Reliability analysis of uncertain dynamic systems

Uncertainty in a structural system will invariably affect the system responses. For example, the responses of an uncertain linear system subjected to a Gaussian excitation will not be Gaussian. This complicates any attempt to characterize fully the responses or even estimate the system failure probability. Numerical schemes that are more efficient than direct simulation or integration, such as the First- and Second-Order Reliability Methods (FORM/SORM), have been used to estimate the failure probability of an uncertain linear system. This paper explores the potential applications of variance reduction techniques such as importance sampling and stratified sampling to estimate the probability of failure of an uncertain linear system subjected to a Gaussian excitation. Knowledge of the dynamic behavior of the system is used to help in the sampling process. Results of a single degree-of-freedom (dof) system and a 2-dof primary-secondary system are presented.