Bayesian probabilistic propagation of hybrid uncertainties

Estimation of response expectation function, its variable importance and bounds

authored by: Chao Dang, Pengfei Wei, Matthias G.R. Faes, Michael Beer
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.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): Northwestern Polytechnical University
TU Dortmund University
University of Liverpool
Tongji University
Type: Article
Journal: Computers and Structures
Volume: 270
ISSN: 0045-7949
Publication date: 01.10.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Civil and Structural Engineering, Modelling and Simulation, Materials Science(all), Mechanical Engineering, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.compstruc.2022.106860 (Access: Closed)