# On Site Investigation and Health Monitoring of a Historic Tower in Mantua, Italy
## 5 Monitoring Results and Data Analysis
The estimate--shown in Figure 14 for modes B\({}_{1}\), B\({}_{2}\), and T\({}_{1}\)--is based on a normal kernel function, which was evaluated at 100 equally-spaced frequency bins covering the range of variation of each identified frequency. The probability density functions presented in Figure 14 refer to the six months before (from 17/12/2012 to 20/06/2013, solid line) and the six months after the earthquake (dashed line). The inspection of the plots reveals that the frequency distributions change after the seismic event and indicates that the identified frequencies slightly shift towards lower values after the earthquake;
2. The general decrease of the statistics of the natural frequencies (mean value, standard deviation, extreme values) summarized in Table 2 and, again, demonstrating the occurrence of abnormal structural changes induced by the seismic event. Figure 11: Mode B\({}_{1}\): (**a**) variation of the natural frequency between 01/06/2013 and 10/07/2013; and (**b**) change in the frequency-temperature correlation induced by the seismic event of 21/06/2013. Figure 12: Mode B\({}_{2}\): (**a**) variation of the natural frequency between 01/06/2013 and 10/07/2013; and (**b**) change in the frequency-temperature correlation induced by the seismic event of 21/06/2013. Based on the previous evidence, it can be stated that the limited number of accelerometers and temperature sensors installed in the tower and the automatic system identification allowed for the assessment of the effects of changing temperature on modal frequencies and to detect the occurrence of abnormal structural behavior under changing environment. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{\(f_{\text{mean}}\) (Hz)} & \multicolumn{2}{c}{\(\sigma_{f}\) (Hz)} & \multicolumn{2}{c}{\(f_{\text{min}}\) (Hz)} & \multicolumn{2}{c}{\(f_{\text{max}}\) (Hz)} \\ \cline{2-9}  & **Before** & **After** & **Before** & **After** & **Before** & **After** & **Before** & **After** \\ \hline
1 (B\({}_{1}\)) & 0.985 & 0.968 & 0.038 & 0.031 & 0.910 & 0.897 & 1.102 & 1.070 \\
2 (B\({}_{2}\)) & 1.024 & 1.012 & 0.032 & 0.025 & 0.961 & 0.953 & 1.148 & 1.110 \\
3 (B\({}_{3}\)) & 3.941 & 3.929 & 0.075 & 0.063 & 3.758 & 3.742 & 4.194 & 4.137 \\
4 (T\({}_{1}\)) & 4.754 & 4.727 & 0.077 & 0.066 & 4.621 & 4.600 & 5.010 & 4.982 \\
5 (L\({}_{1}\)) & 9.222 & 8.937 & 0.554 & 0.433 & 8.385 & 8.332 & 10.327 & 9.862 \\ \hline \hline \end{tabular} B = bending mode; T = torsion mode; L = local mode.  
\end{table} 
Table 2: Statistics of the modal frequencies identified before and after the seismic event of 21/06/2013. Figure 14: Probability density function of the natural frequency identified from 17/12/2012 to 20/06/2013 (solid line) and after 21/06/2013 (dashed line): (**a**) Mode B\({}_{1}\); (**b**) Mode B\({}_{2}\); and (**c**) Mode T\({}_{1}\). Figure 13: Mode T\({}_{1}\): (**a**) variation of the natural frequency between 01/06/2013 and 10/07/2013; and (**b**) change in the frequency-temperature correlation induced by the seismic event of 21/06/2013.