Research Papers

Multiresponse Metamodeling in Simulation-Based Design Applications

[+] Author and Article Information
David A. Romero1 n2

 Universidad del Zulia, Escuela de Ingeniería Mecánica, Laboratorio de Simulación Computacional, Apartado Postal 4011-A-526 Maracaibo, Venezuelaprof.david.romero@gmail.com

Cristina H. Amon

Dean Faculty of Applied Science and Engineering,  University of Toronto, 35 St. George Street, Toronto, ON, M5S 1A4, Canadacristina.amon@utoronto.ca

Susan Finger

Department of Civil and Environmental Engineering, Institute for Complex Engineered Systems,  Carnegie Mellon University, Pittsburgh, PA 15213sfinger@ri.cmu.edu


Corresponding author.


2 Present address: Postdoctoral Fellow at the Department of Mechanical and Industrial Engineering, University of Toronto, Canada (d.romero@utoronto.ca)

J. Mech. Des 134(9), 091001 (Aug 06, 2012) (15 pages) doi:10.1115/1.4006996 History: Received August 01, 2009; Revised June 06, 2012; Published August 06, 2012; Online August 06, 2012

The optimal design of complex systems in engineering requires the availability of mathematical models of system’s behavior as a function of a set of design variables; such models allow the designer to search for the best solution to the design problem. However, system models (e.g., computational fluid dynamics (CFD) analysis, physical prototypes) are usually time-consuming and expensive to evaluate, and thus unsuited for systematic use during design. Approximate models of system behavior based on limited data, also known as metamodels, allow significant savings by reducing the resources devoted to modeling during the design process. In this work in engineering design based on multiple performance criteria, we propose the use of multi-response Bayesian surrogate models (MR-BSM) to model several aspects of system behavior jointly, instead of modeling each individually. To this end, we formulated a family of multiresponse correlation functions, suitable for prediction of several response variables that are observed simultaneously from the same computer simulation. Using a set of test functions with varying degrees of correlation, we compared the performance of MR-BSM against metamodels built individually for each response. Our results indicate that MR-BSM outperforms individual metamodels in 53% to 75% of the test cases, though the relative performance depends on the sample size, sampling scheme and the actual correlation among the observed response values. In addition, the relative performance of MR-BSM versus individual metamodels was contingent upon the ability to select an appropriate covariance/correlation function for each application, a task for which a modified version of Akaike’s Information Criterion was observed to be inadequate.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 2

Test functions used in this work. (a) Pacheco’s Function, f1 [38], (b) Osio’s Function, f2 [33], (c) Sasena’s Function, f3 [58], (d) Modified Pacheco’s Function, f4 (present work).

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Figure 1

Schematic representation of the cross-flow heat exchanger design problem

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Figure 3

Comparison of covariance functions for the 18+07 (f1 , f3 ) test case. (a) Distribution of sum of maximum errors, (b) AICc metric.

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Figure 4

The IRFPA system. (a) Schematic representation and (b) Bottom view of the computational model.

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Figure 5

Comparison of adaptive sampling sets for multiresponse (circles) and single-response (triangles) metamodels. Each subplot represents a projection of the samples in the corresponding 2D subspace

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Figure 6

Main effects of the input variables on the response variables. (a) TTF, (b) τ, and (c) TTF/ τ.

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Figure 7

Comparison of predictive performance of MR-BSM versus FFNN



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