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Bounds optimization of model response moments: a twin-engine Bayesian active learning method

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Abstract

The efficient propagation of imprecise probabilities through expensive simulators has emerged to be one of the great challenges for mixed uncertainty quantification in computational mechanics. An active learning method, named Collaborative and Adaptive Bayesian Optimization (CABO), is developed for tackling this challenge by combining Bayesian Probabilistic Optimization and Bayesian Probabilistic Integration. Two learning functions are introduced as engines for CABO, where one is introduced for realizing the adaptive optimization search in the epistemic uncertainty space, and the other one is developed for adaptive integration in the aleatory uncertainty space. These two engines work in a collaborative way to create optimal design points adaptively in the joint uncertainty space, by which a Gaussian process regression model is trained and updated to approach the bounds of model response moments with pre-specified error tolerances. The effectiveness of CABO is demonstrated using a numerical example and two engineering benchmarks.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (NSFC 51905430) and the grant number of the mobility programme 2020 of Sino-German Center is M-0175. The first author is also supported by the Alexander von Humboldt Foundation of Germany and the Top International University Visiting Program for Outstanding Young Scholars of Northwestern Polytechnical University. The third author extends his appreciation to the Institute for Risk and Reliability, Leibniz University, and the Humboldt award from the Alexander von Humboldt Foundation for providing the support to complete this paper. The authors would also like to thank Assist. Prof. Dr. Jingwen Song for the extensive and helpful discussions.

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, China

    Pengfei Wei & Fangqi Hong

  2. Institute for Risk and Reliability, Leibniz Universität Hannover, Hannover, 30167, Germany

    Pengfei Wei & Michael Beer

  3. Department of Civil and Environmental Engineering, National University of Singapore, Singapore, Singapore

    Kok-Kwang Phoon

  4. Institute for Risk and Uncertainty, University of Liverpool, Liverpool, L69 7ZF, UK

    Michael Beer

  5. International Joint Research Center for Engineering Reliability and Stochastic Mechanics, Tongji University, Shanghai, 200092, China

    Michael Beer

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  1. Pengfei Wei
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  4. Michael Beer
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Correspondence to Pengfei Wei.

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Wei, P., Hong, F., Phoon, KK. et al. Bounds optimization of model response moments: a twin-engine Bayesian active learning method. Comput Mech 67, 1273–1292 (2021). https://doi.org/10.1007/s00466-021-01977-8

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  • DOI: https://doi.org/10.1007/s00466-021-01977-8

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