## 2 Method
### Reference Assemblies  
Assembly I consists of two metal parts. Three weld segments connect the parts together on the cross section of the two parts as butt welds. Figure 1 visualizes the prepared FEM model of the assembly. The basic geometry of the plates allows for understanding the locating scheme and welding sequence behavior. The positioning points for a near-optimal locating scheme are shown in Figure 1, with the thick arrows marked with A-B-C flags representing A, B, and C datum points. The welding paths and forward direction are  
Figure 1: Assembly I—assembly of two INCONEL 718 metal plates with three weld segments F, G, and H.  
shown with the black arrows specified by Welds F-H, and the initial starting points and end points are shown by P1 and P2 for each segment. The sheet thickness for both parts is 3 mm. An ellipsoidal heat source, with a front length of 2, rear length of 4, width of 4, and depth of 1 mm, is utilized in this model. The weld geometry is considered as having a length of 1, width of 1, and height of 3 mm. The liquid and solid temperatures are set to 1523 and 1512 \({}^{\circ}\)C, respectively, and for the transient hull, the max temperature is set to 2000 \({}^{\circ}\)C with a keyhole feature of size 0.1 with a width of 4 and depth of 1 mm.  
Assembly II consists of two metal parts. Three butt-weld segments connect the parts together at the position of the interface of the two parts. Figure 2 visualizes the prepared FEM model of the assembly. This assembly has more curvature and complex geometries and has an industrial use case in the aerospace industry. The positioning points for the near-optimal locating scheme, the welding paths in the forward direction of Welds F-H, and the initial starting points and end points are shown. The thickness for both parts is 3 mm. An ellipsoidal heat source, with a front length of 2, rear length of 4, width of 4, and depth of 1 mm, is utilized in this model. The weld geometry is considered as having a length of 0.2, width of 6, and height of 0.4 mm. The liquid and solid temperatures are set to 1300 \({}^{\circ}\)C, and for the transient hull, the max temperature is set to 2000 \({}^{\circ}\)C with a keyhole feature of size 0.1 with a width of 4 and depth of 1 mm. The material of the parts for both assemblies is nickel-chrome-based super alloy INCONEL 718.  
In order to identify three levels of the locating scheme, an isolated screening of the parameter is performed. For this, the 6 locating points and their directions are considered as a decision variable in a Bayesian optimization routine to minimize the root mean square (RMS) of displacements in all the FEM nodes in the assembly. This displacement corresponds to the displacement of the assembly after welding and releasing the parts from the given locating scheme. Therefore the reported displacements are after cooling and springback. This screening was performed with a CVS approach where the simulation is not time-dependent, and thereby, the influence of the sequences and weld path direction is not taken into consideration. For Assembly I, 100 runs were performed to screen the behavior of the assembly using the different locating scheme inputs. For Assembly II, this screening was performed for 500 runs due to the geometric complexity of the assembly. The outcome of this screening is presented in Figure 3. For Assemblies I and II, three and two locating schemes from the lower and upper bounds and the mean of the screening outcome were chosen, respectively, representing near-optimal (N-O), mean, and non-ideal (N-I) solutions for the DOE presented in the next section. These levels for both assemblies are shown in Figure 3a,b.  
Figure 2: Assembly II—assembly of two INCONEL 718 metal parts with three weld segments F, G, and H.