## 4 Results and Validation
### Small-Scale Testing
#### 4.1.1 Shaking Table Tests  
The acceleration spectra and fitting equations for the vibration dataset recorded from the 0.10 cm displacement frequency chirp by every accelerometer are presented in Figure 11. The first frequency of excitation (0.5 Hz) caused acceleration values higher than the acceleration amplitudes detected for the next three excitation frequencies (1.0, 1.5, and 2.0 Hz) in all accelerometers. This particular trend may be associated with an electric or mechanical issue on the shaking table that reproduces sinusoidal motions with low amplitude concerning these specific frequency levels. Despite the outlier accelerations registered for low excitation frequencies, the tendency of vibration data for every type of acceleration spectrum fit a linear pattern. The acceleration ranges, coefficients of determination R\({}^{2}\) of fitting equations, and RMS error for the set of 0.10 cm displacement acceleration spectra are shown in Table 3.  
For the 0.25 cm displacement frequency chirp, the acceleration spectra and fitting equations for the vibration dataset according to every accelerometer are presented in Figure 12. The sinusoidal motion provided a more consistent acceleration value at 0.5 Hz of excitation, regarding the three excitation frequencies mentioned before, to all accelerometers. Unlike the linear trend fitted for the previous frequency chirp analysis, the acceleration spectra of each accelerometer showed amplitude increments following an exponential pattern. Table 4 summarizes the acceleration ranges, coefficients of determination R\({}^{2}\) of fitting equations, and RMS error for the set of 0.25 cm displacement acceleration spectra. Figure 10: Railway bridge monitoring: (**a**) Location of measurement channel 1. (**b**) Base station of testing. For the 0.50 cm displacement frequency chirp, the acceleration spectra and fitting equations for the vibration dataset recorded by every accelerometer are presented in Figure 13. As occurred in the 0.25 cm displacement frequency chirp, the tendency of vibration data depicted for each type of acceleration spectrum fit an exponential pattern. The acceleration ranges, coefficients of determination R\({}^{2}\) of fitting equations, and RMS error for the set of 0.50 cm displacement acceleration spectra are shown in Table 5.  
Figure 11: Acceleration spectra for the 0.10 cm displacement frequency chirp: (**a**) Maximum acceleration spectrum from original sampling frequency. (**b**) Maximum acceleration spectrum from 100 Hz resampling frequency. (**c**) Acceleration spectrum for the mean of the highest 100 acceleration peaks from 100 Hz resampling frequency. Figure 12: Acceleration spectra for the 0.25 cm displacement frequency chirp: (**a**) Maximum acceleration spectrum from original sampling frequency. (**b**) Maximum acceleration spectrum from 100 Hz resampling frequency. (**c**) Acceleration spectrum from the mean of the highest 100 acceleration peaks from 100 Hz resampling frequency. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Acceleration Spectrum** & **Accelerometer** & \ \begin{tabular}{c} **Accelerations** \\ **Range (g)** \\ \end{tabular}  & \(\mathbf{R^{2}}\) & \begin{tabular}{c} **RMS** \\ **Error (g)** \\ \end{tabular}  \\ \hline Original sampling frequency & PCB L74 ADXL355 RBP4 ADXL3  
The acceleration spectra and fitting equations for the vibration dataset from the 0.75 cm displacement frequency chirp according to every accelerometer are presented in Figure 14. The acceleration spectra for every accelerometer suggested amplitude increments following an exponential pattern. Table 6 summarizes the acceleration ranges, coefficients of determination R\({}^{2}\) of fitting equations, and RMS error for the set of 0.75 cm displacement acceleration spectra.