# On Site Investigation and Health Monitoring of a Historic Tower in Mantua, Italy
## 5 Monitoring Results and Data Analysis
### Damage Detection under Changing Environment  
As stated in Section 4.2, the temperature effects on the natural frequency of each global mode have been described by means of DR models, with the outdoor temperature measured on the S-W front as its only input. Based on the classic loss function (LF) and the final prediction error (FPE) criteria [23], regression models depending on the current and 13 previous hourly-averaged values (\(p-1=13\)) of the external temperature have been established. As the main goal was to mitigate the environmental effects in order to verify if the structural changes induced by the earthquake of 21/06/2013 are still detected, the models were trained over the six months preceding that seismic event (from 17/12/2012 to 16/06/2013), where the process is supposed to be in control. The dynamic regression models were subsequently used to predict the natural frequencies after the training period and to detect the changes in the structural behavior. The relevant results--in terms of cleaned natural frequencies of modes B\({}_{1}\), B\({}_{2}\) and T\({}_{1}\)--are presented in Figure 15 with the confidence limits at plus and minus three times the standard deviation of the frequency estimated obtained over the training period. Figure 15: Change in the cleaned natural frequency (Dynamic Regression model) induced by the seismic event of 21/06/2013: (**a**) Mode B\({}_{1}\); (**b**) Mode B\({}_{2}\); and (**c**) Mode T\({}_{1}\). It is worth noting that the representation in Figure 15 is centered on the earthquake date (21/06/2013), in order to better highlight the different trends before and after the seismic event. The inspection of the cleaned modal frequencies (Figure 15) allows the following comments:  
1. the natural frequencies still exhibit some correlation, meaning that they are still affected by common factors;
2. before the seismic events, each frequency oscillates around its mean value and stays within the confidence interval; and
3. a sudden drop is detected corresponding to the earthquake, along with a clear variation of the previous trend. More specifically, in the months after 21/06/2013, the mean value of the cleaned natural frequency changes and the confidence interval, estimated in the training period, is exceeded. Therefore, the correction of the natural frequencies provided by the adopted regression model still indicates that non-reversible structural changes took place after the Garfagnana earthquake. The DR models, so far discussed, allowed for partially modeling the thermal effects on the natural frequencies of the investigated tower. On one hand, the DR relationship proved to be effective in reproducing the fluctuations of the experimental frequencies due to the daily effect of temperature and in distinguishing the slight damage induced by the Garfagnana earthquake (Figure 15). On the other hand, the model could not as accurately predict the long-term oscillations due to the influence of the average temperature (conceivably combined with the effects of other unobserved factors). In order to improve the prediction, ARX models have been developed. ARX models assume the value \(f_{k}\) of the natural frequency at time \(k\) to be affected by outdoor temperatures at the same time \(k\) and at previous time instants, as well as by previous experimental estimates of the input. In particular, the use of past values of the output is expected to indirectly take into account the effects of unmeasured factors that cannot be modeled otherwise (e.g., wind, humidity, _etc._) leading, in principle, to more accurate predictions. Since several models can be fitted to the experimental data, depending on the amount of previous time instants considered for the input and the output, a comparative study of the performances has been carried out by using the same LF and FPE criteria [23] adopted for establishing the DR models.