## 3 Results
### Entropy-Energy Representation  
The representations of mean velocity and entropy-energy data are basically complementary, that is, they provide different information, which are correlated. The entropy of a signal coming from a structural system defines its propensity to follow a deterministic behavior. That is to say, a lower entropy corresponds to a higher deterministic behavior. An output signal can change its characteristics due to: (i) system properties changes, and (ii) variation of input source. The interest here is only to input independent features; thus, what matters is how the entropy changes in relation to its energy value. This allows for discarding input-related variations, which are not of interest for SHM. When the entropy changes its value (in relation to its energy level) this means that the system changes its internal correlation (since entropy is used to estimate system complexity). Importantly, this can also happen if the mean velocities of the points remain constant; however, the  
Figure 4: Map showing the dispersion of the average annual velocity along the LOS in the period from 2014 to 2016.  
opposite is not true, since an increase in the mean velocity would lead to higher energy and thus lower entropy. Thus, the mean velocity cannot change if the entropy-energy level remains constant. Therefore, the energy-entropy representation implicitly carries more information than the mean velocity. The mean velocity is only representative of the displacement trend over time. Instead, any variation in the trend, frequency content, amplitude and phase is reflected in the entropy-energy representation. An example is when a signal with zero mean increases its amplitude (e.g., due to a loss of stiffness). In this case, the mean velocity, being unchanged, would not allow for any novelty (thus, damage) detection. On the contrary, an increase in amplitude with constant mean velocity would lead to a change in entropy-energy values, and thus to a potential change of the complexity of the system. The mean velocity, however, is still an important datum to monitor because its straightforward physical meaning is connected to the rate of displacement in time (e.g., subsidence or swelling of the soil). While it is true that entropy-energy representations cannot be adopted for the description of a whole urban area if the systems falling in the area are too different from a structural point of view, in the paper, the entropy-energy representation is used to study individual buildings. From the point scatter regression and probability distribution, it was possible to derive the limit curves (threshold 0.3% and 99.7%, according to the 3-sigma rule) and use them for the identification of outliers, i.e., points at which the signal deviates from the global analytical model and therefore requires further investigation. In order to quantify this deviation, the use of the Mahalanobis distance has been adopted. The points at which the entropy displays a low distance from the mean model can be interpreted as less stochastic (more deterministic). Conversely, if the entropy has a higher distance from the model, it indicates a less deterministic point. The following results refer to the building complex at the intersection of Via Emanuele Filiberto and Via Castrense (Figure 6), adjacent to San Giovanni's station, in the period from 2017 to 2019. It has been analyzed as, according to the velocity, this area presents a concentration of points that are outside the subsidence threshold shown in Figure 5.  
Figure 5: Map showing the points with velocity outside the imposed lower threshold, with respect to the subway route and the proximity boundaries. Figure 7 shows the dispersion of points and the mean model, which has a quadratic trend on a logarithmic scale. It also shows the analytical model's probability distribution function (PDF) and allows the evaluation of the outliers.