Probability Density Evolution Method for Seismic Reliability Evaluation of Structural Systems
A structural system reliability evaluation approach based on the idea of equivalent extreme-value event and the probability density evolution method is presented. Using the idea of equivalent extreme-value event, for a compound random event as combination of a set of random events, an equivalent extreme-value event could be constructed. So, this makes it possible to transform computation of the probability of the compound random event to a one-dimensional integration of the probability density function of the equivalent extreme-value random variable. In conjunction with the probability density evolution method, which is capable of evaluating the extreme-value distribution of a set of random variables or stochastic processes, the structural system reliability could be evaluated through computing the probability of the equivalent extreme-value event. The proposed approach is discussed in detail on how to construct the equivalent extreme-value event and then implement the procedure numerically. On the other hand, based on the orthogonal expansion method, the stochastic process of earthquake ground motion can be represented as a linear combination of deterministic functions modulated by a set of mutually independent random variables. Combining the above methods, the reliability of structures under earthquake excitations could be successfully evaluated. An example, of which deals with a linear frame structure subjected to non-stationary seismic loading, is illustrated to validate the proposed method.
Y. L. Lei and Z. J. Liu, "Probability Density Evolution Method for Seismic Reliability Evaluation of Structural Systems", Advanced Materials Research, Vols. 255-260, pp. 2606-2611, 2011