# Application-Oriented Data Analytics in Large-Scale Metal Sheet Bending
## 4 Methods and Results
### Classification Based on DTW and K-Medoids  
To analyze the pressure signals in the roller during the bending of sheet metal, a methodology based on signal classification using the DTW technique combined with k-medoids technique was employed. It is important to note that in the signals of the seven bent sheets, the process underwent multiple active bending phases and periods of inactivity. This can be seen in Figure 4a, which shows the signal for one of the thinner sheets. The evolution of the signals during bending shows how the displacement of the rear roller (Z_CPD) and the pressure in the cylinder (Z_CPD_P) increase and then return to the same level when the sheet is released from contact with the roller. As for the rotation of the main motor (Z_MP_V), the movement is indeterminate in terms of direction and level, as it is manually operated. Figure 3: Application of visual analytics to the metal-sheet-bending signal. Considering the values during the active process, a total of 47 peaks were identified in the signals of sheet metal bending. The peaks of the signals corresponding to the thinnest sheet and the thickest sheet were analyzed. Figure 4b shows the train of active bending peaks in the thinnest sheet, while Figure 4c presents the train of active bending peaks in the thickest sheet. It can be observed that the peaks in both sheets have similar shapes; however, the maximum pressure levels are higher in the thickest sheet. This analysis provides valuable information about the deformation experienced by each type of sheet during the bending process, which can be useful for optimizing the process and improving the quality of the final product. Figure 4b,\(c\) show the trains of active bending peaks. This graphical representation is based on the horizon-graphs technique, which allows visualizing the temporal evolution of the pressure signal in the cylinder during the bending of the sheet to form the collar. The active peaks indicate the moments when the pressure in the cylinder exceeds a certain threshold, indicating the presence of bending in the sheet. The train representation allows identifying patterns and trends in the evolution of bending over time. First, the peaks of the pressure signal were classified using the DTW technique. This technique was chosen for its ability to measure the similarity between two signals that have different lengths and shapes. In this case, each pressure peak was compared to a predefined template, which allowed for the identification of characteristic pressure patterns  
Figure 4: Analysis and classification of (**a**) segments of the signal where the bending of the collar occurs, (**b**) train of active bending peaks in thinner sheet, and (**c**) train of active bending peaks in thicker sheet. for each bending, as it can be seen in Figure 5. Finally, the k-medoids technique was applied to classify the pressure peaks into different clusters based on their similarity in shape and amplitude. This technique grouped the pressure peaks into categories with similar characteristics, enabling the identification of specific pressure patterns for each type of bending. In summary, the employed methodology combined the use of visual analytics for exploratory data analysis, the DTW technique for the classification of pressure peaks [18], and the k-medoids technique for grouping the pressure peaks into different clusters based on their similarity. This methodology allowed for the identification of specific pressure patterns for each type of bending, which can be highly useful for quality control in the metal-sheet-bending process. The pressures recorded on the roller exclusively during the metal-sheet-bending process were considered, resulting in a total of 47 peaks in the pressure diagram. These peaks were aligned using the dynamic-time-warping (DTW) technique and clustered using the k-medoids algorithm. A comparative analysis was conducted among the peaks obtained from the signals corresponding to the three thickest sheets and the four thinnest sheets.