Reliability Optimization With Mixed Continuous-Discrete Random Variables and Parameters

[+] Author and Article Information
Subroto Gunawan1

Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48109

Panos Y. Papalambros

Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48109pyp@umich.edu


Corresponding author.

J. Mech. Des 129(2), 158-165 (Jan 25, 2006) (8 pages) doi:10.1115/1.2406085 History: Received May 09, 2005; Revised January 25, 2006

Engineering design problems frequently involve a mix of both continuous and discrete random variables and parameters. However, most methods in the literature deal with only the continuous or the discrete type, but not both. In particular, no method has yet addressed problems for which the random components (variables and∕or parameters) are categorically discrete. This paper develops an efficient optimization method for problems involving mixed continuous-discrete random variables and parameters. The method reduces the number of function evaluations performed by systematically filtering the discrete combinations used for estimating reliability based on their importance. This importance is assessed using the spatial distance from the feasible boundary and the probability of the discrete components. The method is demonstrated in examples and is shown to be very efficient with only small errors.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Graphical representation of discrete reliability

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Figure 4

Influence functions for different σ̂gj

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Figure 5

Illustration of negligible importance

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Figure 6

Illustration of concentrated importance

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Figure 7

A Belleville spring

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Figure 2

Graphical representation of mixed continuous-discrete reliability

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Figure 3

Different importance of density distributions



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