Probabilistic Damage Detection Using Markov Chain Simulation with Application to a Benchmark Problem

A Markov chain simulation method is presented to evaluate the integrals giving the probability of damage and updated reliability based on dynamic data in a Bayesian probabilistic approach to damage detection and assessment. The method is based on the Metropolis-Hastings algorithm and an adaptive procedure to gain information about the important regions of the updated probability distribution in an efficient manner. Statistical averaging over the Markov chain samples is used to estimate the damage probability for each substructure and the updated reliability. The method is illustrated by applying it to modal data from the ASCE four-story benchmark structure to perform damage detection and assessment by giving the likely locations of the damage, its severity and its impact on the interstory-drift reliability of the structure.