Page 62 - MSAM-4-3

Materials Science in Additive Manufacturing Bead geometry prediction in laser-arc AM

A B

Figure 3. Sketch of three-factor three-level experimental designs. (A) Full factorial design. (B) Box–Behnken design

Table 2. Process parameters of the laser‑CMT process
Heat source Parameter Value
CMT Wire feeding speed (m/min) 6
Travel speed (mm/min) 600
Laser Laser power (kW) 3
Defocusing length (mm) 171.5
Abbreviation: CMT: Cold metal transfer.

Table 3. Wire and substrate chemical compositions

Alloy Chemical components (wt.%)
Si Fe Cu Mn Mg Zn V Ti Zr
ER2319 0.106 0.156 5.950 0.273 0.009 0.012 0.068 0.104 0.104
(wire)
2219-T6 0.021 0.100 6.060 0.270 <0.01 0.024 0.092 0.039 0.130
(substrate)
Figure 4. The actual morphology of the 46 weld beads in the training Abbreviations: Si: Silicon; Fe: Iron; Cu: Copper; Mn: Manganese;
dataset Mg: Magnesium; Zn: Zinc; V: Vanadium; Ti: Titanium; Zr: Zirconium.

In traditional methods (Figure 5A), weights are usually
expressed as a D-dimensional continuous vector: Table 4. Process control parameters and their levels
Parameters Units Notation Factor levels
D
D ∑
X =[, 2 x ], x =1 (III) −1 0 1
x x ,...
i
1
i=1 Wire feed speed m/min v 6 7 8
w
Welding speed mm/min v t 500 600 700
Traditional methods usually encode the weight vector Arc length correction % l 5 10 15
as a D-dimensional continuous variable and perform
iterative updates of particle velocities and positions in this Pulse correction % f 0 1 2
high-dimensional space. Nevertheless, this design entails Laser power kW p 1 2 3
two principal drawbacks: On the one hand, owing to the
excessive dimensionality of the search space, PSO tends to In the ODIE workflow (Figure 5B), every particle is
converge slowly when optimizing in a D-dimensional encoded as an integer sequence of length k:
continuous domain. On the other hand, to enforce the
D
normalization constraint x 1, the weights must be X = [x , x .,x ], x ∈{0,1.,D−1} (IV)
2
k
i
1
i
i1
projected back or a penalty term introduced after every In this setting, D represents the total count of base
iteration, thereby complicating implementation and learners, and x indicates the index of the base model
i
further burdening hyperparameter tuning. chosen at position i. The weight of each base model j can be
Volume 4 Issue 3 (2025) 5 doi: 10.36922/MSAM025220036