Variable-Fidelity Aerodynamic Shape Optimization

Aerodynamic shape optimization (ASO) plays an important role in the design of aircraft, turbomachinery and other fluid machinery. Simulation-driven ASO involves the coupling of computational fluid dynamics (CFD) solvers with numerical optimization methods. Although being relatively mature and widely used, ASO is still being improved and numerous challenges remain. This chapter provides an overview of simulation-driven ASO methods, with an emphasis on surrogate-based optimization (SBO) techniques. In SBO, a computationally cheap surrogate model is used in lieu of an accurate high-fidelity CFD simulation in the optimization process. Here, a particular focus is given to SBO exploiting surrogate models constructed from corrected physics-based low-fidelity models, often referred to as variable- or multi-fidelity optimization.

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

[2]  Robert Haimes,et al.  Strategies for Multifidelity Optimization with Variable-Dimensional Hierarchical Models , 2006 .

[3]  Jacques Periaux,et al.  Multi-objective robust design optimisation using hierarchical asynchronous parallel asynchronous evolutionary algorithms , 2005 .

[4]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[5]  Mesut Güner,et al.  Energy saving device of stator for marine propellers , 2007 .

[6]  T. Pulliam,et al.  Multipoint and Multi-Objective Aerodynamic Shape Optimization , 2002 .

[7]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[8]  Meng Wang,et al.  Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework , 2003 .

[9]  Antony Jameson,et al.  Viscous Aerodynamic Shape Optimization of Wings including Planform Variables , 2003 .

[10]  Antony Jameson,et al.  Control theory based airfoil design using the Euler equations , 1994 .

[11]  Tang Zhi,et al.  Control theory based airfoil design using Euler equations , 2001 .

[12]  Bernard Grossman,et al.  Noisy Aerodynamic Response and Smooth Approximations in HSCT Design , 1994 .

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

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

[15]  Marian Nemec,et al.  Optimization of High-Lift Configurations Using a Newton-Krylov Algorithm , 2003 .

[16]  F. Guibault,et al.  Optimized Nonuniform Rational B-Spline Geometrical Representation for Aerodynamic Design of Wings , 2001 .

[17]  P. A. Newman,et al.  Optimization with variable-fidelity models applied to wing design , 1999 .

[18]  R. W. Derksen,et al.  Bezier-PARSEC: An optimized aerofoil parameterization for design , 2010, Adv. Eng. Softw..

[19]  Marcus Redhe,et al.  Using space mapping and surrogate models to optimize vehicle crashworthiness design , 2002 .

[20]  Theresa Dawn Robinson,et al.  Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping , 2008 .

[21]  R. Lewis,et al.  An Overview of First-Order Model Management for Engineering Optimization , 2001 .

[22]  Slawomir Koziel Efficient optimization of microwave circuits using shape-preserving response prediction , 2009, 2009 IEEE MTT-S International Microwave Symposium Digest.

[23]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[24]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer. By D. A ANDERSON, J. C. TANNEHILL and R. H. PLETCHER. Hemisphere, 1984. 599 pp. $39.95. , 1986, Journal of Fluid Mechanics.

[25]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[26]  Michael S. Eldred,et al.  OVERVIEW OF MODERN DESIGN OF EXPERIMENTS METHODS FOR COMPUTATIONAL SIMULATIONS , 2003 .

[27]  A. Jameson,et al.  Design Optimization of High-Lift Configurations Using a Viscous Continuous Adjoint Method , 2002 .

[28]  F. Wubs Notes on numerical fluid mechanics , 1985 .

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

[30]  Wei Shyy,et al.  Membrane wing aerodynamics for micro air vehicles , 2003 .

[31]  Andy J. Keane,et al.  Optimization using surrogate models and partially converged computational fluid dynamics simulations , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[32]  M. J. Rimlinger,et al.  Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers , 1997 .

[33]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[34]  Afzal Suleman,et al.  Design of a Morphing Airfoil Using Aerodynamic Shape Optimization , 2006 .

[35]  J. Anderson,et al.  Fundamentals of Aerodynamics , 1984 .

[36]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[37]  Andy J. Keane,et al.  Airfoil Design and Optimization Using Multi-Fidelity Analysis and Embedded Inverse Design , 2006 .

[38]  Francis Noblesse,et al.  Hydrodynamic optimization of ship hull forms , 2001 .

[39]  S. Gunn Support Vector Machines for Classification and Regression , 1998 .

[40]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[41]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[42]  Michael S. Eldred,et al.  Second-Order Corrections for Surrogate-Based Optimization with Model Hierarchies , 2004 .

[43]  K. D. Lee,et al.  High-Lift Design Optimization Using Navier-Stokes Equations , 1996 .

[44]  P. W. Hemker,et al.  Space Mapping and Defect Correction , 2005 .

[45]  I. H. Abbott,et al.  Theory of Wing Sections , 1959 .

[46]  J. Katz,et al.  Low-Speed Aerodynamics , 1991 .

[47]  Tamara G. Kolda,et al.  Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods , 2003, SIAM Rev..

[48]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[49]  S. Koziel,et al.  A Space-Mapping Framework for Engineering Optimization—Theory and Implementation , 2006, IEEE Transactions on Microwave Theory and Techniques.

[50]  S. Koziel,et al.  Space mapping , 2008, IEEE Microwave Magazine.

[51]  René Van den Braembussche,et al.  Numerical Optimization for Advanced Turbomachinery Design , 2008 .

[52]  C. P. van Dam,et al.  The aerodynamic design of multi-element high-lift systems for transport airplanes , 2002 .

[53]  G. Janiga,et al.  Optimization and Computational Fluid Dynamics , 2008 .

[54]  J.W. Bandler,et al.  Space mapping: the state of the art , 2004, IEEE Transactions on Microwave Theory and Techniques.

[55]  Ilan Kroo,et al.  OPTIMIZING AIRCRAFT AND OPERATIONS FOR MINIMUM NOISE , 2002 .

[56]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[57]  Slawomir Koziel,et al.  Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction , 2010, J. Comput. Sci..

[58]  Sergey Peigin,et al.  Robust optimization of 2D airfoils driven by full Navier–Stokes computations , 2004 .

[59]  Singiresu S. Rao Engineering Optimization : Theory and Practice , 2010 .

[60]  A. Jameson,et al.  Control theory based airfoil design for potential flow and a finite volume discretization , 1994 .

[61]  P. Spalart A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[62]  Huyse Luc,et al.  Robust airfoil optimization to achieve consistent drag reduction over a mach range , 2001 .

[63]  H. Sobieczky Parametric Airfoils and Wings , 1999 .

[64]  Kyriakos C. Giannakoglou,et al.  Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence , 2002 .

[65]  Robert Haimes,et al.  Multifidelity Optimization for Variable-Complexity Design , 2006 .

[66]  Kyriakos C. Giannakoglou,et al.  Adjoint Methods for Shape Optimization , 2008 .

[67]  Nicolas R. Gauger Efficient Deterministic Approaches for Aerodynamic Shape Optimization , 2008 .

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

[69]  R. Gebart,et al.  Influence from numerical noise in the objective function for flow design optimisation , 2001 .

[70]  Man Mohan Rai,et al.  Robust Optimal Design With Differential Evolution , 2004 .

[71]  M. J. Rimlinger,et al.  Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers , 1997 .

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