Probabilistic uncertainty analysis by mean-value first order Saddlepoint Approximation

In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. For example, the random load of a bridge may have two peaks, with a distribution consisting of a weighted sum of two normal distributions, suggested by traffic load data. When binomial variables are involved, traditional reliability methods, such as the First Order Second Moment (FOSM) method and the First Order Reliability Method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation for bimodal variables and then employs a mean value reliability method to accurately predict the reliability. A limit-state function is at first approximated with the first order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The saddlepoint approximation is then applied to estimate the reliability. Examples show that the new method is more accurate than FOSM and FORM.

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Notice of Retraction Mean-value first order saddlepoint approximation based collaborative optimization for multidisciplinary problems under aleatory uncertainty

2013 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (QR2MSE) ◽

10.1109/qr2mse.2013.6625619 ◽

2013 ◽

Author(s):

Debiao Meng ◽

Xiaoling Zhang ◽

Hong-Zhong Huang ◽

Zhonglai Wang ◽

Ningcong Xiao

Keyword(s):

Saddlepoint Approximation ◽

Mean Value ◽

Collaborative Optimization ◽

Aleatory Uncertainty ◽

First Order

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MOSAIQUE – A network based software for probabilistic uncertainty analysis of computerized simulation models

Nuclear Engineering and Design ◽

10.1016/j.nucengdes.2011.01.021 ◽

2011 ◽

Vol 241 (5) ◽

pp. 1776-1784 ◽

Cited By ~ 10

Author(s):

Ho-Gon Lim ◽

Sang-Hoon Han ◽

Jae Jun Jeong

Keyword(s):

Uncertainty Analysis ◽

Simulation Models ◽

Probabilistic Uncertainty ◽

Computerized Simulation

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Some Important Issues on First-Order Reliability Analysis With Nonprobabilistic Convex Models

Journal of Mechanical Design ◽

10.1115/1.4026261 ◽

2014 ◽

Vol 136 (3) ◽

Cited By ~ 4

Author(s):

C. Jiang ◽

G. Y. Lu ◽

X. Han ◽

R. G. Bi

Keyword(s):

Reliability Analysis ◽

Reliability Index ◽

Probability Model ◽

Mean Value ◽

Convex Model ◽

First Order ◽

Reliability Method ◽

Complex Engineering ◽

Mean Value Method ◽

Form Type

Compared with the probability model, the convex model approach only requires the bound information on the uncertainty, and can make it possible to conduct the reliability analysis for many complex engineering problems with limited samples. Presently, by introducing the well-established techniques in probability-based reliability analysis, some methods have been successfully developed for convex model reliability. This paper aims to reveal some different phenomena and furthermore some severe paradoxes when extending the widely used first-order reliability method (FORM) into the convex model problems, and whereby provide some useful suggestions and guidelines for convex-model-based reliability analysis. Two FORM-type approximations, namely, the mean-value method and the design-point method, are formulated to efficiently compute the nonprobabilistic reliability index. A comparison is then conducted between these two methods, and some important phenomena different from the traditional FORMs are summarized. The nonprobabilistic reliability index is also extended to treat the system reliability, and some unexpected paradoxes are found through two numerical examples.

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