Estimation of time variant reliability of randomly parametered non-linear vibrating systems

• Development of a Monte Carlo simulation based approach to analyze reliability of randomly parametered non-linear dynamical systems under random excitations.
• Combing two powerful variance reduction strategies, namely, Girsanov's transformation and subset simulations, within a single framework.
• Illustrations include non-linear randomly parametered dynamical systems and non-stationary excitations.

The problem of time variant reliability analysis of randomly parametered and randomly driven nonlinear vibrating systems is considered. The study combines two Monte Carlo variance reduction strategies into a single framework to tackle the problem. The first of these strategies is based on the application of the Girsanov transformation to account for the randomness in dynamic excitations, and the second approach is fashioned after the subset simulation method to deal with randomness in system parameters. Illustrative examples include study of single/multi degree of freedom linear/non-linear inelastic randomly parametered building frame models driven by stationary/non-stationary, white/filtered white noise support acceleration. The estimated reliability measures are demonstrated to compare well with results from direct Monte Carlo simulations.