# Spatial Data Analysis for Deformation Monitoring of Bridge Structures
## 4 The Liberty Bridge--A Case Study
### Deformation Analysis Using Ground-Based Radar Interferometry
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Monitored Point**} & \multicolumn{4}{c}{**Vertical Displacement [mm]**} \\ \cline{2-5}  & **No Load** & **Walking** & **Running** & **Jumping** \\ \hline P01 & 0.57 & 0.59 & 0.60 & 2.55 \\ P02 & 0.71 & 0.74 & 0.76 & 4.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum vertical displacements obtained by G-B radar. Figure 9: Range bin profile. epoch was executed when one person was jumping synchronously at the middle of the bridge's main span. The vibrations with a frequency of 1.82 Hz with minimum phase shift are caused purely by a person jumping. The identified frequency is close to the 22 nd vibration mode defined by FEM. To verify the results, measurements using accelerometers were also performed. Two HBM B12/200 one-axial accelerometers were installed at the measured points, P01 and P02. The accelerometers were levelled in a vertical position using Zeiss tribraches, as shown in Figure 10, to ensure the measurement of the acceleration in the vertical direction. The accelerometers used were inductive sensors with a relative error of up to \(\pm\)2%. The frequency of the data registration was 100 Hz, as in the case of G-B radar, and it was performed using a HBM Spider 8 A/D transducer and Catman Easy software. The relative displacements from the data measured were calculated by double integration. The drift of the accelerometers and the errors caused by the integration were minimized by a Butterworth high-pass filter with a cut-off frequency of 0.5 Hz. The reduction of the spectrum's magnitude by the filter (0.7% at 1 Hz) had no significant influence on the determined displacements. Table 3 shows the results of the measurements by the accelerometers. The values of the vertical displacements are very close to the displacements obtained by the G-B radar measurements in all four epochs of the experiment (Table 3). The maximum vertical displacements were indicated by one person jumping at the middle of the superstructure, with values of 2.34 mm (P01) and 4.82 mm (P02). In the 1 st measurement epoch (without any load), no significant frequencies were identified from the measured data (Table 4). During the epoch with one person walking, the structure's 22 nd and 44 th vibration modes with frequencies 2.05 Hz and 3.99 Hz were determined. The results of the 3 rd epoch (running person), 2.90 Hz and 4.59 Hz, correspond to the 23 rd and 59 th vibration modes and are in accordance with the results of the G-B radar measurements. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Vibration Mode**} & \multirow{2}{*}{**Modal Frequency [Hz]**} & \multicolumn{4}{c}{**Dominant Frequencies [Hz]**} \\ \cline{3-6}  & & **No Load** & **Walking** & **Running** & **Jumping** \\ \hline
2 nd & 1.63 & 1.53 & - & 1.53 & - \\
22 nd & 2.15 & - & 2.01 & - & 1.82 \\
23 rd & 2.49 & - & - & 2.97 & - \\
44 th & 3.76 & - & 3.71 & - & 3.51 \\
59 th & 4.69 & - & - & 4.56 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dominant frequencies of structural deformation identified by GB-radar. Figure 10: HBM B12/200 accelerometer at the middle (P02) of the bridge’s main span. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Monitored Point**} & \multicolumn{4}{c}{**Vertical Displacement [mm]**} \\ \cline{2-5}  & **No Load** & **Walking** & **Running** & **Jumping** \\ \hline P01 & 0.61 & 0.54 & 0.56 & 2.34 \\ P02 & 0.69 & 0.73 & 0.72 & 4.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum vertical displacements obtained by accelerometers.