Stochastic Simulation Algorithm for Robust Reliability Updating of Structural Dynamic Systems Based on Incomplete Modal Data

This paper presents an approach for updating the robust structural reliability that any particular response of a structural dynamic system will not reach some specific failure or unfavorable state when it is subjected to future stochastic excitation. In particular, the updating approach is based on incomplete modal data identified from the structural system. Uncertainties arising from structural modeling and modeling of the stochastic excitation that the structure will experience during its lifetime are considered. 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 a constrained multigroup Metropolis within Gibbs (CMMG) sampling algorithm is developed by the authors. Another appealing feature of the proposed method is that it provides not only the exceedance probability estimates but also conditional samples that allow in-depth failure analysis in a single simulation run. The proposed method provides a substantial improvement in efficiency over estimators based on crude Monte Carlo simulation (MCS) for the updated robust reliability and is robust to the number of random variables and uncertain parameters and the amount of modal data involved in the problem. The effectiveness and efficiency of the proposed approach are shown by two illustrative examples.