# Model Updating of Bridges Using Measured Influence Lines
## 3 Results
### Updated FE Model
#### 3.2.1 Frequency-Based EDMF  
In the frequency-based EDMF shown in Figure 17, all eight frequencies were considered. Thresholds for all frequencies were set as a multiplier of the experimental values; in this case, the [0.80, 1.20] interval, representing the \(0.80\cdot f_{i,\text{exp}}\) as the lower bound and \(1.20\cdot f_{i,\text{exp}}\) as the upper bound. The candidates had frequencies within \(\pm 20\%\) of the measured values for this case. For a good correlation between the FE model and measurements, the relative difference between frequencies should be less than 5% [31]. In the initial phases of this study, it was necessary to apply threshold values somewhat higher than usual to identify viable candidates. While this may seem unrealistic, it was essential to obtain any candidates at all. Although the thresholds were subsequently reduced to 5% or less in later steps, we retained this stage to illustrate how the process of FEMU using EDMF was structured to facilitate the identification of the mode with the greatest deviation, and that finally guided us towards understanding the underlying cause. Note that, although strain IL-based (RMSE values) and MAC-based outputs (MAC values) are shown in this EDMF plot, in this case, they do not determine the candidates because of the large thresholds. B-Y-1 frequencies were underestimated and B-Z-3 overestimated compared with the measurements, as shown in Figure 17. Analysis of the EDMF's outputs was performed, where mean values of the modelled frequencies were compared with the experimental values, as shown in Figure 18.  
The greatest absolute deviation between the mean modelled and measured values of frequencies was observed for B-Y-1 and B-Z-3 (Figure 18). Recalling the sensitivity study  
Figure 17: Frequency-based EDMF results. Experimental values are denoted by red markers, red horizontal lines indicate thresholds, candidates are represented in blue, and models that have been falsified are noted in grey. Figure 18: Difference between mean modelled (EDMF) and experimental frequencies. results, fixed boundary conditions importantly reduce the objective function for natural frequencies and could significantly influence the B-Y-1 frequency. Contrary, fixed boundary conditions have a negligible effect on the strain ILs' objective functions. In the following, all analyses were performed on the FE model with fully fixed boundary conditions, where all degrees of freedom were constrained for bearings at both abutments. The investigation of B-Z-3 overestimation revealed that the reason was the unreliable mode pairing strategy, which often paired the modelled B-Z-3 with the experimental B-Z-4 mode. By using the EDMF approach, it is possible to identify suspicious outputs caused by, for example [32], faulty sensors. A similar process was followed in this study, where the B-Z-3 mode was eliminated for all following analyses. Although still present in the EDMF plots, the B-Z-3 mode was excluded by setting the falsification threshold range for the B-Z-3 frequency between the minimum and maximum values of the modelled frequencies, allowing all FE models to pass through the B-Z-3 frequency thresholds. Figure 19 shows the frequency-based EDMF analysis on the FE models with fully restrained bearings at abutments and with B-Z-3 frequency eliminated. The threshold for all frequencies was set to [0.975, 1.025], allowing the frequencies to deviate to \(\pm\)2.5%. Considering fully restrained bearings at the abutments was essential for improving the B-Y-1 frequency results. This approach showed a minimal impact on the E_MG1 and E_MG2 strain IL responses, as illustrated in Figure 18. Previous studies, such as those referenced in [30; 33], have also documented limited or restrained movements in bearings during ambient vibration tests. Although this effect was not measured directly, it was observed that clogged expansion joints and corroded bearings, as shown in Figure 4, limit movement, which is contrary to the original design specifications.