Details
| Original language | English |
|---|---|
| Article number | 106860 |
| Journal | Computers and Structures |
| Volume | 270 |
| Early online date | 6 Jul 2022 |
| Publication status | Published - 1 Oct 2022 |
Abstract
Uncertainties existing in physical and engineering systems can be characterized by different kinds of mathematical models according to their respective features. However, efficient propagation of hybrid uncertainties via an expensive-to-evaluate computer simulator is still a computationally challenging task. In this contribution, estimation of response expectation function (REF), its variable importance and bounds under hybrid uncertainties in the form of precise probability models, parameterized probability-box models and interval models is investigated through a Bayesian approach. Specifically, a new method, termed “Parallel Bayesian Quadrature Optimization” (PBQO), is developed. The method starts by treating the REF estimation as a Bayesian probabilistic integration (BPI) problem with a Gaussian process (GP) prior, which in turn implies a GP posterior for the REF. Then, one acquisition function originally developed in BPI and other two in Bayesian global optimization are introduced for Bayesian experimental designs. Besides, an innovative strategy is also proposed to realize multi-point selection at each iteration. Overall, a novel advantage of PBQO is that it is capable of yielding the REF, its variable importance and bounds simultaneously via a pure single-loop procedure allowing for parallel computing. Three numerical examples are studied to demonstrate the performance of the proposed method over some existing methods.
Keywords
- Bayesian experimental design, Bayesian global optimization, Bayesian probabilistic integration, Hybrid uncertainties, Parallel computing, Response expectation function
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Mathematics(all)
- Modelling and Simulation
- Materials Science(all)
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Computers and Structures, Vol. 270, 106860, 01.10.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bayesian probabilistic propagation of hybrid uncertainties
T2 - Estimation of response expectation function, its variable importance and bounds
AU - Dang, Chao
AU - Wei, Pengfei
AU - Faes, Matthias G.R.
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). Chao Dang, Pengfei Wei and Michael Beer also would like to appreciate the support of Sino-German Mobility Program under Grant No. M-0175.
PY - 2022/10/1
Y1 - 2022/10/1
N2 - Uncertainties existing in physical and engineering systems can be characterized by different kinds of mathematical models according to their respective features. However, efficient propagation of hybrid uncertainties via an expensive-to-evaluate computer simulator is still a computationally challenging task. In this contribution, estimation of response expectation function (REF), its variable importance and bounds under hybrid uncertainties in the form of precise probability models, parameterized probability-box models and interval models is investigated through a Bayesian approach. Specifically, a new method, termed “Parallel Bayesian Quadrature Optimization” (PBQO), is developed. The method starts by treating the REF estimation as a Bayesian probabilistic integration (BPI) problem with a Gaussian process (GP) prior, which in turn implies a GP posterior for the REF. Then, one acquisition function originally developed in BPI and other two in Bayesian global optimization are introduced for Bayesian experimental designs. Besides, an innovative strategy is also proposed to realize multi-point selection at each iteration. Overall, a novel advantage of PBQO is that it is capable of yielding the REF, its variable importance and bounds simultaneously via a pure single-loop procedure allowing for parallel computing. Three numerical examples are studied to demonstrate the performance of the proposed method over some existing methods.
AB - Uncertainties existing in physical and engineering systems can be characterized by different kinds of mathematical models according to their respective features. However, efficient propagation of hybrid uncertainties via an expensive-to-evaluate computer simulator is still a computationally challenging task. In this contribution, estimation of response expectation function (REF), its variable importance and bounds under hybrid uncertainties in the form of precise probability models, parameterized probability-box models and interval models is investigated through a Bayesian approach. Specifically, a new method, termed “Parallel Bayesian Quadrature Optimization” (PBQO), is developed. The method starts by treating the REF estimation as a Bayesian probabilistic integration (BPI) problem with a Gaussian process (GP) prior, which in turn implies a GP posterior for the REF. Then, one acquisition function originally developed in BPI and other two in Bayesian global optimization are introduced for Bayesian experimental designs. Besides, an innovative strategy is also proposed to realize multi-point selection at each iteration. Overall, a novel advantage of PBQO is that it is capable of yielding the REF, its variable importance and bounds simultaneously via a pure single-loop procedure allowing for parallel computing. Three numerical examples are studied to demonstrate the performance of the proposed method over some existing methods.
KW - Bayesian experimental design
KW - Bayesian global optimization
KW - Bayesian probabilistic integration
KW - Hybrid uncertainties
KW - Parallel computing
KW - Response expectation function
UR - http://www.scopus.com/inward/record.url?scp=85133548675&partnerID=8YFLogxK
U2 - 10.1016/j.compstruc.2022.106860
DO - 10.1016/j.compstruc.2022.106860
M3 - Article
AN - SCOPUS:85133548675
VL - 270
JO - Computers and Structures
JF - Computers and Structures
SN - 0045-7949
M1 - 106860
ER -