## 2 Materials and Methods
### Method
#### 2.2.2 Designing and Conducting the Experiment  
In this section, the single-factor experiment scheme was used to determine the selection range of each input parameter separately. The criteria were used to determine a reasonable range of parameters so that the welding process was stable and had no defect on the weld bead. In order to ensure the sequential and rotational properties of the experiment, the CCD method was used to design the experiment matrix. It is worth noting that sequential properties ensure the consistency and extensibility of the experiment, while the rotational properties ensure whether the designed experiment points are on the same sphere as the central point. Moreover, the rotational properties also ensure the consistency of the prediction variance of the experiment point. In the present study, five levels were considered for each input parameter, and each level was defined with a code named \(-\beta\), \(-1\), \(0\), \(+1\), \(+\beta\). The value of \(\beta\) can be calculated using the following expression:  
\[\beta=\left(2^{k}\right)^{1/4} \tag{1}\]  
In this article, five input parameters are considered in the experiments, so \(k\) is set to 5 and \(\beta\) = 2.38. Therefore, the upper limit and lower limit of the design code are \(+2.38\) and \(-2.38\), respectively. The relationship between the actual value and code value for each parameter is shown in Table 2.  
The experiment matrix obtained from Design-Expert software is presented in Table 3. The experiment was carried out in accordance with the experimental matrix. The measured weld-bead geometry is presented in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Factors**} & \multirow{2}{*}{**Unit**} & \multicolumn{5}{c}{**Code Value**} \\ \cline{3-8}  & & \(-\)**2.38** & \(-\)**1** & **0** & **+1** & **+2.38** \\ \hline \(W_{f}\) & \(\text{m}\cdot\text{min}^{-1}\) & 7.6 & 8.7 & 9.5 & 10.3 & 11.4 \\ \(V\) & \(\text{V}\) & 19.7 & 21.5 & 24 & 22.75 & 25.7 \\ \(W_{s}\) & \(\text{mm}\cdot\) & 281 & 350 & 400 & 450 & 518 \\ \(\alpha\) & \(\overset{\circ}{}\) & 1.69 & 52 & 88.5 & 125 & 175 \\ \(O_{\text{W}}\) & \(\text{mm}\) & 0.74 & 1.5 & 2.05 & 2.6 & 3.36 \\ \hline \end{tabular}
\end{table}
Table 2: Code value of the input parameters.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**Std**} & \multirow{2}{*}{**Run**} & \multicolumn{5}{c}{**Code Variables**} & \multicolumn{5}{c}{**Response Parameters**} \\ \hline  & & \(W_{f}\) & \(V\) & \(W_{s}\) & \(O_{W}\) & \(\alpha\) & \(S_{p}\) & \(D_{p}\) & \(W_{h}\) & \(C\) \\  & & \(W_{f}\) & \(V\) & \(W_{s}\) & \(O_{W}\) & \(\alpha\) & **(mm)** & **(mm)** & **(mm)** & **(mm)** \\ \hline
1 & 31 & \(-1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & 0.31 & 2.03 & 2.60 & \(-0.97\) \\
2 & 47 & \(1\) & \(-1\) & \(-1\) & \(-1\) & \(-1\) & 0.42 & 1.92 & 3.46 & \(-1.21\) \\
3 & 42 & \(-1\) & \(1\) & \(-1\) & \(-1\) & \(-1\) & 0.43 & 1.90 & 3.13 & \(-1.01\) \\
4 & 4 & \(1\) & \(1\) & \(-1\) & \(-1\) & \(-1\) & 0.59 & 2.30 & 3.28 & \(-1.42\) \\
5 & 12 & \(-1\) & \(-1\) & \(1\) & \(-1\) & \(-1\) & 0.28 & 1.85 & 2.15 & \(-0.77\) \\
6 & 40 & \(1\) & \(-1\) & \(1\) & \(-1\) & \(-1\) & 0.25 & 2.44 & 2.53 & \(-1.00\) \\
7 & 10 & \(-1\) & \(1\) & \(1\) & \(-1\) & \(-1\) & 0.34 & 2.38 & 2.00 & \(-1.11\) \\
8 & 15 & 1 & \(1\) & \(1\) & \(-1\) & \(-1\) & 0.37 & 2.23 & 2.60 & \(-1.32\) \\
9 & 39 & \(-1\) & \(-1\) & \(-1\) & \(1\) & \(-1\) & 0.43 & 1.73 & 2.84 & \(-1.09\) \\
10 & 20 & 1 & \(-1\) & \(-1\) & \(1\) & \(-1\) & 0.40 & 1.93 & 3.31 & \(-1.42\) \\
11 & 1 & \(-1\) & \(1\) & \(-1\) & \(1\) & \(-1\) & 0.53 & 2.63 & 2.10 & \(-1.48\) \\
12 & 5 & 1 & \(1\) & \(-1\) & \(1\) & \(-1\) & 0.51 & 2.55 & 2.63 & \(-1.33\) \\
13 & 46 & \(-1\) & \(-1\) & \(1\) & \(1\) & \(-1\) & 0.35 & 2.19 & 1.72 & \(-0.99\) \\
14 & 44 & 1 & \(-1\) & \(1\) & \(1\) & \(-1\) & 0.26 & 2.92 & 1.94 & \(-1.07\) \\ \hline \end{tabular}
\end{table}
Table 3: Designed experiment matrix and measured responses.