Details
| Original language | English |
|---|---|
| Article number | 103474 |
| Journal | Probabilistic Engineering Mechanics |
| Volume | 73 |
| Publication status | Published - Jul 2023 |
Abstract
The traditional methods for probabilistic analysis of physical systems often follow a non-intrusive scheme with, random samples for stochastic model parameters generated in the outer loop, and for each sample, physical model (described by PDEs) solved in the inner loop using, e.g., finite element method (FEM). Two of the biggest challenges when applying probabilistic methods are the high computational burden due to the repeated calls of the expensive-to-estimate computational models, and the difficulties of integrating the numerical errors from both loops. To overcome these challenges, we present a new framework for transforming the PDEs with stochastic parameters into equivalent deterministic PDEs, and then devise a statistical inference method, called Bayesian Augmented Space Learning (BASL), for inferring the probabilistic descriptors of the model responses with the combination of measurement data and physical models. With the two sources of information available, only a one-step Bayesian inference needs to be performed, and the numerical errors are summarized by posterior variances. The method is then further extended to the case where the values of the parameters of the test pieces for measurement are not precisely known. The effectiveness of the proposed methods is demonstrated with academic and real-world physical models.
Keywords
- Augmented space, Bayesian learning, Gaussian process regression, Parameter identification, Probabilistic analysis
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Engineering(all)
- Civil and Structural Engineering
- Energy(all)
- Nuclear Energy and Engineering
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
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In: Probabilistic Engineering Mechanics, Vol. 73, 103474, 07.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Combining data and physical models for probabilistic analysis
T2 - A Bayesian Augmented Space Learning perspective
AU - Hong, Fangqi
AU - Wei, Pengfei
AU - Song, Jingwen
AU - Faes, Matthias G.R.
AU - Valdebenito, Marcos A.
AU - Beer, Michael
N1 - Funding Information: Pengfei Wei acknowledges the supports of the National Natural Science Foundation of China under grant number 72171194 and the Sino-German Mobility Programme under grant number M-0175 (2021–2023). Matthias Faes acknowledges the support of the Research Foundation Flanders (FWO), Belgium under grant 12P3519N , as well as of the Humboldt foundation.
PY - 2023/7
Y1 - 2023/7
N2 - The traditional methods for probabilistic analysis of physical systems often follow a non-intrusive scheme with, random samples for stochastic model parameters generated in the outer loop, and for each sample, physical model (described by PDEs) solved in the inner loop using, e.g., finite element method (FEM). Two of the biggest challenges when applying probabilistic methods are the high computational burden due to the repeated calls of the expensive-to-estimate computational models, and the difficulties of integrating the numerical errors from both loops. To overcome these challenges, we present a new framework for transforming the PDEs with stochastic parameters into equivalent deterministic PDEs, and then devise a statistical inference method, called Bayesian Augmented Space Learning (BASL), for inferring the probabilistic descriptors of the model responses with the combination of measurement data and physical models. With the two sources of information available, only a one-step Bayesian inference needs to be performed, and the numerical errors are summarized by posterior variances. The method is then further extended to the case where the values of the parameters of the test pieces for measurement are not precisely known. The effectiveness of the proposed methods is demonstrated with academic and real-world physical models.
AB - The traditional methods for probabilistic analysis of physical systems often follow a non-intrusive scheme with, random samples for stochastic model parameters generated in the outer loop, and for each sample, physical model (described by PDEs) solved in the inner loop using, e.g., finite element method (FEM). Two of the biggest challenges when applying probabilistic methods are the high computational burden due to the repeated calls of the expensive-to-estimate computational models, and the difficulties of integrating the numerical errors from both loops. To overcome these challenges, we present a new framework for transforming the PDEs with stochastic parameters into equivalent deterministic PDEs, and then devise a statistical inference method, called Bayesian Augmented Space Learning (BASL), for inferring the probabilistic descriptors of the model responses with the combination of measurement data and physical models. With the two sources of information available, only a one-step Bayesian inference needs to be performed, and the numerical errors are summarized by posterior variances. The method is then further extended to the case where the values of the parameters of the test pieces for measurement are not precisely known. The effectiveness of the proposed methods is demonstrated with academic and real-world physical models.
KW - Augmented space
KW - Bayesian learning
KW - Gaussian process regression
KW - Parameter identification
KW - Probabilistic analysis
UR - http://www.scopus.com/inward/record.url?scp=85173470706&partnerID=8YFLogxK
U2 - 10.1016/j.probengmech.2023.103474
DO - 10.1016/j.probengmech.2023.103474
M3 - Article
AN - SCOPUS:85173470706
VL - 73
JO - Probabilistic Engineering Mechanics
JF - Probabilistic Engineering Mechanics
SN - 0266-8920
M1 - 103474
ER -