## 1 Introduction
Over the past few years, a growing body of research has focused on exploiting this capability for SHM in civil engineering systems. Various studies have advanced this field, each contributing to the different aspects of AE application. [PERSON] et al. [11] proposed an AE-based deep-learning framework to model the relationship between the structural vibration characteristics and the physical properties of the structure. Similarly, [PERSON] et al. [12] employed energy levels of standardized time series data as the inputs of an AE to monitor the health state of a bridge and a three-story building. [PERSON] et al. [13] developed a convolution AE-based novelty detection approach for detecting tendon damage in prestressed concrete bridges. [PERSON] et al. [14] applied a variational auto encoder technique to the damage identification of a beam-like bridge subjected to a moving vehicle and validated their methodology through both numerically simulated and experimental data. [PERSON] et al. [15] presented a multi-domain indicator-based optimized stacked deep AE to perform fault identification of rolling bearings. [PERSON] et al. [16] proposed an unsupervised deep learning-based method for structural damage detection based on convolutional AEsthat employs acceleration signals from the structure and is trained by the signals solely acquired from the healthy state of the structure. [PERSON] and [PERSON] [17] employed a deep AE to extract damage-sensitive features from measured acceleration response data of a healthy structure. These features were then used by a one-class support vector machine for damage detection. [PERSON] et al. [18] demonstrated the effectiveness of a convolutional auto encoder-based methodology for detecting damage using the acceleration and strain data from field experiments on an actual bridge structure. [PERSON] et al. [19] proposed an approach that employs two deep AEs: an undercomplete AE in the latent domain to capture the low-dimensional manifold of the signal and an overcomplete AE in the time domain to extract reconstruction error-based damage indicators. [PERSON] et al. [20] proposed a stacked AE approach that uses modal parameters extracted from measured vibration data as input as the first level features used to train the stacked auto encoder to perform a second-level feature extraction from the bottleneck layer as the damage-sensitive features. [PERSON] et al. [21] used a deep convolutional denoising AE-based strategy to reconstruct cross correlations of the vibration data extracting the desired features and identifying minor damage through the control charts established for these features. [PERSON] et al. [22] exploited a convolutional variational auto-encoder for tunnel damage detection, employing wavelet packet energy to pinpoint damage locations. [PERSON] et al. [23] investigated the effectiveness of four AE-based methodologies--conventional, sparse, variational, and convolutional--across three different test structures. Using a statistical tool to analyze damage detection and progression, reflected by an increase in the quantified reconstruction error, the study found that the variational AE demonstrated superior performance compared to the other methods. [PERSON] et al. [24] highlighted the suitability of AEs trained with time series data for damage localization under ambient conditions. In the frequency domain, an unsupervised deep AE model was trained on the response of a vehicle passing a healthy bridge, and the effectiveness of a damage index--based on the difference between the original and reconstructed responses--was explored [25]. [PERSON] et al. [26] proposed a generalized AE approach integrated with a statistical pattern recognition strategy, utilizing power cepstral coefficients of structural acceleration responses as damage-sensitive features for structural damage assessment. [PERSON] et al. [27] constructed a variational AE network model for detecting bridge damage utilizing response data from limited sensors.