## 3 Bridge and Monitoring System Descriptions
The dominant frequency of both signals was the same (2.88 Hz); thus, the wavelet filter was directly applied to estimate the dynamic strain of the bridge. Figure 7, also, shows that the dynamic strain did not contain any semi-static responses with one filter applied in this case. Accordingly, the double filters were sufficient for this kind of bridges to extract the dynamic behavior from strain measurements. Furthermore, the relationship between the semi-static behaviors of the strain and displacement measurements are shown in Figure 8a; where the second polynomial fitting model (\(D=5.69\times 10^{-4}\times S^{2}-0.133\times S+0.31\times 10^{-2}\)) was able to demonstrate the relation between these responses. The linear polynomial fitting (\(A=4.5\times 10^{-3}\times S-7.57\times 10^{-5}\)) represents well the relationship between the dynamic responses collected and extracted from the acceleration and strain measurements (Figure 8b). Therefore, the second and first degrees of polynomial models were used to estimate the displacement and acceleration performances of the bridge from strain observation, respectively. The two polynomial models were used to convert the semi-static strain and extracted dynamic responses to displacement and acceleration, respectively. Therefore, after eliminating the noises of the semi-static and dynamic strain measurements, the two models were applied to predict or extract the bridge responses. Figure 6: Measurements and filtration under 20 km/h (**a**) strain, (**b**) displacement and (**c**) acceleration. Then, the two models were evaluated using the strain, displacement and accelerometer measurements of the sensors under 20 km/h truck speed. The prediction values were assessed to estimate the accuracy of the developed models during the design stage. The predicted displacement and acceleration responses of the bridge were evaluated (Figure 9). The R\({}^{2}\) of the displacement and acceleration models were 0.99 and 0.95, respectively. The RMSE values of the models' displacement and acceleration errors were 0.029 mm and 0.0042 g, respectively. In addition, the MAE values of the models' displacement and acceleration errors were 0.024 mm and 0.0024 g, respectively. From these results, it can be concluded that the performance of two models was accurate and thus could be used to predict the displacement and acceleration of the bridge. Moreover, to check the performance of the two models, the strain sensors' measurements for the same point under different conditions were evaluated as well. Figure 8: Scatterplot of (**a**) the semi-static strain and displacement and (**b**) the acceleration and dynamic strain. Figure 7: Acceleration and dynamic strains measurements. For the frequency domain evaluation and estimation, the FFT, Hilbert transform and autocorrelation function methods were used to extract the dynamic characteristics (frequency and damping ratio) of the bridge from the acceleration and dynamic strain measurements. Figure 10 demonstrates the dynamic response of the bridge with 20 km/h truck using strain and acceleration measurements. The time series of the frequency during the measurement time is shown in Figure 10a. As shown in the figure, the performance of the two sensors was almost similar (the mean frequency calculation for acceleration and dynamic strain was 3.54 and 3.69 Hz, respectively). Moreover, the frequency phase was highly correlated with the constant shift (Figure 10b). These results indicate that the frequency contents during the measurement time could be accurately detected using strain observations. The fundamental frequency of the bridge is shown in Figure 10c, and the results suggest that the dominant frequency of the bridge was 2.88 Hz for both the acceleration and dynamic strain measurements. Finally, the autocorrelation function (AF) was used to estimate the damping ratio (Figure 10d), which showed a high correlation of 0.95. In addition, the calculated damping ratio was 0.32, and 0.37 of the dynamic strain and acceleration measurements, respectively.