## 3 The Results of Experiments
### Seam Tracking
In Figure 17, the trace welding line oscillates around the reference line during the trace welding process within in straightness error \(\pm\)1 mm, which is the distance of the offset from the weld seam. The welding deviation statistical analysis is shown in Table 5. The mean deviation was found to be \(-0.1155\) mm, indicating that the overall trend of deviation is minimal and close to zero throughout the welding process. The standard deviation was measured at 0.2654 mm and indicated a certain degree of volatility in the deviation during the welding process. The mean absolute error is approximately 0.1979 mm. The deviation values were small and relatively stable for most of the welding process. The Root Mean Square Error is 0.2891 mm. Although there is some fluctuation in the welding process, the overall error was kept at a relatively low level. The deviation value changes and gradually becomes smaller within a deviation of 1 mm, which is permissible in industrial welding processes. The back bead and image processing result without control is shown in Figure 18. Specifically, when the welding starts, the weld line aligns with the weld seam near the start point and then deviates from the desired trajectory without control during the subsequent welding process. The orange arrow indicates the distance relationship between the weld seam and the weld line; the distance increases in the experiment without control, and the weld line deviates from the weld seam. The deviation between the controllable red center and the white weld seam of the weld pool obtained by image processing becomes wider. The deviation between the weld line and the weld seam in the diagram can be clearly seen. As illustrated in the weld pool image, the weld pool boundaries exhibit an asymmetrical distribution with an increase in deviation angle over time during the welding process. This results in the formation of an asymmetrical weld bead. On the other hand, the situation with control is applied in Figure 19. The end position of the weld bead is coincident with the weld seam. When the control has been applied, the deviations between the white weld seam and red center points get smaller and smaller, coinciding with each other in a steady state. Finally, the center of the weld boundary in the bead image becomes a line with the reference center. There is an asymmetry state in the  
Figure 17: U-Net tracking results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mean Deviation** & **Standard Deviation** & **Mean Absolute Error** & **Root Mean Square Error** \\ \hline \(-0.1155\) mm & 0.2654 mm & 0.1979 mm & 0.2891 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Welding deviation statistical analysis. boundary of the weld pool at the start of the welding. However, as the welding process is regulated, the weld line approaches the center of the weld pool. Subsequently, the weld boundary evolves into a state of symmetry at the end of the welding. It indicates that tracking in the welding experiment was successful. This study proposed a prediction method to provide a more accurate weld line than image processing techniques in the welding process. The boundaries can be obtained more directly and accurately on the weld pool than with other prediction models. Moreover, the control experiments have been conducted to verify the validity of the method. It could be experimentally verified to improve welding quality significantly. In this experiment, the weld boundary is employed as a predictive feature. It has been demonstrated that the formation of the weld boundary is not destroyed by a reasonable range of changes in the welding conditions of the welding material in PAW. Furthermore, it has been shown that the keyhole will change, but the weld boundary will not change in the existing gap. Furthermore, the adaptive control method is applicable to plasma butt welding and gap welding for materials of any thickness.