## 4 Results and Validation
### Full-Scale Testing
#### 4.2.2 Railway Bridge Monitoring
As an example of the different kinds of trains tested, the transverse vibration record of a 48 km/h empty-load train from measurement channel 3 is presented in Figure 32. For transverse forced vibrations of this train tested, the absolute maximum acceleration detected by the PCB B4 accelerometer was 1.662 g, and the absolute maximum acceleration measured from the ADXL355 RBP4 accelerometer was 1.464 g.  
The modal damping ratio, related to the first vertical and transverse dominant vibration modes, was calculated using the logarithmic decrement method to analyze sixteen forced and free-vibration datasets. The vertical and transverse free-vibration responses of  
Figure 31: Modal assurance criteria for the mode shapes estimated of the structure: (**a**) Vertical mode correlation. (**b**) Transverse mode correlation. Figure 32: Transverse forced vibration record of a 48 km/h empty-load train on measurement channel 3.  
the railway bridge of a 48 km/h empty-load train and a 52 km/h empty-load train, respectively, were selected to calculate the damping ratios since the free-decay signals thereof were well-defined exponentially. As explained for the damping estimation of the flexible structure, the Butterworth signal processing filter was used on the free-vibration signals using the band-pass specification based on the frequencies of interest. In the damping estimation for the 6.83 Hz vertical vibration mode, the cut-off frequencies were 5.0 and 8.0 Hz. While for the 2.93 Hz transverse vibration mode, the cut-off frequencies were 1.0 and 5.0 Hz. Figure 33 indicates the transverse exponential free-decay window extracted from both SHM systems on the DOF 4 of the steel bridge and a group of representative acceleration peaks from the ADXL355 RBP4 accelerometer. Once the vertical and transverse free-vibration signals from all the measurements channels got filtered, the damping ratio of the first vertical and transverse vibration modes was estimated by the logarithmic decrement method following the procedure stated earlier in the small-scale testing damping estimation. After elaborating a comprehensive dataset from the damping ratios estimated, the mean damping ratio and its coefficient of variation, related to the vertical and transverse vibration modes, were calculated with both SHM systems and are indicated in Table 11. The vertical mean damping ratio determined from the low-cost SHM system had a relative error of 2.68% compared to the result of the reference SHM system. On the other hand, the transverse mean damping ratio calculated by the low-cost SHM system presented a relative error of 2.51% regarding the approach from the reference SHM system. The vertical and transverse mean damping ratio variation from both SHM monitoring systems was within the state-of-the-art limit considered previously. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Vertical Vibration Mode 1**} \\ \hline \multicolumn{2}{c}{**Reference System**} & \multicolumn{2}{c}{**Low-Cost System**} \\ \hline
**Mean** & **Coefficient of** & **Mean** & **Coefficient of** \\
**Damping** & **Variation (\%)** & **Damping** & **Variation (\%)** \\
**Ratio (\%)** & & **ratio (\%)** & \\ \hline
3.54 & 19.2 & 3.63 & 22.8 \\ \hline \multicolumn{4}{c}{**Transverse Vibration Mode 1**} \\ \hline \multicolumn{4}{c}{**Reference System**} & \multicolumn{2}{c}{**Low-cost System**} \\ \hline
**Mean** & **Coefficient of** & **Mean** & **Coefficient of** \\
**Damping** & **Variation (\%)** & **Damping** & **Variation (\%)** \\
**Ratio (\%)** & & **ratio (\%)** & \\ \hline
1.553 & 21.1 & 1.514 & 24.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Mean damping ratios and coefficients of variation calculated for both monitoring systems. Figure 33: Transverse free-vibration response of the steel structure for DOF 4: (**a**) Exponential free-decay window. (**b**) Representative acceleration peaks from the filtered free-vibration signal of the ADXL355 RBP4 accelerometer.