A new stochastic simulation algorithm for updating robust reliability of linear structural dynamic systems subjected to future Gaussian excitations

In this paper, we are interested in using system response data to update the robust failure probability that any particular response of a linear structural dynamic system exceeds a specified threshold during the time when the system is subjected to future Gaussian dynamic excitations. Computation of the robust reliability takes into account uncertainties from structural modeling in addition to the modeling of the uncertain excitations that the structure will experience during its lifetime. In partial, modal data from the structure are used as the data for the updating. By exploiting the properties of linear dynamics, a new approach based on stochastic simulation methods is proposed to update the robust reliability of the structure. The proposed approach integrates the Gibbs sampler for Bayesian model updating and Subset Simulation for failure probability computation. A new efficient approach for conditional sampling called 'Constrained Metropolis within Gibbs sampling' algorithm is developed by the authors. It is robust to the number of uncertain parameters and random variables and the dimension of modal data involved in the problem. The effectiveness and efficiency of the proposed approach are illustrated by two numerical examples involving linear elastic dynamic systems.