## 2 Materials and Methods
### Generation of Datasets  
In order to generate a data set for analyzing and predicting multipass welding distortion, welding experiments were performed using a Fronius CMT Advanced 4000 R welding power source (Fronius International GmbH, Austria), with the welding torch being guided by a KUKA KR-22 6-axis robotic system (KUKA Deutschland GmbH, Germany). This multipass welding is typical for usage in IM and forms the basis for larger additive welding structures. Single and multipass welding procedures were carried out on 1.0330 mild steel  
Figure 1: The methodical approach of this study. substrates (200 \(\times\) 52 \(\times\) 2 mm). A weld seam length of 150 mm was deposited using a 1.5130 solid wire electrode with a diameter of 1.2 mm. The chemical compositions of the used materials are given in Table 1. All welding experiments were performed using a conventional short arc process and an Argon (99.996%) shielding gas flow of 14 L/min. The contact-tip to workpiece distance was set to 10 mm. For the welding of pre-heated samples, the samples were tempered on a heating plate. Prior to welding, the temperature was verified on the sample surface using type-k thermocouples. To describe the influence of the main process parameter's pre-heating temperature, energy input, and number of layers on the resulting distortion of the baseplate, full fractional parameter variations were conducted according to Table 2. Therefore, there are 48 cases for three different amounts of layers resulting in 144 data points as a potential input for the machine-learning algorithm. During welding and subsequent cooling sequence, the specimens were positioned using a floating bearing arrangement without clamping, allowing free deformation (see Figure 2a). This arrangement was chosen to solely consider the welding distortion under idealized conditions without influences of the clamping conditions. Three stops were used for repeatable positioning of the specimens on the welding table. Only minor deviations of the position in the x-y plane were detected due to the distortion of the samples. Deviations in the z-plane resulted in a change of the contact-tip to workpiece distance along the predetermined weld path. Based on the measurements of welding voltage and current, these showed no significant influences on the deposition process. For the determination of the energy input per layer, welding voltage and current were measured using a weld process data scanner (HKS Prozestechnik GmbH, Germany) and integrated over the welding time. Welding distortion has three primary components in x, y, and z directions. This study is focused on the main distortion in the y-z-plane as distortions in x-z-plane were found to be considerably low. The distortion in the y-z-plane (Figure 2b) was measured after cooling the sample using a dial gauge. For the measurement procedure, the sample was positioned on a measurement table with the curvature from distortion facing upwards. Further, the distortion was determined as the highest point (minus sample thickness) at four points along the x-direction using a dial gauge. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Alloy**} & \multicolumn{5}{c}{**Chemical Composition (wt\%)**} \\ \cline{2-7}  & **Fe** & **C** & **Mn** & **Si** & **P** & **S** \\ \hline Welding wire: & bal & 0.1 & 1.7 & 1.0 & \textless{}0.025 & \textless{}0.025 \\ Substrate: & 1.0330 & bal & \textless{}0.12 & \textless{}0.6 & - & \textless{}0.045 & \textless{}0.045 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The nominal composition of welding wire and substrate material. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Symbol** & **Unit** & \multicolumn{3}{c}{**Variation**} \\ \hline Pre-heating Temperature & t\({}_{\text{i}}\) & \({}^{\circ}\)C & 23 & 80 & 140 & 200 \\ \hline Wire feed & v\({}_{\text{W}}\) & m/min & 2.0 & 2.5 & 3.0 & 3.5 \\ \hline Welding speed & v\({}_{\text{S}}\) & cm/min & 60 & 70 & 80 \\ \hline Number of layers & n & - & 1 & 2 & 4 \\ \hline \hline \end{tabular}
\end{table}