Uncertainty quantification in the damage assessment of ancient masonry towers through Bayesian discrete-model updating of a cantilever beam

The dynamic monitoring of structures represents an emerging tool for their damage assessment. Changes of some relevant dynamic properties of the structures provide a valuable guide in damage identification. Ancient structures, in which only non-destructive investigations are allowed, represent good candidates for damage assessment through vibration-based techniques. The presence of uncertainties in the measurements as well as the lack of knowledge on the modeling of masonry structures, preclude a deterministic estimation of the damage. This work deals with a procedure for the uncertainty quantification on the damage assessment of a masonry tower. The procedure starts by subdividing the tower in N elements, characterized by a prior joint probability density function of their elastic moduli. Bayesian inference is used to update the prior distribution by incorporating the information provided by measurements of the natural frequencies and modal shapes. The measurements are simulated by using a finite element model of the tower with a known damage (i.e., an element with reduced elastic modulus). The Metropolis algorithm is used to sample the posterior joint probability density function. The capability of the procedure in identifying the damage, in terms of intensity and position, represents the main scope of the work.