Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables

Abstract The reliability analysis of structural systems with multiple failure modes and mixed variables is a critical problem because of complex nonlinear correlations among failure modes (or components), huge computational burden of time-consuming implicit functions, and complex failure regions. In this paper, aleatory and epistemic uncertainties are considered simultaneously, and an efficient adaptive kriging-based reliability method is proposed for structural systems with multiple failure modes and mixed variables. Two new learning functions are developed as guidelines for selecting new training samples at each iteration. The proposed learning functions and corresponding stopping criteria are directly linked to system probability of failure; this allows the proposed method to select new training samples efficiently To determine the lower and upper bounds of system probability of failure, the limit-state functions in the entire uncertainty space of interest are accurately constructed while avoiding complicated nested optimizations. The proposed method has the following advantages: (1) the learning functions and stopping criteria are directly linked to system probability of failure, and the structure importance of components is also considered; (2) it requires fewer samples to achieve accurate results, and can be applied to small system probability of failure; (3) it is easy to use for extremely complex systems (e.g., bridge systems); (4) it can be applied to a system with multiple failure modes and mixed variables (e.g., mixture of random and p-box variables). The capabilities and efficiency of the proposed method are validated through four numerical examples; results show that it has high applicability and accuracy.