多学科设计优化代理模型技术的研究和应用
|
摘要
代理模型是多学科设计优化中一种包含试验设计和近似方法等多项内容的建模方法，它通过在系统中用数学模型来替代原有分析模块的方式，实现了分析模块与MDO计算框架的集成，使复杂系统的多学科设计优化变的切实可行。本文系统分析了多学科设计优化方法中代理模型的构造过程，比较了几种相关的试验设计方法和数学近似方法。通过对比分析，我们认为要构造代理模型就必须引入能够大大减少试验次数的试验设计方法和能够解决高维非线性问题的近似方法。为此本文中分别介绍了正交试验，均匀试验以及中心复合试验等几种试验设计方法，以及多项式响应面，Kriging，和径向基函数等几种数学近似方法。并且通过构造描述机翼展向升力分布的代理模型，对上述几种方法作了对比分析。算例的结果表明，试验设计方法的选取与要解决问题的规模直接相关。同时计算结果还显示，Kriging模型和径向基函数模型作为两种通用模型，可以很好的解决一般的高维非线性代理模型的构造问题；另外，从算例问题的物理本质出发所构造的广义多项式响应面模型也能够满足精度要求。
Surrogate model is an important component of Multidiscipline Design Optimization (MDO). A surrogate model is created with experiment design methods and approximation approaches, and it can be easily integrated into a MDO Framework. This article describes the development process of surrogate models and introduces some experiment design methods and approximation approaches that can be used for a MDO surrogate model, they are Full Factorial Experiment Design, Orthogonal Experiment Design, Uniform Experiment Design, Central-Composite Experiment Design, and Polynomial Response Surface method, Kriging method, Radial Basis Function method and Artificial Neural Network. At the end of this article, a surrogate model is created to describe the lift distribution of a wing. Result shows that Kriging method and RBF method are two useful approximation approaches, especially for high dimension problem. In addition, this article created a generalized polynomial response surface model, and result shows that it can be also used to describe the lift distribution.
Surrogate model is an important component of Multidiscipline Design Optimization (MDO). A surrogate model is created with experiment design methods and approximation approaches, and it can be easily integrated into a MDO Framework. This article describes the development process of surrogate models and introduces some experiment design methods and approximation approaches that can be used for a MDO surrogate model, they are Full Factorial Experiment Design, Orthogonal Experiment Design, Uniform Experiment Design, Central-Composite Experiment Design, and Polynomial Response Surface method, Kriging method, Radial Basis Function method and Artificial Neural Network. At the end of this article, a surrogate model is created to describe the lift distribution of a wing. Result shows that Kriging method and RBF method are two useful approximation approaches, especially for high dimension problem. In addition, this article created a generalized polynomial response surface model, and result shows that it can be also used to describe the lift distribution.
引文
[1] Current State of the Art on Multidisciplinary Design Optimization, An AIAA White Paper,
September 1991
[2] Multidisciplinary Design Practices from the F-16 Agile Falcon, Michael H. Love (Lockheed Martin). http://endo.sandia.gov/AIAA_MDOTC/sponsored/mike_love.pdf
[3] A Description of the F/A-18E/F Design and Design Process, James A. Young, Ronald D. Anderson, and Rudolph N. Yurkovich (Boeing, St. Louis). http://endo.sandia.gov/AIAA_MDOTC/sponsored/fl 8boeing.pall
[4] The F-22 Structural/Aeroelastic Design Process with MDO Examples, Nick Radovcich and David Layton (Lockheed Martin). http://endo.sandia.gov/AIAA_MDOTC/sponsored/f221ockmart.pdf
[5] 余雄庆 多学科设计优化算法及其在飞机设计中的应用研究．南京航空航天大学 工学博士学位论文．1999年4月．
[6] 余雄庆 飞机多学科设计优化算法及其在飞行器设计中的应用[J]．航空学报2000，21(1)：1-6
[7] Vladimir O. Balabanov. Development of approximations for HSCT bending material weight using response surface methodology. A dissertation submitted to the faculty of Virginia polytechnic institute and state university in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Aerospace Engineering, September,1998.
[8] Ilan Kroo, Steve Altus, Robert Braun, Peter Gage, and Ian Sobieski. Multidisciplinary Optimization Methods for Aircraft Preliminary Design. Fifth AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. AIAA 94-4325,
[9] Braun, R. D. and Kroo, I. M. Development and application of the Collaborative Optimization architecture in a multidisciplinary design environment. Multidisciplinary Design Optimization: State of the Art (Alexandrov, N. M. and Hussaini, M. Y., eds.), SIAM, 1997.
[10] Braun, R. D., Moore, A. A. and Kroo, I. M. Collaborative architecture for launch vehicle design. Journal of Spacecraft and Rockets, Vol. 34, No. 4,1997, pp. 478-486.
[11] http://www.engineous.com/
[12] http://www.phoenix-int.com/
[13] 蔡苗 多学科设计优化分布式计算环境的研究．南京航空航天大学 硕士学位论文．2003年1月
[14] 石磊，王学仁，孙文爽．试验设计基础[M]．重庆：重庆大学出版社，1997
[15] Rasch Herrendorfer,Bock Victor Guiard．试验设计方法手册(Ⅰ)[M]．北京：中国统计出版社，2000
[16] Timothy W. Simpson, Dennis K. J. Lin and Wei Chen. "Sampling Strategies for Computer Experiments: Design and Analysis" [J]. International Journal of Reliability and Applications, 2001.2(3): 209-240
[17] Golovidov, Oleg B and Mason, William H and Grossman, Bernard and Watson, Layne T and Haftka, Raphael T (1997) "Response Surface Approximations for Aerodynamic Parameters in
High Speed Civil Transport Optimization." Technical Report ncstrl.vatech_cs//TR-97-15, Computer Science, Virginia Polytechnic Institute and State University. http://historical.ncstrl.org/tr/ps/vatech_cs/TR-97-15.ps
[18] Knill, D. L., Giunta, A. A., Baker, C. A., Grossman, B., Mason, W. H., Haftka, R. T., Watson, L. T., "Multidisciplinary HSCT Design Using Response Surface Approximations of Supersonic Euler Aerodynamics"(AIAA 98-0905) 36th Aerospace Sciences Meeting and Exhibit, January 12-15, 1998, Reno, NV.
[19] Knill, D. L., Giunta, A. A., Baker, C. A., Grossman, B., Mason, W. H., Haftka, R. T. and Watson, L. T. "Response Surface Models Combining Linear and Euler Aerodynamics for Supersonic Transport Design" [J], J. Aircraft, 36, No. 1, Jan.-Feb. 1999, pp. 75-86.
[20] Unal, R., Lepsch, R.A. and McMillin, M., " Response Surface Model Building and Multidisciplinary Optimization Using D-Optimal Designs," (AIAA-98-4759), Collection of Technical Papers for 7th Annual AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 405-411, September 1998
[21] Simpson, T. W., Mauery, T. M., Korte, J. J., and Mistree, F., 1998, September 2-4, "Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization," 7th Symposium on Multidisciplinary Analysis and Optimization, St. Louis, MO, AIAA-98-4755.
[22] Giunta, A.A., Dudley, J.M., Narducci, R., Grossman, B., Haftka, R.T., Mason, W.H., and Watson, L.T. "Noisy Aerodynamic Response and Smooth Approximations in HSCT Design," in Proceedings of the 5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 1117-1128, Panama City Beach, FL, AIAA Paper94-4376 (Sept. 1994).
[23] Giunta, A.A. and Watson, L. T., "A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models," 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, St, Louis, MO, AIAA, Vol. 1, September 2-4, 1998, pp. 392-404.
[24] Jin, R., Chen, W. and Simpson, T. W., "Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria," [J]. Journal of Structural and Multidisciplinary Optimization, Vol. 23, No. 1, 2001, pp. 1-13
[25] Anthony A. Giunta. "Aircraft Multidisciplinary Design Optimization Using Design of Experiments Theory and Response Surface Modeling Methods." PhD dissertation, Virginia Polytechnic Institute, May 1997.
[26] Meckesheimer M., Barton R.R., Simpson T.W., Limayem F., Yannou B., (2001), "Metamodeling of Combined Discrete/Continuous Responses." AIAA Journal (American Institute of Aeronautics and Astronautics), vol. 39(10 (October 2001)): p. 1950-1959.
September 1991
[2] Multidisciplinary Design Practices from the F-16 Agile Falcon, Michael H. Love (Lockheed Martin). http://endo.sandia.gov/AIAA_MDOTC/sponsored/mike_love.pdf
[3] A Description of the F/A-18E/F Design and Design Process, James A. Young, Ronald D. Anderson, and Rudolph N. Yurkovich (Boeing, St. Louis). http://endo.sandia.gov/AIAA_MDOTC/sponsored/fl 8boeing.pall
[4] The F-22 Structural/Aeroelastic Design Process with MDO Examples, Nick Radovcich and David Layton (Lockheed Martin). http://endo.sandia.gov/AIAA_MDOTC/sponsored/f221ockmart.pdf
[5] 余雄庆 多学科设计优化算法及其在飞机设计中的应用研究．南京航空航天大学 工学博士学位论文．1999年4月．
[6] 余雄庆 飞机多学科设计优化算法及其在飞行器设计中的应用[J]．航空学报2000，21(1)：1-6
[7] Vladimir O. Balabanov. Development of approximations for HSCT bending material weight using response surface methodology. A dissertation submitted to the faculty of Virginia polytechnic institute and state university in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Aerospace Engineering, September,1998.
[8] Ilan Kroo, Steve Altus, Robert Braun, Peter Gage, and Ian Sobieski. Multidisciplinary Optimization Methods for Aircraft Preliminary Design. Fifth AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. AIAA 94-4325,
[9] Braun, R. D. and Kroo, I. M. Development and application of the Collaborative Optimization architecture in a multidisciplinary design environment. Multidisciplinary Design Optimization: State of the Art (Alexandrov, N. M. and Hussaini, M. Y., eds.), SIAM, 1997.
[10] Braun, R. D., Moore, A. A. and Kroo, I. M. Collaborative architecture for launch vehicle design. Journal of Spacecraft and Rockets, Vol. 34, No. 4,1997, pp. 478-486.
[11] http://www.engineous.com/
[12] http://www.phoenix-int.com/
[13] 蔡苗 多学科设计优化分布式计算环境的研究．南京航空航天大学 硕士学位论文．2003年1月
[14] 石磊，王学仁，孙文爽．试验设计基础[M]．重庆：重庆大学出版社，1997
[15] Rasch Herrendorfer,Bock Victor Guiard．试验设计方法手册(Ⅰ)[M]．北京：中国统计出版社，2000
[16] Timothy W. Simpson, Dennis K. J. Lin and Wei Chen. "Sampling Strategies for Computer Experiments: Design and Analysis" [J]. International Journal of Reliability and Applications, 2001.2(3): 209-240
[17] Golovidov, Oleg B and Mason, William H and Grossman, Bernard and Watson, Layne T and Haftka, Raphael T (1997) "Response Surface Approximations for Aerodynamic Parameters in
High Speed Civil Transport Optimization." Technical Report ncstrl.vatech_cs//TR-97-15, Computer Science, Virginia Polytechnic Institute and State University. http://historical.ncstrl.org/tr/ps/vatech_cs/TR-97-15.ps
[18] Knill, D. L., Giunta, A. A., Baker, C. A., Grossman, B., Mason, W. H., Haftka, R. T., Watson, L. T., "Multidisciplinary HSCT Design Using Response Surface Approximations of Supersonic Euler Aerodynamics"(AIAA 98-0905) 36th Aerospace Sciences Meeting and Exhibit, January 12-15, 1998, Reno, NV.
[19] Knill, D. L., Giunta, A. A., Baker, C. A., Grossman, B., Mason, W. H., Haftka, R. T. and Watson, L. T. "Response Surface Models Combining Linear and Euler Aerodynamics for Supersonic Transport Design" [J], J. Aircraft, 36, No. 1, Jan.-Feb. 1999, pp. 75-86.
[20] Unal, R., Lepsch, R.A. and McMillin, M., " Response Surface Model Building and Multidisciplinary Optimization Using D-Optimal Designs," (AIAA-98-4759), Collection of Technical Papers for 7th Annual AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 405-411, September 1998
[21] Simpson, T. W., Mauery, T. M., Korte, J. J., and Mistree, F., 1998, September 2-4, "Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization," 7th Symposium on Multidisciplinary Analysis and Optimization, St. Louis, MO, AIAA-98-4755.
[22] Giunta, A.A., Dudley, J.M., Narducci, R., Grossman, B., Haftka, R.T., Mason, W.H., and Watson, L.T. "Noisy Aerodynamic Response and Smooth Approximations in HSCT Design," in Proceedings of the 5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 1117-1128, Panama City Beach, FL, AIAA Paper94-4376 (Sept. 1994).
[23] Giunta, A.A. and Watson, L. T., "A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models," 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, St, Louis, MO, AIAA, Vol. 1, September 2-4, 1998, pp. 392-404.
[24] Jin, R., Chen, W. and Simpson, T. W., "Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria," [J]. Journal of Structural and Multidisciplinary Optimization, Vol. 23, No. 1, 2001, pp. 1-13
[25] Anthony A. Giunta. "Aircraft Multidisciplinary Design Optimization Using Design of Experiments Theory and Response Surface Modeling Methods." PhD dissertation, Virginia Polytechnic Institute, May 1997.
[26] Meckesheimer M., Barton R.R., Simpson T.W., Limayem F., Yannou B., (2001), "Metamodeling of Combined Discrete/Continuous Responses." AIAA Journal (American Institute of Aeronautics and Astronautics), vol. 39(10 (October 2001)): p. 1950-1959.