Improved chance index and its solutions for quantifying the structural safety degree under twofold random uncertainty

For the twofold random uncertainty problem of the random input variables with random distribution parameters, there still lacks a reasonable index to measure its safety degree. Aiming to this issue and starting from the characteristics of the failure probability function varying with the random distribution parameters under the twofold random uncertainty, an improved chance index (ICI) is proposed to quantify the safety degree of the structure. The proposed ICI takes into account the bilateral information of the statistical distribution of the failure probability function, and it uses the average of the upper and lower bilateral fractiles of the failure probability function with respect to a given confidence as the ICI. Compared with the existing primitive chance index (PCI), the information extracted by the ICI is more comprehensive. The ICI has self-duality, which can avoid the self-contradiction judgement resulted from the PCI. After the specific properties of the proposed ICI are proved, a differential interval approximation combined with numerical simulation is established for solving ICI, in which an adaptive Kriging model is nested for improving the efficiency, and multi-training-point based on cluster analysis and candidate sample pool reduction strategy are employed to improve the efficiency of constructing the Kriging model.