## 1 Introduction
Any representation coming from that region of latent space turns out to be difficult to handle, unless encoded objects coming from that area have been included during training. Different alternatives have been proposed in the past to artificially generate new data consistent with existing data and that contribute to improving the robustness of the proposed ML model [24; 25], addressing the topic of class imbalance [26]. One of these alternatives is based on the use of variational autoencoders (VAEs) [27; 28]. VAEs are able to generate new data covering under-represented classes with the purpose of balancing the dataset. In this work, a VAE model was implemented to generate synthetic data corresponding to damage patterns apparently not observed in the training dataset. Synthetic data were fed into the trained autoencoder, with the original data balancing the clustering network derived from the latent representations of the dataset. Finally, three health indicators, density, volume of the convex hull, and ellipse overlap, were defined for classification on the latent space representation of all data points, original and synthetic. These metrics are crucial, as they reveal invariants within the latent space (invariant manifolds), which are not dependent on the specific axes or the mapping generated by the AE. Understanding such invariants is essential, since the configuration of the latent space is influenced by the training process and the hyperparameters of the network. For instance, the distance between points corresponding to significantly different input functions highlights consistent characteristics that are preserved across various training setups [29]. Each of these indicators cover different features of the analyzed data in the latent space, and their ensemble application provides a robust framework for SHM. The proposed approach was tested on an external FRP (fiber-reinforced polymer)-strengthened reinforced concrete (RC) specimen, monitored with some piezo-electric ceramic PZT (lead zirconate titanate) transducers bonded on the FRP strip [30]. Typical failures of this type of strengthening originate locally and occur in a sudden and brittle way because of FRP debonding [31; 32; 33]. Therefore, periodic inspections of this type of structure are needed to identify minor potential damage which might arise in its future failures. PZT transducers are frequently used for damage detection purposes [34; 35]. PZTs are electrically excited by an external voltage that, due to the inverse piezoelectric effect, give rise to a mechanical strain acting on the host structure. The mechanical response of the target structure to this mechanical action excites at the same time as the PZT sensor to produce an electric signal, the electromechanical impedance (EMI) signature, due to the direct piezoelectric effect. Because of the electromechanical coupling of the piezoelectric transducer and the inspected structure, damage and anomalies occurring on the host structure can be identified by the variations experienced by the EMI spectrum. EMI spectra captured with the different PZT transducers during different loading stages applied on the analyzed structure were used to feed a deep autoencoder model and to verify the methodology proposed in this research. The organization of this paper is as follows. The main details of the method are presented in Section 2. Section 3 is mainly focused on the presentation of the datasets, the results, and the architecture of the used autoencoder. Finally, conclusions and possible future research lines are presented in Section 4.