## 3 Experimental Validation
### VAE Configuration: Data Augmentation  
Damage identification, based on the classification of points defined in the latent space of an autoencoder model, requires a considerable amount of EMI signals, which are usually limited if only experimental tests are used. Therefore, a data augmentation technique should be applied to generate massive synthetic data, which will reduce overfitting issues and improve network performance. As noted in Section 2.3, VAEs are capable of managing complex data distributions and generating new data artificially. In our problem, from a sampling of the latent space, VAEs can generate synthetic data covering a wide range of variations in the input data by  
Figure 8: Failure mode of the strengthened beam. leveraging probabilistic latent space and exploring all its dimensions. Data augmentation allows for the tackling of limited and imbalanced real-world experimental datasets. In this work, a VAE model was fed with datasets belonging to the different analyzed loading stages and PZT sensors, which means distinct impedance input distributions with varying levels of class imbalance were used. This will serve to test the robustness of the VAE model when synthesizing realistic class imbalance datasets. The configuration of the VAE model was obtained with a batch size, learning rate, and number of epochs of 16, 0.0001, and 4600, respectively, with the purpose of optimizing its performance. An encoder block and a decoder block were used to define its architecture (Table 2). The encoder maps the input data corresponding to the impedance spectra dataset of dimension 7201 into a lower-dimensional latent space by means of successive dense layers which comprise 2000, 1000, 100, and 50 neurons, respectively. The parametric rectified linear unit (PReLU) activation function was used in all the layers. With this architecture, the essential information of the data is retained while reducing dimensionality progressively until reaching the latent space, whose dimension is 50. Although a smaller dimension provides a more compact representation of the input data, it might also cause the loss of important information. The dimension of the latent space must represent a compromise between the degree of compression of the data and the critical information they retain. The latent space distribution is given by two parallel dense linear layers, which correspond to the mean and log-variance of the latent space distribution. The size of both layers agrees and is equal to the latent dimensionality which, in this case, was adjusted to 25. This hyperparameter was experimentally adjusted with the purpose of capturing the complexity of the input data, avoiding the loss of important information and maintaining computational efficiency. Both values, the mean and log-variance, are used for sampling the latent space and for the generation of a probabilistic latent space representation. Beginning with the latent space, the decoder block is also defined with dense layers and using PReLU activation. Its architecture mirrors that of the encoder, with the aim of reconstructing the input data points by reversing the encoding steps. In this case, the loss function used to control the training process has two components, the reconstruction loss, evaluated using MSE (mean squared error), and the Kullback-Leibler Divergence (KLD). While MSE measures the difference between the original and reconstructed data, KLD penalizes the model if the latent space distribution deviates from a standard normal distribution. A hyperparameter, \(\beta\), weights the importance of MSE and KLD in the loss function. In this study, the same weight was given to both components of the loss function. The minimization of the loss function as well as the updating of the weights of the model were performed with the Adam optimization algorithm, which can be considered as