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TECHNICAL BRIEFS

Integration of Possibility-Based Optimization and Robust Design for Epistemic Uncertainty

[+] Author and Article Information
Byeng D. Youn1

Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, Houghton, MI 49931bdyoun@mtu.edu

Kyung K. Choi

Department of Mechanical & Industrial Engineering, College of Engineering, The University of Iowa, Iowa City, IA 52242kkchoi@ccad.uiowa.edu

Liu Du

Department of Mechanical & Industrial Engineering, College of Engineering, The University of Iowa, Iowa City, IA 52242liudu@ccad.uiowa.edu

David Gorsich

AMSTA-TR-N (MS 263), U.S. Army National Automotive Center, Warren, MI 48397gorsichd@tacom.army.mil

“Statistically equivalent” means under the condition that probability-possibility consistency and least conservative principles are satisfied.

1

Corresponding author.

J. Mech. Des 129(8), 876-882 (May 04, 2006) (7 pages) doi:10.1115/1.2717232 History: Received July 28, 2005; Revised May 04, 2006

In practical engineering applications, there exist two different types of uncertainties: aleatory and epistemic uncertainties. This study attempts to develop a robust design optimization with epistemic uncertainty. For epistemic uncertainties, a possibility-based design optimization improves the failure rate, while a robust design optimization minimizes the product quality loss. In general, product quality loss is described using the first two statistical moments for aleatory uncertainty: mean and standard deviation. However, there is no metric for product quality loss defined when having epistemic uncertainty. This paper first proposes a new metric for product quality loss with epistemic uncertainty, and then a possibility-based robust design optimization. For numerical efficiency and stability, an enriched performance measure approach is employed for possibility-based robust design optimization, and the maximal possibility search is used for a possibility analysis. Three different types of robust objectives are considered for possibility-based robust design optimization: smaller-the-better type (S-Type), larger-the-better type (L-Type), and nominal-the-better type (N-Type). Examples are used to demonstrate the effectiveness of possibility-based robust design optimization using the proposed metric for product quality loss with epistemic uncertainty.

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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 4

Membership function of fuzzy random variables Z1 and Z2

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Figure 5

Optimization history of possibility-based robust design for N-Type

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Figure 6

Optimization history of possibility based robust design for S-Type

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Figure 7

Optimization history of possibility-based robust design for L-Type

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Figure 3

Quality improvement of product with aleatory and epistemic uncertainties

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Figure 2

Membership function from Temporary-PDF of Z. (a) Quality improvement of product with aleatory uncertainty. (b) Quality improvement of product with epistemic uncertainty.

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Figure 1

Temporary-PDF using normal distribution fitting Z

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