## 3 Bridge and Monitoring System Descriptions
The accuracy of the designed model when estimating the damping ratio was 86.5%. The results show that the developed model could be used to accurately detect the bridge responses in both the time and frequency domains. Figure 10: Cont. Figure 9: Models prediction in the time domain: (**a**) semi-static displacement and (**b**) dynamic acceleration. To estimate and check the designed model, the displacement and acceleration values of the bridge were predicted, and the identification models were assessed using the truck speeds of 30, 40 and 50 km/h for the same monitoring point (testing stage). The strain measurements were used to estimate the semi-static displacement and dynamic acceleration using the developed model. Figures 11 and 12 show the performance of the designed models in the time and frequency domains, respectively, for truck A with a speed of 40 km/h. In this stage, the strain measurements were used only to estimate the semi-static and acceleration; then, the displacement and acceleration measurements were compared with the predicted values. Figure 11 presents the observed and predicted values for the semi-static and acceleration of the bridge. The evaluation of the displacement shows that the R\({}^{2}\), RMSE and MAE were 0.98, 0.066 mm and 0.054 mm, respectively. Moreover, the R\({}^{2}\), RMSE and MAE of the acceleration model were 0.87, 0.0036 g and 0.0018 g. These results show a high correlation between the observed and the predicted values, which means a high accuracy in estimating the bridge's responses in the time domain. Figure 11: Prediction values in the time domain of the testing stage for a truck speed of 40 km/h; (**a**) semi-static and (**b**) acceleration. Figure 10: Frequency domain evaluation of (**a**) time–frequency, (**b**) time–phase, (**c**) fast Fourier transformation (FFT), (**d**) autocorrelation and damping ratio of the dynamic strain and acceleration. The dominant frequency and damping ratio were calculated and presented for the testing stage (Figure 12). The dominant frequency with 40 km/h truck speed was identical (2.86 Hz) to the dynamic strain and acceleration measurements. In addition, the damping ratios were 0.79 and 0.59 for the strain and acceleration measurements, respectively. This indicates an accurate performance of the model in assessing this kind of bridge in the frequency domain. Accordingly, the model can be used with strain measurements only to estimate the future behavior of the bridge, thereby leading to a decrease of the monitoring system cost. Table 3 summarizes the load cases, including the maximum semi-static absolute displacement and acceleration and the dominant frequency and damping ratio. From Table 3, it can be seen that the variation between the observed and estimated semi-static displacements was very small (maximum variation was 0.07 mm), which means very high model accuracy (99%). Meanwhile, the maximum change of acceleration was 0.02 g (accuracy was 72.6%), indicating that the model accuracy in the time domain was acceptable and could be used to assess the bridge behavior under different kinds of dynamic loads. On the other hand, the dominant frequency estimations for both observed and predicted accelerations were equal. The maximum damping ratio variation change was 0.24 (with accuracy 69%). Therefore, the developed model could be used to precisely estimate the semi-static displacement and frequency with acceptable dynamic acceleration and damping ratio changes using a low-cost monitoring system. On the other hand, the model was tested to check its capacity to estimate the displacements of other points not considered in the design stage. In this part, the displacements of girders G1 to G5 were evaluated. Table 4 shows the maximum absolute values of the extracted and the observed semi-static displacements of the girders under the speeds of 20, 30, 40 and 50 km/h.