Details
| Original language | English |
|---|---|
| Article number | 116068 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 412 |
| Early online date | 15 May 2023 |
| Publication status | Published - 1 Jul 2023 |
Abstract
Line sampling (LS) has proved to be a highly promising advanced simulation technique for assessing small failure probabilities. Despite the great interest in practical engineering applications, many efforts from the research community have been devoted to improving the standard LS. This paper aims at offering some new insights into the LS method, leading to an innovative method, termed ‘partially Bayesian active learning line sampling’ (PBAL-LS). The problem of evaluating the failure probability integral in the LS method is treated as a Bayesian, rather than frequentist, inference problem, which allows to incorporate our prior knowledge and model the discretization error. The Gaussian process model is used as the prior distribution for the distance function, and the posterior mean, and an upper bound of the posterior variance of the failure probability are derived. Based on the posterior statistics of the failure probability, we also put forward a learning function and a stopping criterion, which enable us to use active learning. Besides, an efficient algorithm is also designed to implement the PBAL-LS method, with the ability to automatically adjust the important direction and efficiently process the lines. Five numerical examples are studied to demonstrate the performance of the proposed PBAL-LS method against several existing methods.
Keywords
- Active learning, Bayesian inference, Failure probability, Gaussian process, Line sampling
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 412, 116068, 01.07.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Estimation of small failure probabilities by partially Bayesian active learning line sampling
T2 - Theory and algorithm
AU - Dang, Chao
AU - Valdebenito, Marcos A.
AU - Song, Jingwen
AU - Wei, Pengfei
AU - Beer, Michael
N1 - Funding Information: Chao Dang is mainly supported by China Scholarship Council (CSC). Jingwen Song acknowledges the financial support from the National Natural Science Foundation of China (grant no. 12202358 and 12220101002 ). Pengfei Wei is grateful to the support from the National Natural Science Foundation of China (grant no. 51905430 and 72171194 ). Chao Dang, Pengfei Wei and Michael Beer also would like to appreciate the support of Sino-German Mobility Program under grant number M-0175 .
PY - 2023/7/1
Y1 - 2023/7/1
N2 - Line sampling (LS) has proved to be a highly promising advanced simulation technique for assessing small failure probabilities. Despite the great interest in practical engineering applications, many efforts from the research community have been devoted to improving the standard LS. This paper aims at offering some new insights into the LS method, leading to an innovative method, termed ‘partially Bayesian active learning line sampling’ (PBAL-LS). The problem of evaluating the failure probability integral in the LS method is treated as a Bayesian, rather than frequentist, inference problem, which allows to incorporate our prior knowledge and model the discretization error. The Gaussian process model is used as the prior distribution for the distance function, and the posterior mean, and an upper bound of the posterior variance of the failure probability are derived. Based on the posterior statistics of the failure probability, we also put forward a learning function and a stopping criterion, which enable us to use active learning. Besides, an efficient algorithm is also designed to implement the PBAL-LS method, with the ability to automatically adjust the important direction and efficiently process the lines. Five numerical examples are studied to demonstrate the performance of the proposed PBAL-LS method against several existing methods.
AB - Line sampling (LS) has proved to be a highly promising advanced simulation technique for assessing small failure probabilities. Despite the great interest in practical engineering applications, many efforts from the research community have been devoted to improving the standard LS. This paper aims at offering some new insights into the LS method, leading to an innovative method, termed ‘partially Bayesian active learning line sampling’ (PBAL-LS). The problem of evaluating the failure probability integral in the LS method is treated as a Bayesian, rather than frequentist, inference problem, which allows to incorporate our prior knowledge and model the discretization error. The Gaussian process model is used as the prior distribution for the distance function, and the posterior mean, and an upper bound of the posterior variance of the failure probability are derived. Based on the posterior statistics of the failure probability, we also put forward a learning function and a stopping criterion, which enable us to use active learning. Besides, an efficient algorithm is also designed to implement the PBAL-LS method, with the ability to automatically adjust the important direction and efficiently process the lines. Five numerical examples are studied to demonstrate the performance of the proposed PBAL-LS method against several existing methods.
KW - Active learning
KW - Bayesian inference
KW - Failure probability
KW - Gaussian process
KW - Line sampling
UR - http://www.scopus.com/inward/record.url?scp=85159208250&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2023.116068
DO - 10.1016/j.cma.2023.116068
M3 - Article
AN - SCOPUS:85159208250
VL - 412
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 116068
ER -