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Research Papers: Design Automation

A New Variable-Fidelity Optimization Framework Based on Model Fusion and Objective-Oriented Sequential Sampling

[+] Author and Article Information
Ying Xiong

Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Tech B224, Evanston, IL 60208-3111

Wei Chen1

Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Tech B224, Evanston, IL 60208-3111weichen@northwestern.edu

Kwok-Leung Tsui

School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA 30332-0205

1

Corresponding author.

J. Mech. Des 130(11), 111401 (Oct 03, 2008) (9 pages) doi:10.1115/1.2976449 History: Received June 20, 2007; Revised June 18, 2008; Published October 03, 2008

Computational models with variable fidelity have been widely used in engineering design. To alleviate the computational burden, surrogate models are used for optimization without directly invoking expensive high-fidelity simulations. In this work, a model fusion technique based on the Bayesian–Gaussian process modeling is employed to construct cheap surrogate models to integrate information from both low-fidelity and high-fidelity models, while the interpolation uncertainty of the surrogate model due to the lack of sufficient high-fidelity simulations is quantified. In contrast to space filling, the sequential sampling of a high-fidelity simulation model in our proposed framework is objective-oriented, aiming for improving a design objective. Strategy based on periodical switching criteria is studied, which is shown to be effective in guiding the sequential sampling of a high-fidelity model toward improving a design objective as well as reducing the interpolation uncertainty. A design confidence metric is proposed as the stopping criterion to facilitate design decision making against the interpolation uncertainty. Examples are provided to illustrate the key ideas and features of model fusion, sequential sampling, and design confidence—the three key elements in the proposed variable-fidelity optimization framework.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Proposed variable-fidelity optimization framework

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Figure 2

The proposed PSC strategy

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Figure 3

The uncertainty of ys(x) at x∗, xa, and xb

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Figure 4

The uncertainty of zx∗(x) at x∗, xa, and xb

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Figure 5

The HF model and the LF model, with three initial HF sampling points (Example 1)

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Figure 6

The plots of ŷs(x) and the HF sampling points (Stage 5)

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Figure 7

The 3D plots of the HF and LF models

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Figure 8

The contour plot of the HF model marked with xHF∗=[0.0912,0.9325] and yh(xHF∗)=−19.142

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Figure 9

The plot of ŷs(x) at Stage 0 (five points) with x∗=[0.694,0.001]

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Figure 10

The plot of ŷs(x) at Stage 10, with x∗=[0.5276,0.2132]: sequential sampling points generated by EI criterion

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Figure 11

The plot of ŷs(x) at Stage 10, with x∗=[0.1011,0.9156]: sequential sampling points generated by PSC strategy

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Figure 12

Comparison of the history plots of ŷs(x∗)

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Figure 13

Comparison of the history plots of DC(x∗) (H=12.0 and CX0=0.95)

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Figure 15

History plot of DC(x∗)

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Figure 14

The plots of ŷs(x) with x∗=[1.0000,0.2103] (one-shot sampling of 5+10=15 points)

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