## 3 Results
### Monitoring of Retrofitted BCJs
#### 3.2.2 Hierarchical Clustering Approach  
This study further explores the implementation of the HCA as an additional method for assessing the performance of retrofitted BCJs. The primary rationale for integrating HCA in this study stemmed from the recognition that conventional damage indices, such as RMSD, evaluate the performance of retrofitted BCJs solely based on scalar values. Frequently, it is noted that similar damage index values may indicate varying structural conditions, leading to potential inaccuracies in alerts. Therefore, the HCA was applied as a supplementary tool for co-evaluating the statistical analysis results. Figure 10 depicts the CCC values from all of the PZTs across the various metric distances examined in this study. The CCC quantifies the degree to which a dendrogram accurately maintains the initial pairwise distances between unmodeled data points and represents how accurately the dendrogram represents the differences between observations. [PERSON] et al. suggest that CCC values exceeding 0.7 indicate a strong fit for a cluster. Thus, it is essential to highlight that every PZT demonstrates CCC values exceeding 0.7 for all of the investigated metric distances. The city block metric exhibits notably higher average CCC values and is, therefore, selected for further analysis. The HCA results are illustrated through dendrograms, which reflect the multilevel hierarchy of the EMI responses of each PZT transducer. The multilevel hierarchy results from the degree of dissimilarity between the EMI responses captured at the end of each loading step. Figure 11 depicts the dendrogram of PZT Left, where HCA separates its EMI responses into two main clusters. The first cluster contains the EMI responses of PZT Left in the healthy condition and up to the third loading step. The EMI measurements captured at the end of the fifth, sixth, and seventh loading steps form the second cluster. The EMI response of the fourth loading step appears to be in a transitional structural state due to the activation of the C-FRP rope to restrain the growing cracks. Additionally, the eighth loading step observation was distinguished from the rest due to the formation of severe damage in the BCJ panel. The HCA promptly identified stress development within the C-FRP rope, which benefits the mechanical response of the retrofitted BCJ. Furthermore, HCA distinguishes the performance of C-FRP into four states based on the variations in EMI responses of PZT Left. HCA also separates the EMI responses of PZT Right into three clusters, as illustrated in Figure 12. The first cluster contains the EMI responses of PZT Right in the healthy condition and up to the end of the third loading step. The fourth, fifth, and sixth loading step observations were placed on the second cluster. During those loading steps, the C-FRP rope successfully restrains the cracks formed within the BCJ body. The rest of the  
Figure 10: The CCC values of utilized metric distances. EMI responses form the third cluster, where the bearing capacity of the BCJ degrades significantly. Although the RMSD values of PZT Left were notably higher than the RMSD values of PZT Right, HCA promptly identified the severe damage of the BCJ panel and the excessive stress developed in the C-FRP rope to mitigate the crack's further growth from both PZT transducers. Furthermore, Figures 13 and 14 present the dendrograms of PZT Left and PZT Right attached to the C-FRP ropes of Specim 2, respectively. The HCA separates the EMI responses of PZT Left into two clusters and three additional measurements. The HCA forms two clusters and three additional measurements, as illustrated in Figure 13. The first cluster contains the EMI responses of PZT Left in the healthy condition up to the end of the third loading step, while the second cluster is formed from the EMI responses of the fourth and fifth loading steps. As mentioned, the bearing capacity of Specim 2 decreases significantly after the sixth loading step, as depicted in Figure 6b.