## 4 Conclusions  
The effects of welding parameters (WS, leading WFR, and trailing WFR) on the bead shape (leg length and penetration depth) were investigated to predict and control the bead shape in tandem GMAW of aluminum 5083-O alloy. The following results and conclusions were obtained from this investigation:  
1. The tandem GMAW process was used in these experiments, and a torch with a 7 mm gap between the tandem torches was designed and applied;
2. The bead shape (leg length and penetration depth) gradually decreased owing to the decrease in heat input as the WS increased within the WS range of 123-157 cm/min;
3. The leading arc directly strikes the solid to form a narrow molten article, which has an effect on the influence of the penetration depth;
4. The trailing arc is transferred to the molten pool created by the leading arc, which expanded the molten pool and influenced the leg length;
5. As a result of observing arc behavior using a high-speed camera, it was confirmed that the leading WFR affects the penetration depth, and the trailing WFR affects the leg length;
6. In the lap fillet joint tandem GMAW process using aluminum 5083-O alloy (thickness: 1.5 mm) for the top plate and aluminum 5083-O alloy (thickness: 2.5 mm) for the bottom plate, a regression equation was derived to predict the bead shape (leg length and penetration depth). The coefficient of determination (R\({}^{2}\)) of the regression models was 0.9414 for the leg length and 0.9924 for the penetration depth;
7. It was validated that the estimated models were effective in predicting the weld bead shape of the aluminum 5083-O alloy single lap joint using the tandem GMAW process.  
Conceptualization, G.-G.K. and T.K.; methodology, T.K. and J.P.; formal analysis, G.-G.K. and D.-Y.K.; investigation, G.-G.K. and T.K.; writing--original draft preparation, G.-G.K. and T.K.; writing--review and editing, G.-G.K. and Y.-M.K.; supervision, Y.-M.K. and J.Y. All authors have read and agreed to the published version of the manuscript.  
This study has been conducted with the support of the Korea Institute of Industrial Technology as \"The dynamic parameter control-based smart welding system module development for the complete joint penetration weld\" (KITECH-EH230007).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Point**} & \multirow{2}{*}{**Welding Parameter**} & \multirow{2}{*}{**Item**} & \multicolumn{2}{c}{**Value**} & \multicolumn{2}{c}{**Deviation**} & \multirow{2}{*}{**Cross-Section**} \\ \cline{3-4} \cline{6-7}  & & & \(Y_{lag}\) & \(Y_{pen}\) & \(Y_{lag}\) & \(Y_{pen}\) \\  & & & **(mm)** & **(mm)** & **(mm)** & **(mm)** \\ \hline \multirow{6}{*}{1} & & Predicted values & 5.9 & 1.2 & & \\  & & Actual value 1 & 6.0 & 1.4 & 0.1 & 0.2 \\  & & (\(X_{3}\)) 5.8 m/min & Actual value 2 & 6.1 & 1.3 & 0.2 & 0.1 \\  & & Actual value 3 & 6.1 & 1.3 & 0.2 & 0.1 \\ \hline \multirow{6}{*}{2} & & Predicted values & 6.0 & 1.9 & & \\  & & Actual value 1 & 5.6 & 1.5 & 0.4 & 0.4 \\  & & (\(X_{3}\)) 8.7 m/min & Actual value 2 & 5.6 & 1.5 & 0.4 & 0.4 \\  & & Actual value 3 & 5.7 & 1.6 & 0.3 & 0.3 \\ \hline \multirow{6}{*}{3} & & Predicted values & 5.5 & 1.5 & & \\  & & Actual value 1 & 5.2 & 1.1 & 0.3 & 0.1 \\ \cline{1-1}  & & (\(X_{3}\)): 3.0 m/min & Actual value 2 & 5.2 & 1.2 & 0.3 & 0.3 \\ \cline{1-1}  & & Actual value 3 & 5.1 & 1.2 & 0.4 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Validation conditions and results.