# Spatial Data Analysis for Deformation Monitoring of Bridge Structures
## 4 The Liberty Bridge--A Case Study
### Deformation Analysis Using Ground-Based Radar Interferometry  
The dynamic measurements were performed during different types of structural load, which were proposed based on the finite element method (FEM) model of the bridge using the structure's technical documentation [29]. Four loading epochs were defined as follows: 1 st--without loading; 2 nd--one person walking; 3 rd--one person running; 4 th--one person jumping in the middle of the bridge's span. Each epoch was performed in three phases. The first phase was the no load state (but the data was recorded). The second phase represented the load (4 types) and the last phase was again the no load state with the aim of determining the structure's damping. The individual loading epochs each took approximately 60 s.  
The main suspended bridge section was measured from a single position of the interferometric radar IDS IBIS-S (Figure 8). Because the FEM model of the structure assumed significant frequencies of the structure's vibration on the level of 10 Hz, the data was registered with a frequency of 100 Hz to ensure higher relevance of the results (relative displacements), although it is sufficient to measure with a frequency that is twice as high as the accepted frequencies for their proper identification. Despite the fact that the G-B radar measurement allows monitoring of the entire structure, the measurement and data processing was focused specifically on two points of the structure. The first point was at the center of the suspended structure and the second one was positioned at the anchorage of the suspension cable. Figure 8: Position of the ground-based radar. Figure 7: Vertical displacement of the monitored points obtained by terrestrial laser scanning (TLS). The data analysis was realized in several steps, and its aim was the determination of the amplitude and the frequency of the vibration of the structure's selected parts. The processing was arranged into following steps:  
1. Radial displacements' transformation to vertical;
2. Identification of the monitored parts (P01, P02);
3. Modal analysis. The displacements were transformed from the radial to the vertical direction on the basis of the position and orientation of the radar in relation to the structure being monitored. This geometry was obtained from the laser scanning data. The second step was the identification of the peaks of the signal that corresponded to the chosen monitored parts of the structure from the range bin profile (Figure 9). The figure shows the estimated signal to ratio (SNR) of the signal's reflection, depending on the structure's range. The last step was the determination of the relative displacements, auto-spectral analysis of the radar data using the approaches described in the chapter 3.1, and the comparison of the results with the FEM model of the structure. The vertical displacements are affected by a only very small extent by the pedestrian walking (Table 1). The fast movement (running) of the pedestrian has almost the same effect on the maximum vertical displacements as that of the walking pedestrian. One person jumping in the center of the span results in the maximum vertical displacement, with values of 2.55 mm (P01) and 4.63 mm (P02). During the measurement epoch without any load on the structure, a frequency of deformation at the level of 1.53 Hz was determined (Table 2). Signals from both monitored points were of low coherence with a relatively high phase delay of around 65.0\({}^{\circ}\). The dominant frequency of vibration determined during the epoch with one person walking corresponds to the structure's 22 nd vibration mode (from the FEM model). The estimated 2.01 Hz corresponds to the frequency of steps of standard walking. A phase shift of 23.0\({}^{\circ}\) is caused by a short delay in the structure's response at points P01 and P02. The 3 rd loading epoch shows the vibration of the structure caused by the running person to be in the range of 1.53-4.56 Hz, which corresponds to the 2 nd, 23 rd, and 59 th vibration modes. The 4 th load