On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems, there are a lot of uncertain variables from different sources. Therefore, it is important to consider these uncertainties in engineering. In addition, time-variant reliability problems typically involve a complex multilevel nested optimization problem, which can result in an enormous amount of computation. To this end, this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model. In this method, the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a time independent reliability problem. Further, to solve the double nested optimization problem in hybrid reliability calculation, an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point (MPP). The limit state function is linearized at these points, and an innovative random variable is defined to solve the equivalent static reliability analysis model. The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.