Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models

This workdiscussesan approach,e rst-orderapproximation and modelmanagementoptimization (AMMO), for solving design optimization problems that involve computationally expensive simulations. AMMO maximizes the use of lower-e delity, cheaper models in iterative procedures with occasional, but systematic, recourse to highere delity, more expensive models for monitoring the progress of design optimization. A distinctive feature of the approach is thatit is globally convergent to a solution oftheoriginal, high-e delity problem. VariantsofAMMObased on three nonlinear programming algorithms are demonstrated on a three-dimensional aerodynamic wing optimization problemand atwo-dimensionalairfoiloptimizationproblem. Euleranalysisonmeshesof varying degrees of ree nement provides a suite of variable-e delity models. Preliminary results indicate threefold savings in terms of high-e delity analyses for the three-dimensional problem and twofold savings for the two-dimensional problem.

[1]  L. Schmit,et al.  Some Approximation Concepts for Structural Synthesis , 1974 .

[2]  Lucien A. Schmit,et al.  Structural Synthesis by Combining Approximation Concepts and Dual Methods , 1980 .

[3]  Philip E. Gill,et al.  Practical optimization , 1981 .

[4]  Michael A. Saunders,et al.  User''s guide for NPSOL (Ver-sion 4.0): A FORTRAN package for nonlinear programming , 1984 .

[5]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[6]  Uri Kirsch,et al.  3 – Approximation concepts for optimum structural design , 1985 .

[7]  E. Turkel,et al.  A multistage time-stepping scheme for the Navier-Stokes equations , 1985 .

[8]  Roger Fletcher,et al.  Practical methods of optimization; (2nd ed.) , 1987 .

[9]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[10]  J. -F. M. Barthelemy,et al.  Approximation concepts for optimum structural design — a review , 1993 .

[11]  Raphael T. Haftka,et al.  Sensitivity-based scaling for approximating. Structural response , 1993 .

[12]  E. Robert,et al.  Rapid Airplane Parametric Input Design (RAPID) , 1995 .

[13]  Art B. Owen,et al.  9 Computer experiments , 1996, Design and analysis of experiments.

[14]  William T. Jones,et al.  Experiences with the application of the ADIC automatic differentiation tool for to the CSCMDO 3-D volume grid generation code , 1996 .

[15]  Robert Lewis,et al.  A trust region framework for managing approximation models in engineering optimization , 1996 .

[16]  Antony Jameson,et al.  Essential Elements of Computational Algorithms for Aerodynamic Analysis and Design , 1997 .

[17]  James L. Thomas,et al.  CFL3D: Its History and Some Recent Applications , 1997 .

[18]  Arthur C. Taylor,et al.  CFL3D.ADII (Version 2.0) - An efficient, accurate, general-purpose code for flow shape-sensitivity analysis , 1997 .

[19]  M. Natalia.  On Managing the Use of Surrogates in General Nonlinear Optimization and MDO , 1998 .

[20]  Gene Hou,et al.  Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations , 1999 .

[21]  W. K. Anderson,et al.  First-Order Model Management With Variable-Fidelity Physics Applied to Multi-Element Airfoil Optimization , 2000 .

[22]  Nicholas I. M. Gould,et al.  Trust Region Methods , 2000, MOS-SIAM Series on Optimization.

[23]  Sharon L. Padula,et al.  Probabilistic approach to free-form airfoil shape optimization under uncertainty , 2002 .