A Time-Variant Reliability Analysis Method Based on the Stochastic Process Discretization under Random and Interval Variables

Abstract

In practical engineering, it is a cost-consuming problem to consider the time-variant reliability of both random variables and interval variables, which usually requires a lot of calculation. Therefore, a time-variant reliability analysis approach with hybrid uncertain variables is proposed in this paper. In the design period, the stochastic process is discretized into random variables. Simultaneously, the original random variables and the discrete random variables are converted into independent normal variables, and the interval variables are changed into standard variables. Then it is transformed into a hybrid reliability problem of static series system. At different times, the limited state functions are linearized at the most probable point (MPP) and at the most unfavorable point (MUP). The transformed static system reliability problem with hybrid uncertain variables can be solved effectively by introducing random variables. To solve the double-loop nested optimization in the hybrid reliability calculation, an effective iterative method is proposed. Two numerical examples and an engineering example demonstrate the validity of the present approach.