# Perspectives on the Structural Health Monitoring of Bridges by Synthetic Aperture Radar
## 3 Analyses of Structural Integrity of Bridges from SAR
### Study Case 1  
\"Ponte dell'Industria\", originally known as \"Ponte S. Paolo\", has been built in between 1862 and 1863 to connect several railway lines to Rome new central railway station called \"Termini\". The bridge, consists of iron and cast iron arches resting on pylons made of cast iron pipes filled with concrete and is higher in the central part to allow steamships and armed ships to freely pass underneath. However, nowadays the bridge is an important junction of the city traffic and therefore it represents a good testbed for SAR monitoring. In Figure 4a the vibration map of the bridge is shown (SLC and ROI stand for Single Look Complex and Region Of Interest). The map is computed at a fixed frequency of about 10 Hz, with right-ascending observation geometry. Our method provides the spectral analysis in terms of vibrations assumed by the material bodies observed. According to the sampling theorem, spectral observation occurs in the frequency range from a few Hz to the physical limit of half the Doppler frequency, used to synthesise the SAR image at full spatial resolution in azimuth. So the results on a given bridge are given by a tensor where each plane represents the observation space for each frequency. In this case we have chosen only one plane with a frequency equal to 10 Hz. Figure 4b shows the same observation area but using the opposite \"right-descending\" geometry. It should be noted that the distortion of the observation geometry, which varies from a \"right-ascending\" to a \"right-descending\" configuration, does not entail any particular distortion and/or limitation to the analysis. Particularly, the points 1, 2 and 3, shown in both figures, represent three singularities on which high vibration energy is observed. The observed bridges have been also observed through optical images. This is done to find a clue that corresponds to the vibrational behavior observed through the proposed method. Precisely, at each anomalous vibrations position corresponds to a dilation joint that is used to allow an adequate thermal expansion of the road surface constituting the deck of the bridge. The comparison with optical images can be performed considering Figure 5 where the expansion joint 1, corresponding to the vibration singularity 1 of Figure 4, is visible in Figure 5a. The expansion joints 2 and 3, corresponding to the vibration singularities 2 and 3 in Figure 4 are shown in Figure 5b,c, respectively. Thus, the analysis of this first case study allows us to detect the position of all thermal expansion joints in the bridge. This is of fundamental importance because a joint, even if artificial, is built as a real crack (a joint) between two road sections constituting the deck of the bridge. Therefore, we deduce that this technique could be able to detect or, at least, provide a clue for possible cracks and lesions, not specifically designed to discharge the thermal energy of the infrastructure. Figure 4: Vibration maps on SLC image ROI in magnitude: (**a**) Right ascending, (**b**) Right descending. Figure 6 represents the trend over time of the oscillations related to point 1 of Figure 4. Observing this trend, it can be noticed that this point has persistent components at low frequencies and others less marked at higher frequencies. The results of the spectral analysis are shown in Figure 7. Figure 7a shows the overall spectrum, represented on the linear scale. Figure 7b represents a detail of the spectrum corresponding to low frequencies (inside the red box 1 shown in subfigure Figure 7a). The spectral mode 1 presents a maximum in oscillations at about 7 Hz in frequency, while mode 2 is anchored at about 21 Hz and mode number 3 and 4 are standing on about 28 Hz and 35 Hz, respectively. Finally, Figure 7c represents the total spectrum in the logarithmic scale where it is possible to notice an average attenuation level of the low-pass characteristic at near \(-50\) dB.