TY - JOUR

T1 - Estimation of Failure Probability Function under Imprecise Probabilities by Active Learning-Augmented Probabilistic Integration

AU - Dang, Chao

AU - Wei, Pengfei

AU - Song, Jingwen

AU - Beer, Michael

N1 - Funding information: 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).

PY - 2021/12

Y1 - 2021/12

N2 - 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.

AB - 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.

KW - Active learning

KW - Bayesian probabilistic integration

KW - Failure probability function (FPF)

KW - Gaussian process regression

KW - Imprecise probability

KW - Probability box

UR - http://www.scopus.com/inward/record.url?scp=85111985174&partnerID=8YFLogxK

U2 - 10.1061/AJRUA6.0001179

DO - 10.1061/AJRUA6.0001179

M3 - Article

AN - SCOPUS:85111985174

VL - 7

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

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

SN - 2376-7642

IS - 4

M1 - 04021054

ER -