Aleatory and epistemic uncertainties analysis based on non-probabilistic reliability and its kriging solution

•A new approach for aleatory and epistemic uncertainties analysis is proposed.•A high efficient algorithm is developed for the proposed approach.•This approach can identify the effect of two types of uncertainties on the response. The uncertainties affecting the capability of the structural system are generally classified into aleatory uncertainty and epistemic uncertainty. In this study, aleatory uncertainty is modeled by probability theory, and epistemic uncertainty is modeled by evidence theory. A new reliability analysis model is developed to analyze both uncertainties. According to evidence theory, the uncertain input space is first partitioned into different focal elements which contain the random variables with their joint probability density function (PDF) and the interval variables with the joint basic probability assignment (BPA). Then, according to the non-probabilistic theory based on interval analysis, the bounds of the failure probability for each focal element can be obtained through a successive construction of the performance function of the focal element in two levels and the corresponding reliability analysis. Furthermore, the belief and plausibility measures are obtained by the random reliability analysis. In order to improve computational efficiency, the kriging method is employed to build the surrogate model for the constructed performance function and then based on this surrogate model to implement the estimation of the failure probability. The features of the proposed approach are demonstrated with two practical examples.