## 2 Experimental Program
### Implementation of the Retrofitting Technique Monitoring Framework
\[\text{RMSD}=\sqrt{\frac{\sum_{\tau=1}^{\text{M}}\left(\left|Z_{(t)}\right|_{ \text{D}}-\left|Z_{(t)}\right|_{0}\right)^{2}}{\sum_{\tau=1}^{\text{M}}\left( \left|Z_{(t)}\right|_{0}\right)^{2}}}, \tag{1}\]  
\(\left|Z_{(t)}\right|_{\text{D}}\) represents the absolute impedance value of the same PZT in the examined state D, \(\left|Z_{(t)}\right|_{0}\) denotes the absolute impedance value of the PZT in its pristine state, and M represents the number of individual excitation frequencies. The statistical index RMSD quantifies PZT's EMI response variation across the recorded spectra. Thus, higher values of RMSD indicate alterations in the monitored area's structural integrity. Although this approach has been proven efficient for damage identification in the published literature, there is a growing concern regarding the performance assessment of retrofitted RC elements. The diversity in the mechanical properties of the materials that coexist in retrofitted RC members increases the complexity of performance evaluation. Therefore, implementing machine learning techniques, such as hierarchical clustering, in retrofitting performance monitoring is gaining popularity in the literature. This study employs the HCA to monitor the performance of retrofitted BCJs. [PERSON] et al. describe the primary hypothesis for the PZT-enabled FRP debonding identification clustering approach, where the abrupt variation in the PZT response strongly indicates a decrease in structural integrity. Hierarchical clustering is an unsupervised machine learning algorithm that identifies a hierarchy of clusters based on the preselected metric distance. This study used the Cophenetic Correlation Coefficient (CCC) to determine the most suitable metric distance among Cityblock, Euclidean, Squared Euclidean, Minkowski, Chebychev, Cosine, and Correlation. Subsequently, the chosen metric's dendrogram was utilized to visually represent the various clustering stages, thereby classifying the dissimilarity among the resulting groups. The equation for CCC is presented in Equation (2). \[\text{CCC}=\frac{\sum_{s<t}\left(d_{st}-\overline{d}\right)\left(d_{st}^{ \text{copph}}-\overline{d}^{\text{copph}}\right)}{\sqrt{\sum_{s<t}\left(d_{st} -\overline{d}\right)^{2}\sum_{s<t}\left(d_{st}^{\text{copph}}-\overline{d}^{ \text{copph}}\right)^{2}}} \tag{2}\]  
where \(d_{st}\) is the distance according to the selected metric between each pair of observations, \(s\) and \(t\), and \(d_{st}^{copph}\) is the cophenetic distances, illustrating the dissimilarity between groups at which the observations \(s\) and \(t\) initially merge into the same cluster. In this study, each measurement was considered an individual cluster by HCA. The similarity degree of each cluster was calculated according to the chosen metric distance. Then, the observations with the highest degree of similarity were combined to form a new cluster. The aforementioned procedure was reiterated through an iterative process until all observations were consolidated into a single cluster with an agglomeration hierarchy. Subsequently, a dendrogram was utilized to provide a visual representation of the various stages of clustering, enabling classification of the dissimilarity among the formed groups.