期刊
RELIABILITY ENGINEERING & SYSTEM SAFETY
卷 242, 期 -, 页码 -出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.ress.2023.109729
关键词
Reliability estimation; Importance sampling; Normalizing flows; Invertible neural networks
We introduce a novel framework called REIN for reliability estimation using importance sampling and normalizing flows. REIN demonstrates effectiveness in high-dimensional reliability estimation with very small failure probabilities.
We introduce a novel framework called REIN: Reliability Estimation by learning an Importance sampling (IS) distribution with Normalizing flows (NFs). The NFs learn probability space maps that transform the probability distribution of the input random variables into a quasi-optimal IS distribution. NFs stack together invertible neural networks to construct differentiable bijections with efficiently computed Jacobian determinants. The NF 'pushes forward' a realization from the input probability distribution into a realization from the IS distribution, with importance weights calculated using the change of variables formula. We also propose a loss function to learn a NF map that minimizes the reverse Kullback-Leibler divergence between the 'pushforward' distribution and a sequentially updated target distribution obtained by modifying the optimal IS distribution. We demonstrate REIN's efficacy on a set of benchmark problems that feature very low failure rates, multiple failure modes and high dimensionality, while comparing against other variance reduction methods. We also consider two simple applications, the reliability analyses of a thirty-four story building and a cantilever tube, to demonstrate the applicability of REIN to practical problems of interest. As compared to other methods, REIN is shown to be useful for high-dimensional reliability estimation problems with very small failure probabilities.
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