Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds. (1st October 2022) - Dang, Chao; Wei, Pengfei; Faes, Matthias G.R.; Beer, Michael
Highlights: An efficient Bayesian framework is presented to tackle the challenge of propagating hybrid uncertainties. Estimation of response expectation function (REF) is treated as a Bayesian inference problem. Under Gaussian process (GP) prior, posterior distribution of REF is proven to be GP. Posterior means and variances of REF and its RS-HDMR are analytically derived in closed form . A multipoint selection strategy is proposed to facilitate parallel distributed processing. 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.