A numerical approach for hybrid reliability analysis of structures under mixed uncertainties using the uncertainty theory

This paper presents a novel numerical method for the hybrid reliability analysis by using the uncertainty theory. Aleatory uncertainty and epistemic uncertainty are considered simultaneously in this method. Epistemic uncertainty is characterized by the uncertainty theory, and the effect of epistemic uncertainty is quantified by the sub-additive uncertain measure. Then, under the framework of the chance theory which can be interpreted as the combination of the probability theory and the uncertainty theory, a general uncertainty quantification model is established to deal with the hybrid reliability analysis problem, then the corresponding reliability metric is defined. After that, to improve the feasibility of the proposed model, by utilizing the polar coordinate transformation based dimension reduction method, a numerical analysis method for the hybrid reliability model are provided. At last, several application cases are presented to prove the effectiveness of the proposed method for the reliability analysis under hybrid uncertainty. The comparisons between the results of the proposed method and the Monte Carlo simulation also illustrate the merit of this method.