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Research Papers

First Order Reliability Method With Truncated Random Variables

[+] Author and Article Information
Xiaoping Du1

Zhen Hu

 Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, 290D Toomey Hall, 400 West 13th Street, Rolla, MO 65409-0500zh4hd@mst.edu

1

Corresponding author.

J. Mech. Des 134(9), 091005 (Aug 09, 2012) (9 pages) doi:10.1115/1.4007150 History: Received December 01, 2011; Revised April 29, 2012; Published August 09, 2012; Online August 09, 2012

In many engineering applications, the probability distributions of some random variables are truncated; these truncated distributions are resulted from restricting the domain of other probability distributions. If the first order reliability method (FORM) is directly used, the truncated random variables will be transformed into unbounded standard normal distributions. This treatment may result in large errors in reliability analysis. In this work, we modify FORM so that the truncated random variables are transformed into truncated standard normal variables. After the first order approximation and variable transformation, saddlepoint approximation is then used to estimate the reliability. Without increasing the computational cost, the proposed method is generally more accurate than the original FORM for problems with truncated random variables.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Failure region and limit-state function in original random space

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Figure 2

Failure region and limit-state function in transformed random space

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Figure 3

Transformation of truncated random variables

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Figure 4

Transformation of truncated normal distribution

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Figure 5

Transformation of truncated lognormal distribution

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Figure 6

Transformation of truncated exponential distribution

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Figure 7

Flow chart of the numerical procedure

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Figure 8

River flow loading on a hydrokinetic turbine blade

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