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

Abstract

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 and boundary conditions, numerical models can fail to predict the static and dynamic behavior of such structures. In order to achieve more reliable predictions, important information can be obtained measuring the structural response under ambient vibrations. This wholly non-destructive technique allows obtaining very accurate information on the structure’s dynamic properties (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 model updating procedures. This work presents two different model updating procedures. 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 (Girardi et al. (2018)). The second has been developed within a Bayesian statistical framework and uses both frequencies and mode shapes (Yuen (2015)). Both algorithms are used in conjunction with the NOSA-ITACA code for calculation of the eigenfrequencies and eigenvectors. These procedures are illustrated in the case study of the medieval Maddalena Bridge in Borgo a Mozzano (Italy). Experimental data, frequencies and mode shapes, acquired in 2015 (Azzara et al. (2017)) have enabled calibration of the bridge’s constituent materials and boundary condition