# Interpretation of Bridge Health Monitoring Data from Satellite InSAR Technology
## 4 Results and Discussion
### Correlation between Displacements and Temperature Variations
Marking the negative peaks of the correlation (see the black dashed lines in Figure 16), we can notice that they correspond  
Figure 14: Linear correlation between air temperature variation and displacement time series of PSs identified on (**a**) the A22 Po River Bridge and (**b**) the portion of the bridge in the floodplain. Magenta arrows highlight the yellow–red coloured PS groups. Figure 15: Scatterplots of the variables _Displacements_ (\(d_{\text{LoS}}\)) and _Temperature_ with the least-squares reference line (magenta line) and correlation coefficient (\(\rho\)) for PS 4894, PS 4970, PS 5857, PS 5885.  
to the right (northern) joint of the suspended span--the one with monodirectional and multidirectional bearing (thus, roller supports). To confirm the periodicity in the correlation variation along the bridge length observed in Figures 14 and 16, we fitted the three PS lines highlighted in Figure 16 with the sine function \(A\cdot\sin(\omega\cdot x+\varphi)\), where \(A\), \(\omega\), and \(\varphi\) are free parameters, and \(x\) is the longitudinal coordinate along the bridge. The estimated parameters are reported in Table 2, along with the estimated periodicity \(T=2\pi/\omega\). The estimated periodicity results between 72.72 m and 73.15 m, almost equal to the spacing of the spans (72.80 m, see Figure 3), and thus the distance between two consecutive roller supports. This result is in line with the expected longitudinal response of the bridge deck to temperature variation: the longitudinal displacements are zero over the piers and increase along the cantilevers until the joints as we move away from the piers; the suspended spans move longitudinally in the direction of the cantilever which supports it with fixed bearings. The possibility of noticing it with such clarity from satellite measurements is quite sensational. Let us discuss more in-depth why we can observe such periodic correlation. As shown in Figure 17a, the correlation is negative in the northern portion of the pier as the longitudinal displacements have an opposite sign to the temperature variation. Conversely, the correlation is positive in the southern portion of the pier as displacements and temperature variations share the same sign. Figure 17b illustrates this result with the correlations obtained for the A22 Po River Bridge. This result allows us to conclude that, for the A22 \begin{table}
\begin{tabular}{c c c c c} \hline
**PS Line** & \(A\) [\(-\)] & \(\omega\) [1/m] & \(\varphi\) [\(-\)] & \(T\) [m] \\ \hline PS Line 1 & 0.385 & 0.0859 & 30.2 & 73.15 \\ PS Line 2 & 0.435 & 0.0862 & 30.2 & 72.89 \\ PS Line 3 & 0.476 & 0.0864 & 30.2 & 72.72 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters \(A\), \(\omega\), \(\varphi\) estimated by fitting the sine function \(A\cdot\sin(\omega\cdot x+\varphi)\) to the correlation variation along the PS lines highlighted in Figure 16; \(x\) is the longitudinal coordinate along the bridge; \(T\) is the estimated period \(T=2\pi/\omega\). Figure 16: Linear correlation between PS displacement time series and temperature variation plotted against the length of the bridge. PSs are divided into three lines. Po River Bridge, the horizontal longitudinal displacements in response to temperature variation can be clearly observed with satellite InSAR-based SHM. Moreover, and most importantly, it is possible to identify different spans of the bridge simply by studying the sign of the correlation between displacement and temperature variation and its periodicity along the length of the bridge. This finding is quite important in view of using this type of monitoring to detect anomalous bridge behaviour on a large scale automatically. Regarding displacements in the riverbed, a certain periodicity in the colours of the PSs is maintained, suggesting that the observations made for the floodplain portion can be extended, even though in a purely qualitative manner, to the riverbed portion.