A new Bayesian probabilistic integration framework for hybrid uncertainty propagation

Efficient propagation of uncertainty is one of the most critical tasks for uncertainty quantification and reliable design in the presence of multi-source uncertainties. This work presents a new methodology framework, termed as “mixed imprecise probabilistic integration”, for efficient propagation of the uncertainties characterized by non-probabilistic models, imprecise probability models and precise probability models. In this paper, the mixed-high dimensional model representation combining the cut-high dimensional model representation and random sampling-high dimensional model representation is firstly proposed, which conserves all the advantages of these two methods. Secondly, the proposed method is realized by using mixed-high dimensional model representation and Bayesian inference. The estimations and the posterior variances of the proposed method are analytically derived of high accuracy. With the proposed method, all the three kinds of uncertainty models can be efficiently propagated with one set of function evaluations. The effectiveness of the proposed methods is demonstrated by three engineering examples.