## 1 Introduction
Nevertheless, according to [PERSON] and [PERSON] (2018) [23], the high dimensionality of the involved variables in actual monitored systems and the structure's complexity can significantly compromise the damage detection algorithms' performance. There are a few techniques to reduce the dimension of large data sets, e.g., Principal Component Analysis (PCA), Independent Component Analysis (ICA), t-Distributed Stochastic Neighbor Embedding (t-SNE), etc. [24; 25; 26] However, since their success depends mainly on the nature and quality of the data, empirical analysis is still essential for determining the most appropriate, which can be time-consuming within an actual SHM context. Thus, developing a more autonomous, accurate, and robust approach to identify structural alterations remains a challenge. With this in mind, many SHM methodologies have been developed based on Deep Learning (DL). DL algorithms are known for their ability to handle large volumes of data. They consist of modeling representative data information using complex abstractions through linear and nonlinear mapping with multiple processing layers. Among all of the possible DL algorithms, the Sparse Auto-Encoder (SAE) is a promising alternative for the SHM community. This method attempts to reduce and learn the data characteristics by itself. Generally speaking, the SAE may be interpreted as a type of ANN whose aim is to output an approximate reproduction of the input data through an internal codification that transforms the input variables (theoretically of higher dimension) into new variables with a lower dimension (see [PERSON] et al. (2016) [27]). Due to the learning autonomy of their models, DL-based techniques can extract features more robustly than traditional data processing techniques and adapt to different types of problems. Such factors facilitate the automatic processing of dynamic signals, encouraging its application in an SHM approach. In so doing, [PERSON] et al. (2019) [28] studied the Sparse Auto-Encoder (SAE) to diagnose the presence of damage based on modal parameters of the structures. It is important to highlight that the parameters obtained by the SAE are not directly correlated with the modal data of the structure. Instead, they carry characteristics that model the structural behavior for the health state, type of loading and environmental factors for which the SAE was trained. Numerical and experimental studies were carried out considering uncertainties in the finite element modeling of a steel frame and the noise effects on the measured signals in a prestressed concrete bridge prototype. In the work of [PERSON] and [PERSON] (2021) [29], the authors proposed a method based on the One-Class Support Vector Machine (OC-SVM) to discover structural changes directly from measurement acceleration. The method's performance was evaluated on a 12-story numerical building model and a laboratory-built scaled-down steel bridge. [PERSON] et al. (2019) [30] investigated a detection strategy in which acceleration data from a cable-stayed bridge are transformed into image vectors and are then analyzed by an Auto-Encoder and classified by an ANN. In turn, [PERSON] et al. (2021) [31] adopted modal parameters as input attributes of the Auto-Encoder to distinguish between different structural scenarios in a highway viaduct. SHM methodologies with two other variations of the Auto-Encoder algorithm are discussed in [PERSON] et al. (2020) [32] and [PERSON] et al. (2021) [33], both focused on the extraction of signal characteristics in the time domain. While [PERSON] et al. (2020) [32] presented a damage detection method based on a Variational Auto-Encoder (VAE), [PERSON] et al. (2021) [33] bet on the theory of the Deep Convolutional Denoising Auto-Encoder (DCDAE). The first strategy was evaluated for a bridge subjected to moving vehicles (numerical simulation and laboratory experiment), and the second considered a beam structure (numerical simulation and laboratory experiment).