Estimation of Failure Probability Function under Imprecise Probabilities by Active Learning-Augmented Probabilistic Integration

authored by

Chao Dang, Pengfei Wei, Jingwen Song, Michael Beer

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.

Organisation(s)

Institute for Risk and Reliability

External Organisation(s)

Northwestern Polytechnical University
Tokyo City University
University of Liverpool
International Joint Research Center for Engineering Reliability and Stochastic Mechanics
Tongji University

Type

Article

Journal

ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering

Volume

7

No. of pages

16

ISSN

2376-7642

Publication date

12.2021

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Civil and Structural Engineering, Building and Construction, Safety, Risk, Reliability and Quality

Electronic version(s)

https://doi.org/10.1061/AJRUA6.0001179 (Access: Closed)