## 3 Damage Detection and Localization Scheme  
In most transmissibility-based techniques using unlabeled data, the detection aspect of the damage identification problem is often bypassed, with the focus placed on a damage index that reflects transmissibility changes relative to an undamaged baseline for damage localization. In the relatively few studies that explicitly tackle the damage detection problem, distance measures are the most commonly applied metrics. Techniques like Euclidean distance [52] and Mahalanobis distance [26; 29; 30], coupled with deterministic threshold values, have been used to differentiate damaged states from baseline conditions. An alternative approach, similar to the modal assurance criterion (MAC) in modal analysis, was also proposed by [PERSON] et al. [53], based on correlations of transmissibility functions for damage detection. Other techniques, such as outlier analysis using the Monte Carlo method or threshold determination based on training data [54; 55] for a specific significance level, as well as statistical process control using control charts [56], have also been employed to de tect damage. However, these methods often rely on deterministic thresholds or assume Gaussian distributions for the selected features. These assumptions can limit both their computational efficiency and reliability when applied to complex, real-world scenarios. In contrast, the unsupervised one-class learning approach proposed in this study removes these constraints, enabling a fully data-driven framework. This allows for more flexible detection, as the system can adapt to a broader range of damage types without the need for pre-labeled data or assumptions about specific feature distributions. Building on the core principles of unsupervised one-class learning, the proposed methodology for damage diagnosis is implemented in two stages: training and inspection. The first stage of training includes a learning process with the features built from the data corresponding to the undamaged or baseline state of the structure, while the second stage of inspection refers to the evaluation of data corresponding to the unknown structural state that attempts to classify it as an 'outlier' or 'belonging' to the trained class. Damage detection is based on tracking the difference in amplitudes of the transmissibility functions selected as the DSFs. The selected transmissibility functions, or more specifically, the sum of the amplitudes of the transmissibility over the frequency range of interest, are tracked for detecting anomalies in the data patterns as an indication of structural changes. Hence, DSF is expressed as:  
\[\left(DSF\right)_{k}=\frac{\sum_{\omega_{1}}^{\omega_{2}}\left|\left(T_{k,k+1 }^{k}\right)^{State}1-\left(T_{k,k+1}^{k}\right)^{State}2\right|}{\sum_{\omega_ {1}}^{\omega_{2}}\left|\left(T_{k,k+1}^{k}\right)^{State}1\right|} \tag{9}\]  
where \(k=1,\ldots,N-1\), \(N\) is the number of sensors, and \(\left[\omega_{1},\;\omega_{2}\right]\) is the frequency band of interest. For each consecutive sensor combination, this normalized measure compares the two states not only through the peaks at certain frequencies but over a specific frequency range which helps reduce the effect of noise and enhance damage detection accuracy. Subsequently, the outlier estimation methods developed can be implemented to distinguish the dataset belonging to the healthy state ('normal') from that belonging to the damaged state ('outlier'). The local outlier factor (LOF) is an algorithm based on the concept of the local density that is well-suited for this purpose. Instead of comparing the density of an observation with respect to the entire data distribution, LOF compares it to its neighbors. Outliers are defined as points with significantly lower density than their neighbors [57]. The algorithm utilizes the nearest neighbor search starting by calculating the distance between data point \(p\) and all other observations using a selected distance measure, \(d(p,o)\), such as Euclidean, Manhattan or Minkowski.