A comparative study of two interval-random models for hybrid uncertainty propagation analysis

Abstract

Abstract A wide variety of uncertainty propagation methods have been developed to deal with the single uncertainty; however, different kinds of uncertainties may exist simultaneously in many engineering practices. By using random variables and interval variables to quantify the probabilistic and non-probabilistic uncertainties respectively, this paper proposes two different interval-random models and a universal numerical approach for hybrid uncertainty propagation analysis. In the first model, uncertain parameters are treated as either random variables or interval variables with deterministic distributions, which exist independently. In the second model, uncertain parameters are quantified as random interval variables, where the bounds of interval variables are expressed as random variables instead of deterministic values. In both models, the effect of input hybrid uncertainties on output response is interpreted by an interval number with random bounds. To predict the moments of random bounds of interval response, a double-loop numerical analysis framework is constructed, where the outer loop is executed to traverse the discrete points for random variables and the inner loop is implemented to capture the response extreme values for interval variables. To further solve the computationally expensive issue caused by the full-scale finite element simulations, a cross validation-based adaptive surrogate model is introduced as an approximation, which can achieve an acceptable accuracy through a small number of sample points. Finally, a transient heat conduction example demonstrates the feasibility of the proposed models and method.