## 1 Introduction
In the time-frequency domain, a deep convolutional AE model was proposed to utilize wavelet transmissibility pattern spectra as input data for characterizing damage information, combined with an unsupervised clustering algorithm for damage classification [28]. The success of these varied approaches to SHM largely depends on how well the AE can capture and reconstruct key features from the input data as accurately as possible by encoding them. To enhance the accuracy of this encoding, input data must be carefully selected to ensure effective representation of the information. [PERSON] et al. [29] have shown that compressions and reconstructions performed by the AEs were more accurate in the frequency domain compared to the time domain since a Fourier transformation algorithm serves as an initial parameter extractor that facilitates this encoding. Another critical factor for the reliability of these approaches is the quality and usefulness of the collected data. The effectiveness of the monitoring system depends not only on data processing techniques but also on optimal sensor placement, which influences the accuracy of the acquired information [30; 31]. Strategic sensor placement--both in terms of number and distribution--ensures that critical structural behaviors are captured, the signal-to-noise ratio is optimized, and meaningful changes in the structural response can be detected. Moreover, considering the structural topology when deploying sensors enhances the damage localization capabilities, further improving the robustness of the monitoring system [32; 33]. In this context, the transmissibility function (TF) stands out as a promising candidate to be processed as the input to be reconstructed by the AE. Transmissibility is a frequency-domain representation that relates the output response at one measurement point to the response at another, independent of excitation measurements. This characteristic makes it particularly suitable for SHM, as it enables damage detection by capturing localized changes in dynamic properties. The concept of transmissibility for damage detection has been explored extensively. A critical review on the use of TFs for damage detection and localization from an analytical standpoint is presented by [PERSON] and [PERSON] [34]. [PERSON] et al. [35] developed the power spectral density transmissibility concept for response reconstruction and damage identification within the model-update framework. [PERSON] et al. [36] explored the damage sensitivities of TFs on a lumped mass model in their research, using inversion of a tri-diagonal matrix. The following study by [PERSON] et al. [37] developed a methodology utilizing TFs in conjunction with principal component analysis (PCA) and validated the approach on both numerically simulated data and experimental data. [PERSON] et al. [38] provided a comprehensive review on the fundamentals of TFs as a mathematical representation of output-to-output relationships as well as TF-based system identification and damage detection. [PERSON] et al. [39] employed TFs with one-dimensional convolutional neural networks in a deep learning strategy. [PERSON] et al. [40] proposed an approach for detecting structural damage subject to unknown seismic excitation with wavelet-based transmissibility of structural response data utilized as inputs to the pre-trained convolutional neural network. Despite extensive research on damage detection using machine learning, several challenges remain unaddressed. In particular, the effectiveness of AE-based methods is often hindered by the nature of the input data, reliance on subjective thresholding, and the need for labeled datasets in supervised approaches. Additionally, many studies focus on detecting damage but do not explicitly address localization. To contextualize the contributions of this study, key research gaps are outlined below:  
* Many studies use raw vibration signals as inputs to AE models.