Model parameter estimation using Bayesian and deterministic approaches: the case study of the Maddalena Bridge

Finite element modeling has become common practice for assessing the structural health of historic constructions. However, because of the uncertainties typically affecting our knowledge of the geometrical dimensions, material properties, boundary conditions and so forth, numerical models can fail to predict the static and dynamic behavior of such structures. In order to achieve more reliable predictions of structural performance, important information can be obtained via in situ experimental tests. More specifically, measurements of the structural response under ambient vibrations represent an effective, wholly non-destructive technique, which allows obtaining very accurate information on the structure’s dynamic properties (natural frequencies, mode shapes, damping ratios) (Brincker and Ventura (2015)). Moreover, when experimental data is coupled with a finite element model, an estimate of the boundary conditions and the mechanical properties of the constituent materials can also be obtained via suitable model updating procedures. In this work two different model updating procedures are presented. The first relies on construction of local parametric reduced-order models embedded in a trust region scheme to minimize the distance between the natural frequencies experimentally determined and the corresponding numerically evaluated ones, as described in Girardi et al. (2018). The second has been developed within a Bayesian statistical framework and uses modal properties (both frequencies and mode shapes) to obtain parameter estimates (Yuen (2015)). Both algorithms are used in conjunction with the NOSA-ITACA code for calculation of the eigenfrequencies and eigenvectors. Some advantages of these procedures are illustrated through the case study of the medieval Maddalena Bridge in Borgo a Mozzano (Italy). Experimental data on the bridge’s dynamic properties was acquired in 2015, using four three-axial seismometers placed on the structure in different layouts, as described in Azzara et al. (2017). The natural frequencies and mode shapes deduced by the experiment have enabled calibration of the bridge’s constituent materials and boundary conditions.