Seismic Reliability Assessment of Structures via Subset Simulation and Bayesian Updating

The reliability assessment of building constructions is one of the most important research topics in structural engineering. Among the various methods proposed to solve the problem, Monte Carlo Simulation has successfully been employed over the past decades; its success is due to the ability of taking into account all the uncertainties involved in the assessment. Recently, advanced stochastic simulation algorithms have been discussed and applied, with the aim of increasing the computational efficiency, especially when the probability of failure to be estimated is low. One of the more recent and efficient techniques of stochastic simulation is the Subset Simulation. In this paper, an application of Subset Simulation is illustrated to the evaluation of the probability of failure of a structure damaged by an earthquake. The structural response is analysed in time domain by considering the time-histories of the ground acceleration as input; each time-history is a sample of a stochastic model which is able to represent the uncertainties of the seismic action. Uncertainty in structural model is defined by the posterior probability density functions of the stiffness and damping associated to each degree of freedom. The posterior density functions of the model parameters are obtained by implementing an identification technique with unknown input in the frequency domain, that is based on a Bayesian Model Updating approach. The sampling of the uncertain parameters for Subset Simulation is carried out according to Markov Chain Monte Carlo simulation, which relies on a modified version of the Metropolis-Hastings algorithm. The main purpose of the proposed approach is to include in a unique probabilistic framework for structural health monitoring the results coming from damage detection and reliability assessment.