Estimation of Failure Probability Function under Imprecise Probabilities by Active Learning–Augmented Probabilistic Integration
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 4
Abstract
Imprecise probabilities have gained increasing popularity for quantitatively modeling uncertainty under incomplete information in various fields. However, it is still a computationally challenging task to propagate imprecise probabilities because a double-loop procedure is usually involved. In this contribution, a fully decoupled method, termed as active learning–augmented probabilistic integration (ALAPI), is developed to efficiently estimate the failure probability function (FPF) in the presence of imprecise probabilities. Specially, the parameterized probability-box models are of specific concern. By interpreting the failure probability integral from a Bayesian probabilistic integration perspective, the discretization error can be regarded as a kind of epistemic uncertainty, allowing it to be properly quantified and propagated through computational pipelines. Accordingly, an active learning probabilistic integration (ALPI) method is developed for failure probability estimation, in which a new learning function and a new stopping criterion associated with the upper bound of the posterior variance and coefficient of variation are proposed. Based on the idea of constructing an augmented uncertainty space, an imprecise augmented stochastic simulation (IASS) method is devised by using the random sampling high-dimensional representation model (RS-HDMR) for estimating the FPF in a pointwise stochastic simulation manner. To further improve the efficiency of IASS, the ALAPI is formed by an elegant combination of the ALPI and IASS, allowing the RS-HDMR component functions of the FPF to be properly inferred. Three benchmark examples are investigated to demonstrate the accuracy and efficiency of the proposed method.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request (MATLAB code of the proposed ALPI method, ALAPI method, IASS method and three numerical examples; OpenSees model of the 120-bar space truss structure in the third example).
Acknowledgments
The first author would like to appreciate the financial support from China Scholarship Council (CSC). The second author is grateful to the support from the National Natural Science Foundation of China (Grant No. NSFC 51905430) and the Alexander von Humboldt Foundation. The second and forth authors would also like to show their thankfulness to the support of Mobility Program 2020 from Sino-German Center (Grant No. M-0175).
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ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 4 • December 2021
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© 2021 American Society of Civil Engineers.
History
Received: Dec 17, 2020
Accepted: May 26, 2021
Published online: Aug 5, 2021
Published in print: Dec 1, 2021
Discussion open until: Jan 5, 2022
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