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Research Papers

Reliability-Based Design Optimization With Confidence Level for Non-Gaussian Distributions Using Bootstrap Method

[+] Author and Article Information
Yoojeong Noh, David Gorsich

Kyung K. Choi1

Ikjin Lee

Department of Mechanical and Industrial Engineering,  College of Engineering, The University of Iowa, Iowa City, IA 52242ilee@engineering.uiowa.edu

David Lamb

 US Army RDECOM/TARDEC, Warren, MI 48397-5000david.lamb@us.army.mil

1

Corresponding author

J. Mech. Des 133(9), 091001 (Sep 07, 2011) (12 pages) doi:10.1115/1.4004545 History: Received February 13, 2011; Revised June 28, 2011; Published September 07, 2011; Online September 07, 2011

For reliability-based design optimization (RBDO), generating an input statistical model with confidence level has been recently proposed to offset inaccurate estimation of the input statistical model with Gaussian distributions. For this, the confidence intervals for the mean and standard deviation are calculated using Gaussian distributions of the input random variables. However, if the input random variables are non-Gaussian, use of Gaussian distributions of the input variables will provide inaccurate confidence intervals, and thus yield an undesirable confidence level of the reliability-based optimum design meeting the target reliability βt. In this paper, an RBDO method using a bootstrap method, which accurately calculates the confidence intervals for the input parameters for non-Gaussian distributions, is proposed to obtain a desirable confidence level of the output performance for non-Gaussian distributions. The proposed method is examined by testing a numerical example and M1A1 Abrams tank roadarm problem.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

βt–contours using true and estimated input model

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Figure 2

Histograms of upper bound of confidence interval for standard deviation

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Figure 3

βt–contours for four cases

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Figure 4

Optimum design point using true input model for Eq. 24

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Figure 5

Box plot for estimated parameters

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Figure 6

Box plot for adjusted parameters

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Figure 7

Finite element model of roadarm

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Figure 8

Joint PDF contours of Gaussian and Frank copula identified from 29 paired data of SAE 950X

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