Details
| Original language | English |
|---|---|
| Article number | 102259 |
| Journal | Structural safety |
| Volume | 99 |
| Early online date | 18 Jul 2022 |
| Publication status | Published - Nov 2022 |
Abstract
Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation, as opposed to the classical frequentist perspective. For this purpose, a principled Bayesian Failure Probability Inference (BFPI) framework is first developed, which allows to quantify, propagate and reduce numerical uncertainty behind the failure probability due to discretization error. Especially, the posterior variance of the failure probability is derived in a semi-analytical form, and the Gaussianity of the posterior failure probability distribution is investigated numerically. Then, a Parallel Adaptive-Bayesian Failure Probability Learning (PA-BFPL) method is proposed within the Bayesian framework. In the PA-BFPL method, a variance-amplified importance sampling technique is presented to evaluate the posterior mean and variance of the failure probability, and an adaptive parallel active learning strategy is proposed to identify multiple updating points at each iteration. Thus, a novel advantage of PA-BFPL is that both prior knowledge and parallel computing can be used to make inference about the failure probability. Four numerical examples are investigated, indicating the potential benefits by advocating a Bayesian approach to failure probability estimation.
Keywords
- Bayesian inference, Failure probability, Gaussian process, Numerical uncertainty, Parallel computing
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Building and Construction
- Engineering(all)
- Safety, Risk, Reliability and Quality
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In: Structural safety, Vol. 99, 102259, 11.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Structural reliability analysis
T2 - A Bayesian perspective
AU - Dang, Chao
AU - Valdebenito, Marcos A.
AU - Faes, Matthias G.R.
AU - Wei, Pengfei
AU - Beer, Michael
N1 - Funding Information: Chao Dang is mainly supported by China Scholarship Council (CSC) . Pengfei Wei is grateful to the support from the National Natural Science Foundation of China (grant no. 51905430 and 72171194 ). Marcos Valdebenito acknowledges the support by ANID (National Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271 . Chao Dang, Pengfei Wei and Michael Beer also would like to appreciate the support of Sino-German Mobility Program, PR China under grant number M-0175 .
PY - 2022/11
Y1 - 2022/11
N2 - Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation, as opposed to the classical frequentist perspective. For this purpose, a principled Bayesian Failure Probability Inference (BFPI) framework is first developed, which allows to quantify, propagate and reduce numerical uncertainty behind the failure probability due to discretization error. Especially, the posterior variance of the failure probability is derived in a semi-analytical form, and the Gaussianity of the posterior failure probability distribution is investigated numerically. Then, a Parallel Adaptive-Bayesian Failure Probability Learning (PA-BFPL) method is proposed within the Bayesian framework. In the PA-BFPL method, a variance-amplified importance sampling technique is presented to evaluate the posterior mean and variance of the failure probability, and an adaptive parallel active learning strategy is proposed to identify multiple updating points at each iteration. Thus, a novel advantage of PA-BFPL is that both prior knowledge and parallel computing can be used to make inference about the failure probability. Four numerical examples are investigated, indicating the potential benefits by advocating a Bayesian approach to failure probability estimation.
AB - Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation, as opposed to the classical frequentist perspective. For this purpose, a principled Bayesian Failure Probability Inference (BFPI) framework is first developed, which allows to quantify, propagate and reduce numerical uncertainty behind the failure probability due to discretization error. Especially, the posterior variance of the failure probability is derived in a semi-analytical form, and the Gaussianity of the posterior failure probability distribution is investigated numerically. Then, a Parallel Adaptive-Bayesian Failure Probability Learning (PA-BFPL) method is proposed within the Bayesian framework. In the PA-BFPL method, a variance-amplified importance sampling technique is presented to evaluate the posterior mean and variance of the failure probability, and an adaptive parallel active learning strategy is proposed to identify multiple updating points at each iteration. Thus, a novel advantage of PA-BFPL is that both prior knowledge and parallel computing can be used to make inference about the failure probability. Four numerical examples are investigated, indicating the potential benefits by advocating a Bayesian approach to failure probability estimation.
KW - Bayesian inference
KW - Failure probability
KW - Gaussian process
KW - Numerical uncertainty
KW - Parallel computing
UR - http://www.scopus.com/inward/record.url?scp=85134368709&partnerID=8YFLogxK
U2 - 10.1016/j.strusafe.2022.102259
DO - 10.1016/j.strusafe.2022.102259
M3 - Article
AN - SCOPUS:85134368709
VL - 99
JO - Structural safety
JF - Structural safety
SN - 0167-4730
M1 - 102259
ER -