A Bayesian Approach to Reliability-Based Optimization With Incomplete Information

[+] Author and Article Information
Subroto Gunawan

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

Panos Y. Papalambros

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

J. Mech. Des 128(4), 909-918 (Jan 25, 2006) (10 pages) doi:10.1115/1.2204969 History: Received September 15, 2005; Revised January 25, 2006

In engineering design, information regarding the uncertain variables or parameters is usually in the form of finite samples. Existing methods in optimal design under uncertainty cannot handle this form of incomplete information; they have to either discard some valuable information or postulate existence of additional information. In this article, we present a reliability-based optimization method that is applicable when information of the uncertain variables or parameters is in the form of both finite samples and probability distributions. The method adopts a Bayesian binomial inference technique to estimate reliability, and uses this estimate to maximize the confidence that the design will meet or exceed a target reliability. The method produces a set of Pareto trade-off designs instead of a single design, reflecting the levels of confidence about a design’s reliability given certain incomplete information. As a demonstration, we apply the method to design an optimal piston-ring/cylinder-liner assembly under surface roughness uncertainty.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 3

Feasible-infeasible realization of a (Xs,Ps) sample given (Xt,Pt) pdf’s

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Figure 7

The N-R-ζsmax diagram; (a) ζsmax as ordinate, (b) N as ordinate

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Figure 9

Pareto optima for different sample numbers N

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Figure 2

Beta-distributed Fgj(0) estimate for different r(N=10)

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Figure 4

Probability distribution of X1

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Figure 5

Actual and estimate reliability of (μX1,μX2)=(−2,0.5)

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Figure 6

Beta distribution of Fg(0) for increasing N

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Figure 8

Probability distributions of X1

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Figure 10

Pareto optima in the design variable space

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Figure 11

Optima obtained by fitting a Gaussian distribution to X1 samples

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Figure 1

Uncertainty quantification based on information content

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Figure 12

The piston-ring/cylinder-liner model

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Figure 13

Pareto optima of the ring-liner design problem



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