Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations

[+] Author and Article Information
Beiqing Huang

Department of Mechanical and Aerospace Engineering,University of Missouri–Rolla

Xiaoping Du1

Department of Mechanical and Aerospace Engineering,University of Missouri–Rolladux@umr.edu


Corresponding author.

J. Mech. Des 128(1), 26-33 (Mar 30, 2005) (8 pages) doi:10.1115/1.2118667 History: Received January 21, 2005; Revised March 29, 2005; Accepted March 30, 2005

Uncertainty analysis, which assesses the impact of the uncertainty of input variables on responses, is an indispensable component in engineering design under uncertainty, such as reliability-based design and robust design. However, uncertainty analysis is an unaffordable computational burden in many engineering problems. In this paper, an uncertainty analysis method is proposed with the purpose of accurately and efficiently estimating the cumulative distribution function (CDF), probability density function (PDF), and statistical moments of a response given the distributions of input variables. The bivariate dimension reduction method and numerical integration are used to calculate the moments of the response; then saddlepoint approximations are employed to estimate the CDF and PDF of the response. The proposed method requires neither the derivatives of the response nor the search of the most probable point, which is needed in the commonly used first and second order reliability methods (FORM and SORM) and the recently developed first order saddlepoint approximation. The efficiency and accuracy of the proposed method is illustrated with three example problems. With the same computational cost, this method is more accurate for reliability assessment and much more efficient for estimating the full range of the distribution of a response than FORM and SORM. This method provides results as accurate as Monte Carlo simulation, with significantly reduced computational effort.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Procedure of the proposed method

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Figure 2

CDF of Y obtained by various methods when n=4

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Figure 3

CDF of Y obtained by various methods when n=20

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Figure 4

CDF of the burst margin of disk

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Figure 5

PDF of the burst margin of disk



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