USE OF ADAPTIVE METAMODELING FOR DESIGN OPTIMIZATION

This paper describes a method to implement an adaptive metamodeling procedure during simulation- based design. Metamodels can be used for design space visualization and design optimization applications when model evaluation performance is critical. The proposed method uses a sequential technique to update a kriging metamodel. This sequential technique will determine the point of the metamodel's design space with the maximum mean square error and select this as the next point to use to update the metamodel. At each iteration the quality of the metamodel is assessed using a leave- k-out cross-validation technique with three different values for k. The method is intended to permit continuous updating of the metamodel to investigate the entire design space without concern of finding an optimal value in the metamodel or model.

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

[2]  D. Dennis,et al.  A statistical method for global optimization , 1992, [Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics.

[3]  John R. Rice,et al.  An Agent-Based Netcentric Framework for Multidisciplinary Problem Solving Environments (MPSE) , 2000, Int. J. Comput. Eng. Sci..

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

[5]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[6]  Jack P. C. Kleijnen,et al.  A Comment on Blanning's “Metamodel for Sensitivity Analysis: The Regression Metamodel in Simulation” , 1975 .

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

[8]  Timothy W. Simpson,et al.  Multidimensional Visualization and Its Application to a Design by Shopping Paradigm , 2002 .

[9]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[10]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .

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

[12]  Timothy W. Simpson,et al.  REQUIREMENTS ON MDO IMPOSED BY THE UNDERSEA VEHICLE CONCEPTUAL DESIGN PROBLEM , 2000 .

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

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

[15]  Cristina H. Amon,et al.  An engineering design methodology with multistage Bayesian surrogates and optimal sampling , 1996 .

[16]  T. Simpson,et al.  Comparative studies of metamodeling techniques under multiple modeling criteria , 2000 .

[17]  V. Markine,et al.  Refinements in the multi-point approximation method to reduce the effects of noisy structural responses , 1996 .

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

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

[20]  Farrokh Mistree,et al.  Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization , 2001 .

[21]  John E. Renaud,et al.  Concurrent Subspace Optimization Using Design Variable Sharing in a Distributed Computing Environment , 1996 .

[22]  L. Watson,et al.  Adaptive Experimental Design for Construction of Response Surface Approximations , 2001 .

[23]  T. Simpson,et al.  Computationally Inexpensive Metamodel Assessment Strategies , 2002 .

[24]  Jack P. C. Kleijnen,et al.  Kriging for interpolation in random simulation , 2003, J. Oper. Res. Soc..

[25]  Pierre Montés,et al.  Smoothing noisy data by kriging with nugget effects , 1994 .

[26]  L. Watson,et al.  Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization , 1998 .

[27]  J. Renaud,et al.  Approximation in nonhierarchic system optimization , 1994 .

[28]  J. H. Starnes,et al.  Construction of Response Surface Approximations for Design Optimization , 1998 .