Processing parameter optimization of fiber laser beam welding using an ensemble of metamodels and MOABC

doi:10.1007/s11465-022-0703-5

Front. Mech. Eng.

2022, Vol. 17

Issue (4) : 47 https://doi.org/10.1007/s11465-022-0703-5

RESEARCH ARTICLE

Processing parameter optimization of fiber laser beam welding using an ensemble of metamodels and MOABC

Jianzhao WU^1,², Chaoyong ZHANG¹(

), Kunlei LIAN³, Jiahao SUN¹, Shuaikun ZHANG¹

¹. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
². Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore
³. Walmart Global Technology, Walmart Inc., Bentonville, AR 72712, USA

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Abstract

In fiber laser beam welding (LBW), the selection of optimal processing parameters is challenging and plays a key role in improving the bead geometry and welding quality. This study proposes a multi-objective optimization framework by combining an ensemble of metamodels (EMs) with the multi-objective artificial bee colony algorithm (MOABC) to identify the optimal welding parameters. An inverse proportional weighting method that considers the leave-one-out prediction error is presented to construct EM, which incorporates the competitive strengths of three metamodels. EM constructs the correlation between processing parameters (laser power, welding speed, and distance defocus) and bead geometries (bead width, depth of penetration, neck width, and neck depth) with average errors of 10.95%, 7.04%, 7.63%, and 8.62%, respectively. On the basis of EM, MOABC is employed to approximate the Pareto front, and verification experiments show that the relative errors are less than 14.67%. Furthermore, the main effect and the interaction effect of processing parameters on bead geometries are studied. Results demonstrate that the proposed EM-MOABC is effective in guiding actual fiber LBW applications.

Keywords laser beam welding parameter optimization metamodel multi-objective

Corresponding Author(s): Chaoyong ZHANG

Just Accepted Date: 27 May 2022 Issue Date: 12 December 2022

Cite this article:

Jianzhao WU,Chaoyong ZHANG,Kunlei LIAN, et al. Processing parameter optimization of fiber laser beam welding using an ensemble of metamodels and MOABC[J]. Front. Mech. Eng., 2022, 17(4): 47.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-022-0703-5
https://academic.hep.com.cn/fme/EN/Y2022/V17/I4/47

Tab.1 Chemical composition of AISI 316L stainless steel

Fig.1 Fiber laser beam welding platform.

Fig.2 Processing schematic and welding bead profile.

Tab.2 LBW experimental factors and levels

Tab.3 Corresponding relationship between foraging and function optimization

Fig.3 Workflow of multi-objective artificial bee colony algorithm.

Fig.4 Proposed data-driven framework combining the ensemble of metamodels with multi-objective artificial bee colony algorithm. MOABC: multi-objective artificial bee colony algorithm, KRG: kriging, RBF: radial basis function, SVR: support vector regression.

Fig.5 Error evaluations of the three metamodels for different responses: (a) W_b, (b) D_p, (c) W_n, and (d) D_n.

Fig.6 EMs for the four output responses: (a) W_b, (b) D_p, (c) W_n, and (d) D_n.

Fig.7 Comparison of experimental and predicted results for (a) W_b, (b) D_p, (c) W_n, and (d) D_n.

Fig.8 Main effects of processing parameters on bead geometries: (a) W_b, (b) D_p, (c) W_n, and (d) D_n.

Fig.9 First-order interaction diagrams of the processing parameters on (a) W_b, (b) D_p, (c) W_n, and (d) D_n.

Tab.4 Parameter settings of MOABC in the optimization

Fig.10 Pareto front for the bead geometries.

Fig.11 Bead geometry of the two optimal solutions selected.

Tab.5 Validation results of the No. 1 optimal solution

Tab.6 Validation results of the No. 2 optimal solution

Fig.12 Cross-sections using random process parameters.

Fig.13 Microstructures of the welding bead for the No. 1 optimal solution.

Fig.14 Bead geometries in the No. 3 Taguchi L₂₅ experiment.

Fig.15 Microstructures of the welding bead profiles beside the centerline: (a) No. 2 optimal solution and (b) No. 3 Taguchi L₂₅ experiment.

Abbreviations
ABC	Artificial bee colony
DOE	Design of experiment
EM	Ensemble of metamodel
KRG	Kriging
LBW	Laser beam welding
LOO	Leave-one-out
MOABC	Multi-objective artificial bee colony algorithm
PDAS	Primary dendrite arm spacing
RBF	Radial basis function
RSM	Response surface method
SVR	Support vector regression
Variables
C₀	Specific heat at constant pressure of the workpiece
C_m	Predetermined maximum cycle number of the searching processes for the bees
C_r	Repeated cycle number of the searching processes for the bees
D	Defocus distance
D_n	Neck depth
$D n +$ , $D n ?$	Maximum and minimum values of D_n in the Pareto optimal solutions, respectively
D_p	Depth of penetration
$\| D p ? H \| +$ , $\| D p ? H \| ?$	Maximum and minimum values of $\| D p ? H \|$ in the Pareto optimal solutions, respectively
$E 1 k$ , $E 2 k$	LOO errors of the first and second metamodels selected for the variable k, respectively
E_al	Generalized relative maximum absolute error under the leave-one-out method
E_r	Relative error of the four outputs
E_sl	Generalized root mean square error under the leave-one-out method
$f^(?)$	Approximation approach using the metamodel
$f^i (x)$	Predictive response of the ith individual metamodel at sample point x
$f (x i)$	Actual experimental value of the ith sample point
$f^(x ? i)$	Predictive response from the metamodel trained using the full data sets with the ith sample point excluded out
$f^1 k (x)$ , $f^2 k (x)$	First and second metamodel selected for the variable k, respectively
$f^E k (x)$	Prediction value of the integrated EM for the variable k
$f^E D n (x)$	Integrated EM for the variable D_n
fitness(X_i)	Quality (fitness value) of the food source of X_i
H	Thickness of the workpiece
k	Output response variable
K	Thermal conductivity of the workpiece
m	Number of sample points
P	Laser power
P_i	Probability value for onlooker bees to select the ith food source
Q	u feasible solutions (food sources)
rand(0, 1)	A random number between 0 and 1
S	Welding speed
S_n	Sum of normalized bead geometries
t	Duration of temperature variation
T	Reference temperature
T₀	Room temperature
u	Number of the initial solution population in colony initialization phase
v	Dimension of each initial solution in colony initialization phase
V_e	Experimental values of the four outputs
V_p	Predicted values of the four outputs
w₁, w₂, w₃, w₄	Weighting values of the four optimization objectives
W_b	Bead width
$W b +$ , $W b ?$	Maximum and minimum values of W_b in the Pareto optimal solutions, respectively
W_n	Neck width
$W n +$ , $W n ?$	Maximum and minimum values of W_n in the Pareto optimal solutions, respectively
x	Input value of the metamodel
x_i,j	jth dimension of the ith feasible solution
x_p,j	One of the u food sources other than x_i,j
x_max,j, x_min,j	Upper and lower bounds of the jth dimension, respectively
X_i	ith feasible solution (food source) in MOABC
Y	Output response of the metamodel
α	Coefficient vector of the metamodel
δ	Difference between the maximum and minimum mean bead geometries
ε	Stochastic factor of the metamodel
θ_i,j	Neighborhood of x_i,j for searching a better food source
ρ	Material density of the workpiece
$? i, j$	Change rate of food sources during the employed bees phase
$ω 1 k$ , $ω 2 k$	Weights of first and second metamodel for the variable k, respectively

Table A1 Fiber LBW processing parameters and experimental results

1	L J Huang , X M Hua , D S Wu , Y X Ye . Role of welding speed on keyhole-induced porosity formation based on experimental and numerical study in fiber laser welding of Al alloy. The International Journal of Advanced Manufacturing Technology, 2019, 103(1): 913–925 https://doi.org/10.1007/s00170-019-03502-x
2	K M Hong , Y C Shin . Prospects of laser welding technology in the automotive industry: a review. Journal of Materials Processing Technology, 2017, 245: 46–69 https://doi.org/10.1016/j.jmatprotec.2017.02.008
3	J Stavridis , A Papacharalampopoulos , P Stavropoulos . Quality assessment in laser welding: a critical review. The International Journal of Advanced Manufacturing Technology, 2018, 94(5): 1825–1847 https://doi.org/10.1007/s00170-017-0461-4
4	Z Zeng , B Panton , J P Oliveira , A Han , Y N Zhou . Dissimilar laser welding of NiTi shape memory alloy and copper. Smart Materials and Structures, 2015, 24(12): 125036 https://doi.org/10.1088/0964-1726/24/12/125036
5	J P Oliveira , F M Braz Fernandes , R M Miranda , N Schell , J L Ocana . Effect of laser welding parameters on the austenite and martensite phase fractions of NiTi. Materials Characterization, 2016, 119: 148–151 https://doi.org/10.1016/j.matchar.2016.08.001
6	J P Oliveira , J J Shen , J D Escobar , C A F Salvador , N Schell , N Zhou , O Benafan . Laser welding of H-phase strengthened Ni-rich NiTi-20Zr high temperature shape memory alloy. Materials & Design, 2021, 202: 109533 https://doi.org/10.1016/j.matdes.2021.109533
7	A Ruggiero , L Tricarico , A G Olabi , K Y Benyounis . Weld-bead profile and costs optimisation of the CO2 dissimilar laser welding process of low carbon steel and austenitic steel AISI316. Optics & Laser Technology, 2011, 43(1): 82–90 https://doi.org/10.1016/j.optlastec.2010.05.008
8	J P Oliveira , J J Shen , Z Zeng , J M Park , Y T Choi , N Schell , E Maawad , N Zhou , H S Kim . Dissimilar laser welding of a CoCrFeMnNi high entropy alloy to 316 stainless steel. Scripta Materialia, 2022, 206: 114219 https://doi.org/10.1016/j.scriptamat.2021.114219
9	P Jiang , C C Wang , Q Zhou , X Y Shao , L S Shu , X B Li . Optimization of laser welding process parameters of stainless steel 316L using FEM, Kriging and NSGA-II. Advances in Engineering Software, 2016, 99: 147–160 https://doi.org/10.1016/j.advengsoft.2016.06.006
10	E Assunção , L Quintino , R Miranda . Comparative study of laser welding in tailor blanks for the automotive industry. The International Journal of Advanced Manufacturing Technology, 2010, 49(1): 123–131 https://doi.org/10.1007/s00170-009-2385-0
11	C Kumar , M Das , C P Paul , K S Bindra . Comparison of bead shape, microstructure and mechanical properties of fiber laser beam welding of 2 mm thick plates of Ti−6Al−4V alloy. Optics & Laser Technology, 2018, 105: 306–321 https://doi.org/10.1016/j.optlastec.2018.02.021
12	M Sokolov , A Salminen . Improving laser beam welding efficiency. Engineering, 2014, 6(09): 559–571 https://doi.org/10.4236/eng.2014.69057
13	T E Abioye , N Mustar , H Zuhailawati , I Suhaina . Prediction of the tensile strength of aluminium alloy 5052-H32 fibre laser weldments using regression analysis. The International Journal of Advanced Manufacturing Technology, 2019, 102(5): 1951–1962 https://doi.org/10.1007/s00170-019-03310-3
14	M J Zhang , T T Liu , R Z Hu , Z Y Mu , S Chen , G Y Chen . Understanding root humping in high-power laser welding of stainless steels: a combination approach. The International Journal of Advanced Manufacturing Technology, 2020, 106(11): 5353–5364 https://doi.org/10.1007/s00170-020-05021-6
15	G Shanthos Kumar , K Raghukandan , S Saravanan , N Sivagurumanikandan . Optimization of parameters to attain higher tensile strength in pulsed Nd: YAG laser welded Hastelloy C-276–Monel 400 sheets. Infrared Physics & Technology, 2019, 100: 1–10 https://doi.org/10.1016/j.infrared.2019.05.002
16	Y Du , T Mukherjee , T DebRoy . Physics-informed machine learning and mechanistic modeling of additive manufacturing to reduce defects. Applied Materials Today, 2021, 24: 101123 https://doi.org/10.1016/j.apmt.2021.101123
17	Z Huang , H J Cao , D Zeng , W W Ge , C M Duan . A carbon efficiency approach for laser welding environmental performance assessment and the process parameters decision-making. The International Journal of Advanced Manufacturing Technology, 2021, 114(7): 2433–2446 https://doi.org/10.1007/s00170-021-07011-8
18	A P Mackwood , R C Crafer . Thermal modelling of laser welding and related processes: a literature review. Optics & Laser Technology, 2005, 37(2): 99–115 https://doi.org/10.1016/j.optlastec.2004.02.017
19	S T Peng , T Li , J L Zhao , S P Lv , G Z Tan , M M Dong , H C Zhang . Towards energy and material efficient laser cladding process: modeling and optimization using a hybrid TS-GEP algorithm and the NSGA-II. Journal of Cleaner Production, 2019, 227: 58–69 https://doi.org/10.1016/j.jclepro.2019.04.187
20	M Akbari , M H Shojaeefard , P Asadi , A Khalkhali . Hybrid multi-objective optimization of microstructural and mechanical properties of B4C/A356 composites fabricated by FSP using TOPSIS and modified NSGA-II. Transactions of Nonferrous Metals Society of China, 2017, 27(11): 2317–2333 https://doi.org/10.1016/S1003-6326(17)60258-9
21	M Akbari , P Asadi , P Zolghadr , A Khalkhali . Multicriteria optimization of mechanical properties of aluminum composites reinforced with different reinforcing particles type. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2018, 232(3): 323–337 https://doi.org/10.1177/0954408917704994
22	S Srivastava , R K Garg . Process parameter optimization of gas metal arc welding on IS:2062 mild steel using response surface methodology. Journal of Manufacturing Processes, 2017, 25: 296–305 https://doi.org/10.1016/j.jmapro.2016.12.016
23	Y M Rong , Z Zhang , G J Zhang , C Yue , Y F Gu , Y Huang , C M Wang , X Y Shao . Parameters optimization of laser brazing in crimping butt using Taguchi and BPNN-GA. Optics and Lasers in Engineering, 2015, 67: 94–104 https://doi.org/10.1016/j.optlaseng.2014.10.009
24	S H Wang , L D Zhu , J Y H Fuh , H Q Zhang , W T Yan . Multi-physics modeling and Gaussian process regression analysis of cladding track geometry for direct energy deposition. Optics and Lasers in Engineering, 2020, 127: 105950 https://doi.org/10.1016/j.optlaseng.2019.105950
25	G G Wang , S Shan . Review of metamodeling techniques in support of engineering design optimization. Journal of Mechanical Design, 2007, 129(4): 370–380 https://doi.org/10.1115/1.2429697
26	T Goel , R T Haftka , W Shyy , N V Queipo . Ensemble of surrogates. Structural and Multidisciplinary Optimization, 2007, 33(3): 199–216 https://doi.org/10.1007/s00158-006-0051-9
27	A Younis , Z M Dong . Trends, features, and tests of common and recently introduced global optimization methods. Engineering Optimization, 2010, 42(8): 691–718 https://doi.org/10.1080/03052150903386674
28	H C Dong , C S Li , B W Song , P Wang . Multi-surrogate-based Differential Evolution with multi-start exploration (MDEME) for computationally expensive optimization. Advances in Engineering Software, 2018, 123: 62–76 https://doi.org/10.1016/j.advengsoft.2018.06.001
29	A Díaz-Manríquez , G Toscano , Coello C A Coello . Comparison of metamodeling techniques in evolutionary algorithms. Soft Computing, 2017, 21(19): 5647–5663 https://doi.org/10.1007/s00500-016-2140-z
30	R Jin , W Chen , T W Simpson . Comparative studies of metamodelling techniques under multiple modelling criteria. Structural and Multidisciplinary Optimization, 2001, 23(1): 1–13 https://doi.org/10.1007/s00158-001-0160-4
31	E Acar . Effect of error metrics on optimum weight factor selection for ensemble of metamodels. Expert Systems with Applications, 2015, 42(5): 2703–2709 https://doi.org/10.1016/j.eswa.2014.11.020
32	X G Song , G Y Sun , G Y Li , W Z Gao , Q Li . Crashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate models. Structural and Multidisciplinary Optimization, 2013, 47(2): 221–231 https://doi.org/10.1007/s00158-012-0820-6
33	Z M Gao , X Y Shao , P Jiang , L C Cao , Q Zhou , C Yue , Y Liu , C M Wang . Parameters optimization of hybrid fiber laser-arc butt welding on 316L stainless steel using kriging model and GA. Optics & Laser Technology, 2016, 83: 153–162 https://doi.org/10.1016/j.optlastec.2016.04.001
34	W A Ayoola , W J Suder , S W Williams . Parameters controlling weld bead profile in conduction laser welding. Journal of Materials Processing Technology, 2017, 249: 522–530 https://doi.org/10.1016/j.jmatprotec.2017.06.026
35	Y J Huang , X D Gao , B Ma , G Q Liu , N F Zhang , Y X Zhang , D Y You . Optimization of weld strength for laser welding of steel to PMMA using Taguchi design method. Optics & Laser Technology, 2021, 136: 106726 https://doi.org/10.1016/j.optlastec.2020.106726
36	X W Cai , H B Qiu , L Gao , X K Li , X Y Shao . A hybrid global optimization method based on multiple metamodels. Engineering Computations, 2018, 35(1): 71–90 https://doi.org/10.1108/EC-05-2016-0158
37	D Karaboga , B Basturk . A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization, 2007, 39(3): 459–471 https://doi.org/10.1007/s10898-007-9149-x
38	H F Jia , H Z Miao , G D Tian , M C Zhou , Y X Feng , Z W Li , J C Li . Multiobjective bike repositioning in bike-sharing systems via a modified artificial bee colony algorithm. IEEE Transactions on Automation Science and Engineering, 2020, 17(2): 909–920 https://doi.org/10.1109/TASE.2019.2950964
39	W J Wang , G D Tian , M N Chen , F Tao , C Y Zhao , A AI-Ahmari , Z W Li , Z G Jiang . Dual-objective program and improved artificial bee colony for the optimization of energy-conscious milling parameters subject to multiple constraints. Journal of Cleaner Production, 2020, 245: 118714 https://doi.org/10.1016/j.jclepro.2019.118714
40	B K Verma , D Kumar . A review on artificial bee colony algorithm. International Journal of Engineering and Technology, 2013, 2(3): 175–186 https://doi.org/10.14419/ijet.v2i3.1030
41	Y P Ren , H Y Jin , F Zhao , T Qu , L L Meng , C Y Zhang , B Zhang , G Wang , J W Sutherland . A multiobjective disassembly planning for value recovery and energy conservation from end-of-life products. IEEE Transactions on Automation Science and Engineering, 2021, 18(2): 791–803 https://doi.org/10.1109/TASE.2020.2987391
42	K Manikya Kanti , P Srinivasa Rao . Prediction of bead geometry in pulsed GMA welding using back propagation neural network. Journal of Materials Processing Technology, 2008, 200(1–3): 300–305 https://doi.org/10.1016/j.jmatprotec.2007.09.034
43	M Ragavendran , N Chandrasekhar , R Ravikumar , R Saxena , M Vasudevan , A K Bhaduri . Optimization of hybrid laser—TIG welding of 316LN steel using response surface methodology (RSM). Optics and Lasers in Engineering, 2017, 94: 27–36 https://doi.org/10.1016/j.optlaseng.2017.02.015
44	F Zhang , T T Zhou . Process parameter optimization for laser-magnetic welding based on a sample-sorted support vector regression. Journal of Intelligent Manufacturing, 2019, 30(5): 2217–2230 https://doi.org/10.1007/s10845-017-1378-3
45	P Jiang , L C Cao , Q Zhou , Z M Gao , Y M Rong , X Y Shao . Optimization of welding process parameters by combining kriging surrogate with particle swarm optimization algorithm. The International Journal of Advanced Manufacturing Technology, 2016, 86(9): 2473–2483 https://doi.org/10.1007/s00170-016-8382-1
46	H M Soltani , M Tayebi . Comparative study of AISI 304L to AISI 316L stainless steels joints by TIG and Nd:YAG laser welding. Journal of Alloys and Compounds, 2018, 767: 112–121 https://doi.org/10.1016/j.jallcom.2018.06.302
47	J Y Shao , G Yu , X L He , S X Li , R Chen , Y Zhao . Grain size evolution under different cooling rate in laser additive manufacturing of superalloy. Optics & Laser Technology, 2019, 119: 105662 https://doi.org/10.1016/j.optlastec.2019.105662
48	Z Y Yang , K N Jin , H Fang , J S He . Multi-scale simulation of solidification behavior and microstructure evolution during vacuum electron beam welding of Al-Cu alloy. International Journal of Heat and Mass Transfer, 2021, 172: 121156 https://doi.org/10.1016/j.ijheatmasstransfer.2021.121156
49	N Kumar , M Mukherjee , A Bandyopadhyay . Comparative study of pulsed Nd:YAG laser welding of AISI 304 and AISI 316 stainless steels. Optics & Laser Technology, 2017, 88: 24–39 https://doi.org/10.1016/j.optlastec.2016.08.018
50	R Lenart , M Eshraghi . Modeling columnar to equiaxed transition in directional solidification of Inconel 718 alloy. Computational Materials Science, 2020, 172: 109374 https://doi.org/10.1016/j.commatsci.2019.109374
51	E M F de Souza Silva , G S da Fonseca , E A Ferreira . Microstructural and selective dissolution analysis of 316L austenitic stainless steel. Journal of Materials Research and Technology, 2021, 15: 4317–4329 https://doi.org/10.1016/j.jmrt.2021.10.009
52	M Ragavendran , M Vasudevan . Laser and hybrid laser welding of type 316L(N) austenitic stainless steel plates. Materials and Manufacturing Processes, 2020, 35(8): 922–934 https://doi.org/10.1080/10426914.2020.1745231
53	G R Mohammed , M Ishak , S N Aqida , H A Abdulhadi . Effects of heat input on microstructure, corrosion and mechanical characteristics of welded austenitic and duplex stainless steels: a review. Metals, 2017, 7(2): 39 https://doi.org/10.3390/met7020039
54	W D Huang , X G Geng , Y H Zhou . Primary spacing selection of constrained dendritic growth. Journal of Crystal Growth, 1993, 134(1–2): 105–115 https://doi.org/10.1016/0022-0248(93)90015-O
55	W Kurz , D J Fisher . Dendrite growth at the limit of stability: tip radius and spacing. Acta Metallurgica, 1981, 29(1): 11–20 https://doi.org/10.1016/0001-6160(81)90082-1
56	D G McCartney , J D Hunt . Measurements of cell and primary dendrite arm spacings in directionally solidified aluminium alloys. Acta Metallurgica, 1981, 29(11): 1851–1863 https://doi.org/10.1016/0001-6160(81)90111-5

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