# Model Updating of Bridges Using Measured Influence Lines
## 3 Results
### Updated FE Model
#### 3.2.5 Comparison of EDMF Results  
Table 7 presents outputs; RMSE values for E_MG1 and E_MG2 sensors, and natural frequencies and mode shapes for the initial FE model and all four EDMF analyses. The measured values are added for comparison. 'Bottom' and 'Upper' denote both range thresholds the candidates provided. The RMSE values for both sensors were set to 0, and the MAC values for all mode shapes were set to 1.00. For each output, the cell value in a row that deviated most from the measured value is coloured red, and the one closest to the measured value is green. B-Z-3 frequencies and mode shapes are coloured grey because they were not considered in the EDMF study. Again, the results of all EDMF studies were calculated in the FE model with all restrained degrees of freedom at the ABUT1 and ABUT2 bearings. In contrast, the initial FE model enabled longitudinal movements. The comparison of the EDMF results in Table 7 yielded the following conclusions:  
* Setting bearings ABUT1 and ABUT2 to fixed improved the B-Y-1 and B-Y-2 modelled vs. measured frequency values;
* Frequency-based EDMF primarily improved the frequency values; a minor improvement was also seen for E_MG1 and E_MG2 strain ILs. The MAC values decreased;
* MAC-based improved MAC values, improvement in E_MG1 and E_MG2 strain ILs was greater than that in the frequency-based EDMF;
* Frequency and MAC-based EDMF improved frequencies and MACs, closely matching the results of frequency-based EDMF (for frequencies) and MAC-based EDMF (for MAC values), while both strain ILs did not align more closely with the measured ones;  
Figure 22: Strain IL-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. * Strain-based EDMF only improved both strain ILs. Frequency and MAC values were even worse than for the initial FE model. Table 8 presents the updated variables for all EDMF studies performed. The initial values of 1, obtained from the initial FE model, are added for comparison. Comparing the values from Tables 7 and 8 yielded the conclusion that combining frequencies and MACs into EDMF was reasonable because it has significantly narrowed the range of the candidates' variables. The updated approximately 25 and 20% increases in the MG1 and MG2 main girders' stiffnesses and 10% decrease in the stiffnesses of all other elements are also in line with the expectations. Some updated MAC values are still lower than 0.90, and it should be noted that future research is needed to investigate the cause. The strain IL-based EDMF narrowed the MG1 and MG2 stiffness increases to more reasonable values of 35 and 50%. The \(\alpha_{\text{OTHER}}\) range, however, remained wide as the E_MG1 and E_MG2 strain ILs were not sensitive to OTHER elements. The strain IL-based EDMF generally resulted in approximately 10-15% higher values of frequencies (Figure 22) than those from the frequency and MAC-based EDMF (Figure 21) or measured ones. A similar trend can be seen for the RMSE values from the frequency and MAC-based EDMF. They were higher than the strain IL-based EDMF values, because the MG1 and MG2 stiffnesses were underestimated. Figure 23 compares the strain ILs of the  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Output**} & \multirow{2}{*}{**Experiment**} & \multirow{2}{*}{**Initial**} & \multicolumn{2}{c}{**Frequency-**} & \multicolumn{2}{c}{**MAC-**} & \multicolumn{2}{c}{**Frequency and**} & \multicolumn{2}{c}{**Strain IL-**} \\  & & & **FEC Model** & & **Based** & & **Based** & & **MAC-Based** & & **Based** \\ \hline RMSE E\_MG1 & & & & & & & & & & & \\ (\(\mu\)m/m)/kN) & 0 & 0.00821 & 0.00208 &  
initial FE model with the frequency and MAC-based and strain IL-based updated models for E_MG1 (Figure 23a) and E_MG2 (Figure 23b). The initial FE model overestimated the maximum modelled E_MG1 IL strains by 43% compared with the measured values.