Multifidelity Analysis and Optimization for Supersonic Design

Supersonic aircraft design is a computationally expensive optimization problem and multifidelity approaches offer a significant opportunity to reduce design time and computational cost. This report presents tools devloped to improve supersonic aircraft design capabilities including: aerodynamic tools for supersonic aircraft configurations; a systematic way to manage model uncertainty; and multifidelity model management concepts that incorporate uncertainty. The aerodynamic analysis tools developed are appropriate for use in a mutltifidelity optimization framework, and include four analysis routines to estimate the lift and drag of a supersonic airfoil, a multifidelity supersonic drag code that estimates the drag of aircraft configurations with three different methods: an area rule method, a panel method, and an Euler solver. In addition, five multifidelity optimization methods are developed, which include local and global methods as well as gradient-based and gradient-free techniques.

[1]  O. SIAMJ..  A DERIVATIVE-FREE ALGORITHM FOR INEQUALITY CONSTRAINED NONLINEAR PROGRAMMING VIA SMOOTHING OF AN ∞ PENALTY FUNCTION∗ , 2009 .

[2]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[3]  Christine A. Shoemaker,et al.  ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions , 2008, SIAM J. Sci. Comput..

[4]  Wu Li,et al.  A Mixed-Fidelity Approach for Design of Low-Boom Supersonic Aircraft * , 2010 .

[5]  D. Dennis,et al.  SDO : A Statistical Method for Global Optimization , 1997 .

[6]  M. Aftosmis.  Solution adaptive cartesian grid methods for aerodynamic flows with complex geometries , 1997 .

[7]  Karen Willcox,et al.  Convergent Multifidelity Optimization using Bayesian Model Calibration , 2010 .

[8]  Katya Scheinberg,et al.  Geometry of interpolation sets in derivative free optimization , 2007, Math. Program..

[9]  Christine A. Shoemaker,et al.  Derivative-free optimization algorithms for computationally expensive functions , 2009 .

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

[11]  Charles Audet,et al.  A Pattern Search Filter Method for Nonlinear Programming without Derivatives , 2001, SIAM J. Optim..

[12]  A. O'Hagan,et al.  Predicting the output from a complex computer code when fast approximations are available , 2000 .

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

[14]  Hiroshi Akima,et al.  A method of univariate interpolation that has the accuracy of a third-degree polynomial , 1991, TOMS.

[15]  Ilan Kroo,et al.  A Multifidelity Gradient-Free Optimization Method and Application to Aerodynamic Design , 2008 .

[16]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[17]  Katya Scheinberg,et al.  Global Convergence of General Derivative-Free Trust-Region Algorithms to First- and Second-Order Critical Points , 2009, SIAM J. Optim..

[18]  P. A. Newman,et al.  Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models , 2001 .

[19]  Patricia Diane Hough,et al.  Developing a computationally efficient dynamic multilevel hybrid optimization scheme using multifidelity model interactions. , 2006 .

[20]  Ilan Kroo,et al.  Multi-fidelity Design Optimization of Low-boom Supersonic Business Jets , 2004 .

[21]  Andy J. Keane,et al.  A Knowledge-Based Approach To Response Surface Modelling in Multifidelity Optimization , 2003, J. Glob. Optim..

[22]  N. M. Alexandrov,et al.  A trust-region framework for managing the use of approximation models in optimization , 1997 .

[23]  D. Anderson,et al.  Algorithms for minimization without derivatives , 1974 .

[24]  H. Ashley,et al.  Aerodynamics of Wings and Bodies , 1965 .

[25]  Ilan Kroo,et al.  An interactive system for aircraft design and optimization , 1992 .

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

[27]  Robert J. Mack,et al.  Determination of Extrapolation Distance With Pressure Signatures Measured at Two to Twenty Span Lengths From Two Low-Boom Models , 2006 .

[28]  R. Carter.  On the global convergence of trust region algorithms using inexact gradient information , 1991 .

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

[30]  Mathias Wintzer,et al.  Adjoint-Based Adaptive Mesh Refinement for Complex Geometries , 2008 .

[31]  Robert Michael Lewis,et al.  A Direct Search Approach to Nonlinear Programming Problems Using an Augmented Lagrangian Method with Explicit Treatment of Linear Constraints , 2010 .

[32]  Donald R. Jones,et al.  Global versus local search in constrained optimization of computer models , 1998 .

[33]  Ilan Kroo,et al.  Conceptual Design of Conventional and Oblique Wing Configurations for Small Supersonic Aircraft , 2006 .

[34]  John L. Nazareth,et al.  Introduction to derivative-free optimization , 2010, Math. Comput..

[35]  Daniel M. Dunlavy,et al.  Formulations for Surrogate-Based Optimization with Data Fit, Multifidelity, and Reduced-Order Models , 2006 .

[36]  Jiawei Han,et al.  Efficient and Effective Clustering Methods for Spatial Data Mining , 1994, VLDB.

[37]  F. Jose,et al.  Convergence of Trust Region Augmented Lagrangian Methods Using Variable Fidelity Approximation Data , 1997 .

[38]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[39]  T. Kolda,et al.  A generating set direct search augmented Lagrangian algorithm for optimization with a combination of general and linear constraints , 2006 .

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

[41]  Ilan Kroo,et al.  Probability Collectives for Optimization of Computer Simulations , 2007 .

[42]  J. Bezdek,et al.  FCM: The fuzzy c-means clustering algorithm , 1984 .

[43]  R. Oeuvray.  Trust-region methods based on radial basis functions with application to biomedical imaging , 2005 .

[44]  M. Sasena,et al.  Exploration of Metamodeling Sampling Criteria for Constrained Global Optimization , 2002 .

[45]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[46]  Ilan Kroo,et al.  Optimization Under Uncertainty Using Probability Collectives , 2006 .