Estimation of response expectation function under hybrid uncertainties by parallel Bayesian quadrature optimization

Multiple types of uncertainty characterization models usually coexist within a single practical uncertainty quantification (UQ) problem. However, efficient propagation of such hybrid uncertainties still remains one of the biggest computational challenges to be tackled in the UQ community. In this study, a novel Bayesian approach, termed ‘Parallel Bayesian Quadrature Optimization’ (PBQO), is proposed to estimate the response expectation function (REF) under hybrid uncertainties in the form of probability models, parametric p-box models and interval models. By assigning a Gaussian process (GP) prior over the augmented (transformed) response function, the posterior distribution of the REF w.r.t. interval parameters is also proven to be a GP. The posterior mean and variance functions of the induced GP are derived in closed form. Besides, a novel strategy is proposed to select multiple points at each iteration so as to take advantage of parallel computing. The efficiency and accuracy of the proposed method is demonstrated by a numerical example.