Application of directional importance sampling for estimation of first excursion probabilities of linear structural systems subject to stochastic Gaussian loading

This contribution addresses the estimation of first excursion probabilities of linear structural systems subject to stochastic Gaussian loading by means of simulation. This probability is estimated by combining existing knowledge on the geometry of the associated failure domain with Directional Importance Sampling. In this way, the space associated with the stochastic loading is explored by generating some random directions according to a prescribed importance sampling distribution; then, each random direction is analyzed taking advantage of the linearity of the response with respect to the stochastic loading. Such an approach allows estimating small failure probabilities with high accuracy and precision while requiring a reduced number of samples. The application of Directional Importance Sampling is illustrated by means of a series of examples, indicating that failure probabilities in the order of 10^-3 or less can be estimated reliably with a reduced number of samples, even in problems comprising involved structural models.