.

关键词:

作者及机构信息

罗佳奇¹,
刘锋^{1 2}

1.
北京大学工学院, 北京 100871;

2.
加州大学Irvine分校机械与宇航工程系, CA 92697-3975

基金项目: 国家自然科学基金(批准号:51206003,51376009)和中国博士后科学基金(批准号:2012M510267,2013T60035)资助的课题.

参考文献

[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

施引文献

[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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物理学报. 2013, 62(19): 190201.

doi: 10.7498/aps.62.190201.

基于梯度响应面模型的优化设计

罗佳奇¹
刘锋^{1 2}

1. 北京大学工学院, 北京 100871;
2. 加州大学Irvine分校机械与宇航工程系, CA 92697-3975

基金项目:

国家自然科学基金(批准号:51206003,51376009)和中国博士后科学基金(批准号:2012M510267,2013T60035)资助的课题.

收稿日期: 2013-04-19
修回日期: 2013-05-24
刊出日期: 2013-10-05

摘要: 本文主要研究一种梯度响应面模型及其在气动优化设计中的应用. 目前应用广泛的多项式响应面模型是连续可导的, 采用梯度信息构造完全二阶多项式响应面模型, 所需样本数与设计参数个数呈线性关系. 首先通过改进实验设计方法, 快速生成满足精度要求的样本并确定梯度响应面模型. 随后通过函数实验验证梯度响应面模型的精度, 及该模型在多极值函数最值搜索中的有效性. 最后由伴随方法快速求解气动优化设计目标函数的梯度信息, 并开展基于梯度响应面模型和复合形法的叶片压力反设计和效率优化设计. 结果表明: 基于梯度响应面模型的优化方法在全局最优及提高优化效率两方面均有出色表现, 基于该优化方法的气动优化设计能够显著改善叶片的气动性能.

关键词:

English Abstract

Gradient-based response surface approximations for design optimization

Luo Jia-Qi¹,
Liu Feng^{1 2}

1.
College of Engineering, Peking University, Beijing 100871, China;

2.
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA

Fund Project:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51206003, 51376009), and the China Postdoctoral Science Foundation (Grant Nos. 2012M510267, 2013T60035).

Received Date: 19 April 2013
Accepted Date: 24 May 2013
Published Online: 05 October 2013

Abstract: 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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