Searching optimal process parameters for desired layer geometry in wire-laser directed energy deposition based on machine learning

Figures & data

Figure 1. Schematic diagram of the intelligent metal AM system.

Table 1. Summary of research on data modelling between process parameters and layer geometries in metal AM.

Prediction objects	Ref. & Process	Forward models	Forward inputs	Forward outputs	Reverse systems
Layer geometry	Hong et al. 2023; LPBF.	RF & ANN	Laser power & Scanning velocity.	Layer height & width & Penetration depth.	\
	Zhu et al., 2023; Powder-laser DED.	SVR	Laser power &Travel speed & Powder feed rate.	Layer height & width.	\
	Liu et al., 2022; Wire-laser DED.	NB	Laser power &Travel speed & Wire feed rate.	Layer height & width.	\
Layer geometry & Process parameters	Xiong et al. 2013; Wire arc DED.	ANN	Arc voltage &Travel speed & Wire feed rate.	Layer height & width.	Parameter iterative optimisation based on preset adjusting rules.
	Zhao et al., 2023; LPBF.	MLP	Laser power &Travel speed.	Layer width & Penetration depth.	Step-wise parameter prediction based on the ML model.

Figure 2. Schematic diagram of the wire-laser DED system.

Table 2. The values of process parameters at different levels.

Parameters	Factor levels
	Level 1	Level 2	Level 3	Level 4	Level 5	Level 6
Travel speed V (mm/s)	2.3	2.5	2.7	2.9	3.1	3.3
Laser power P (kW)	2.2	2.4	2.6	2.8	3.0	3.2
Wire feed rate F (cm/min)	120	140	160	180	200	220

Figure 3. Schematic diagram of the deposited layer geometry.

Table 3. Parameter design and results of the training experiments.

No.	P (kW)	V (mm/s)	F (cm/min)	H (mm)	W (mm)
1	2.2	2.3	160	2.77	5.20
2	2.2	2.5	200	3.28	4.72
3	2.2	2.9	140	2.09	5.04
4	2.2	3.1	180	2.64	4.50
5	2.2	3.3	220	3.09	4.17
6	2.4	2.3	140	2.09	6.24
7	2.4	2.5	180	2.79	5.87
8	2.4	2.9	120	1.69	5.84
9	2.4	3.1	160	2.17	5.42
10	2.4	3.3	200	2.53	5.32
11	2.6	2.3	120	1.86	6.75
12	2.6	2.5	160	2.50	6.73
13	2.6	2.7	200	2.88	6.21
14	2.6	3.1	140	1.69	6.28
15	2.6	3.3	180	2.20	5.68
16	2.8	2.5	140	1.77	7.31
17	2.8	2.7	180	2.43	6.71
18	2.8	2.9	220	2.75	6.51
19	2.8	3.1	120	1.47	6.42
20	2.8	3.3	160	1.96	6.59
21	3	2.3	220	3.01	7.24
22	3	2.5	120	1.44	7.95
23	3	2.7	160	1.94	7.56
24	3	2.9	200	2.40	7.17
25	3	3.3	140	1.47	7.07
26	3.2	2.3	200	2.71	7.97
27	3.2	2.7	140	1.73	7.78
28	3.2	2.9	180	2.16	7.59
29	3.2	3.1	220	2.57	6.95
30	3.2	3.3	120	1.25	7.10

Table 4. Parameter design and measured layer geometries of the testing experiments.

No.	P (kW)	V (mm/s)	F (cm/min)	H (mm)	W (mm)
1	2.3	2.5	140	1.98	6.05
2	2.5	2.6	200	2.88	5.85
3	2.6	2.4	220	3.14	6.31
4	2.7	2.8	180	2.55	6.22
5	2.7	3	200	2.72	6.48
6	2.9	2.6	180	2.35	7.15
7	2.9	3.1	160	2.05	6.83
8	3	2.3	200	2.97	7.20

Figure 4. Schematic diagram of the SVR model displaying the maximising ϵ-interval among the samples furthest from the hyperplane f(x).

Table 5. Parameters of various ML models for layer geometry regressions.

Models	Parameters	Value
Ridge	Alpha	1
Lasso	Alpha	0.02
GPR	Kernel	C(1, (0.01, 0.1)) * RBF(1, (1e-3, 1000))
RF	n_estimators	500
XGBoost	n_estimators colsample_bytree	1000 0.3
SVR	Kernel C	RBF 1000

Figure 5. Schematic of non-dominated sorting and crowded distance. (a) Non-dominated sorting. (b) Crowded distance.

Figure 6. Flowchart of the process parameter optimisation for desired layer geometries.

Figure 7. Accuracy and MAE results of various ML models for layer height prediction on training and testing datasets.

Figure 8. Accuracy and MAE results of various ML models for layer width prediction on training and testing datasets.

Figure 9. Predicted results of the H_pred and W_pred models based on the training data. (a) H_pred model. (b) W_pred model.

Figure 10. The APE values of the H_pred and W_pred models based on the training data.

Figure 11. Scatter diagrams of actual and predicted layer geometries and prediction accuracy distribution based on the testing data. (a) Layer height. (b) Layer width.

Figure 12. Pareto front plots of multiple objective functions under different training experiments selected in Table 3. (a) No. 10. (b) No. 15. (c) No. 20. (d) No. 25.

Table 6. Analysis of actual and predicted layer geometries.

No.	Actual geometries		Predicted parameters			Predicted geometries		Error
	H (mm)	W (mm)	P (kW)	V (mm/s)	F (cm/min)	H (mm)	W (mm)	H (%)	W (%)
10	2.53	5.32	2.60	2.83	203	2.53	5.31	0	0.19
15	2.20	5.68	2.89	3.06	157	2.20	5.68	0	0
20	1.96	6.59	2.94	2.56	142	1.96	6.59	0	0
25	1.47	7.07	2.94	2.99	120	1.47	7.06	0	0.14

Figure 13. Cross-sections of single layers deposited by the predicted process parameters in Table 7. (a) No. 1. (b) No. 2. (c) No. 3. (d) No. 4. (e) No. 5. (f) No. 6. (g) No. 7. (h) No. 8.

Figure 14. Scatter diagrams of desired and actual layer geometries and corresponding error distribution maps. (a) Layer height. (b) Layer width.

Table 7. Desired layer geometries and predicted process parameters.

No.	Desired layer geometries		Predicted process parameters
	H (mm)	W (mm)	P (kW)	V (mm/s)	F (cm/min)
1	2.5	7.0	2.86	2.52	180
2	2.0	6.5	2.74	3.21	160
3	1.6	6.0	2.58	2.96	121
4	2.3	5.7	2.77	3.20	182
5	2.7	6.8	2.89	2.57	201
6	2.0	5.0	2.20	3.04	139
7	1.5	6.5	2.82	3.15	120
8	3.0	4.8	2.20	2.67	201

Figure 15. Flowchart of the collaborative optimisation framework of forming quality, microstructure, and mechanical property in laser-DED.

Table 8. Controllable parameters and optimisation objectives in metal laser-DED.

Variables	Objectives
Laser power	Layer geometries
Travel speed	Surface roughness
Powder feed rate	Geometric distortion
Wire feed rate	Grain size
Laser spot size	Phase content
Layer thickness	Density
Layer numbers	Microhardness
Shielding gas flow rate	Tensile strength
Deposition trajectory	Elongation rate
Inter-layer temperature	Corrosion resistance
Materials	Fatigue properties

Data availability statement

Data available on request from the authors.