Multi-Objective Optimization of Laser Cladding Parameters Based on BP Neural Network

Dewei Deng; Hao Jiang; Zhenhua Li; Xueguan Song; Qi Sun; Yong Zhang

doi:10.3788/LOP221821

Laser & Optoelectronics Progress, Volume. 60, Issue 17, 1714001(2023)

Multi-Objective Optimization of Laser Cladding Parameters Based on BP Neural Network

Dewei Deng^1,3、*, Hao Jiang¹, Zhenhua Li¹, Xueguan Song², Qi Sun³, and Yong Zhang³

¹Research Center of Laser 3D Printing Equipment and Application Engineering Technology (Liaoning Province), School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, Liaoning , China

²School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, Liaoning , China

³Shenyang Blower Group Corporation, Shenyang 110869, Liaoning , China

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Figures & Tables(25)

Fig. 1. Morphology of cladding powder

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Fig. 2. Schematic diagram of laser cladding system

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Fig. 3. Schematic diagram of laser cladding coating

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Fig. 4. Pareto and main effects plots of dilution rates. (a) Pareto chart; (b) main effects chart

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Fig. 5. Residual and main effects plots of micro hardness. (a) Pareto diagram; (b) main effect diagram

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Fig. 6. Pareto and main effects plots of height. (a) Pareto chart; (b) main effects chart

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Fig. 7. Pareto and main effects plots of width. (a) Pareto chart; (b) main effects chart

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Fig. 8. Schematic diagram of BP neural network

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Fig. 9. GA-BP neural network flow chart

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Fig. 10. Comparison curves of response volume test and predicted values with coefficient of determination R².(a) Height; (b) width; (c) dilution rate; (d) hardness

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Fig. 11. Plot of predicted and expected value fit of response volume.(a) Width; (b) height; (c) dilution rate; (d) hardness

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Fig. 12. Relationship between the refined process parameters and gray correlation degree

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Fig. 13. Relative error of validation sample performance data for neural networks

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Table 1. Chemical composition of the substrate and Ferro 55 alloy powder
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Table 1. Chemical composition of the substrate and Ferro 55 alloy powder
Material Mass fraction /%
C Mn P S Si Cr Ni Fe Mo
304 stainless steel ≤0.08 ≤2.00 ≤0.045 ≤0.030 ≤1.00 18.0-20.0 8.0-11.0 Bal. —
Ferro 55 0.35 1.1 — — 0.3 7 — Bal. 2

Table 2. Full factor experiment level table
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Table 2. Full factor experiment level table
Process parameter Notation Level
Laser power /W LP 1000 1200 1400 1600 1800
Scanning speed /（mm·s^-1） SS 4 5 6 7 8
Flow rate of protective gas /（L·min^-1） FG 6 7 8 9 10

Table 3. Morphological data and hardness data of some samples

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Table 3. Morphological data and hardness data of some samples

No.	LP /W	SS /（mm·s^-1）	FG /（L·min^-1）	W /μm	H /μm	η /%	DH /HV
1	1000	4	6	3775.811	1085.781	18.394	893.50
2	1000	4	7	3839.020	1230.670	19.766	640.44
3	1000	4	8	3653.007	1149.451	24.586	816.16
4	1000	4	9	3749.740	1101.470	26.765	631.60
5	1000	4	10	3843.952	963.0877	33.214	643.54
6	1000	5	6	3620.063	1200.113	17.523	878.22
7	1000	5	7	3589.932	1429.445	6.577	951.22
8	1000	5	8	3632.841	1128.766	17.657	847.00
9	1000	5	9	3633.135	1113.519	20.976	822.62
10	1000	5	10	3395.680	1021.660	23.473	832.60
11	1000	6	6	3378.067	1241.917	11.610	848.58
12	1000	6	7	3380.289	1159.290	13.168	833.76
13	1000	6	8	3549.465	1399.060	3.687	954.66
14	1000	6	9	3596.015	1002.324	20.108	749.00
15	1000	6	10	3431.845	986.5434	23.052	665.12
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
116	1800	7	6	3983.089	1296.855	28.123	705.48
117	1800	7	7	3904.384	1268.997	28.857	667.70
118	1800	7	8	3624.623	1208.514	34.520	566.60
119	1800	7	8	4292.723	1396.216	19.470	821.52
120	1800	7	10	3374.230	746.500	46.727	480.96
121	1800	8	6	3842.054	1322.708	24.122	814.26
122	1800	8	7	3834.420	1294.360	21.603	762.53
123	1800	8	8	3917.358	1266.675	26.265	733.98
124	1800	8	9	3280.512	1314.897	24.122	575.80
125	1800	8	10	3953.457	984.4884	31.864	595.90

Table 4. Analysis of variance results for dilution rates

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Table 4. Analysis of variance results for dilution rates

Source	df	Adjusted SSD	Adjusted MS	F value	P value
S=4.17128 R²=87.21% Adjusted R²=86.21% Predicted R²=84.98%
Model	9	13640.0	1515.56	87.10	0.000
LP	1	451.4	451.37	25.94	0.000
SS	1	60.6	60.61	3.48	0.065
FG	1	47.6	47.59	2.74	0.101
LP×LP	1	429.8	429.80	24.70	0.000
SS×SS	1	47.5	47.50	2.73	0.101
FG×FG	1	126.3	126.29	7.26	0.008
LP×SS	1	4.7	4.67	0.27	0.605
LP×FG	1	23.8	23.83	1.37	0.244
SS×FG	1	64.0	64.01	3.68	0.058
Residual	115	2001.0	17.40
Lack of fit	114	1887.7	16.56	0.15	0.990
Pure error	1	113.3	113.25
Cor total	124	15641.0

Table 5. Analysis of variance results for micro hardness

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Table 5. Analysis of variance results for micro hardness

Source	df	Adjusted SSD	Adjusted MS	F value	P value
S=94.5079 R²=63.26% Adjusted R²=60.38% Predicted R²=57.00%
Model	9	1768213	196468	22.00	0.000
LP	1	64966	64966	7.27	0.008
SS	1	35281	35281	3.95	0.049
FG	1	0	0	0.00	0.998
LP×LP	1	63104	63104	7.07	0.009
SS×SS	1	32684	32684	3.66	0.058
FG×FG	1	153	153	0.02	0.896
LP×SS	1	768	768	0.09	0.770
LP×FG	1	6929	6929	0.78	0.380
SS×FG	1	40	40	0.00	0.947
Residual	115	1027151	8932
Lack of fit	114	994659	8725	0.27	0.944
Pure error	1	32492	32492
Cor total	124	2795364

Table 6. Analysis of variance results for height

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Table 6. Analysis of variance results for height

Source	df	Adjusted SSD	Adjusted MS	F value	P value
S=99.1298 R²=49.66% Adjusted R²=45.72% Predicted R²=39.58%
Model	9	1114720	123858	12.60	0.000
LP	1	12319	12319	1.25	0.265
SS	1	3196	3196	0.33	0.570
FG	1	95049	95049	9.67	0.002
LP×LP	1	8421	8421	0.86	0.357
SS×SS	1	612	612	0.06	0.803
FG×FG	1	137532	137532	14.00	0.000
LP×SS	1	273	273	0.03	0.868
LP×FG	1	10017	10017	1.02	0.315
SS×FG	1	31	31	0.00	0.955
Residual	115	1130072	9827
Lack of fit	114	1112456	9758	0.55	0.818
Pure error	1	17616	17616
Cor total	124	2244792

Table 7. Analysis of variance results for width

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Table 7. Analysis of variance results for width

Source	df	Adjusted SSD	Adjusted MS	F value	P value
S=171.605 R²=78.09% Adjusted R²=76.38% Predicted R²=74.06%
Model	9	12073380	1341487	45.55	0.000
LP	1	218954	218954	7.44	0.007
SS	1	123178	123178	4.18	0.043
FG	1	19186	19186	0.65	0.421
LP×LP	1	33293	33293	1.13	0.290
SS×SS	1	154	154	0.01	0.943
FG×FG	1	6926	6926	0.24	0.629
LP×SS	1	28494	28494	0.97	0.327
LP×FG	1	200091	200091	6.79	0.010
SS×FG	1	43861	43861	1.49	0.225
Residual	115	3386568	29448
Lack of fit	114	3163389	27749	0.12	0.995
Pure error	1	223179	223179
Cor total	124	15459948

Table 8. Gray correlation degree of some samples

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Table 8. Gray correlation degree of some samples

No.	LP /W	SS /（mm·s^-1）	FG /（L·min^-1）	GRC
1	1000	4	6	0.5455
2	1000	4	7	0.4814
3	1000	4	8	0.5468
4	1000	4	9	0.5495
5	1000	4	10	0.5891
6	1000	5	6	0.5075
7	1000	5	7	0.4698
8	1000	5	8	0.5105
9	1000	5	9	0.5254
10	1000	5	10	0.5506
11	1000	6	6	0.4564
12	1000	6	7	0.4691
13	1000	6	8	0.4647
14	1000	6	9	0.5239
15	1000	6	10	0.5242
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
25	1000	8	10	0.3947
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
106	1800	4	6	0.6250
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
116	1800	7	6	0.5705
117	1800	7	7	0.5704
118	1800	7	8	0.5028
119	1800	7	8	0.5482
120	1800	7	10	0.5502
121	1800	8	6	0.5344
122	1800	8	7	0.5060
123	1800	8	8	0.5505
124	1800	8	9	0.4607
125	1800	8	10	0.6033

Table 9. Parameter level design
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Table 9. Parameter level design
Process parameter Parameter range Upward gradient Number of levels
LP /W 1000-1800 10 81
SS /（mm·s^-1） 4-8 0.1 41
FG /（L·min^-1） 6-10 0.5 9

Table 10. Sample parameters for validation
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Table 10. Sample parameters for validation
Sample number LP /W SS /（mm·s^-1） FG /（L·min^-1）
T₁ 1370 5.0 7.5
T₂ 1410 6.5 8.0
T₃ 1060 6.2 6.0
T₄ 1700 7.5 9.0
T₅ 1500 4.0 7.0
H₁ 1090 4.4 10.0
H₂ 1090 4.4 10.0
H₃ 1090 4.4 10.0

Table 11. Test and predicted values of the validated samples by neural networks

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Table 11. Test and predicted values of the validated samples by neural networks

Sample	W /μm	H /μm	η /%	DH /HV
T₁	3882.1	1287.5	24.069	715.30
T₁′	3993.5	1234.3	30.000	602.05
T₂	3885.3	1301.9	21.143	754.24
T₂′	3723.9	1198.0	25.800	707.74
T₃	3405.7	1299.4	12.671	772.44
T₃′	3504.1	1277.9	12.732	905.74
T₄	3907.8	1259.2	27.893	660.16
T₄′	3771.5	1200.0	32.221	610.27
T₅	4129.7	1191.8	32.907	529.98
T₅′	4225.3	1209.1	38.730	535.17

Table 12. Test and predicted values of the validated samples by neural networks
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Table 12. Test and predicted values of the validated samples by neural networks
Sample W /μm H /μm η /% DH /HV GRC
H₁ 3715.3 1112.5 32.564 518.72 0.5448
H₂ 3459.6 925.1 41.638 530.90 0.5668
H₃ 3666.2 1030.9 35.639 525.47 0.5403
H’ 3714.2 967.4 29.972 611.42 0.6797

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Dewei Deng, Hao Jiang, Zhenhua Li, Xueguan Song, Qi Sun, Yong Zhang. Multi-Objective Optimization of Laser Cladding Parameters Based on BP Neural Network[J]. Laser & Optoelectronics Progress, 2023, 60(17): 1714001

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