Research Papers

On Estimating the Reliability of Multiple Failure Region Problems Using Approximate Metamodels

[+] Author and Article Information
Ramon C. Kuczera1

Department of Mechanical Engineering, Oakland University, Rochester, MI 48309ramon.kuczera@gkndriveline.com

Zissimos P. Mourelatos2

Department of Mechanical Engineering, Oakland University, Rochester, MI 48309mourelat@oakland.edu


Present address: Engineering Director-Americas, GKN Driveline, Auburn Hills, MI 48326.


Corresponding author.

J. Mech. Des 131(12), 121003 (Nov 09, 2009) (11 pages) doi:10.1115/1.4000326 History: Received December 19, 2007; Revised August 10, 2009; Published November 09, 2009; Online November 09, 2009

In a complex system it is desirable to reduce the number of expensive function evaluations required for an accurate estimation of the probability of failure. An efficient reliability estimation method is presented for engineering systems with multiple failure regions and potentially multiple most probable points. The method can handle implicit nonlinear limit state functions with correlated or noncorrelated random variables, which can be described by any probabilistic distribution. It uses a combination of approximate or “accurate-on-demand,” global and local metamodels, which serve as indicators to determine the failure and safe regions. Sample points close to limit states define transition regions between safe and failure domains. A clustering technique identifies all transition regions, which can be, in general, disjoint, and local metamodels of the actual limit states are generated for each transition region. Importance sampling generates sample points only in the identified transition and failure regions, thus, allowing the method to focus on the areas near the failure region and not expend computational effort on the sample points in the safe domain. A robust maximin “space-filling” sampling technique is used to construct the metamodels. Two numerical examples highlight the accuracy and efficiency of the method.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

(a) Maximin with 5 sample points, (b) maximin with 20 sample points, and (c) maximin with 50 sample points

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Figure 9

Clusters with η=10%

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Figure 10

Samples in each cluster for vibration absorber

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Figure 11

Clusters with η=58%

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Figure 12

Two-bar bracket

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Figure 13

Clusters for two-bar bracket

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Figure 14

Description of terms in probability of failure calculation for the two-bar bracket example

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Figure 2

Left tail sampling

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Figure 3

Right tail sampling

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Figure 4

Middle region sampling

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Figure 5

(a) Clustering with η=η1, (b) clustering with η2>η1, and (c) clustering with η3>η2

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Figure 6

Tuned vibration absorber

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Figure 7

Plot of normalized amplitude y versus β1 and β2

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Figure 8

Samples for vibration absorber



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