Abstract
In the process of multidisciplinary design optimization, there exits the calculation complexity problem due to frequently calling high fidelity system analysis models. The high fidelity system analysis models can be surrogated by approximate models. The sensitivity analysis and numerical noise filtering can be done easily by coupling approximate models to optimization. Approximate models can reduce the number of executions of the problem’s simulation code during optimization, so the solution efficiency of the multidisciplinary design optimization problem can be improved. Most optimization methods are based on gradient. The gradients of the objective and constrain functions are gained easily. The gradient-based Kriging (GBK) approximate model can be constructed by using system response value and its gradients. The gradients can greatly improve prediction precision of system response. The hybrid optimization method is constructed by coupling GBK approximate models to gradient-based optimization methods. An aircraft aerodynamics shape optimization design example indicates that the methods of this paper can achieve good feasibility and validity.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Sacks J, Schiller S B, Welch W J. Design for computer experiments. Technometrics, 1989, 31(1): 41–47
Dyck D N, Lowther D A. Response surface modeling of magnetic device performance using function value and gradient. Int J Appl Electrom, 1998, 9(2): 241–248
Sacks J, Welch W J, Mitchell T J, et al. Design and analysis of computer experiments. Stat Sci, 1989, 4(4): 409–435
Cressie N A C. Statistics for Spatial Data. New York: Wiley, 1993
Montes P. Smoothing noisy data by Kriging with nugget effects. In: Laurent P J, Peters A K, et al., eds. Int Conf Curves and Surfaces on Wavelets, Images, and Surface Fitting. Wellesley: Adams-Blake Publishing, 1994. 371–378
Cox D D, John S. SDO: A statistical method for global optimization. In: Alexandrov N M, Hussaini M Y, eds. Proc ICASE/NASA Langley Workshop on Multidisciplinary Optimization. Hampton: Society for Industrial and Applied Mathematics, 1995. 315–329
Torczon V, Trosset M W. Using approximations to accelerate engineering design optimization. In: Proc 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. Reston: AIAA, 1998. 738–748
Trosset M W, Torczon V. Numerical Optimization Using Computer Experiments. Technical Report, Department of Computational and Applied Mathematics, Rice University, Houston, TR97-02. 1997
Simpson T W, Mauery T M, Korte J J, et al. Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA J, 2001, 39(12): 2233–2241
Han Y Z, Gao H S, Li L Z, et al. Kriging model-based multidisplinary design optimization framework for turbine blade. J Aerospace Power, 2007, 22(7): 1055–1059
Jeong S, Obayashi S, Yamamoto K. Aerodynamic optimization design with Kriging model. T Jpn Soc Aeronaut Space Sci, 2005, 48(161): 161–168
Keane A J. Wing optimization using design of experiment, response surface, and data fusion methods. J Aircraft, 2003, 40(4): 741–750
Wang X F, Xi G. Aerodynamic optimization design for airfoil based on Kriging model (in Chinese). Acta Aeronautica et Astronautica Sinica, 2005, 26(5): 545–549
Wang S G, Shi J H, Yin S J, et al. Theory on Linear Model (in Chinese). Beijing: Science Press, 2004
Lu D. Random Process with Applications (in Chinese). Beijing: Tsinghua University Press, 1986
Mckay M D, Beckman R J, Conover W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 1979, 21(2): 239–245
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National High Technology Research and Development Program of China (“863” Program)
Rights and permissions
About this article
Cite this article
Xuan, Y., Xiang, J., Zhang, W. et al. Gradient-based Kriging approximate model and its application research to optimization design. Sci. China Ser. E-Technol. Sci. 52, 1117–1124 (2009). https://doi.org/10.1007/s11431-009-0096-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-009-0096-2