Directional importance sampling for dynamic reliability of linear structures under non-Gaussian white noise excitation

Reliability analysis of dynamic structural systems and its implications for structural design have garnered increasing attention. Sample-based methods prove insensitive to the dimension of the probability integral. Nontheless, a substantial number of realizations is necessary for estimating small failure probabilities, resulting in time-consuming computations. Recently, the Directional Importance Sampling (DIS) was introduced for linear structural systems subjected to Gaussian loads, showcasing the ability to accurately estimate small failure probabilities with a reduced number of simulations. However, this Gaussian assumption on the load makes the method inapplicable for realistic loading scenarios as they might be of non-Gaussian nature. This contribution develops the DIS method for linear structural systems subjected to loading characterized as non-Gaussian white noise. To take the advantage of both linearity in physical space and simplicity of Gaussian space, directional importance sampling is conducted in Gaussian space and the failure probability is estimated with the aid of physical space. The information is dynamically exchanged between physical and Gaussian spaces with the aid of normal and inverse-normal transformation techniques. The whole procedure of the developed DIS method is straightforward, and it provides an explicit estimator of the failure probability. The application of the developed DIS method is presented through three examples, illustrating its accuracy and efficiency for dynamic reliability analysis.