Details
| Original language | English |
|---|---|
| Article number | 116410 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 417 |
| Early online date | 6 Sept 2023 |
| Publication status | Published - 1 Dec 2023 |
Abstract
Uncertainty quantification (UQ) has been widely recognized as of vital importance for reliability-oriented analysis and design of engineering structures, and three groups of mathematical models, i.e., the probability models, the imprecise probability models and the non-probabilistic models, have been developed for characterizing uncertainties of different forms. The propagation of these three groups of models through expensive-to-evaluate simulators to quantify the uncertainties of outputs is then one of the core, yet highly challenging task in reliability engineering, as it involves a demanding double-loop numerical dilemma. For addressing this issue, the Collaborative and Adaptive Bayesian Optimization (CABO) has been developed in our previous work, but it only applies to imprecise probability models and is only capable of bounding the output expectation. We present a substantial improvement of CABO to incorporate all three categories of uncertainty models and to bound arbitrary probabilistic measures such as output variance and failure probability. The algorithm is based on a collaborative active learning mechanism, that is, jointly performing Bayesian optimization in the epistemic uncertainty subspace and Bayesian cubature in the aleatory uncertainty subspace, thus allowing to adaptively produce training samples in the joint uncertainty space. An efficient conditional Gaussian process simulation algorithm is embedded in CABO for acquiring training points and Bayesian inference in both uncertain subspaces. Benchmark studies show that CABO exhibits a remarkable performance in terms of numerical efficiency, accuracy, and global convergence.
Keywords
- Bayesian optimization, Imprecise probabilities, Interval analysis, Machine learning, Non-probabilistic model, Uncertainty quantification
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. 417, 116410, 01.12.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Collaborative and Adaptive Bayesian Optimization for bounding variances and probabilities under hybrid uncertainties
AU - Hong, Fangqi
AU - Wei, Pengfei
AU - Song, Jingwen
AU - Valdebenito, Marcos A.
AU - Faes, Matthias G.R.
AU - Beer, Michael
N1 - Funding Information: This work is supported by the National Natural Science Foundation of China under grant number 72171194 and 12202358 , as well as the Sino-German Mobility Programme under grant number M-0175 (2021–2023) .
PY - 2023/12/1
Y1 - 2023/12/1
N2 - Uncertainty quantification (UQ) has been widely recognized as of vital importance for reliability-oriented analysis and design of engineering structures, and three groups of mathematical models, i.e., the probability models, the imprecise probability models and the non-probabilistic models, have been developed for characterizing uncertainties of different forms. The propagation of these three groups of models through expensive-to-evaluate simulators to quantify the uncertainties of outputs is then one of the core, yet highly challenging task in reliability engineering, as it involves a demanding double-loop numerical dilemma. For addressing this issue, the Collaborative and Adaptive Bayesian Optimization (CABO) has been developed in our previous work, but it only applies to imprecise probability models and is only capable of bounding the output expectation. We present a substantial improvement of CABO to incorporate all three categories of uncertainty models and to bound arbitrary probabilistic measures such as output variance and failure probability. The algorithm is based on a collaborative active learning mechanism, that is, jointly performing Bayesian optimization in the epistemic uncertainty subspace and Bayesian cubature in the aleatory uncertainty subspace, thus allowing to adaptively produce training samples in the joint uncertainty space. An efficient conditional Gaussian process simulation algorithm is embedded in CABO for acquiring training points and Bayesian inference in both uncertain subspaces. Benchmark studies show that CABO exhibits a remarkable performance in terms of numerical efficiency, accuracy, and global convergence.
AB - Uncertainty quantification (UQ) has been widely recognized as of vital importance for reliability-oriented analysis and design of engineering structures, and three groups of mathematical models, i.e., the probability models, the imprecise probability models and the non-probabilistic models, have been developed for characterizing uncertainties of different forms. The propagation of these three groups of models through expensive-to-evaluate simulators to quantify the uncertainties of outputs is then one of the core, yet highly challenging task in reliability engineering, as it involves a demanding double-loop numerical dilemma. For addressing this issue, the Collaborative and Adaptive Bayesian Optimization (CABO) has been developed in our previous work, but it only applies to imprecise probability models and is only capable of bounding the output expectation. We present a substantial improvement of CABO to incorporate all three categories of uncertainty models and to bound arbitrary probabilistic measures such as output variance and failure probability. The algorithm is based on a collaborative active learning mechanism, that is, jointly performing Bayesian optimization in the epistemic uncertainty subspace and Bayesian cubature in the aleatory uncertainty subspace, thus allowing to adaptively produce training samples in the joint uncertainty space. An efficient conditional Gaussian process simulation algorithm is embedded in CABO for acquiring training points and Bayesian inference in both uncertain subspaces. Benchmark studies show that CABO exhibits a remarkable performance in terms of numerical efficiency, accuracy, and global convergence.
KW - Bayesian optimization
KW - Imprecise probabilities
KW - Interval analysis
KW - Machine learning
KW - Non-probabilistic model
KW - Uncertainty quantification
UR - http://www.scopus.com/inward/record.url?scp=85170435509&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2023.116410
DO - 10.1016/j.cma.2023.116410
M3 - Article
AN - SCOPUS:85170435509
VL - 417
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 116410
ER -