Collaborative and Adaptive Bayesian Optimization for bounding variances and probabilities under hybrid uncertainties

authored by

Fangqi Hong, Pengfei Wei, Jingwen Song, Marcos A. Valdebenito, Matthias G.R. Faes, Michael Beer

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.

Organisation(s)

Institute for Risk and Reliability

External Organisation(s)

Northwestern Polytechnical University
TU Dortmund University
University of Liverpool
International Joint Research Center for Engineering Reliability and Stochastic Mechanics
Tongji University

Type

Article

Journal

Computer Methods in Applied Mechanics and Engineering

Volume

417

ISSN

0045-7825

Publication date

01.12.2023

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications

Electronic version(s)

https://doi.org/10.1016/j.cma.2023.116410 (Access: Closed)