A time-variant reliability analysis method for non-linear limit-state functions with the mixture of random and interval variables

Most of the current time-variant reliability analysis methods are applicable for only random variables. However, some of the uncertain parameters can only be easily modeled by interval variables in many engineering applications. The main contribution of this paper is to propose a new time-variant reliability analysis method for nonlinear limit state function with the coexistence of random variables and interval uncertain variables. Three primary strategies are put forward. Firstly, the stochastic process in the time-variant limit-state function is discretized, equivalently gaining several static limit-state functions at different time. Secondly, each static limit-state function is linearized at the most probable point (MPP) and the worst-case point (WCP) of interval variable, by doing which, the ordinary time-dependent reliability problem is equally transformed into a static reliability one with mixed uncertain variables. Finally, complex nested optimization problems using sequential iterations are effectively solved in mixed reliability calculation. The proposed method can obtain structural reliability considering time effects and mixed uncertainties. The effectiveness and the efficiency of the proposed method are demonstrated by four numerical examples.