## 4 Conclusions  
This paper presented a methodology to determine the replacement cycle of welding electrode tips using dynamic resistance data. The proposed methodology consists of three key steps: (1) waveform imaging; (2) unsupervised feature extraction; and (3) welding electrode condition assessment. First, 1D waveforms are converted into 2D images. This study proposed a novel imaging method that is modified from the original recurrence plot (RP) imaging method. The proposed RP imaging method was devised to improve sensitivity to weak changes in a nonstationary signal and to enhance the method's robustness to external noise. Convolutional neural networks (CNNs) were used for unsupervised feature engineering. A pre-trained CNN was used to develop activation maps. Finally, a health indicator that assesses the condition of welding electrode tips was built using Mahalanobis distance (MD), which was calculated from the outputs of the activation maps.  
The performance of the proposed RP was evaluated with two different types of waveform signals, including (1) the positive half cycle of the sinusoidal waveforms and (2) the waveforms that emulate the evolution of dynamic resistance during resistance spot welding. From visual inspection and quantitative evaluation, it was found that the proposed RP is sensitive to amplitude changes of the simulated waveform, while being robust to random noise. For example, with the simulated dynamic  
Figure 19: Feature-based degradation curve of a welding electrode: (a) five features and (b) eight features.  
resistance waveforms, the increase of the yellow area's ratio between \(f_{1}(x)\) and \(f_{3}(x)\) using the proposed RP was 21.75%; whereas, the increase using the original RP was only 45.06%. The proposed RP showed double the sensitivity of the original RP.  
A case study was conducted with a testbed using a real spot welding machine. From the case study, it was concluded that the methodology with the proposed RP imaging method outperformed the original RP imaging method and outperformed handcrafted, feature-based approaches. The results of presented methodology demonstrated the feasibility of monitoring a welding electrode condition in real time. It is anticipated that this study will help to determine the optimal replacement interval of electrode tips in spot welding systems subjected to variable working conditions.  
The proposed methodology has two limitations. First, the threshold of \(N\) in the proposed RP should be determined by the user. Second, a criterion that determines the failure of welding electrodes was chosen based on the data from a single experiment. A statistical test method such as the sequential probability ratio test (SPRT) may help select the criterion. In the future, the proposed method will be further evaluated with data from real spot welding machines in the field.  
Conceptualization, H.O.; methodology, W.J.; validation, D.H.Y. and Y.G.K.; resources, J.P.Y. and J.H.P.; writing--original draft preparation, W.J.; writing--review and editing, H.O.; supervision, H.O. All authors have read and agreed to the published version of the manuscript.  
This research was supported in part by Korea Ministry of Planning and Budget Foundation through Korea Institute of Industrial Technology (Project Number: JH190001) and in part by the Cross-Ministry Giga KOREA Project grant funded by the Korea Government (MSIT), (GK20P0700, 5G-Based Production/Logistics Service and Machine-Learning Platform Development for Cloud Manufacturing).  
The authors declare no conflict of interest.