Bayesian-based model updating using natural frequency data for historic masonry towers

Model updating procedures are commonly used to identify numerical models of a structure to be subsequently used for reliable assessment of its behaviour under environmental loads. In the case of historic masonry buildings, the uncertainties that are involved in the knowledge process (material properties, geometry, boundary conditions, etc.) can severely affect the matching between the experimental data and the corresponding model output. To account for the different sources of uncertainties that are involved in the model updating procedure for historic confined masonry towers, this paper proposes an application of the Bayesian paradigm. Effects of parameter uncertainty, observation errors and model inadequacy are explored by comparing the output of the numerical model against real measured modal data. The proposed methodology aims at obtaining the posterior distribution of unknown quantities to estimate their uncertainty and to identify values of the parameters to be used in the numerical model for subsequent analyses. The comparison among the updated distributions related to different initial probabilistic modelling assumptions (prior distributions, measurement errors and modelling uncertainties) shows significant improvements of the predictive capabilities with a considerable reduction of the initial uncertainties, which confirm the potential of the proposed approach.