Application of line sampling simulation method to reliability benchmark problems

A procedure denoted as Line Sampling (LS) has been developed for estimating the reliability of static and dynamical systems. The efficiency and accuracy of the method is shown by application to the subset of the entire spectrum of the posed benchmark problems [Schuëller GI, Pradlwarter HJ, Koutsourelakis PS. Benchmark study on reliability estimation in higher dimensions of structural systems. In URL: http://www.uibk.ac.at/mechanik/Publications/benchmark.html. Institute of Engineering Mechanics, Leopold-Franzens University, Innsbruck, Austria, 2004], i.e. in particular linear systems with random properties. The notion of design point excitation for non-linear systems is discussed and its use extended for reliability estimations of conservative non-linear MDOF systems considering critical conditional excitation. For solving the hysteretic MDOF system with uncertain structural parameters subjected to general Gaussian excitation, however, the general applicable subset procedure [Au SK, Beck JL. Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 2001;16:263-277] has been used combined with Importance Sampling.