Conditional probability method for dynamic reliability calculation of random structures

Based on Markov hypothesis of a dynamic response spanning process, two kinds of conditional probabilistic solutions are established for compound random reliability problems. One is the second order Taylor expansion expressions deduced for the dynamic reliability calculation of a stochastic structure. Another is a numerical sampling method based on Kriging model established by the concept of mathematical statistics. Among them, the sampling method by Kriging interpolation model fits the nonlinear relationship between dynamic reliability and structural random parameters. Therefore, the influence of random structural parameters on dynamic reliability can be analyzed directly by using the finite element method, which avoids the cumbersome and difficult problem of theoretical deduction. The numerical results show that the Kriging sampling method is not only insensitive to the size of the coefficient of variation, but also has the advantages of accuracy and computational efficiency.