Details
| Original language | English |
|---|---|
| Article number | 04021054 |
| Number of pages | 16 |
| Journal | ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering |
| Volume | 7 |
| Issue number | 4 |
| Early online date | 5 Aug 2021 |
| Publication status | Published - Dec 2021 |
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.
Keywords
- Active learning, Bayesian probabilistic integration, Failure probability function (FPF), Gaussian process regression, Imprecise probability, Probability box
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Building and Construction
- Engineering(all)
- Safety, Risk, Reliability and Quality
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, Vol. 7, No. 4, 04021054, 12.2021.
Research output: Contribution to journal › Article › Research › peer review
}
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 -