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

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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.

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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

C 0 :

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 Dn in the Pareto optimal solutions, respectively

D p :

Depth of penetration

|D p−H|+, |D p−H|− :

Maximum and minimum values of |Dp−H| in the Pareto optimal solutions, respectively

E k1 , E k2 :

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

\(\hat f\left(\cdot \right)\) :

Approximation approach using the metamodel

\({{\hat f}_i}\left(x \right)\) :

Predictive response of the ith individual metamodel at sample point x

f(x i):

Actual experimental value of the ith sample point

\(\hat f\left({{x_{- i}}} \right)\) :

Predictive response from the metamodel trained using the full data sets with the ith sample point excluded out

\(\hat f_1^k\left(x \right),\,\hat f_2^k\left(x \right)\) :

First and second metamodel selected for the variable k, respectively

\(\hat f_{\rm{E}}^k\left(x \right)\) :

Prediction value of the integrated EM for the variable k

\(\hat f_{\rm{E}}^{{D_{\rm{n}}}}\left(x \right)\) :

Integrated EM for the variable Dn

fitness(X i):

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

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

T 0 :

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

w 1, w 2, w 3, w 4 :

Weighting values of the four optimization objectives

W b :

Bead width

W +b , W −b :

Maximum and minimum values of Wb in the Pareto optimal solutions, respectively

W n :

Neck width

W +n , W −n :

Maximum and minimum values of Wn 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 xi,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 xi,j for searching a better food source

ρ :

Material density of the workpiece

ϕ i,j :

Change rate of food sources during the employed bees phase

ω k1 , ω k2 :

Weights of first and second metamodel for the variable k, respectively

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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.

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Authors and Affiliations

  1. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jianzhao Wu, Chaoyong Zhang, Jiahao Sun & Shuaikun Zhang

  2. Department of Mechanical Engineering, National University of Singapore, Singapore, 117575, Singapore

    Jianzhao Wu

  3. Walmart Global Technology, Walmart Inc., Bentonville, AR, 72712, USA

    Kunlei Lian

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  1. Jianzhao Wu
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  2. Chaoyong Zhang
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Correspondence to Chaoyong Zhang.

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Wu, J., Zhang, C., Lian, K. et al. Processing parameter optimization of fiber laser beam welding using an ensemble of metamodels and MOABC. Front. Mech. Eng. 17, 47 (2022). https://doi.org/10.1007/s11465-022-0703-5

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