Reliability analysis of linear dynamical systems with uncertain structural parameters subject to discrete white noise excitation

The estimation of first excursion probabilities for dynamical systems remains as one of the most challenging problems of computational stochastic mechanics. Hence, this contribution introduces an approach for estimating first excursion probabilities for a particular class of problems, i.e. linear dynamical systems involving uncertain structural parameters subject to discrete white noise excitation. The proposed approach is based on Importance Sampling. The Importance Sampling density (ISD) function related with uncertainty in stochastic loading is selected based on the work reported in [1]. In addition, a novel ISD function associated with uncertainty in structural parameters is introduced. This novel ISD function is defined such that it is proportional to the probability density function of the uncertain structural parameters and also to a parameter related with the probability of excursion at specific time instants. The application of the proposed approach is illustrated by means of a simple structural model involving two uncertain structural parameters and a stochastic excitation comprising a large number of random variables. The efficiency and accuracy of the proposed approach is analyzed in terms of failure probability estimators, the associated coefficient of variation and the number of samples required. Results obtained indicate that the proposed approach is accurate and also numerically efficient.