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

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.

Graphical abstract

Keywords

laser beam welding / parameter optimization / metamodel / multi-objective

References

[1] Huang L J , Hua X M , Wu D S , Ye Y X . 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

[2] Hong K M , Shin Y C . Prospects of laser welding technology in the automotive industry: a review. Journal of Materials Processing Technology, 2017, 245: 46–69

[3] Stavridis J , Papacharalampopoulos A , Stavropoulos P . Quality assessment in laser welding: a critical review. The International Journal of Advanced Manufacturing Technology, 2018, 94(5): 1825–1847

[4] Zeng Z , Panton B , Oliveira J P , Han A , Zhou Y N . Dissimilar laser welding of NiTi shape memory alloy and copper. Smart Materials and Structures, 2015, 24(12): 125036

[5] Oliveira J P , Braz Fernandes F M , Miranda R M , Schell N , Ocana J L . Effect of laser welding parameters on the austenite and martensite phase fractions of NiTi. Materials Characterization, 2016, 119: 148–151

[6] Oliveira J P , Shen J J , Escobar J D , Salvador C A F , Schell N , Zhou N , Benafan O . Laser welding of H-phase strengthened Ni-rich NiTi-20Zr high temperature shape memory alloy. Materials & Design, 2021, 202: 109533

[7] Ruggiero A , Tricarico L , Olabi A G , Benyounis K Y . 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

[8] Oliveira J P , Shen J J , Zeng Z , Park J M , Choi Y T , Schell N , Maawad E , Zhou N , Kim H S . Dissimilar laser welding of a CoCrFeMnNi high entropy alloy to 316 stainless steel. Scripta Materialia, 2022, 206: 114219

[9] Jiang P , Wang C C , Zhou Q , Shao X Y , Shu L S , Li X B . Optimization of laser welding process parameters of stainless steel 316L using FEM, Kriging and NSGA-II. Advances in Engineering Software, 2016, 99: 147–160

[10] Assunção E , Quintino L , Miranda R . Comparative study of laser welding in tailor blanks for the automotive industry. The International Journal of Advanced Manufacturing Technology, 2010, 49(1): 123–131

[11] Kumar C , Das M , Paul C P , Bindra K S . 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

[12] Sokolov M , Salminen A . Improving laser beam welding efficiency. Engineering, 2014, 6(09): 559–571

[13] Abioye T E , Mustar N , Zuhailawati H , Suhaina I . 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

[14] Zhang M J , Liu T T , Hu R Z , Mu Z Y , Chen S , Chen G Y . 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

[15] Shanthos Kumar G , Raghukandan K , Saravanan S , Sivagurumanikandan N . 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

[16] Du Y , Mukherjee T , DebRoy T . Physics-informed machine learning and mechanistic modeling of additive manufacturing to reduce defects. Applied Materials Today, 2021, 24: 101123

[17] Huang Z , Cao H J , Zeng D , Ge W W , Duan C M . 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

[18] Mackwood A P , Crafer R C . Thermal modelling of laser welding and related processes: a literature review. Optics & Laser Technology, 2005, 37(2): 99–115

[19] Peng S T , Li T , Zhao J L , Lv S P , Tan G Z , Dong M M , Zhang H C . 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

[20] Akbari M , Shojaeefard M H , Asadi P , Khalkhali A . 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

[21] Akbari M , Asadi P , Zolghadr P , Khalkhali A . 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

[22] Srivastava S , Garg R K . 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

[23] Rong Y M , Zhang Z , Zhang G J , Yue C , Gu Y F , Huang Y , Wang C M , Shao X Y . Parameters optimization of laser brazing in crimping butt using Taguchi and BPNN-GA. Optics and Lasers in Engineering, 2015, 67: 94–104

[24] Wang S H , Zhu L D , Fuh J Y H , Zhang H Q , Yan W T . Multi-physics modeling and Gaussian process regression analysis of cladding track geometry for direct energy deposition. Optics and Lasers in Engineering, 2020, 127: 105950

[25] Wang G G , Shan S . Review of metamodeling techniques in support of engineering design optimization. Journal of Mechanical Design, 2007, 129(4): 370–380

[26] Goel T , Haftka R T , Shyy W , Queipo N V . Ensemble of surrogates. Structural and Multidisciplinary Optimization, 2007, 33(3): 199–216

[27] Younis A , Dong Z M . Trends, features, and tests of common and recently introduced global optimization methods. Engineering Optimization, 2010, 42(8): 691–718

[28] Dong H C , Li C S , Song B W , Wang P . Multi-surrogate-based Differential Evolution with multi-start exploration (MDEME) for computationally expensive optimization. Advances in Engineering Software, 2018, 123: 62–76

[29] Díaz-Manríquez A , Toscano G , Coello Coello C A . Comparison of metamodeling techniques in evolutionary algorithms. Soft Computing, 2017, 21(19): 5647–5663

[30] Jin R , Chen W , Simpson T W . Comparative studies of metamodelling techniques under multiple modelling criteria. Structural and Multidisciplinary Optimization, 2001, 23(1): 1–13

[31] Acar E . Effect of error metrics on optimum weight factor selection for ensemble of metamodels. Expert Systems with Applications, 2015, 42(5): 2703–2709

[32] Song X G , Sun G Y , Li G Y , Gao W Z , Li Q . Crashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate models. Structural and Multidisciplinary Optimization, 2013, 47(2): 221–231

[33] Gao Z M , Shao X Y , Jiang P , Cao L C , Zhou Q , Yue C , Liu Y , Wang C M . 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

[34] Ayoola W A , Suder W J , Williams S W . Parameters controlling weld bead profile in conduction laser welding. Journal of Materials Processing Technology, 2017, 249: 522–530

[35] Huang Y J , Gao X D , Ma B , Liu G Q , Zhang N F , Zhang Y X , You D Y . Optimization of weld strength for laser welding of steel to PMMA using Taguchi design method. Optics & Laser Technology, 2021, 136: 106726

[36] Cai X W , Qiu H B , Gao L , Li X K , Shao X Y . A hybrid global optimization method based on multiple metamodels. Engineering Computations, 2018, 35(1): 71–90

[37] Karaboga D , Basturk B . A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization, 2007, 39(3): 459–471

[38] Jia H F , Miao H Z , Tian G D , Zhou M C , Feng Y X , Li Z W , Li J C . 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

[39] Wang W J , Tian G D , Chen M N , Tao F , Zhao C Y , AI-Ahmari A , Li Z W , Jiang Z G . 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

[40] Verma B K , Kumar D . A review on artificial bee colony algorithm. International Journal of Engineering and Technology, 2013, 2(3): 175–186

[41] Ren Y P , Jin H Y , Zhao F , Qu T , Meng L L , Zhang C Y , Zhang B , Wang G , Sutherland J W . 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

[42] Manikya Kanti K , Srinivasa Rao P . Prediction of bead geometry in pulsed GMA welding using back propagation neural network. Journal of Materials Processing Technology, 2008, 200(1–3): 300–305

[43] Ragavendran M , Chandrasekhar N , Ravikumar R , Saxena R , Vasudevan M , Bhaduri A K . Optimization of hybrid laser—TIG welding of 316LN steel using response surface methodology (RSM). Optics and Lasers in Engineering, 2017, 94: 27–36

[44] Zhang F , Zhou T T . Process parameter optimization for laser-magnetic welding based on a sample-sorted support vector regression. Journal of Intelligent Manufacturing, 2019, 30(5): 2217–2230

[45] Jiang P , Cao L C , Zhou Q , Gao Z M , Rong Y M , Shao X Y . 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

[46] Soltani H M , Tayebi M . 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

[47] Shao J Y , Yu G , He X L , Li S X , Chen R , Zhao Y . Grain size evolution under different cooling rate in laser additive manufacturing of superalloy. Optics & Laser Technology, 2019, 119: 105662

[48] Yang Z Y , Jin K N , Fang H , He J S . 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

[49] Kumar N , Mukherjee M , Bandyopadhyay A . Comparative study of pulsed Nd:YAG laser welding of AISI 304 and AISI 316 stainless steels. Optics & Laser Technology, 2017, 88: 24–39

[50] Lenart R , Eshraghi M . Modeling columnar to equiaxed transition in directional solidification of Inconel 718 alloy. Computational Materials Science, 2020, 172: 109374

[51] de Souza Silva E M F , da Fonseca G S , Ferreira E A . Microstructural and selective dissolution analysis of 316L austenitic stainless steel. Journal of Materials Research and Technology, 2021, 15: 4317–4329

[52] Ragavendran M , Vasudevan M . Laser and hybrid laser welding of type 316L(N) austenitic stainless steel plates. Materials and Manufacturing Processes, 2020, 35(8): 922–934

[53] Mohammed G R , Ishak M , Aqida S N , Abdulhadi H A . Effects of heat input on microstructure, corrosion and mechanical characteristics of welded austenitic and duplex stainless steels: a review. Metals, 2017, 7(2): 39

[54] Huang W D , Geng X G , Zhou Y H . Primary spacing selection of constrained dendritic growth. Journal of Crystal Growth, 1993, 134(1–2): 105–115

[55] Kurz W , Fisher D J . Dendrite growth at the limit of stability: tip radius and spacing. Acta Metallurgica, 1981, 29(1): 11–20

[56] McCartney D G , Hunt J D . Measurements of cell and primary dendrite arm spacings in directionally solidified aluminium alloys. Acta Metallurgica, 1981, 29(11): 1851–1863

Nomenclature

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
Cm	Predetermined maximum cycle number of the searching processes for the bees
Cr	Repeated cycle number of the searching processes for the bees
D	Defocus distance
Dn	Neck depth
D_{\text{n}}^{+}, D_{\text{n}}^{-}	Maximum and minimum values of Dn in the Pareto optimal solutions, respectively
Dp	Depth of penetration
{\left|D_{\text{p}}-H\right|}^{+}, {\left|D_{\text{p}}-H\right|}^{-}	Maximum and minimum values of \left|D_{\text{p}}-H\right| 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
Eal	Generalized relative maximum absolute error under the leave-one-out method
Er	Relative error of the four outputs
Esl	Generalized root mean square error under the leave-one-out method
\hat{f}(\cdot )	Approximation approach using the metamodel
{\hat{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
\hat{f}(x_{-i})	Predictive response from the metamodel trained using the full data sets with the ith sample point excluded out
{\hat{f}}_1^k(x), {\hat{f}}_2^k(x)	First and second metamodel selected for the variable k, respectively
{\hat{f}}_{\mathrm{E}}^k(x)	Prediction value of the integrated EM for the variable k
{\hat{f}}_{\mathrm{E}}^{D_{\text{n}}}(x)	Integrated EM for the variable Dn
fitness(Xi)	Quality (fitness value) of the food source of Xi
H	Thickness of the workpiece
k	Output response variable
K	Thermal conductivity of the workpiece
m	Number of sample points
P	Laser power
Pi	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
Sn	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
Ve	Experimental values of the four outputs
Vp	Predicted values of the four outputs
w1, w2, w3, w4	Weighting values of the four optimization objectives
Wb	Bead width
W_{\text{b}}^{+}, W_{\text{b}}^{-}	Maximum and minimum values of Wb in the Pareto optimal solutions, respectively
Wn	Neck width
W_{\text{n}}^{+}, W_{\text{n}}^{-}	Maximum and minimum values of Wn in the Pareto optimal solutions, respectively
x	Input value of the metamodel
xi,j	jth dimension of the ith feasible solution
xp,j	One of the u food sources other than xi,j
xmax,j, xmin,j	Upper and lower bounds of the jth dimension, respectively
Xi	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
θi,j	Neighborhood of xi,j for searching a better food source
ρ	Material density of the workpiece
{\varphi }_{i,j}	Change rate of food sources during the employed bees phase
{\omega }_1^k, {\omega }_2^k	Weights of first and second metamodel for the variable k, respectively

Acknowledgements

This research was partially supported by the Project of International Cooperation and Exchanges NSFC (Grant No. 51861165202), the National Natural Science Foundation of China (Grant Nos. 51575211, 51705263, and 51805330), and the 111 Project of China (Grant No. B16019). The authors thank the technical support from the Experiment Center for Advanced Manufacturing and Technology in the School of Mechanical Science & Engineering of HUST.

Appendix

Table A1 Fiber LBW processing parameters and experimental results

No.	Processing parameters				Experimental results
	P/kW	S/(m·min−1)	D/mm		Wb/mm	Dp/mm	Wn/mm	Dn/mm
1	2.000	3.50	0.0		1.055	1.686	0.679	0.410
2	2.000	3.25	−0.5		1.204	1.823	0.583	0.601
3	2.000	3.00	−1.0		1.266	1.702	0.569	0.625
4	2.000	2.75	−1.5		1.195	1.950	0.512	0.806
5	2.000	2.50	−2.0		1.546	2.241	0.655	0.624
6	2.375	3.25	0.0		1.266	2.123	0.628	0.700
7	2.375	3.00	−0.5		1.323	2.059	0.608	0.691
8	2.375	2.75	−1.0		1.301	2.168	0.631	0.724
9	2.375	2.50	−1.5		1.538	2.225	0.651	0.699
10	2.375	3.50	−2.0		1.306	2.152	0.629	0.470
11	2.750	3.00	0.0		1.567	2.289	0.670	0.780
12	2.750	2.75	−0.5		1.497	2.339	0.717	0.684
13	2.750	2.50	−1.0		1.777	2.265	0.601	0.847
14	2.750	3.50	−1.5		1.510	2.534	0.712	0.561
15	2.750	3.25	−2.0		1.576	2.340	0.672	0.628
16	3.125	2.75	0.0		1.579	2.720	0.668	0.965
17	3.125	2.50	−0.5		1.587	2.921	0.669	1.046
18	3.125	3.50	−1.0		1.518	2.228	0.671	0.631
19	3.125	3.25	−1.5		1.637	2.804	0.724	0.668
20	3.125	3.00	−2.0		1.599	2.863	0.599	0.914
21	3.500	2.50	0.0		1.927	2.820	0.789	0.792
22	3.500	3.50	−0.5		1.418	2.447	0.825	0.576
23	3.500	3.25	−1.0		1.875	2.759	0.696	0.812
24	3.500	3.00	−1.5		1.719	2.966	0.738	0.871
25	3.500	2.75	−2.0		1.798	2.917	0.884	0.718

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