*Corr. Author’s Address: University of Zanjan, Zanjan, Iran, dafshari@znu.ac.ir 485
Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 485-492 Received for review: 2022-04-25
© 2022 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2022-06-20
DOI:10.5545/sv-jme.2022.174 Original Scientific Paper Accepted for publication: 2022-07-08
Optimization in the Resistant Spot-Welding Process  
of AZ61 Magnesium Alloy
Afshari, D. – Ghaffari, A. – Barsum, Z.
Davood Afshari
1,*
 – Ali Ghaffari
1
 – Zuheir Barsum
2
1 
University of Zanjan, Iran 
2 
Royal Institute of Technology, Sweden
In this paper, an integrated artificial neural network (ANN) and multi-objective genetic algorithm (GA) are developed to optimize the resistance 
spot welding (RSW) of AZ61 magnesium alloy. Since the stability and strength of a welded joint are strongly dependent on the size of the 
nugget and the residual stresses created during the welding process, the main purpose of the optimization is to achieve the maximum size of 
the nugget and minimum tensile residual stress in the weld zone. It is identified that the electrical current, welding time, and electrode force 
are the main welding parameters affecting the weld quality. The experiments are carried out based on the full factorial design of experiments 
(DOE). In order to measure the residual stresses, an X-ray diffraction technique is used. Moreover, two separate ANNs are developed to predict 
the nugget size and the maximum tensile residual stress based on the welding parameters. The ANN is integrated with a multi-objective GA 
to find the optimum welding parameters. The findings show that the integrated optimization method presented in this study is effective and 
feasible for optimizing the RSW joints and process.
Keywords: resistance spot welding, residual stresses, artificial neural network, genetic algorithm, AZ61 magnesium alloy
Highlights
• 	 A full factorial design of experiments has been utilized to investigate the effects of the welding parameters on the nugget size 
and the residual stresses in the AZ61 resistance spot welded joint.
• 	 The nugget size and the residual stresses have been measured experimentally based on the DOE.
• 	 Two separate ANN models have been created to predict the nugget size and the maximum residual stress using the welding 
parameters.
• 	 An integrated ANN-ANN-GE algorithm has been developed to optimize the welding process.
• 	 The results show that the welding current and the welding time have significant effects on the nugget size and the maximum 
residual stress, respectively.
• 	 The findings confirm that the presented algorithm is effective and feasible to optimize the RSW process. 
0  INTRODUCTION
In recent years, alloys of Magnesium (Mg) have 
become of great attraction and significance as easy-to-
machine metals with exceptional strength-to-weight 
ratios, for various sectors including automotive, 
aerospace, and structural applications [1]. Magnesium 
is the lightest of all commonly used structural metals; 
with a density that is approximately two thirds that of 
aluminium and one quarter that of steels. Other than 
this, magnesium alloys have a high strength-to-density 
ratio, high specific heat, low melting temperature, and 
good castability, hot formability, recyclability, and 
sound-damping capabilities [1] to [5]. These properties 
bring a significant interest in many industrial 
applications to reduce the weight of the structures. 
Despite these considerable interests, using magnesium 
alloys in the industry remains limited compared with 
aluminium and steel alloys due to some technical 
problems. For example, the resistance spot welding 
(RSW) of magnesium alloys is more complex than 
in steel and aluminium alloys and needs different 
welding parameters. 
Although many new welding processes have 
been developed and presented for magnesium alloys 
(such as friction stir welding [6] to [9], laser welding 
[10] and [11]), RSW remains the most common joining 
process. In RSW, a high electric current is passed 
through the sheets via electrodes for a short time, 
which results in the generation of a melting zone 
between the sheets. After switching off the electrical 
current and undergoing a cooling process, a nugget 
is created in the welding area. Studies have shown 
that the nugget size is the most important controlling 
factor to determine the mechanical strength of the 
joint. The larger nugget results in higher mechanical 
strength [12] to [14]. In addition, when the molten 
metal starts cooling down to room temperature, a 
large temperature gradient occurs in the heat-affected 
zone (HAZ). This non-uniform temperature change 
leads to residual stresses in the welded joint. The 
residual stresses significantly affect stress corrosion 
cracking, hydrogen-induced cracking, and fatigue 
strength. Regardless of the loading conditions on spot-
welded joints, tensile residual stress deteriorates the 
fatigue strength and the quality of the joint [15] to [17]. 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 485-492
486 Afshari, D. – Ghaffari, A. – Barsum, Z.
Therefore, selecting the optimum welding parameters 
to achieve the maximum nugget size and the minimum 
tensile residual stress is the key factor in obtaining 
high-quality welding and joint strength.
Yi et al. [18] introduced a non-linear multiple 
orthogonal regression assembling model to optimize 
the welding parameters of RSW on galvanized steel 
sheet. They evaluated the effects of the welding 
parameters on the nugget size and optimized the 
parameters to maximize it. Hamidinejad et al. [19] 
predicted the mechanical strength of the RSW in 
the galvanized steel joints based on the welding 
parameters. They also optimized the welding 
parameters with a genetic algorithm (GA) to 
improve the tensile-shear strength. A multi-objective 
Taguchi method was applied to optimize the welding 
parameters in RSW of low-carbon steel by Muhammad 
et al. [20]. The main purpose of the study was to select 
the optimum RSW parameters to increase the nugget 
size and decrease the heat-affected zone (HAZ). Zhao 
et al. [21] utilized the response surface methodology 
(RSM) to optimize the nugget size, the mechanical 
strength, and the failure load in small-scale RSW of 
titanium alloy.
A hybrid ANN-GA model was developed by 
Pashazadeh et al. [22] to optimize the welding 
parameters of RSW on AISI 1008 steel alloy and 
achieve the maximum nugget size. Mirzaei et al. [23] 
developed a finite element (FE) model to predict the 
nugget size in RSW on galvanized steel. They used the 
RSM to optimize the welding parameters and obtain 
the maximum nugget size and maximum mechanical 
strength. Valera et al. [24] applied the Taguchi design 
of experiments to optimize the RSW of TRIP steel. 
The optimized electrical parameters were presented 
to increase the tensile-shear strength of the welded 
joints. The dissimilar RSW of AISI 316L austenitic 
stainless steel and 2205 duplex stainless steel were 
optimized by Vignesh et al. [25] using Taguchi’s L27 
orthogonal array (OA) design. Their results revealed 
that the welding current is the most dictating factor 
in achieving the highest tensile strength with superior 
weld quality.
The literature indicates that the optimization in 
the RSW of magnesium alloys has not been studied 
extensively. The purpose of this study is to contribute 
to the optimization of the welding parameters: 
electrical current, welding time, and electrode force 
of AZ61 magnesium alloy RSW joints. A full factorial 
design of the experimental (DOE) results is carried 
out and then two separate ANN models are developed 
to predict the nugget size and the maximum residual 
stress. Finally, an integrated ANN-ANN-GA algorithm 
is developed to optimize the welding parameters.
1  METHODS
In this study, AZ61 magnesium alloy has been used 
to prepare the welded samples. The nugget size has 
been measured experimentally for all the samples 
and an X-ray method has been utilized to measure 
the residual stresses. To predict the nugget size and 
the residual stresses, two ANN models have been 
developed. Finally, the welding parameters have been 
optimized by an integrated ANN-ANN-GE to obtain 
the maximum nugget size and the minimum tensile 
residual stress.
2  EXPERIMENTAL
AZ61 magnesium alloy sheets have been used to 
prepare the welding samples and their chemical 
composition is given in Table 1. 
Table 1.  Chemical compositions of AZ61 Mg alloy [wt.%]
Ca Cu Fe Si Mn Zn Al Mg
0.001 0.001 0.003 0.04 0.19 0.72 6.3 92.7
Fig. 1 shows the specification of the specimens 
(100 mm × 25 mm × 1.2 mm) and the welded joints. 
Fig. 1.  The dimensions of welded samples  
(dimensions in mm, not to scale) and the welded joints
The surfaces of the specimens have been cleaned 
using a hard brush before welding. RSW has been 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 485-492
487 Optimization in the Resistant Spot-Welding Process of AZ61 Magnesium Alloy 
performed by using a Novin Sazan Company Machine 
(model SSA014, IRAN, Fig. 2) with a CU08 controller 
and nominal welding power of 120 kVA. Both copper 
electrodes were cooled by circulating water during 
the welding. The welded samples have been cut along 
the centreline and the nugget size has been measured 
using an optical microscope (Fig. 3). A SEIFERT 
X-ray diffractometer (model 3000PTS, Fig. 4) has 
been utilized for the residual stress measurements. 
Measurements have been performed in the centre 
of the welded zone where the maximum tensile 
residual stress occurs [17]. The residual stresses have 
been measured on both sides of the welded samples 
in radial and transverse directions. The average of 
measured residual stresses has been reported as the 
maximum tensile residual stress in the welded zone.
Fig. 2.  The RSW machine, Novin Sazan model SSA014
Fig. 3.  The measurement of the nugget size
Fig. 4.  The SEIFERT X-ray diffractometer model 3000PTS
3  RESULTS AND DISCUSSION
3.1  The Full Factorial Experiment Design
In this study, a full factorial design of an experiment 
has been used to design the welding parameters 
schedule. Electrical current, welding time, and 
electrode force have been considered to be the main 
influencing welding parameters. The lower bond 
of each welding parameter was selected to achieve 
the nugget size recommended by AWS [26], and 
the higher bond was chosen to prevent weld splash 
and spatter. The appropriate ranges of the welding 
parameters are given in Table 2. The full factorial 
2
k
 design of experiments has been designed, k is the 
number of variables, which is 3 here with lower and 
higher bonds of −1 and +1, respectively. According to 
the full factorial DOE, a total of 8 combinations of the 
input parameters were considered. 
Table 2.  The higher and lower bond of RSW parameters
Welding 
current [kA]
Welding 
time [cycle]
Electrode 
force [N]
Higher bond (+1) 12 12 848
Lower bond (−1) 16 16 1130
The samples have been welded based on the 
welding parameters given in Table 3, and the results 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 485-492
488 Afshari, D. – Ghaffari, A. – Barsum, Z.
obtained from the nugget and the residual stress 
measurement are displayed in Table 3.
Fig. 5 illustrates the results of the DOE analysis 
for the nugget size. The Pareto diagram shows that 
although the electrical current, welding time, and their 
interaction affect the nugget size, the electrode force 
and its interaction with other variables have almost no 
effect. In addition, the electrical current is the most 
influential parameter on the nugget size. The Normal 
diagram confirms the results obtained from the Pareto 
diagram. The electrical current is the furthest point 
from the normal line, which means it is the most 
significant parameter. The points close to the normal 
line have no impact on the output. Similar results have 
been reported in previous studies for other materials 
[12] to [15] and [18] to [24].
The results of the DOE analysis for the residual 
stress are displayed in Fig. 6. According to the Pareto 
and Normal diagrams, the welding time and the 
electrode force affect the residual stresses. Although 
the welding time is the most influential parameter on 
the residual stress, the electrical current has almost 
no effect. The results are similar to those previously 
reported for RSW of Al joints [16]. 
3.2  The Artificial Neural Networks
ANN is a powerful and reliable model to predict 
complex phenomena with multiple variables. ANN is 
also very flexible in terms of the number of variables, 
the training algorithm, transfer functions, and the 
structure. An ANN consists of several layers: an input 
layer, some hidden layers, and an output layer. In 
addition, each layer involves some neurons. 
The number of hidden layers is usually one or, 
in specific cases, two. Using more than two layers is 
rarely done and is not recommended [27].
Two separate multilayer backpropagation 
feedforward ANNs have been used to predict the 
nugget size and the maximum tensile residual stress. 
Theses ANNs have been implemented using Matlab. 
Table 3.  The full factorial DOE
Sample Welding current [kA] Welding time [cycles] Electrode force [N] Nugget size [mm] Maximum residual stress [MPa]
1 12 12 848 4.54 276
2 16 12 1130 5.76 255
3 12 12 1130 4.42 254
4 16 16 1130 6.34 216
5 16 12 848 5.75 280
6 12 16 1130 4.64 213
7 12 16 848 4.68 234
8 16 16 848 6.33 238
a) 
Term
Effect
BC
ABC
C
AC
B
AB
A
2.0 1.5 1.0 0.5 0.0
0.332
F actor Name
A C urrent
B Time
C F orce
Pareto Chart of the Effects
(response is Nugget, Alpha = .05)
Lenth's PSE = 0.088125
b) 
Effect
Percent
2.0 1.5 1.0 0.5 0.0
99
95
90
80
70
60
50
40
30
20
10
5
1
F actor Name
A C urrent
B Time
C F orce
Effect Type
Not Significant
Significant
AB
B
A
Normal Probability Plot of the Effects
(response is Nugget, Alpha = .05)
Lenth's PSE = 0.088125
Fig. 5.  a) Pareto chart of the graph, and  
b) normal probability plot of the effect for the nugget size
a) 
Term
Effect
BC
ABC
AB
AC
A
C
B
70 60 50 40 30 20 10 0
6.35
F actor Name
A C urrent
B Time
C F orce
Pareto Chart of the Effects
(response is Residual, Alpha = .05)
Lenth's PSE = 1.6875
b) 
Effect
Percent
0 -10 -20 -30 -40 -50 -60 -70
99
95
90
80
70
60
50
40
30
20
10
5
1
F actor Name
A C urrent
B Time
C F orce
Effect Type
Not Significant
Significant
C
B
Normal Probability Plot of the Effects
(response is Residual, Alpha = .05)
Lenth's PSE = 1.6875
Fig. 6.  a) Pareto chart of the graph, and b) normal probability plot 
of the effect for the maximum residual stress

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 485-492
489 Optimization in the Resistant Spot-Welding Process of AZ61 Magnesium Alloy 
The Levenberg-Marquardt training algorithm has been 
utilized to train the ANNs. This algorithm minimizes 
a combination of squared errors and weights and then 
determines the correct combination. The transfers 
between layers have been done by using a combination 
of Tansig and Purelin transfer functions. Finally, the 
mean square error (MSE) function determines the 
ability of the ANNs to predict the outputs.
According to the number of the welding 
parameters and the output, the number of neurons in 
the input and output layers of both ANNs are three 
and one, respectively. The performance of the ANNs 
depends on the number of hidden layers and the 
number of their neurons. Hence, many trials need to 
be made to find the optimum structure for the ANN 
by changing the number of hidden layers and their 
neurons. Since there were two different ANN, two 
different structures have been considered. The proper 
structure for the first ANN to predict the nugget size 
was 3×6×1. The best structure for the second ANN to 
predict the maximum residual stress has been found 
to be 3×10×1 using a trial-and-error procedure. In 
addition, the values of the variables and outputs have 
been normalized between 1 and 2 (Eq. (1)) in order to 
increase the accuracy and speed of training the ANNs.
 P
PP
PP
n




min
maxm in
, 1 (1)
where P is the real value of each parameter, P
n
 is the 
normalized value, P
min
 and P
max
 are the minimum and 
maximum values respectively. Eq. (2) also has been 
used to de-normalize the results obtained from the 
model.
 P
P
PP
P
n
n




1
maxm in
min
. (2)
According to the DOE results, the electrical 
current is the most effective parameter on the nugget 
size, and the welding time has the most influential 
impact on the residual stress. Although the electrode 
force has almost no effect on the nugget size, it affects 
the residual stress. To run the ANNs, the five levels 
have been considered for both electrical current and 
welding time and just three levels have been selected 
for the electrode force. A total of 75 sets of welding 
parameters have been chosen to run the ANNs. Table 
4 displays the level of the RSW parameters considered 
to run the ANNs. However, the nugget sizes have 
been measured experimentally; the maximum residual 
stresses have been obtained from the FE model [6] 
since the experimental testing would have been time 
consuming.
Table 4.  The levels of RSW parameters for running the ANNs
RSW Parameters Levels
Welding current [kA] 12-13-14-15-16
Welding time [cycles] 12-13-14-15-16
Electrode force [N] 848-990-1130
The overfitting is the usual phenomenon that 
may occur in the training of ANN. It happens when 
the ANN memorizes the training data instead of 
building input-output mapping for the problem. Thus, 
determining the number of training and test data has 
a very important role in avoiding overfitting. In this 
study, approximately 10 % of the total tests (i.e., 7 
tests) have been randomly selected as the test data, 
and the remaining 68 tests have been considered for 
training data.
Fig. 7 illustrates the results obtained from the 
training and testing of the first ANN to predict the 
nugget size. The results indicate that the ANN has been 
trained successfully, and the first ANN can predict the 
nugget size very well. Table 5 displays the comparison 
between the results predicted from the first ANN and 
the results obtained from the experimental test.
a) 
6.5 6.0 5.5 5.0 4.5 4.0 3.5
6.5
6.0
5.5
5.0
4.5
4.0
3.5
Measured nugget diameter [mm]
Predicted nugget diameter [mm]
b) 
Fig. 7.  The compression results of measured and predicted nugget 
diameter by the first ANN model a) train samples and b) test 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 485-492
490 Afshari, D. – Ghaffari, A. – Barsum, Z.
The results obtained from the second ANN model 
are almost similar to the first model. The results 
indicate that the second ANN model can predict the 
residual stress based on the RSW parameters with high 
accuracy. Fig. 8 presents the results of the training and 
testing of the second ANN model.
a) 
245 240 235 230 225 220 215 210
245
240
235
230
225
220
215
210
205
Measured residual stress [MPa]
Predicted residual stress [MPa]
b) 
Fig. 8.  The compression results of measured and predicted 
residual stress by the second ANN model;  
a) train samples, and b) test 
3.3  The Multi-Objective Genetic Algorithm
The genetic algorithm (GA) is a repeat-based 
optimization method and its principles are adapted 
from genetic science. In the GA, a set of design 
variables are encoded by fixed-length or variable-
length strings, which the biological systems refer to 
them as chromosomes or individuals. GA is based on 
natural and biological science, and it is widely used to 
solve optimization problems in engineering.
A non-dominated sorting genetic algorithm 
II (NSGA II) has been developed to optimize the 
RSW parameters to obtain a set of desired values 
for maximizing the nugget size and minimizing 
the residual stress. Since the GA is the minimizing 
algorithm, Eq. (3) has been used as the fitness function 
to achieve the desired goal.
 MinM = αR – βd, (3)
where R is the residual stress, d is the nugget size, α 
and β are the weight coefficients for the residual stress 
and the nugget size, respectively. Because in this 
study there is no priority between the nugget size and 
residual stress, both α and β have been considered 1⁄2. 
Thus, the final fitness function is as follows:
 MinM = 1/2 R – 1/2 d. (4)
The flowchart of the developed multi-objective 
ANN-ANN-GA algorithm is presented in Fig. 
10. The initial population size was 100 and was 
the same for each generation. According to this 
presented optimization algorithm, the nugget size 
and the residual stress were predicted by the ANNs. 
A different set of RSW parameters were born in each 
generation, and the nugget size and residual stress 
were predicted by ANNs inside of the integrated 
optimization algorithm. A two-point crossover rate of 
0.5 and a uniform mutation probability of 0.05 were 
considered for the GA. In addition, 300 generations 
were chosen as the maximum generation and the 
condition for ending the algorithm.
Fig. 10.  The flowchart of the multi-objective ANN-ANN-GA 
Fig. 11 displays the results of running the 
integrated optimization algorithm. The optimized 
RSW parameters are displayed in Fig. 12. Since 
all the variables and outputs have been normalized 
between 1 and 2, the normalized parameters have 
been used in both ANNs and multi-objective GA. 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 485-492
491 Optimization in the Resistant Spot-Welding Process of AZ61 Magnesium Alloy 
high accuracy, and the optimum RSW parameters lead 
to high strength and good joint quality.
Fig. 12.  The optimized-normalized RSW parameters obtained from 
the integrated algorithm
4  CONCLUSIONS
In this study, the RSW parameters of the electric 
current intensity, welding time, and electrode force 
have been optimized to achieve the largest nugget 
along with the lowest tensile residual stress in the 
RSW of the magnesium alloy AZ61. The full factorial 
DOE has been employed to investigate the effects of 
the RSW parameters on the nugget and the residual 
stress. The results of the DOE have been used to 
develop two separated ANN models. The ANN 
models have been utilized to predict the dimensions 
of the nugget and the maximum tensile residual 
stress in the welded zone. The results display that the 
proposed ANNs have a high accuracy in predicting 
the dimensions of the nugget and the residual stress. 
Finally, an integrated multi-objective ANN-ANN-GA 
has been developed to optimize the RSW parameters. 
The results show that the presented optimization 
model can be used very well to optimize the RSW 
parameters.
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Table 5.  The optimized RSW parameters
Welding parameters
Welding current [kA] 12
Welding time [cycles] 16
Electrode force [N] 1130
Nugget size
Measured [mm] 4.74
Predicted [mm] 4.77
Error [%] 0.6
Maximum residual 
stress
Measured [MPa] 213
Predicted [MPa] 207
Error [%] 2.8
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