Journal
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
Volume 100, Issue -, Pages 782-801Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ymssp.2017.07.040
Keywords
Lower and upper probabilities of failure; Imprecise probabilities; Random set theory; Copulas; Interval Monte Carlo; Subset simulation; Isoprobabilistic transformation
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Funding
- Universidad Nacional de Colombia
- Deutsche Forschungsgemeinschaft (DFG) through the TUM International Graduate School of Science and Engineering (IGSSE)
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Random set theory is a general framework which comprises uncertainty in the form of probability boxes, possibility distributions, cumulative distribution functions, Dempster-Shafer structures or intervals; in addition, the dependence between the input variables can be expressed using copulas. In this paper, the lower and upper bounds on the probability of failure are calculated by means of random set theory. In order to accelerate the calculation, a well-known and efficient probability-based reliability method known as subset simulation is employed. This method is especially useful for finding small failure probabilities in both low- and high-dimensional spaces, disjoint failure domains and nonlinear limit state functions. The proposed methodology represents a drastic reduction of the computational labor implied by plain Monte Carlo simulation for problems defined with a mixture of representations for the input variables, while delivering similar results. Numerical examples illustrate the efficiency of the proposed approach. (C) 2017 Elsevier Ltd. All rights reserved.
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