Robust Reliability of Stochastic Structural Systems under Stochastic Excitation

Abstract

This paper presents the concept of robust dynamic reliability where the uncertainties in the dynamic loading and structural modelling are treated probabilistically. Efficient evaluation of this robust reliability, which is formulated as a multi-dimensional probability integral, requires advanced computational methodologies other than numerical integration or standard Monte Carlo simulation. Some advanced simulation methods that have been recently developed by the authors are reviewed, namely, ISEE (Importance Sampling using Elementary Events) and adaptive importance sampling and subset simulation, both of which use Markov chain Monte Carlo simulation. In particular, ISEE is dedicated to, and is extremely efficient for, evaluating first-passage probabilities for linear dynamical systems. Subset simulation, on the other hand, is applicable for general dynamical systems and is most suitable for a combined treatment of both loading and structural parameter uncertainties in high dimensions.