# Dynamic Identification on an Irregular Structure
## 4 Identification Results and Up-Dating Procedure
### Optimization Updating Procedure  
The FE model has been updated to match the experimental results; the adopted criterion is to minimize the errors of the frequency values of the first three modes. The main uncertainties are related to the masses and the stiffnesses. Two different updating procedures have been conducted on the finite element model of the structure. In the first model, the masonry infills have been modelled only by inserting their contribution on the seismic mass acting on the beams of the r.c. frame. In the second model, starting from the same assumptions on the involved masses, the updating was firstly conducted by inserting diagonal strut in the positions of the infill walls. In the model without the infills (Figure 6), due to the particular condition which was conducted during an out-of-service period of the structure, an accurate evaluation of the masses was possible, and the uncertainties were expected to be of low amplitude; in addition, a not significant influence of such uncertainties was reasonably expected on the natural frequency values. Thus, on the first model, the updating procedure was performed by changing the elastic modulus of the concrete to match the experimental frequency results. In this way the concrete elastic modulus was set equal to 38,640 MPa. In the second model, starting from the same assumptions on the involved masses, the updating procedure was firstly conducted by inserting diagonal struts in the positions of the infills whose properties have been established according to [32]. In particular, the gross cross-sectional area of the equivalent diagonal strut was defined starting assuming a depth equal to the real size of the infill walls, while the other dimension of the transversal section was established according to [32], whereas the elastic modulus E adopted for the equivalent strut is that of the masonry itself equal to 2.9 MPa. The diagonal strut was not inserted only in the windowed walls. Thus, the updating strategy was to modify the elastic modulus of the concrete, which at the end of the updating was set equal to 33,640 MPa, i.e., a reduction of 13% of such value. It is worth noting that this new value is close to the survey campaign values  
The first three modes are equal to 4.94 Hz, 7.67 Hz and 8.44 Hz. Following the plots of the first three mode shapes are reported in Figures 16-18. The second FE model has been improved considering including the infill walls into the model as shown in Figure 19. This has allowed us to consider the contribution of the masonry infill walls as regards the stiffness and not only the mass as in the first FE model. Figure 16: First mode is a torsional-bending mode along x axis with frequency equal to 4.94 Hz (in grey the un-deformed configuration and in blue the mode shape): (**a**) 3D view; (**b**) plan view. The infill walls were modelled as diagonal strut with axial stiffness only and their properties have been established according to [32]. In particular, the gross cross-sectional area of the equivalent diagonal strut was defined starting to the real size of the infill walls, whereas the elastic modulus E adopted for the equivalent strut is that of the masonry itself equal to 2.9 MPa. The diagonal strut was not inserted only in the windowed walls. The updating strategy was to modify the r.c. elastic modulus E of the concrete starting from the same assumptions of the first model for the involved masses. The final r.c. elastic modulus was set equal to 33,640 MPa, i.e., a reduction of 13% of such a value from the first FE model. It is worth noting that this new value is close to the survey campaign values. Table 4 shows the results of the two FE models and the comparison with these frequencies with the ARTeMIS values; it highlights the influence of masonry infill walls. The mode shapes do not change between the FE models with and without the infill walls.