Research Papers

Reducible Uncertain Interval Design by Kriging Metamodel Assisted Multi-Objective Optimization

[+] Author and Article Information
Joshua M. Hamel

Department of Mechanical and Aerospace Engineering, California State University, Long Beach, CA 90840jhamel@csulb.edu

Shapour Azarm

Department of Mechanical Engineering, University of Maryland, College Park, MD 20472azarm@umd.edu

J. Mech. Des 133(1), 011002 (Dec 29, 2010) (10 pages) doi:10.1115/1.4002974 History: Received May 12, 2010; Revised October 15, 2010; Published December 29, 2010; Online December 29, 2010

Sources of reducible uncertainty present a particular challenge to engineering design problems by forcing designers to make decisions about how much uncertainty to consider as acceptable in final design solutions. Many of the existing approaches for design under uncertainty require potentially unavailable or unknown information about the uncertainty in a system’s input parameters, such as probability distributions, nominal values, and/or uncertain intervals. These requirements may force designers into arbitrary or even erroneous assumptions about a system’s input uncertainty. In an effort to address these challenges, a new approach for design under uncertainty is presented that can produce optimal solutions in the form of upper and lower bounds (which specify uncertain intervals) for all input parameters to a system that possess reducible uncertainty. These solutions provide minimal variation in system objectives for a maximum allowed level of input uncertainty in a multi-objective sense and furthermore guarantee as close to deterministic Pareto optimal performance as possible with respect to the uncertain parameters. The function calls required by this approach are kept to a minimum through the use of a kriging metamodel assisted multi-objective optimization technique performed in two stages. The capabilities of this approach are demonstrated through three example problems of varying complexity.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Input parameter uncertainty

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Figure 2

Uncertainty propagation

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Figure 3

Variation of deterministic optima

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Figure 4

RUID anchor point set

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Figure 6

RUID inner problem

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Figure 7

RUID solutions for TNK problem

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Figure 8

Tube design problem

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Figure 9

RUID solutions for tube problem

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Figure 10

Shell and tube heat exchanger

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Figure 11

RUID solutions for heat exchanger problem




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