Building Surrogate Models Based on Detailed and Approximate Simulations

[+] Author and Article Information
Zhiguang Qian

School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Carolyn Conner Seepersad

Mechanical Engineering Department, The University of Texas at Austin, Austin, TX 78750

V. Roshan Joseph

 School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Janet K. Allen

 The Systems Realization Laboratory, The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

C. F. Jeff Wu1

 School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332jeffwu@isye.gatech.edu

Seepersad and co-authors (4) describe the details of the finite difference and FLUENT models for this example, including grid sizes and boundary conditions.


Corresponding author.

J. Mech. Des 128(4), 668-677 (Jun 07, 2005) (10 pages) doi:10.1115/1.2179459 History: Received August 30, 2004; Revised June 07, 2005

Preliminary design of a complex system often involves exploring a broad design space. This may require repeated use of computationally expensive simulations. To ease the computational burden, surrogate models are built to provide rapid approximations of more expensive models. However, the surrogate models themselves are often expensive to build because they are based on repeated experiments with computationally expensive simulations. An alternative approach is to replace the detailed simulations with simplified approximate simulations, thereby sacrificing accuracy for reduced computational time. Naturally, surrogate models built from these approximate simulations are also imprecise. A strategy is needed for improving the precision of surrogate models based on approximate simulations without significantly increasing computational time. In this paper, a new approach is taken to integrate data from approximate and detailed simulations to build a surrogate model that describes the relationship between output and input parameters. Experimental results from approximate simulations form the bulk of the data, and they are used to build a model based on a Gaussian process. The fitted model is then “adjusted” by incorporating a small amount of data from detailed simulations to obtain a more accurate prediction model. The effectiveness of this approach is demonstrated with a design example involving cellular materials for an electronics cooling application. The emphasis is on the method and not on the results per se.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Diagram of the proposed approach for combining detailed and approximate data into a surrogate model

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Figure 2

Compact, forced convection heat exchanger with graded rectangular linear cellular alloys

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Figure 3

Sixty four points of an orthogonal array-based Latin Hypercube sample. In each plot, there is one point in each of the square bins bounded by dashed lines.

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Figure 4

yd vs ya for the same design values, where the straight line is yd=ya

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Figure 5

δ̂ for different pairs of factors



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