The equivalent extreme-value event and evaluation of the structural system reliability

The idea of equivalent extreme-value event and accordingly a new approach to evaluate the structural system reliability are elaborated. For any type of compound random event as combination of a set of random events represented by inequalities, an equivalent extreme-value event is defined. Elaborated investigations show that correlative information among the component random events is inherent in the equivalent extreme-value event. Since the probability density function of the equivalent extreme value could be obtained through the probability density evolution method, the idea of equivalent extreme-value event leads to a new uniform approach to evaluate the structural system reliability for both static and dynamic problems. Particularly, the investigation points out that computation of the dynamic reliability essentially involves dealing with infinite-dimensional correlation information and that is why the widely-used out-crossing process theory could be only an approximate and somewhat empirical reliability evaluation rather than an exact approach. The proposed approach is discussed in detail on how to construct the equivalent extreme-value event and then implement the procedure numerically. Two examples, of which one deals with static problem comparing the results with exact solution, the other deals with a nonlinear frame structure subjected to stochastic ground motions, are illustrated to validate the proposed method. The investigations show that the proposed approach is of satisfactory accuracy and applicable to the structural reliability analysis of various structures.