## 4 Results of the Bridge Dynamic Responses
### Dynamic Vibration of the 192-m Span
This result was compared to the synchronized hydrostatic leveling measurements at the same position. We summarize below the main results:  
1. As far as the train-induced displacement procedures are considered, the radar and hydrostatic leveling results are quite consistent in the six different load cases;
2. The hydrostatic leveling results about the train-induced displacements miss the real peak in most instances. By contrast, the radar results provide a higher detail in the description of the displacement behavior. This is due to the higher sampling frequency (53.845 Hz) with respect to leveling sensor (1 Hz). This can help the engineers to capture the maximum value of the train-induced displacements of bridge;
3. The displacements occur as soon as the given train reaches the main bridge, and they decrease to the normal state as far as the loading disappears. This is evident by calculating the duration of the loading on the main bridge. For instance, in Case 1 the displacement lasts for about 25 s. Considering the velocity of the train (237.7 km/h), the main bridge length (1272 m) and the train length (400 m, 16 carriages of 25 m each), the total time for the train passing the bridge is about 25.3 s. The same result can be achieved for the metro, considering the 6 carriages of 20 m each, with a speed of about 80 km/h;  
Figure 8: Time series of the horizontal displacements. (**a**) Lateral displacement in the middle of the 192-m span; (**b**) longitudinal displacement and temperature at pier #8 from the existing structure health monitoring (SHM) system. 4. The temporal evolution of the displacements is related to the direction of the passing train. When the train arrives, small displacements are detected at the beginning; then they transmit like a sine wave, while the displacement amplitude becomes larger and larger; when the train leaves the bridge, the displacements disappear quickly. The behavior is symmetric for the trains coming from north to south (N2S) and from south to north (S2N);
5. The vertical displacements achieve the maximum value when the train is running on the measuring point. In all cases, the displacement magnitude is less than 12 mm;
6. The magnitude of vertical displacement, as well as the duration, does not significantly increase when two trains are running simultaneously on the bridge. This is in agreement with the structural characteristic of NDHRB, which is a rigid bridge. Bins corresponding to the bridge deck were analyzed to detect the main frequencies of the displacement measured by the radar. In Figure 10 we show the displacement retrieved for bin 83, bin 84 and 85. The power spectral density (PSD) calculated using the periodogram procedure with the Welch method [34], after filtering the time sample using a Butterworth bandpass filter of third order whose bandpass (0.3 Hz-3 Hz) is shown for bin 83 and bin 84 in Figure 11. The goal of using this filter is to emphasize the stationary response with respect to the pulse response due to the train passage. The entire sample was divided into two, partially overlapping, signals to also evaluate the stationarity of the acquisition. Observing Figure 11 we can clearly find out some peaks at frequencies close to that measured by the accelerometers (Figure 12), in which the data were filtered (0-20 Hz) in frequency domain. Table 3 report the main value compared to those from the accelerograms. Observing the values of table we can make some comments: The lowest (0.267 Hz) clearly appears only for bin 83, so we can discard it as a vibration not of the main structure of the bridge; The two set of data agree within less than 10% of error between the two techniques results, although radar results are noisier; According to the frequencies obtained by the radar, the main/similar frequencies of the bridge were recognized by the radar, hence the results are credible. Figure 9: Vertical displacement time histories in the middle of 192-m span monitored by IBIS-S (blue lines) and the hydrostatic leveling system (red triangles).