## 3 Results
### Comparison of the Two Representations
The comparison between the two periods is subsequently carried out by observing the variation in the parameters governing the fitting curves. A rational function of the second degree (Equation (2)) is used to fit the entropy-velocity dispersion (\(S\)-\(v\)) shown in Figures 11a and 12a, and a nonlinear regression model is used, starting from null initial parameters. Thus, the mean model of the dispersion of the points is obtained. Subsequently, the regression model of the deviations from the mean model is studied, using the same type of equation:  
\[S=p_{1}\frac{p_{2}v^{2}+1}{p_{3}v^{2}+1} \tag{2}\]  
It can be observed that Equation (2) is symmetrical with respect to the axis (\(v=0\)). This condition derives from the intention to study the structural response in the range of  
Figure 12: Correlation between LOS velocity and entropy-energy dispersion in the period from 2015 to 2019 for a building complex near San Giovanni station: (**a**) Entropy-velocity dispersion; (**b**) Energy-velocity dispersion. Figure 13: Entropy-energy dispersion, mean model and thresholds for a building complex near San Giovanni station: (**a**) period from 2011 to 2015; (**b**) period from 2015 to 2019.  
small displacements, for which the structure is deemed to exhibit linear elastic behavior. In addition, it is assumed that the effect of settlements is also linear. The first parameter of the mean model, which represents the value of the curve for null velocity, is subjected to a slight reduction, which is related to a global decrease in the system entropy in the second period. Instead, the ratio between \(p_{2}\) and \(p_{3}\) represents the limit value assumed by the function for high speed (in absolute value), normalized with respect to the \(p_{1}\) value. In addition, an increase in the values of \(p_{2}\) and \(p_{3}\), while maintaining the same ratio, corresponds to a reduction in the amplitude of the curve with respect to the vertical axis, as the inflection points tend to be closer to the axis (\(v=0\)). It occurs for the entropy in the second period, as shown by Figure 14a, where the two parameters increase, making the curve narrower with respect to the origin, so it tends toward the horizontal asymptotes more rapidly. For the system's variance (Figure 14b), the three parameters decrease from the first period to the second, reducing variance, especially for high velocity modules. It is worth noting that the parameters fitting guarantees positive variance. Figure 15 shows the parameters derived from a nonlinear regression model to construct the mean and standard deviation fittings of the energy-velocity (\(E\)-\(v\)) dispersion. A second-order polynomial model is used for the evaluation of the mean curve and the standard deviation, as a parabolic shape can easily be identified in the dispersion, especially in Figure 12b. As previously stated, the curves follow the hypothesis of linear elastic behavior; therefore, the vertices of the parabolic curves are fixed on the axis (\(v=0\)). The two average curves are similar, but higher energy values are reached in the second period at the same velocities. This effect is represented by the increase in the second parameter of the mean curve in Figure 15a. As shown by the second parameter in Figure 15b, there is a significant reduction in the standard deviation between the first and second periods for higher velocity values in modulus. Figure 14: Fitting parameters of the entropy-velocity dispersions in the two periods for a building complex near San Giovanni station: (**a**) parameters of the mean model; (**b**) parameters of the standard deviation model. Figure 16 represents the parameters used to construct the mean and standard deviation model of the entropy-energy (\(S\)-\(E\)) dispersion. These parameters are evaluated using a nonlinear constrained minimization, where \(p_{1}\) must be positive.