Adaptive kriging model for fuzzy safety degree analysis to time-dependent structure

Time-dependent failure possibility (TDFP) has the capability to measure the safety degree of a structure under fuzzy uncertainty over a service time interval of interest. To improve the computational efficiency in estimating TDFP, an adaptive kriging model is developed in this paper. In the proposed method, TDFP is first represented as a bilevel problem, where the outer level is a one-dimensional rooting problem with respect to the membership level of fuzzy variables and the inner level is a minimum optimization of the model response function where the interval parameters and time are regarded as the same level. Second, the dichotomy instead of the interpolation technique is employed to solve the one-dimensional rooting problem. Third, the numerical simulation replacing the optimization technique is used to settle the optimization problem. Finally, to greatly reduce the computational cost in estimating the TDFP especially involved in numerical simulations, an adaptive kriging model is proposed for TDFP analysis. Additionally, the proposed kriging model can be used to estimate the safety life based on the TDFP constraint. The results of a mathematical example and two aerospace engineering examples show that the proposed method significantly improves the efficiency in estimating the TDFP and the TDFP-based safety life with acceptable precision.