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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2016017441
pages 445-466


Zigan Zhao
National University of Defense Technology
Xiaojun Duan
Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha, Hunan, HN 731, People's Republic of China
Zhengming Wang
College of Science, National University of Defense Technology, Changsha, Hunan Province 410000, China


In engineering applications, an important challenge of structural reliability analysis is to minimize the number of calls to the performance function, which is expensive to evaluate. In recent years, metamodels have been introduced to solve this problem and the methods combining the Kriging model and Monte Carlo simulation have widely gained attention, because they sample training points sequentially. Two essential issues should be considered in these kinds of methods: the selection of the next training point and the stopping criterion of the iteration. EGRA (efficient global reliability analysis) and AK-MCS (active learning reliability method combining Kriging and Monte Carlo simulation) are two representative approaches, whose strategy of sampling training points and stopping criterion are based on evaluations of each Monte Carlo sample under certain learning functions. However, these proposed learning functions are based on the individual performance of each Monte Carlo sample, causing the methods to focus more on the local optimization. As a result, the idea of globally solving the problem was proposed and applied to the GSAS method in 2015. In this paper, a new global reliability analysis method is proposed. Unlike GSAS, a new learning function called the uncertainty reduction quantification function (URQF) is put forward. Specifically, a new random variable proposed in GSAS that helps simplify the statistical feature of Monte Carlo samples is inherited from GSAS, and a weighting function that establishes the connection between any point and the next training point is proposed. These two functions are combined to build URQF, which quantifies the uncertainty reduction of predicted failure probability after a new training point is added. Meanwhile, a novel stopping criterion is proposed by calculating a prediction of an upper bound of failure probability's relative error; the iteration stops when this prediction reaches a preset bound. In the end, a series of examples are performed, which indicates that both URQF and the novel stopping criterion can improve the efficiency of the method, more or less.