# Spatial Data Analysis for Deformation Monitoring of Bridge Structures
## 3 Structural Health Monitoring Using Ground-Based Radar  
Ground-based radar interferometry is an innovative and rapidly evolving technique for the dynamic deformation analysis of engineering structures, even those of large investments such as dams and bridge structures [23; 24; 25]. The radar measurements use the stepped frequency continuous wave (SF-CW) approach in microwave bandwidth [26]. This approach allows determination of the monitored object's displacements in the radar's field of view in a radial direction (from the instrument to the object). The measurement is based on the transmission of a set of pulses created by a beam of frequency modulated electromagnetic signals (waves). To get radial resolution (range resolution), the instrument emits short pulses of beams. The relationship between the pulse duration and the radial resolution is defined by the formula:  
\[\Delta r=\frac{c\cdot\tau}{2} \tag{5}\]  
where \(c\) is the light's speed in vacuum (empty space) and \(\tau\) is the time of flight (ToF) of the measuring signal. The frequency response is then determined by comparison of the emitted and received signal. By the application of inverse Fourier transformation (IFT), this response can be transformed from the frequency domain to the time domain. After this procedure, the radar creates a so-called range bin profile, which is a one-dimensional (1D) image representing the signal to noise ratio (SNR) at individual radial distances from the instrument (Figure 2). In this range bin profile, the peaks of the reflected signal are detected. Each peak represents an average reflection from the whole range resolution area, e.g., when the range resolution is 0.5 m then the corresponding signal peak represents the average reflection from the parts of the structure monitored, which is in this 0.5 m range interval (radial resolution area).  
After the range bin profile is created and the targets are identified, the changes in the position of the monitored parts are determined by differential interferometry (DI). The DI determines the radial displacements by comparison of the phase shift of the emitted and received measuring signal on the base of the formula:  
\[d_{p}=\frac{\lambda}{4\cdot\pi}.(\varphi_{2}-\varphi_{1}) \tag{6}\]  
Figure 2: Principle of the targets’ identification in the radial direction.  
where \(\lambda\) is the wavelength of the signal and \(\varphi_{1}\) and \(\varphi_{2}\) are the phase shifts of the signal in first and subsequent epoch.  
As the basic principle of the radar interferometry indicates, the displacements of the monitored structure are determined in the radial direction (from the instrument to the structure being monitored). In practice, it is almost impossible to ensure the direct deformation monitoring in a required direction, e.g., vertical or horizontal. The solution can be the transformation of the displacement from the radial direction to the required one based on the known geometry of the measurements (relationship between the instrument and the object monitored); e.g., the transformation to the vertical direction is illustrated in Figure 3.