## 6 Interpretation of the Results and Discussion  
For a hypogeum pavilion, vertical modes are relatively more amplified than horizontal ones, especially in the presence of important slab spans. Consequently, the identification of horizontal modes can be affected by unfavorable levels of signal-to-noise ratio (SNR), with respect to the vertical ones. This resulted from a comparison between the normalized spectral entropy of vertical and horizontal channels data, which indicates how close is a spectrum to the Gaussian noise condition. For further details about the relation between entropy and SNR, one can refer to [30,31]. Furthermore, in [PERSON]'s pavilion, the roofing system is connected at the extrados by non-structural materials, including waterproofing layers. In particular, while the expansion joints between the blocks measure about 0.04 m, the blocks are connected by a thin concrete screed (approximately 0.05 m tick) to create continuity on the walking surface. It was precisely the uncertainty described above that prompted the authors to aid the identifications with the analytical model reported in Section 2. As said before, since the model admits only diaphragmatic degrees of freedom, to compare the experimental results with the model prediction, the horizontal components of the first horizontal mode (identified at 2.57 Hz) have been estimated with the least squares method, also to reduce spillover effects. If \(\mathbf{\Theta}_{id}\) denotes the identified eigenvector matrix, the equivalent diaphragmatic body mode components of the eigenvectors can be estimated with a linear transformation matrix \(\mathbf{\mathrm{D}}\) as \(\mathbf{\mathrm{\Theta}}_{D,id}=\mathbf{\mathrm{D}}\)\(\mathbf{\mathrm{\Theta}}_{id}\), where \(\mathbf{\mathrm{\Theta}}_{D,id}\) contains the diaphragmatic components, i.e., the two horizontal translations and the rotation about the vertical axis of each block, and \(\mathbf{\mathrm{D}}\) is the linear transformation matrix. In accordance with the theoretical model of Section 2, Figure 13 limits the representation to the horizontal components of the examined mode (undeformed configuration in dashed lines, with sensor positions). Figure 13: Identified mode shape #1 at 2.57 Hz (horizontal components). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Description** & **Mode Id.** & \
\begin{tabular}{c} **Natural** \\ **Frequency (Hz)** \\ \end{tabular} &
\begin{tabular}{c} **Damping** \\ **Ratio (\%)** \\ \end{tabular} \\ \hline Horizontal (with roof bending) mode & 1 & 2.57 & 2.11 \\ Mainly vertical mode & 2 & 2.73 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Identified modes of the entire pavilion. From a preliminary analysis of the first mode, the blocks are not appreciably affected by mutual interaction, this being indicative of the full effectiveness of the joints. In other words, the three blocks are likely to behave as fairly separated dynamic systems. This observation can be extended also to joints with relatively low nominal stiffnesses (see Figures 3-5). On the other hand, this uncoupled behavior is reflected in Figure 13.  
To shed light on the effectiveness of the joints, a numerical analysis was carried out on the nominal values of the model stiffnesses of the joints. The multiplier of the three stiffness components of each joint was varied between 0 and 1. In particular, with reference to Figure 10, two multipliers have been defined as \(k_{var,left}\) and \(k_{var,right}\), respectively. The Modal Assurance Criterion (MAC) [32] between the identified mode shape and the predicted ones was then calculated for each combination of the two multipliers.