Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

Externe Organisationen

  • Northwestern Polytechnical University
  • Technische Universität Dortmund
  • The University of Liverpool
  • Tongji University
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Details

OriginalspracheEnglisch
Aufsatznummer106860
FachzeitschriftComputers and Structures
Jahrgang270
Frühes Online-Datum6 Juli 2022
PublikationsstatusVeröffentlicht - 1 Okt. 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.

ASJC Scopus Sachgebiete

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Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds. / Dang, Chao; Wei, Pengfei; Faes, Matthias G.R. et al.
in: Computers and Structures, Jahrgang 270, 106860, 01.10.2022.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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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.",
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author = "Chao Dang and Pengfei Wei and Faes, {Matthias G.R.} and Michael Beer",
note = "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. ",
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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.

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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.

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