## 3 Experimental Validation
### Analysis  
Figure 12 shows the distribution of all data points (original and synthetic) in the three-dimensional latent space for all the sensors and all the analyzed loading stages (test codes 1 to 11 in Table 1). The clusterability of the latent representations for the different loading stages is evident, allowing for the distinction of intra-class similarities and inter-class dissimilarities. All the variants of the new data points, synthetically generated within the probabilistic framework introduced by the VAE, are perfectly encompassed in the classes defined by the original data. These features, not obvious in the original data, show patterns in the data and provide powerful mathematical signatures that are used in the proposed model to predict the health of the structure. This is one of the main ideas applied in this work. In Figure 12, the data of all PZT transducers are included. If discrimination by the sensors is performed to represent the data points in the latent space, Figure 13 is obtained. With the purpose of remarking the transition from the lower to the higher damage states and to avoid excessive confusion in the figures, only the two higher damage states (tests 16 and 17), corresponding to the last two loading stages prior to the failure of the specimen, are represented in red, while for the other stages, green was used. PZT sensors work in a high frequency range and, therefore, are able to monitor local stiffness changes occurring in the  
Figure 11: Loss function vs. number of epochs of the autoencoder. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Section** & **Layer Type** & **Input** & **Output** & **Activation** \\ \hline \multirow{3}{*}{Encoder} & Fully connected & 7201 & 4000 & PReLU \\ \cline{2-5}  & Fully connected & 4000 & 100 & PReLU \\ \cline{2-5}  & Fully connected & 100 & 3 & PReLU \\ \hline \multirow{3}{*}{Decoder} & Fully connected & 3 & 100 & PReLU \\ \cline{2-5}  & Fully connected & 100 & 4000 & PReLU \\ \cline{1-1}  & Fully connected & 4000 & 7209 & PReLU \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Deep autoencoder architecture. It is evident that the last loading stage (test number 17) formed a cluster far from the previous stages for those sensors located on the left side of the beam. This agreed with the failure mode of the beam, which occurred by debonding of the left side of the FRP strip (Figure 8). For the penultimate loading stage (test number 16), the growth of the damage was progressive. One important point to remark on regards sensor 4, for which three clusters were distinguished, affecting the intermediate loading stages. This phenomenon means that something noticeable occurred before reaching the last loading stages. Debonding originated close to this sensor as a consequence of a strong concentration of stresses that occurred near a major flexural crack. The distance between the red and green clusters served to determine if, in the vicinity of each sensor, the damage grew more or less gradually for the last two stages. However, the graphs in Figure 13 may be misleading, because for some sensors, the data points corresponding to the penultimate loading step were mixed with those of previous loading steps and could not be distinguished. The existence of enough overlapping clusters and decreased cluster homogeneity is, without a doubt, one of the main limitations of clustering when applied to the latent space of autoencoders. The clusterability of latent representations could be the purpose of a deeper future study. Figure 13: Representation of all data points (original and synthetic), sensor by sensor, in the 3D latent space: (**a**) PZT1; (**b**) PZT2; (**c**) PZT3; (**d**) PZT4; (**e**) PZT6; (**f**) PZT7; (**g**) PZT8; (**h**) PZT9; (**i**) PZT10. Figure 14 shows the evolution of the three indicators, average density (blue), volume of the convex hull (red), and ellipse overlap (green), presented in Section 2.4 to identify damage.