## 4 On-Site Experiment and Analysis  
### Site Description and Data Acquisition  
The Fengbei Bridge is located at the junction of the West Fourth Ring Road and the Fengtai North Road in Beijing, China. As shown in Figure 6a, there is a road crossing under the bridge, and the GB-SAR instrument should be located on one side of the bridge as shown in Figure 6b. Inevitably, the different instantaneous vibrations of the equipment itself will be caused by passing vehicles with a different speed and weight on the road, which increases the noise in the obtained time-series displacement of the bridge. Therefore, to validate the accuracy of the improved SOBI signal de-noising method for time-series displacement obtained using GBSAR, the Fengbei Bridge was selected as an experimental bridge. In this study, an Imaging by Interferometric Survey (IBIS-S) instrument--a typical system based on microwave interferometry--was adopted to acquire an accurate dynamic time-series displacement of the bridge dynamic deflection. The IBIS-S instrument consists of a radar unit, a control personal computer, a power supply unit, and a tripod. In typical measurement conditions, the sampling rate is up to 200 Hz, the maximal detection distance is up to 1 km, the range resolution is up to 0.50 m, and the displacement measurement accuracy is up to 0.01 mm [38]. As shown in Figure 6, the IBIS-S instrument was located on one side of the bridge without passive radar reflectors attached to the bridge. The angle of the altitude of the radar unit was set to \(30^{\circ}\) so that the two antennas on the radar unit  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Signal Components**} & \multicolumn{3}{c}{**Correlation Coefficients**} \\ \cline{2-4}  & \(S_{1}(t)\) & \(S_{2}(t)\) & \(S_{3}(t)\) \\ \hline \(Y_{1}(t)\) & 0.9933 & \(-\)0.0173 & 0.0555 \\ \(Y_{2}(t)\) & 0.1155 & 0.9999 & \(-\)0.0133 \\ \(Y_{3}(t)\) & \(-\)0.0016 & 0.0003 & 0.9984 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Correlation coefficient between the separated signal and the source signal.  
Figure 5: Separated signals using the improved SOBI method. (**a**) Separated signal \(Y_{1}(t)\), (**b**) separated signal \(Y_{2}(t)\), and (**c**) separated signal \(Y_{3}(t)\).  
could be aligned to the mid-span point of the central span of the bridge. The range resolution was 0.5 m, the sampling frequency was 200 Hz, and the duration of data acquisition was 45 s.  
Figure 7a shows the obtained time-series displacement (X1, as shown in Figure 6a) of a mid-span point on the Fengbei Bridge. Due to the influences of the surrounding environment and the equipment itself, there was an inevitable increase in the noise information of the obtained time-series displacement. Therefore, to improve the accuracy of the obtained time-series displacement of the mid-span point on the Fengbei Bridge, using a similar noise as the time-series displacements from the mid-span point, two adjacent monitored points before and after the mid-span point were selected as another two observed signal point (X2 and X3, as shown in Figure 6a). This was done to develop signal de-noising for the mid-span point of the Fengbei Bridge using the improved SOBI method. The time-series displacements of the two adjacent monitored points are shown in Figure 7b,c. Obviously, there are some fluctuations in the curves of the obtained three time-series displacements. These were caused by the transient load of vehicles.  
Figure 6: The Fengbei Bridge and the IBIS-S instrument layout. (**a**) The Fengbei Bridge and (**b**) the dynamic deflection measurement of the Fengbei bridge using IBIS-S.  
Figure 7: Three time-series displacements of the mid-span point and two adjacent points. (**a**) Observed signal X1, (**b**) observed signal X2, and (**c**) observed signal X3.