Dynamic reliability analysis model for structure with both random and interval uncertainties

Aiming at analyzing the safety of the dynamic structure involving both input random variables and the interval ones, a new dynamic reliability analysis model is presented by constructing a second level limit state function. Two steps are involved in the construction of the dynamic reliability model. In the first step, the non-probabilistic reliability index is firstly extended to the dynamic structure, in which the uncertainties of interval inputs can be analyzed by fixing random inputs and time parameter. In the second step, the second level limit state function is constructed by considering the fact that the non-probabilistic reliability index larger than one corresponds to the safe state, in which the uncertainties of random inputs are taken into account. Generally, the actual reliability of dynamic structure with both random and interval inputs is an interval variable, and theoretic analysis illustrates that the proposed reliability is equivalent to the lower bound of the actual reliability, which can provide an efficient way for measuring the safety of dynamic structure. For estimating the proposed reliability, a double-loop optimization algorithm combined with Monte Carlo Simulation as well as the active learning Kriging method is established. Several examples involving a cylindrical pressure vessel, an automobile front axle and a planar 10-bar structure are introduced to illustrate the validity and significance of the established reliability model and the efficiency and accuracy of the proposed solving procedure.