## 3 Case Study
### Results and Discussion  
Images with the size of 600 pixels by 600 pixels were obtained by converting the dynamic resistance waveforms using the proposed RP. Representative examples are shown in Figure 16. The yellow area decreases as the weld points increase, as presented from Figure 16a-d. The yellow area increases as the maximum value of dynamic resistance increases. The blue line increases as the slope of dynamic resistance increases. Therefore, the proposed RP can present multiple features of dynamic resistance in a single image. Figure 16e,f shows the images after failure. The domain experts determined that the welding electrode should be replaced after 375 welds were conducted.  
Health indicators (HIs) were compared using the images from the original and proposed RP, as shown in Figure 17. As presented in Figure 17a, the HI curve using the original RP showed a gradual increase until 375 welds were conducted; whereas, the HI value decreased after 375 welds were conducted. As presented in Figure 17b, the HI curve using the proposed RP presented a monotonic increase even after 360 weld points. Therefore, it was concluded that the proposed RP outperforms the  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Data Type** & **Signal** & **Set 1** & **Set 2** & **Set 3** & **Set 4** & **Set 5** & **Set 6** \\ \hline \multirow{3}{*}{Waveform} & Dynamic Resistance & & & & & & 500 welds \\  & Pressure & 100 welds & 100 welds & 100 welds & 100 welds & 100 welds & (sample/ \\  & Current & (sample & (sample & (sample & (sample & (sample & (sample/ \\ \multirow{2}{*}{Image} & Upper Electrode & /veld) & /veld) & /veld) & /veld) & /veld) & 500 welds (sample/ \\  & Lower Electrode & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Database collected from the accelerated testing of welding electrodes.  
Figure 16: Proposed RP images of dynamic resistance after (**a**) one, (**b**) 100, (**c**) 200, (**d**) 300, (**e**) 400, and (**f**) 500 spot welding instances.  
original RP. The instant spatter phenomenon that occurred after 420 weld points was also captured by the HI curve.  
A peel test was conducted to provide direct evidence of failure. The peel test results are shown in Figure 18. The replacement point was determined to be approximately 353 weld points when the nugget size was below 5 mm. When the HI value was 20, the replacement point for the welding electrode tip corresponded to 360 weld points.  
To compare the performance of the proposed methodology with prior methods, handcrafted features were employed. The knowledge-based features consisted of the resistance at each half-cycle  
Figure 17: Proposed degradation curve of a welding electrode: (**a**) original RP and (**b**) proposed RP.  
Figure 18: Peel test result by weld number: (**a**) cross sectional view of welding and (**b**) nugget diameter versus weld number.  
peak, maximum resistance, time of maximum resistance, positive resistance slope, negative resistance slope, mean resistance value, final resistance value, and standard deviation of the resistance [1; 13; 14]. In this study, either five or eight features were incorporated. Depending on the number of features, the degradation curves fluctuated, as shown in Figure 19. It was difficult to decide a particular threshold value since the HI curve was not monotonic. The results showed that the proposed RP-based approach outperformed the handcrafted, feature-based approach.