## 3 Materials and Methods
The background noise, in fact, can be generated in different sources and external conditions. The causes of the noises can be mechanical, electromagnetic, or generated by human action or environmental conditions. Generally, there is a tendency to maintain a low threshold level in order to avoid in the cutting of a large amount of significant data. In this way, it will be possible to subsequently filter the data during the post-processing phase. On the other hand, the preset thresholds for the acquisition must be high enough to avoid saturation of the acquisition memories due to the effect of repetitive signals and due to the background noise. The threshold methods used in the various cases were implemented in the software of the device used and reported by the authors in recent publications [20]. The AE equipment automatically performs different kinds of analyses. The first parameter is represented by the cumulative number of AE signals \(N\), detected during the monitoring time. In addition, the time dependence of the structural damage observed during the monitoring period, identified by parameter \(\eta\), can also be correlated to the rate of propagation of the micro-cracks. If we express the ratio of the cumulative number of AE counts recorded during the monitoring process, \(N\), to the number obtained at the end of the observation period, \(N_{d}\), as a function of time, \(t\), we get the damage versus time dependence [6; 7; 8; 9; 10; 24; 25; 26]:  
\[\eta=\frac{E}{E_{d}}=\frac{N}{N_{d}}=\left(\frac{t}{t_{d}}\right)^{\beta_{t}} \tag{3}\]  
where \(E\) and \(E_{d}\) represented the energy dissipation during micro-crack propagation in general and with respect to the monitoring time. By working out the \(\beta_{t}\) exponent from the data obtained during the observation period, we can make a prediction regarding the structural stability conditions. Damage assessment in the structure may be also investigated by the statistical distribution of the AE signal magnitudes fitted by the Gutenberg-Richter (GR) law. The \(b\)-value is usually computed  
Figure 7: AE signal and AE results of the tower: (**a**) Typical received signal in the time domain during the acoustic emission (AE) monitoring. The AE equipment used in the present paper allow to set the appropriate threshold value due to the monitored structure and the environmental conditions. (**b**) Cumulative number of AE and AE count per day during the monitoring time. (**c**) \(b\)-value diagram representing the evolution of the damage, \(\beta_{\mathrm{t}}\) trend evolution during time. using the cumulative frequency magnitude distribution data and applying the GR law. By analogy with seismic phenomena, in the AE technique, the magnitude may be defined as follows [17]:  
\[m=Log_{10}A_{\text{ max}}+f(r), \tag{4}\]  
where \(A_{max}\) is the amplitude of the signal expressed in \(\mu\)V and \(f(r)\) is a correction coefficient whereby the signal amplitude is taken to be a decreasing function of the distance \(r\) between the source and the AE sensor. According to [PERSON]'s empirical law [17],  
\[Log_{10}n(\geq m)=a-bm \tag{5}\]  
that can be re-written as:  
\[n(\geq m)=10\ ^{a-bm}, \tag{6}\]  
where \(n\) is the cumulative number of earthquakes (AE events) with magnitude \(\geq m\) in a given area and a within specific time range, whilst \(a\) and \(b\) are positive constants varying from a region to another and from a time interval to another. The damage evolution in the masonry structure of the tower is described by the evaluation of the cumulative number of AE and by different parameters able to predict the time dependence of damage, including the \(b\)-value [6; 7; 8; 9; 10; 13; 14]. In particular, since environmental disturbances have been minimized and instrumental noises have been filtered out, the \(b\)-value analysis showed a downward trend to values compatible with the growth of localized macro-cracks in the south side of the tower.