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Research Papers

Interval Uncertainty Reduction and Single-Disciplinary Sensitivity Analysis With Multi-Objective Optimization

[+] Author and Article Information
M. Li

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742

N. Williams

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742; Senior Risk Manager Shell Energy North America, Spokane, WA 99201

S. Azarm1

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742azarm@umd.edu

1

Corresponding author.

J. Mech. Des 131(3), 031007 (Feb 05, 2009) (11 pages) doi:10.1115/1.3066736 History: Received May 29, 2008; Revised November 05, 2008; Published February 05, 2009

Sensitivity analysis has received significant attention in engineering design. While sensitivity analysis methods can be global, taking into account all variations, or local, taking into account small variations, they generally identify which uncertain parameters are most important and to what extent their effect might be on design performance. The extant methods do not, in general, tackle the question of which ranges of parameter uncertainty are most important or how to best allocate Investments to partial uncertainty reduction in parameters under a limited budget. More specifically, no previous approach has been reported that can handle single-disciplinary multi-output global sensitivity analysis for both a single design and multiple designs under interval uncertainty. Two new global uncertainty metrics, i.e., radius of output sensitivity region and multi-output entropy performance, are presented. With these metrics, a multi-objective optimization model is developed and solved to obtain fractional levels of parameter uncertainty reduction that provide the greatest payoff in system performance for the least amount of “Investment.” Two case studies of varying difficulty are presented to demonstrate the applicability of the proposed approach.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Tolerance region in parameter space

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Figure 12

Plots of correlations among α, Investment, and MEP

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Figure 13

Engineering components of an angle grinder

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Figure 14

Obtained optimal solutions for Investment versus Rf

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Obtained optimal solutions, Investment versus MEP

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Figure 16

Plots of correlations among α, Investment, and Rf

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Figure 17

Plots of correlations among α, Investment, and MEP

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Figure 2

Retained tolerance regions

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Figure 3

Mapping from RTR to ROSRs with Rf

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Figure 4

Indifference hypercube

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Figure 5

Parameter realizations in the output space for single versus multiple designs

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Figure 6

Formulation of sensitivity analysis

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Figure 7

Investment versus uncertainty metric

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Figure 8

Solutions for Investment versus Rf for (a) a single design and (b) 35 designs

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Figure 9

Plots of correlations among α, Investment, and Rf

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Figure 10

Solutions for Investment versus MEP for (a) a single design and (b) 35 designs

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Figure 11

Solutions for different indifference hypercubes, Investment versus MEP, and 35 designs

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