Hybrid reliability analysis with uncertain statistical variables, sparse variables and interval variables

There are differences among sampling data and representation types of uncertain statistical variables, sparse variables and interval variables, which increase the complexity of structure reliability analysis. Therefore, a hybrid first order reliability analysis method considering the three types of uncertain variables is demonstrated in this article. First, distribution types and distribution parameters of sparse variables are identified and probabilistically estimated. Secondly, interval variables are transformed into probabilistic types using a uniformity approach. Thirdly, a unified hybrid reliability calculation method considering these uncertain variables simultaneously is demonstrated. The most probable point (MPP) is searched for using the first order reliability method, and then a linear approximation function of performance function is constructed in the neighbourhood of the MPP. Finally, the belief and plausibility measures of the reliability index are efficiently calculated using the theoretical analytical method. Three examples are investigated to demonstrate the effectiveness of the proposed method.