Approximation of multiresponse deterministic engineering simulations: a dependent metamodeling approach

A new approach to metamodeling is introduced whereby a sequential technique is used to construct and simultaneously update mutually dependent metamodels for multiresponse, high-fidelity deterministic simulations. Unlike conventional approaches which produce a single metamodel for each scalar response independently, the present method uses the correlation among different simulation responses in the construction of the metamodel. These dependent metamodels are solved as a system of equations to estimate all individual responses simultaneously. Since several responses contribute to the construction of each individual metamodel, more information from the computed responses is used, thus improving the accuracy of the obtained metamodels. Examples are used to explore the relative performance of the proposed approach and show that the new approach outperforms conventional metamodeling approaches in terms of approximation accuracy. The new method should be particularly useful in problems that require very computationally intensive simulations.

[1]  Douglas C. Montgomery,et al.  Modified Desirability Functions for Multiple Response Optimization , 1996 .

[2]  Raymond H. Myers,et al.  Response Surface Methods and the Use of Noise Variables , 1997 .

[3]  D. Lindley.  On a Measure of the Information Provided by an Experiment , 1956 .

[4]  James M. Lucas,et al.  How to Achieve a Robust Process Using Response Surface Methodology , 1994 .

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

[6]  Noel A Cressie,et al.  Multivariable spatial prediction , 1993 .

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

[8]  M. Hamada,et al.  Analyzing Experiments with Correlated Multiple Responses , 2001 .

[9]  Ruichen Jin,et al.  On Sequential Sampling for Global Metamodeling in Engineering Design , 2002, DAC 2002.

[10]  Dhafer Marzougui,et al.  Validation of a Non-Linear Finite Element Vehicle Model Using Multiple Impact Data , 1997 .

[11]  Jaroslaw Sobieszczanski-Sobieski,et al.  Multidisciplinary design optimisation - some formal methods, framework requirements, and application to vehicle design , 2001 .

[12]  G. Geoffrey Vining,et al.  Combining Taguchi and Response Surface Philosophies: A Dual Response Approach , 1990 .

[13]  Shapour Azarm,et al.  A SEQUENTIAL INFORMATION-THEORETIC APPROACH TO DESIGN OF COMPUTER EXPERIMENTS , 2002 .

[14]  R. H. Myers,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[15]  C. Currin,et al.  A Bayesian Approach to the Design and Analysis of Computer Experiments , 1988 .

[16]  A. I. Khuri.  12 Multiresponse surface methodology , 1996, Design and analysis of experiments.

[17]  Ren-Jye Yang,et al.  Approximation methods in multidisciplinary analysis and optimization: a panel discussion , 2004 .

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

[19]  G. Derringer,et al.  Simultaneous Optimization of Several Response Variables , 1980 .

[20]  T. J. Mitchell,et al.  Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments , 1991 .

[21]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[22]  Alejandro R. Diaz,et al.  Bayesian approximation-assisted optimization applied to crashworthiness design of a pickup truck , 2003, DAC 2003.

[23]  R. Haftka,et al.  Response surface approximations for structural optimization , 1996 .

[24]  Ron Kohavi,et al.  A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection , 1995, IJCAI.

[25]  Shapour Azarm,et al.  Bayesian meta‐modelling of engineering design simulations: a sequential approach with adaptation to irregularities in the response behaviour , 2005 .

[26]  Henry P. Wynn,et al.  Maximum entropy sampling , 1987 .