Improving Adjoint-Based Aerodynamic Optimization via Gradient-Enhanced Kriging

Gradient-based optimization using adjoint method has proved effective for automatic aerodynamic shape optimization via high-fidelity Computational Fluid Dynamics (CFD) methods. Past experience suggests that its optimization efficiency and robustness are crucially affected by the step size along a direction of descending. In this paper, a surrogate modeling method based on gradient-enhanced Kriging is exercised to determinate the step size of adjoint-based optimization and a routine for adjoint-based aerodynamic design has been proposed. Representative results are presented for the inverse design of a RAE 2822 airfoil. It is found that the efficiency as well as robustness of adjoint-based aerodynamic optimization can be dramatically improved. Nomenclature

[1]  Søren Nymand Lophaven,et al.  Aspects of the Matlab toolbox DACE , 2002 .

[2]  Joel Brezillon,et al.  2D and 3D aerodynamic shape optimisation using the adjoint approach , 2004 .

[3]  R. Dwight,et al.  Effect of Approximations of the Discrete Adjoint on Gradient-Based Optimization , 2006 .

[4]  Zhong-Hua Han,et al.  Numerical Study of High-Resolution Scheme Based on Preconditioning Method , 2008 .

[5]  A. Jameson,et al.  Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation , 1996 .

[6]  Juan J. Alonso,et al.  Design of a Low-Boom Supersonic Business Jet Using Cokriging Approximation Models , 2002 .

[7]  W. K. Anderson,et al.  Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation , 1997 .

[8]  G. Gary Wang,et al.  Survey of Modeling and Optimization Strategies for High-Dimensional Design Problems , 2008 .

[9]  A. Jameson.  Optimum aerodynamic design using CFD and control theory , 1995 .

[10]  Juan J. Alonso,et al.  Two-dimensional High-Lift Aerodynamic Optimization Using the Continuous Adjoint Method , 2000 .

[11]  Antony Jameson,et al.  Aerodynamic design via control theory , 1988, J. Sci. Comput..

[12]  B. Kulfan.  Universal Parametric Geometry Representation Method , 2008 .

[13]  Farrokh Mistree,et al.  Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size , 1999 .

[14]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007 .

[15]  R. Radespiel,et al.  Preconditioning Methods for Low-Speed Flows. , 1996 .

[16]  Zhong-Hua Han,et al.  A Preconditioned Multigrid Method for Efficient Simulation of Three-dimensional Compressible and Incompressible Flows , 2007 .

[17]  Zhonghua Han,et al.  Efficient Uncertainty Quantification using Gradient-Enhanced Kriging , 2009 .

[18]  Weiyu Liu,et al.  Gradient-Enhanced Response Surface Approximations Using Kriging Models , 2002 .

[19]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[20]  R. M. Hicks,et al.  Wing Design by Numerical Optimization , 1977 .

[21]  J. Alonso,et al.  Using gradients to construct cokriging approximation models for high-dimensional design optimization problems , 2002 .

[22]  G. Matheron.  Principles of geostatistics , 1963 .

[23]  A. Jameson,et al.  Aerodynamic shape optimization techniques based on control theory , 1998 .

[24]  P. Sagaut,et al.  Building Efficient Response Surfaces of Aerodynamic Functions with Kriging and Cokriging , 2008 .

[25]  D. Mavriplis.  Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes , 2007 .

[26]  D. Krige.  A statistical approach to some basic mine valuation problems on the Witwatersrand, by D.G. Krige, published in the Journal, December 1951 : introduction by the author , 1951 .

[27]  Pierre Sagaut,et al.  Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers , 2010 .

[28]  R. M. Hicks,et al.  An assessment of airfoil design by numerical optimization , 1974 .

[29]  Antony Jameson,et al.  Enhancement of Adjoint Design Methods via Optimization of Adjoint Parameters , 2005 .

[30]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[31]  Dimitri J. Mavriplis,et al.  A Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes , 2006 .