# Spatial Data Analysis for Deformation Monitoring of Bridge Structures
## 4 The Liberty Bridge--A Case Study
### Deformation Analysis Lsign Terrestrial Laser Scanning  
Monitoring using TLS was executed in three epochs of measurement using a Leica ScanStation2 instrument. The surface of the bottom of the main suspended bridge section was scanned from a single instrument's position. The instrument was set up on the longitudinal axis of the structure on the Slovakian riverbank to ensure that the whole structure's rear section could be scanned (Figure 6). The minimum density of the scanned points on the structure was 3 mm. The next two epochs of the measurements were performed using the same Leica ScanStation2 with approximately the same conditions as in the first (initial) epoch.  
Figure 4: Spectral analysis of data: (**a**) displacements of the chosen parts of the monitored structure; (**b**) average normalized spectral density (ANSPD) of the entire structure’s dynamics.  
Figure 5: The Liberty Bridge: (**a**) suspended structure; (**b**) inundation bridge.  
The reference point network consisted of four control points (VB1-VB4), realized by Leica HDS type targets. Two of the reference points were the points of the reference network established for the construction of the bridge, stabilized with concrete pillars. Due to the vegetation and the fact that the whole structure is situated in a protected area of floodplain forest, where cutting out the vegetation (for lines of sight) is not allowed, two of the reference points were stabilized by metallic fasteners on the base of the pillars.  
The scanned data was transformed to a local coordinate system, which was defined for the bridge for the purpose of geodetic monitoring with a local horizon. The reference points defined the coordinate system in each measurement epoch. The aim of the data processing was the identification and quantification of the bridge's main section in discrete points positioned on the bottom of the bridge structure. The vertical displacements were determined using the geometry-based approach of deformation analysis described in Section 2.1. During the data processing, square fences of 75 mm \(\times\) 75 mm were defined around the fixed position of the monitored points (these created fencing boxes for the pre-segmentation of the points in each epoch). The monitored points were situated on the bottom of the transverse girders between the diagonal reinforcements of the supporting girders on both sides of the bridge; there were 23 points on each side (left and right), giving 46 in total.  
The deformation analysis shows the changed position of every monitored point, except for the points on the ends of the bridge (Figure 7). The bridge is anchored to the pillars on both ends, which means there is no displacement is these parts. The standard deviation of the displacements, calculated using the uncertainty propagation law, varied from 1.3 mm to 1.8 mm. The vertical displacements increasing from the ends to the center of the bridge where reach negative values at the level of -13 mm (left side) and -10 mm (right side). The displacements were caused by the structure's temperature difference between the monitoring epochs and by the weight of the layer of fallen snow (approx. 100 mm).  
Figure 6: Position of the laser scanner and the reference points.