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Research Papers: Design Theory and Methodology

A Design-Driven Validation Approach Using Bayesian Prediction Models

[+] Author and Article Information
Wei Chen1

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

Ying Xiong

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

Kwok-Leung Tsui, Shuchun Wang

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

1

Corresponding author.

J. Mech. Des 130(2), 021101 (Dec 27, 2007) (12 pages) doi:10.1115/1.2809439 History: Received August 19, 2006; Revised March 25, 2007; Published December 27, 2007

In most of the existing work, model validation is viewed as verifying the model accuracy, measured by the agreement between computational and experimental results. Due to the lack of resource, accuracy can only be assessed at very limited test points. However, from the design perspective, a good model should be considered the one that can provide the discrimination (with good resolution) between competing design candidates under uncertainty. In this work, a design-driven validation approach is presented. By combining data from both physical experiments and the computer model, a Bayesian approach is employed to develop a prediction model as the replacement of the original computer model for the purpose of design. Based on the uncertainty quantification with the Bayesian prediction and, subsequently, that of a design objective, some decision validation metrics are further developed to assess the confidence of using the Bayesian prediction model in making a specific design choice. We demonstrate that the Bayesian approach provides a flexible framework for drawing inferences for predictions in the intended, but maybe untested, design domain. The applicability of the proposed decision validation metrics is examined for designs with either a discrete or continuous set of design alternatives. The approach is demonstrated through an illustrative example of a robust engine piston design.

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Copyright © 2008 by American Society of Mechanical Engineers
Topics: Design , Computers
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References

Figures

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Figure 1

Design resolution

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Figure 2

Comparison of traditional and proposed validation approaches (UQ)

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Figure 3

Physical and computer experiment data (circles: physical experiments; triangles: computer experiments)

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Figure 4

Prediction of Ŷm(x), interpolating all nine computer experiments

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Figure 5

Prediction of δ̂(x) (dB) and 95% confidence interval

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Figure 6

Prediction of Ŷr(x) (dB) and 95% confidence interval

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Figure 7

Prediction of f̂(x) (dB) and 95% confidence interval (six physical experiments)

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Figure 8

Mean and 95% confidence interval of f(xi) (dB) at five design candidates (six physical experiments)

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Figure 9

Mean and 95% confidence interval of Z(xi) (dB) at five design candidates (six physical experiments)

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Figure 10

Mean and 95% confidence interval of Z(x) (dB) (H=0.5, c=95%)

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Figure 11

Mean and 95% confidence interval of Z(x) (H=0.9, c=95%)

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