Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438 Received for review: 2022-03-10
© 2022 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2022-05-12
DOI:10.5545/sv-jme.2022.111 Original Scientific Paper Accepted for publication: 2022-05-12
*Corr. Author’s Address: Le Quy Don Technical University, 236 Hoang Quoc Viet, Ha Noi, VietNam, trungthanhnguyen@lqdtu.edu.vn 424
Optimization of Friction Stir Welding Operation Using  
Optimal Taguchi-based ANFIS and Genetic Algorithm 
Van, A.-L. – Nguyen, T.-T.
An-Le Van
1
 – Trung-Thanh Nguyen
2,*
1
Nguyen Tat Thanh University, Faculty of Engineering and Technology, Vietnam 
2
Le Quy Don Technical University, Faculty of Mechanical Engineering, Vietnam
The friction stir welding (FSW) process is an effective approach to producing joints of superior quality. Unfortunately, most published 
investigations primarily addressed optimizing process parameters to boost product quality. In the current work, the FSW operation of an 
aluminium alloy has been considered and optimized to decrease the specific welding energy (SWE) and enhance the jointing efficiency 
(JE) as well as micro-hardness at the welded zone (MH). The parameter inputs are the rotational speed (S), welding speed (f), depth of 
penetration (D), and tool title angle (T). The optimal adaptive neuro-based-fuzzy inference system (ANFIS) models were utilized to propose 
the welding responses in terms of the FSW parameters, while the Taguchi method was applied to optimize the ANFIS operating parameters. 
The neighbourhood cultivation genetic algorithm (NCGA) was employed to determine the best solution. The obtained results indicated that 
the optimal values of the S, f, D, and T are 560 rpm, 90 mm/min, 0.9 mm, and 2 deg, respectively. The SWE is decreased by 17 %, while the 
JE and MH are improved by 2.3 % and 6.4 %, respectively, at the optimal solution. The optimal ANFIS models for the welding responses were 
adequate and reliably employed to forecast the response values. The proposed optimization approach comprising the orthogonal array-based 
ANFIS, Taguchi, and NCGA could be effectively and efficiently utilized to save experimental costs as well as human efforts, produce optimal 
predictive models, and select optimum outcomes. The observed findings contributed significant data to determine optimal FSW parameters 
and enhance welding responses.
Keywords: friction stir welding; energy efficiency; jointing efficiency; micro-hardness; NCGA  
Highlights
• 	 FSW operating parameters, including the rotational speed, welding speed, depth of penetration, and tool title angle were 
considered.
• 	 The specific welding energy was minimized, while the jointing efficiency and micro-hardness at the welded zone were maximized. 
• 	 Optimal orthogonal array-based ANFIS models for welding performances were developed.
• 	 An efficient optimization approach comprising the ANFIS, Taguchi, and NCGA was proposed.
0  INTRODUCTION
The friction stir welding (FSW) operation is an 
effective and efficient solid-state joining process in 
which the tool plastically deforms the material and 
mixes it to produce strong welds. The FSW process 
is widely employed to avoid the porosity, hot crack, 
and large deformation due to non-material melting, 
as compared to the other fusion welding processes. 
Moreover, this technology does not require material, 
such as shielding gas, electrodes, and filling materials, 
for generating welded joints. Consequently, the FSW 
operation could be efficiently and effectively applied 
to produce high quality joints for different materials 
with similar and/or dissimilar thicknesses. 
Many attempts have been executed to improve 
the mechanical properties of the joints for different 
FSW operations, in which the conventional welding 
responses are the ultimate tensile strength (TS), yield 
strength (YS), elongation (EL), welding force (WF), 
welding temperature (WT), micro-hardness at the 
welded zone (MH), and grain size (GS). The ratio 
between shoulder and pin diameters (R) of 4, the 
rotational speed (S) of 100 rpm, the welding speed (f) of 
100 mm/min were utilized to improve the TS and EL of 
the AA6082-AA5754 joint [1]. The pin square, the S of 
1400 rpm, the f of 1.75 mm/s, and the axial force (AF) 
of 7.5 KN were applied to enhance the TS, MH, and YS 
of the AA7075 weld [2]. The optimal data of the f, S, and 
T were 25 mm/min, 1250 rpm, and 1 deg, respectively, 
which could be used to obtain the TS of 6.06 MPa for 
the composite joint [3]. Shojaeefard et al. stated that the 
optimal values of the S and f for the FSW operation of 
AA5083 were 1345 rpm and 60.0 mm/min, respectively 
[4]. For the welded magnesium alloy, the S was found 
to be the most effective contribution, followed by the f 
and the AF [5]. The S of 1550 rpm, the T of 4 deg, and 
octagonal pin were applied to boost the TS and EL of the 
aluminium alloy weld [6]. Gou et al. emphasized that 
the maximum TS and MH for the AA6061-T6 could be 
obtained at the D of 0.45 mm [7]. Saju and Narayanan 
revealed that the highest mechanical properties of the 
AA5052-AA6061 weld were achieved with the D of 
0.6 mm [8]. The TS of 2.6 KN and the MH of 70.45 HV 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
425 Optimization of Friction Stir Welding Operation Using Optimal Taguchi-based ANFIS and Genetic Algorithm  
for the dissimilar AA5083-C10100 weld were obtained 
at the S of 1250 rpm, depth of penetration (D) of 1.9 
mm, and dwell time (DT) of 12.5 s, respectively [9]. 
Elyasi et al. emphasized that the T of 2 deg could be 
applied to improve the TS and MH of the AA1100 weld 
[10]. Farzadi et al. indicated that the S of 513 rpm, the f 
of 95 mm/min, the shoulder diameter (SD) of 16.1 mm 
and the D of 5 mm could be applied to maximize the TS 
of the AA7075 weld [11]. The S of 900 rpm, f of 60 mm/
min, SD of 18 mm, and D of 5 mm were employed to 
enhance the TS, MH, and GS for the AA5083-AA6063 
weld [12]. 
Palanivel et al. indicated that the S of 1000 rpm, 
the f of 60 mm/min, and the partial impeller pin were 
applied to improve the TS of AA6351-AA5083 joint 
[13]. The vertical force model of the FSW operation of 
AZ31 magnesium alloy was developed with the aid of 
an artificial neural network (ANN) [14]. Rajendran et 
al. revealed that the defect-free welds were obtained 
using the T of 1 deg to 3 deg [15]. The S of 1005 rpm, f 
of 20 mm/min, and T of 3 deg were utilized to increase 
the TS of the AA2219 joint [16]. The TS of 167 MPa, 
the YS of 145 MPa, and the EL of 8.3 % for the 6063-
T6 joint were achieved using optimum outcomes [17]. 
The maximum TS (135.83  MPa) and EL (4.35 %) of 
the AAA6061-A5083 joint were produced at the T of 
1.11 deg, the S of 1568  rpm, and the f of 39.53 mm/
min, respectively [18]. Boukraa et al. indicated that 
the WT and dissolution time were enhanced by 13.44 
% and 46.5 %, respectively, at the optimal solution 
for the AA2195-T8 joint [19]. Satheesh et al. revealed 
that the taper cylindrical pin geometry, the S of 1045 
rpm, the f of 1.5 mm/s, and the AF of 4.87 kN were 
applied to improve the TS, YS, and EL for the AZ91C 
Mg alloy joint [20]. The distribution of the WT on the 
AZ80A Mg Alloy joint was analysed by Sevvel et 
al., in which the authors stated that the S was named 
as the best contribution, followed by the f and AF, 
respectively [21]. The empirical models of the TS, 
EL, and percentage reduction in area were developed 
in terms of the S, f, and SD for the carbon steel weld 
[22]. A simulation model was developed to investigate 
the impacts of the S and pin geometry on the WT for 
the AZ80A Mg alloy weld, in which the authors stated 
that the maximum WT was obtained by means of 
distinctive geometries [23]. 
As a result, different FSW processes with various 
materials have been considered and optimized 
to enhance welding performances. However, the 
shortcomings of published works can be listed as 
follows.
Quality indicators are primary considerations 
of the aforementioned works. The impacts of FSW 
factors on energy consumption have not been 
analysed.
The energy consumption model regarding the 
FSW parameters has not been developed.
The selection of optimal FSW parameters for 
decreasing energy consumed and improving the 
welding quality (e.g., ultimate tensile strength and 
elongation) has not been addressed.  
To overcome these challenges, the FSW 
operation of the AA6061 has been considered and 
optimized to decrease the specific welding energy 
(SWE) and enhance the jointing efficiency (JE) as 
well as micro-hardness at the welded zone (MH). The 
optimal Taguchi-based ANFIS models were utilized to 
propose FSW performances regarding the S, f, D, and 
T. The optimal outcomes are selected with the aid of 
the NCGA.  
The scientific contributions of the current study 
can be expressed as follows.
The developed optimizing method comprising 
the Taguchi method, ANFIS, and NCGA can be 
considered an effective and efficient approach to 
solving complicated optimization issues and selecting 
optimal outcomes. The developed approach possesses 
various advantages, including low experimental costs, 
decreased human efforts, and easy implementation. 
The developed technique could be effectively and 
efficiently employed to optimize not only welding 
operations but also other machining processes.
The impacts of the FSW parameters on the 
FSW responses have been thoroughly analysed. The 
obtained knowledge can help machine operators 
comprehend the physical insights in the FSW 
operation of the AA6061.
The analysed outcomes of the current study can 
be effectively and efficiently utilized as significant 
references for future investigations and developing 
expert systems regarding FSW processes.
1  OPTIMIZING FRAMEWORK
Traditionally, the primary aim of the FSW process 
is to produce the welds with superior quality, as 
seen in factors such as ultimate tensile strength, 
elongation, micro-hardness at the weld nugget zone, 
yield strength, and grain size. Unfortunately, the rise 
of energy cost and environmental legislation requires 
manufacturers to decrease energy consumed, welding 
noise/fumes, and wastage. In this investigation, three 
technological responses, including the SWE, JE, and 
MH, are listed as important indicators.
The profile of the power consumed for the FSW 
process is shown in Fig. 1, in which three operating 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
426 Van, A.-L. – Nguyen, T.-T.
phases, including the plunge, dwell, and welding states 
are depicted. For the plunge phase, the workpieces are 
tightly clamped on the fixture, while the rotating tool 
is inserted into the joint line of plates. For the dwell 
phase, the rotational motion of the welding tool is kept 
in its position to plasticize the material around the pin. 
For the welding phase, the linear motion of the tool is 
performed to produce the weld in the solid state.
Fig. 1.  The profile of the power consumption
The SWE value is calculated as:
 SWE
P
f
w
= , (1)
where P
w
 and f are the power consumed in the welding 
time and welding speed, respectively. 
The JE value is computed as:
 JF
UTS
UTS
w
b
= , (2)
where UTS
w
 and UTS
b
 denote the ultimate tensile 
strength of the weld and base material, respectively.
The MH value is computed as:
 MH
MH
i
n
i
n


1
, (3)
where MH
i
 and n denotes the micro-hardness at the 
i
th
 
position and the number of measuring points, 
respectively.
The schematic of the FSW operation with the 
four process parameters is shown in Fig. 2. The 
welding tool and materials used are considered fixed 
conditions. Four key process parameters, including 
the S, f, D, and T are listed as optimizing inputs (Table 
1). The ranges of the S and f are primarily selected 
based on the specifications of the machine tool and 
recommendations of the manufacturer of the welding 
tool. The levels of the D and T are determined using the 
configuration of the machine tool and the knowledge 
of the previous publications. The highest and lowest 
values of process parameters were tested by means 
of experimental trials to ensure machinability. These 
values are confirmed by company experts and welding 
handbooks. 
Fig. 2.  The schematic illustration of the FSW operation
Consequently, the optimizing issue is expressed 
as follows:
Finding X = [S, f, D, and T].
Maximizing JE and MH; Minimizing SWE. 
Constraints: 480 ≤ S ≤ 1600 rpm; 
48 ≤  f  ≤ 112 mm/min; 0.6 ≤ D ≤ 1.2 mm; 0 ≤ T ≤ 4 deg
The systematic approach for generating optimal 
FSW parameters is shown in Fig. 3.
Step 1: The physical experiments of the FSW 
operation are then conducted using the orthogonal 
array L
32
. 
Step 2: The ANFIS models of the SWE, JE, and 
MH are developed in terms of the FSW parameters. 
In this investigation, the ANFIS with five layers are 
developed to model welding performances [24].
Layer I: This layer is employed to convert the 
inputs set to fuzzy set with the aid of the assigned 
membership function. The outputs of three welding 
responses are expressed:
 Lx Ax E 1, () ,  (4)
 Ly By T 1, () ,   (5)
 Lz Cz L 1, () ,  (6)
where E, T, and L are the input variable nodes, while x, 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
427 Optimization of Friction Stir Welding Operation Using Optimal Taguchi-based ANFIS and Genetic Algorithm  
y, z, A, B, and C are connected labels having μ(E), μ(S, 
and μ(P) as memberships.
Layer II: This layer is employed to generate the 
fixed function of the input. The node function Π is 
expressed as:
 Lx Ax EB yT Cz L 2, () () () .   (7)
Layer III: This layer contains the fixed node 
labelled N. The output namely the normalized firing 
strength is represented as:
 Lx
i
i
i
i
n
3
1






. (8)
Layer IV: This layer contains an adaptive node. 
The current layer is applied to assign the consequent 
parameters of the rules. The output of this layer is 
expressed as:
 Lx ax bx c
ii i i
4    () ,  (9)
where a
i
, b
i
, and c
i
 are the consequent parameters, 
respectively.
Layer V: This layer comprises only one fixed 
node. The fifth layer is used to calculate the overall 
output of all incoming signals. The output of this layer 
is expressed as:
 Lx f
ii
i
5  . (10)
Step 3: The optimal parameters of the ANFIS 
models are selected using the Taguchi method.
It is necessary to select the proper operating 
factors of each ANFIS model to minimize the 
predictive errors. The aforementioned publications 
randomly determine the operating parameters, 
including the number of inputs, types of input, optimal 
method, and types of output. Practically, a variety of 
each ANFIS parameter changes the mean square error 
(MSE), which is expressed as:
 MSE
n
yy
mp
i
n
 

1
2
1
() , (11)
where y
m
 and y
p
 are the measured and predicted values, 
respectively. 
Step 4: The optimal outcomes of the FSW process 
factors and technical responses are selected with the 
aid of the NCGA. 
The NCGA is an effective solution to solve 
the trade-off analysis between the conflicting 
responses. This algorithm possesses various 
advantages, including easy computational skills, a 
large number of feasible solutions, and producing 
global optimization results. The NCGA provides 
better results than conventional approaches, such as 
multi-objective genetic algorithm (MOGA) and non-
dominated sorting genetic algorithm II (NSGA-II) 
when responses have a multiple peak landscape and 
a higher number of design variables. However, the 
NCGA requires higher computational time to conduct 
the algorithm. The working principle of the NCGA is 
summarized, as follows (Fig. 4):
• Assigning initial population (P
0
) and computing 
fitness of the initial individual.
• Generating and sorting a new generation (P
t
) 
based on the objective purpose.
• Performing crossover and mutation operations for 
generating new child individuals.
• Assembling produced individuals and generating 
a new population.
Fig. 3.  The flow chart of optimization approach
Table 1.  FSW parameters for the experimental work
No. Symbol Parameters Values
1 S Rotational speed [rpm] 480 1120 1600
2 f Welding speed [mm/min] 48 77 112
3 D Depth of penetration [mm] 0.60 0.90 1.20
4 T Tool title angle [deg] 0 2 4
2  EXPERIMENTS AND MEASUREMENTS
The welding specimens with a length of 160 mm, 
a width of 100 mm, and a thickness of 6 mm are 
prepared with the aid of milling process. The joints 
between the AA6061 plates are widely utilized in the 
marine industry to resist the corrosion of seawater. 
The chemical compositions and mechanical properties 
of the AA6061 with the aid of the axial tension test are 
presented in Table 2.
The welding experiments are done with the aid 
of a vertical milling machine and a fabricated fixture 
(Fig. 5). The welding tool with a cylindrical tapered 
pin is applied to perform trials. The hot die steel 
entitled H13 is used as the tool material due to its 
high strength, wear resistance, and stability at higher 
temperatures. The flat bars are employed to clamp the 
workpiece tightly using the bolts.

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
428 Van, A.-L. – Nguyen, T.-T.
Fig. 4.  The operating principle of the NCGA
Table 2.  Chemical compositions and mechanical properties of the AA6061
Element Mn Fe Mg Si Cu Zn Ti Cr Others Al
 [%] 0.12 0.55 0.10 0.60 0.30 0.20 0.10 0.30 0.10 Balance
Mechanical properties
Ultimate tensile strength [MPa] Yield stress [MPa] Elongation [%] Vickers Hardness [HV] Poisson’s ratio Modulus of elasticity [GPa]
241 214 15.2 104 0.33 68.9
A power sensor (Kyoritsu 6305) is used to record 
the variety of power components during the welding 
time. The obtained data is stored in the flashcard and 
visualized with the aid of the KEW6305 software. 
The reading and scaling errors are ±0.3 % and ±0.2 
%, respectively, to improve the measuring precision, 
while the up-dating time of 1 second is utilized to 
visualize the capture data. 
The ultimate tensile strength and elongation are 
obtained with the aid of the Exceed E45 machine 
based on the American Society for Testing of 
Materials (ASTM E8) guidelines. The resolution 
of 0.1 MPa is employed to improve the accuracy of 
the measuring tensile strength. The Vickers Wolperts 
Wilson machine is used to measure the micro-hardness 
with the force of 500d at the dwell time of 20 seconds. 
The resolution of 0.1 HV is applied to capture the 
experimental data.
3  RESULTS AND DISCUSSION
3.1  Development of the Optimal ANFIS Models
The experimental outcomes of the FSW operation are 
shown in Table 3. 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
429 Optimization of Friction Stir Welding Operation Using Optimal Taguchi-based ANFIS and Genetic Algorithm  
a) 
b) 
Fig. 5.  FSW Experiment; a) experimental setting,  
b) representative specimen 
Practically, the optimal architecture of the ANFIS 
model is randomly determined using the decisive 
maker, which decreases the predicting precision. In 
this study, optimal Taguchi-based ANFIS models 
are proposed to render the relations between process 
parameters and FSW performances. Four ANFIS 
operating parameters are the number of input MFs 
(N), types of input MFs (TI), optimal method (O), 
and types of output MFs (TO). The parameter 
combinations of the ANFIS model are produced 
with the support of the Taguchi experimental matrix 
L
16
. The numerical experiments of ANFIS models 
are executed to calculate the MSE values for three 
welding responses. As shown in Fig. 6a, the optimal 
outcomes of the N, TI, O, and TO for the SWE model 
are 2, gaussmf, hybrid, and linear, respectively. As 
shown in Figs. 6b and c, the optimal outcomes of 
the N, TI, O, and TO for the JE and MH models are 
2, gaussmf, hybrid, and constant, respectively. The 
2-2-2-2-2 ANFIS architecture can be used to render 
the relations between welding parameters and the 
responses (Fig. 7). The schematic rules for ANFIS 
models of the SWE, JE, and MH are shown in Figs. 8 
a, b, and c, respectively.
The Gaussian membership function is expressed 
as:
 
Ai
i
i
x
xc
a
() exp , 
 













1
2
2
 (12)
where a
i
 and c
i
 are the definite centre and its width of 
the membership function, respectively.
To investigate the accuracy of developed ANFIS 
models, a set of experiments is performed at random 
points. The comparisons between the obtained and 
ANFIS results are presented in Table 4. The errors of 
the SWE, JE, and MH lie within the range of -1.48 % 
to 0.53 %, -0.86 % to 0.59 %, and -0.11 % to 1.20 
%, respectively. The accepted deviations indicate that 
the developed models performed well in predicting 
welding responses.
a) 
b) 
c) 
Fig. 6.  MSE values for FSW responses; a) for SWE model, b) for JE 
model, c) for MH model
3.2  ANOVA Results for Welding Performances
The ANOVA results of the SWE, JE, and MH models 
are presented in Tables 5 to 7, respectively. The R
2
, 
adjusted R
2
, and predicted R
2
 values indicate that the 
developed models are adequate.

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
430 Van, A.-L. – Nguyen, T.-T.
Fig. 7.  The ANFIS structures for welding performances
Table 3.  Experimental data for the FSW operation
No. S [rpm] f [mm/min] D [mm] T [deg] SWE [J/mm] UTS
w
 [MPa] JE [%] MH [HV]
Experimental 
data for 
developing the 
ANFIS models 
of welding 
responses
1 480 48 0.6 0 1693.64 133.1 55.24 74.2
2 1120 77 0.6 2 1211.24 158.9 65.95 62.8
3 1600 112 0.6 4 960.73 131.2 54.45 60.3
4 480 48 0.6 0 1693.64 133.2 55.28 74.2
5 480 48 0.6 2 1741.24 152.7 63.36 71.4
6 1120 77 0.6 0 1175.54 139.5 57.89 66.2
7 1600 112 0.6 0 909.19 113.8 47.22 69.3
8 480 48 0.6 4 1801.61 151.1 62.68 66.7
9 480 77 0.9 4 1255.48 151.3 62.78 62.8
10 1120 48 0.9 0 1903.33 165.0 68.45 55.3
11 1600 48 0.9 0 2013.54 164.3 68.17 51.1
12 480 112 0.9 2 889.28 139.2 57.78 72.4
13 480 77 0.9 0 1183.62 142.1 58.98 68.3
14 1120 48 0.9 4 2016.12 174.1 72.22 47.5
15 1600 48 0.9 2 2066.76 179.5 74.48 47.5
16 480 112 0.9 0 879.27 124.2 51.53 73.8
17 480 48 1.2 0 1854.52 160.3 66.53 61.2
18 1120 112 1.2 2 934.86 161.1 66.83 60.4
19 1600 77 1.2 4 1461.78 170.3 70.67 43.9
20 480 48 1.2 0 1854.52 160.5 66.58 61.2
21 480 48 1.2 2 1898.37 171.3 71.08 59.9
22 1120 112 1.2 0 922.43 150.3 62.36 62.2
23 1600 77 1.2 0 1378.67 169.9 70.49 51.1
24 480 48 1.2 4 1954.99 161.1 66.86 56.5
25 480 112 0.6 4 860.74 126.4 52.45 74.4
26 1120 48 0.6 0 1800.72 147.8 61.31 63.5
27 1600 48 0.6 0 1910.77 145.7 60.44 59.2
28 480 77 0.6 2 1134.09 146.3 60.71 73.5
29 480 112 0.6 0 824.22 108.9 45.17 80.7
30 1120 48 0.6 4 1917.26 165.6 68.73 54.2
31 1600 48 0.6 2 1965.87 165.2 68.54 54.9
32 480 77 0.6 0 1102.67 126.8 52.63 75.9
Experimental 
data for testing 
the accuracy 
of developed 
ANFIS models
33 560 66 0.8 2 1397.78 160.3 66.52 65.7
34 800 90 1.0 0 1052.33 150.1 62.28 63.1
35 1250 112 1.2 4 973.83 151.1 62.68 55.3
36 1600 66 0.9 0 1557.83 159.2 66.05 53.4
37 1250 90 1.1 4 1178.58 164.2 68.15 50.2
38 1120 90 1.0 4 1151.58 162.1 67.27 52.6

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
431 Optimization of Friction Stir Welding Operation Using Optimal Taguchi-based ANFIS and Genetic Algorithm  
workpiece to be machined, leading to higher friction 
at the interfaces. Greater resistance is produced, which 
requires more power used to overcome the friction 
of the joining materials; hence, the SWE logically 
increases. There are similar impacts of the spindle 
For the SWE model, single terms (S, f, D, and 
T), interactive terms (Sf, fD, and fT), and quadratic 
terms (S
2
, f
2
, and D
2
) are significant factors. The 
contributions of the S, f, D, and T are 7.89 %, 50.59 %, 
5.47 %, and 3.77 %, respectively. The contributions 
of the Sf, fD, and fT are 3.28 %, 2.35 %, and 1.77 %, 
respectively. The contributions of the S
2
, f
2
, and D
2 
are 
1.73 %, 19.74 %, and 2.18 %, respectively.
For the JE model,  single terms (S, f, D, and 
T), interactive term (Sf, SD, and DT), and quadratic 
terms (S
2
, f
2
, D
2
, and T
2
) are significant factors. The 
contributions of the S, f, D, and T are 8.81 %, 20.64 %, 
16.09 %, and 6.64 %, respectively. The contributions 
of the Sf, SD, and DT are 2.78 %, 2.46 %, and 6.29 
%, respectively. The contributions of the S
2
, f
2
, D
2
, 
and T
2  
are 11.16 %, 6.93 %, 2.45 %, and 15.52 %, 
respectively.
For the MH model, single terms (S, f, D, and T), 
interactive term (Sf, ST, fD, and DT), and quadratic 
terms (S
2
, f
2
, D
2
, and T
2
) are significant factors. 
The contributions of the S, f, D, and T are 23.89 %, 
16.87 %, 16.49 %, and 11.49 %, respectively. The 
contributions of the Sf, ST, fD, and DT are 2.94 %, 
2.53 %, 2.29 %, and 2.29 %, respectively. The 
contributions of the S
2
, f
2
, D
2
 and, T
2 
are 7.18 %, 3.86 
%, 5.66 %, and 3.37 %, respectively. 
3.3  The Impacts of FSW Parameters 
The influences of FSW parameters on the specific 
welding energy are shown in Fig. 9. 
Fig. 9a indicates that a higher S increases the SWE, 
while an increased f causes a reduction in the SWE. 
When the S relatively rises from 480 rpm to 1600 rpm, 
the SWE is relatively increased by 13.6 %. At a higher 
S, the momentum of the main spindle increases and 
the spindle system consumes more power consumed 
to satisfy the desired value. The total power consumed 
of the machine tool increases; hence, the SWE 
increases according to Eq. (1). An increased S causes 
higher welding engagement between the tool and 
Table 4. Comparative errors for the welding responses
No. SWE [J/mm] JE [%] MH [HV]
Exp. ANFIS Err. [%] Exp. ANFIS Err. [%] Exp. ANFIS Err. [%]
33 1397.78 1390.42 0.53 66.52 66.14 0.57 65.7 65.2 0.76
34 1052.33 1067.89 -1.48 62.28 62.77 -0.79 63.1 63.8 -1.11
35 973.83 970.12 0.38 62.65 62.28 0.59 55.3 55.7 -0.72
36 1557.83 1552.94 0.31 66.05 66.62 -0.86 53.4 53.8 -0.75
37 1178.58 1172.93 0.48 68.15 68.73 -0.85 50.2 49.6 1.20
38 1151.58 1159.46 -0.68 67.27 67.59 -0.48 52.6 52.1 0.95
Exp.: Experimental value; Err.: Error
Table 5.  ANOVA results for the SWE model 
So SS MS F Value p-value
Mo 343725.7 343725.7 35.3 0.0001
S 598793.7 598793.7 859.8 0.0001
f 383216.9 383216.9 5512.8 0.0001
D 415233.3 415233.3 596.1 0.0001
T 286087.7 286087.7 410.8 0.0001
Sf 248222.2 248222.2 357.4 0.0033
fD 178436.6 178436.6 256.1 0.0046
fT 134269.3 134269.3 192.9 0.0058
S2 131912.9 131912.9 188.5 0.0062
f2 149067.7 149067.7 2151.1 0.0001
D2 164422.1 164422.1 237.5 0.0048
Res 76608.1 6964.4
Cor 351433.8
R
2
 = 0.9782; Adjusted R
2 
= 0.9734; Predicted R
2
 = 0.9622
Table 6.  ANOVA results for JE model 
So SS MS F Value p-value
Mo 892.76 63.769 41.008 < 0.0001
S 26533.5 26533.5 17063.37 < 0.0001
f 62162.5 62162.5 39975.93 < 0.0001
D 48459.1 48459.1 31163.41 < 0.0001
T 199981 199981 12860.47 < 0.0001
Sf 8372.6 8372.6 5384.35 0.0045
SD 7408.9 7408.9 4764.57 0.0048
DT 18943.9 18943.9 12182.58 0.0003
S2 33611.1 33611.1 21614.89 < 0.0001
f2 20871.4 20871.4 13422.15 0.0001
D2 7378.7 7378.7 4745.205 0.0048
T2 46742.4 46742.4 30059.42 < 0.0001
Res 17.105 1.555
Cor 909.865
R
2
 = 0.9812; Adjusted R
2
 = 0.9746; Predicted R
2
 = 0.9622

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
432 Van, A.-L. – Nguyen, T.-T.
speed on the energy consumption for the turning [25], 
milling [26], and burnishing [27] processes. 
As shown in Fig. 9a, when the f relatively changes 
from 47 mm/min to 112 mm/min, the SWE is relatively 
decreased by 52.6 %. An increased f causes higher 
power consumption in the feed driving system; hence, 
the total power used in the machine tool increases. 
Fortunately, the SWE is inversely proportional to f 
according to Eq.1; therefore, higher f decreases the 
SWE value. An increment in the f causes a reduction 
in the welding time, which decreases the machining 
engagement between the tool and workpiece; hence, 
a decreased friction at the interfaces is obtained. Low 
power consumption is required due to low resistance; 
hence, the SWE decreases. Similar impacts of the 
transverse speed on the energy consumption can be 
found in the turning [25], milling [26], and burnishing 
[27] operations.
As shown in Fig. 9b, an increased D causes a 
higher SWE. When the D relatively changes from 0.6 
mm to 1.2 mm, the SWE is relatively increased by 
9.6 %. An increase in the D causes a higher depth of 
shoulder inside the workpiece. This creates hindrances 
for tool movement, leading to higher friction at the 
interfaces between the tool and workpiece. Higher 
power consumed is required to overcome greater 
resistance; hence, the SWE increases. An increased 
energy consumption with a higher depth of penetration 
can be found for the turning [25], milling [26], and 
burnishing [27] processes. 
As shown in Fig. 9b, an increased T causes a 
higher SWE. When the T relatively rises from 0 deg 
mm to 4 deg, the SWE is relatively increased by 6.3 
%. At a higher T, the depth of the shoulder inside the 
specimen increases; which leads to higher friction 
between the tool and workpiece. Greater resistance 
for tool movement is obtained, which requires more 
power consumption; hence, a higher SWE is required. 
Higher energy consumption with an increased T was 
presented in the work of [10].
a) 
b) 
c) 
Fig. 8.  The schematic rules for;  
a) SWE model, b) IF model, and c) MH model
Table 7.  ANOVA results for MH model 
So SS MS F Value p-value
Mo 1446.74 103.34 33.081 < 0.0001
S 1639.87 1639.87 524.963 < 0.0001
f 1158.00 1158.00 370.705 < 0.0001
D 113.91 113.91 362.354 < 0.0001
T 788.70 788.70 252.483 < 0.0001
Sf 201.81 201.81 64.604 0.0056
ST 173.66 173.66 55.595 0.0058
fD 157.19 157.19 50.321 0.0061
DT 157.19 157.19 50.321 0.0061
S2 492.85 492.85 157.775 0.0002
f2 264.96 264.96 84.820 0.0043
D2 388.51 388.51 124.374 0.0003
T2 231.32 231.32 74.053 0.0044
Res 34.36 3.12
Cor 1481.10
R
2
 = 0.9768; Adjusted R
2
 = 0.9691; Predicted R
2
 = 0.9638

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
433 Optimization of Friction Stir Welding Operation Using Optimal Taguchi-based ANFIS and Genetic Algorithm  
a) 
b) 
Fig. 9. The interactive influences; a) SWE versus S and f, and  
b) SWE versus T and D
The influences of FSW parameters on the 
jointing efficiency are shown in Fig. 10. As shown 
in Fig. 10a, the JE increases as the S increases to 
the middle value and decreases thereon. When the S 
rises from 480 rpm to 1120 rpm, the JE is relatively 
increased by 8.4 %. The JE is relatively decreased 
by 0.6 % as the S changes from 1120 rpm to 1600 
rpm. A higher S increases the welding engagement, 
leading to higher heat generation at the interfaces. The 
hardness and strength of the two materials decrease, 
which increases the degree of the mixture; hence, 
the stir zone size and the bonded area enhances. 
Consequently, the tensile strength improves, leading 
to higher jointing efficiency. In contrast, a further S 
causes excessive heat input, which results in grain 
growth in the welded region. The tensile strength of 
the weld decreases, leading to a reduction in the JE. 
The similar influences of the S on the tensile strength 
can be found in the works of [1], [2], [4] and [6].  
As shown in Fig. 10a, a higher f decreases the 
JE. When the f rises from 47 mm/min to 112 mm/
min, the JE is relatively reduced by 15.73 %. A 
higher f increases the velocity of the welding tool and 
decreases the processing time. The heat generation at 
the interfaces decreases, resulting in the lack of proper 
diffusion between the two plates. In other words, the 
degree of the mixture decreases, leading to higher 
grain size in the welded region. The tensile strength 
of the weld decreases, leading to a decreased JE. A 
reduction in the tensile strength with higher welding 
speed can be found in the works of [1], [2], [4], and 
[11].
a) 
b) 
Fig. 10. The interactive influences; a) JE versus S and f;  
and b) JE versus T and D
Fig. 10b indicates that an increase in the D 
increases the JE. When the D relatively rises from 0.6 
mm to 1.2 mm, the JE is relatively increased by 13.9 
%. A higher depth of shoulder inside the workpiece 
is obtained with an increased D. An increase in the 
heat generation is obtained due to higher friction at the 
interfaces between the tool and workpiece increases. 
The consolidation of the weld by effective diffusion 
of atoms between the two plates is enhanced. A better 
mixture between two materials is achieved, leading 
to higher tensile strength; hence, the JE increases. 
Higher tensile strength with an increase in the depth 
of penetration can be found in the publications [8], [9], 
and [11]. 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
434 Van, A.-L. – Nguyen, T.-T.
As shown in Fig. 10b, the JE increases as the T 
increases to the middle value and decreases thereon. 
When the T rises from 0 deg to 2 deg, the JE is 
relatively increased by 10.1 %. The JE is relatively 
decreased by 3.9 % as the tool tile angle changes 
from 2 deg to 4 deg. A higher T causes an increased 
depth of shoulder inside the specimen; which leads to 
higher friction between the tool and workpiece. The 
heat generation increases at the interfaces, leading 
to a better mixture between two materials due to the 
enlargement in the welded zone. Therefore, the tensile 
strength of the joint increases, resulting in a higher JE. 
Further T causes excessive heat generation, leading to 
a coarse grain; hence, the JE decreases. The similar 
impacts of the tool title angle on the tensile strength 
are presented in the works of [3], [6], [16], and [18].
The influences of FSW parameters on the micro-
hardness at the welded zone are shown in Fig. 11. As 
shown in Fig. 11a, a higher S decreases the MH. When 
the S relatively rises from 480 rpm to 1600 rpm, the 
MH is relatively reduced by 21.8 %. An increased S 
causes higher welding engagement at the interfaces 
between the tool and specimen. A higher degree 
of friction increases, leading to an increased heat 
generation in the welding region. The hardness and 
strength of the welded specimen decrease, resulting in 
soft and flexible structures; hence, the MH decreases. 
A decreased micro-hardness with higher welding 
speed can be found in the works of [2], [9], [12], and 
[15].  
As shown in Fig. 11a, a higher f increases the 
MH. When the f relatively rises from 47 mm/min to 
112 mm/min, the MH is relatively enhanced by 19.3 
%. Higher f causes an increased velocity of the tool 
and a reduction in the welding time. The welding 
engagement decreases, leading to a reduction in 
the friction at the interfaces. The heat generation 
decreases, resulting in higher strength and hardness of 
the welded specimen. Therefore, an increased MH is 
obtained. Similar impacts of the welding speed on the 
micro-hardness are presented in the works of [2] and 
[12]. 
As shown in Fig. 11b, the MH decreases with an 
increased D. When the D relatively rises from 0.6 mm 
to 1.2 mm, the MH is relatively decreased by 15.9 %. 
A higher D increases the depth of the shoulder inside 
the workpiece. The friction at the interfaces between 
the tool and workpiece to be machined increases. 
Excessive heat generation is obtained, which causes 
the coarse-graining in welding metal and dissolves of 
sediments in aluminium alloys. Consequently, the MH 
decreases. Low micro-hardness with higher depth of 
penetration can be found in the works of [7] and [8].
As shown in Fig. 11b, the MH decreases with an 
increased T. When the T relatively rises from 0 deg to 
4 deg, the MH is relatively decreased by 11.7 %. At 
a higher T, the depth of shoulder inside the specimen 
increases; which leads to higher friction between the 
tool and workpiece. The heat generation increases 
at the interfaces, leading to a higher grain size at the 
welded region. Consequently, low MH is observed 
with an increased T. The similar impacts of the tool 
title angle on the micro-hardness are presented in the 
works of [10] and [15]. 
a) 
b) 
Fig. 11.  The interactive influences, a) EL versus S and f, 
and b) EL versus T and D
3.4  Optimization Results
The developed ANFIS models are applied to select 
the optimal outcomes with the aid of the NCGA. 
The operating parameters of the NCGA are shown 
in Table 8. In this study, we select the collapse of the 
population ( α) as the convergence parameter, which 
can be expressed as:
 
 










yy
y
maxm in
max
, 100
 (13)

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
435 Optimization of Friction Stir Welding Operation Using Optimal Taguchi-based ANFIS and Genetic Algorithm  
where y
max
 and y
min
 are the maximum and minimum 
responses.
Table 8.  Operating parameters of the NCGA
No. Symbol Parameters Values
1 PO Population size 20 40 60
2 NG Number of generations 20 40 60
3 MR Mutation rate 0.01 0.03 0.05
4 GS Gene size 40 60 80
Fig. 12.  Selection of optimal NCGA parameters
The minimum value of the α is utilized to select 
the convergence, while the SWE is considered as 
the objective function. The computation trials are 
conducted by means of the Taguchi experimental 
matrix L
9
. As shown in Fig. 12, the optimal data of 
the PO, NG, MR, and GS are 60, 60, 0.05, and 80, 
respectively. 
We have simultaneously performed the PSO 
to solve the optimization issue. The Pareto graphs 
produced by the NCGA and PSO are presented in 
Figs. 13a and b, respectively. As a result, the number 
of feasible designs of the NCGA and PSO are 560 
and 301, respectively. Moreover, the NCGA provides 
better results, as compared to the PSO ones (Table 9).
An experimental confirmation is conducted 
at the optimal point to check the reliability of the 
obtained results. The small deviation indicates that the 
proposed approach comprising the ANFIS, Taguchi 
method, and NCGA is feasible and reliable (Table 10).
The microstructure in the nugget zone is shown 
in Fig. 14, in which the grains are entirely transformed 
into fine-sized structure with even distribution and 
equal space. The welding defects, such as porosity, 
voids, flash, and cracks, have not been found in the 
welded zones. It can be stated that the fine grains 
using the recrystallization have been produced with 
the aid of optimal FSW parameters. In other words, 
the joints of AA6061 plates have been successfully 
implemented, leading to high-quality joint.
a) 
b) 
Fig. 13.  Pareto fronts; a) produced by the NCGA,  
b) produced by the PSO
Fig. 14.  The microstructure in the nugget zone
The industrial values can be listed as follows.
The obtained results are effectively applied to 
improve performance measures of the FSW process of 
the aluminium alloy.
The 2-2-2-2-2 ANFIS architectures could be 
used to render the relations between FSW parameters 
and the welding performances. The welding models 
proposed by the ANFIS approach are significant and 
adequate, which are capable of generating accurate 
predictions for the response values of the FSW 
operation of the aluminium alloy.

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)6, 424-438
436 Van, A.-L. – Nguyen, T.-T.
4  CONCLUSIONS
In the current investigation, the friction stir welding 
(FSW) operation of the AA6061 has been addressed 
and optimized to decrease the specific welding energy 
(SWE) and enhance the jointing efficiency (JE) as 
well as the micro-hardness (MH). The optimizing 
FSW parameters are the rotational speed (S), welding 
speed (f), depth of penetration (D), and tool title angle 
(T). The ANFIS models of the welding responses 
were proposed in terms of the optimizing inputs, in 
which optimal operating parameters were optimized 
using the Taguchi method. The NCGA was applied to 
determine optimal values of welding parameters and 
objectives. The finding can be listed as follows.
1. The lowest levels of the S, D, and T could be 
utilized to reduce the SWE, while the highest f was 
recommended. To enhance the JE, higher values of 
the S, D, and T could be utilized, while lower f could 
be applied. Similarly, an increased MH could be 
obtained with higher values of the S, D, and T, while 
a lower f is encouraged.
2. All machining factors have significant 
contributions to the ANFIS models. For the SWE
 
model, the f was named as the most effective 
factor, followed by the S, D, and T, respectively. 
For the JE model, the welding speed was the 
most effective factor, followed by the D, S, and 
T, respectively. For the MH model, the S had the 
highest contribution, followed by the f, D, and T, 
respectively. 
3. The optimal parameters proposed by orthogonal 
array-based ANFIS-Taguchi method-NCGA of 
the S, f, D, and T were 560 rpm, 90 mm/min, 
0.9 mm, and 2 deg, respectively. The SWE was 
decreased by 17 %, while the JE and MH were 
enhanced by 2.3 % and 6.4 %, respectively.
4. This investigation addressed the specific welding 
energy, jointing efficiency, and micro-hardness 
at the welded zone under the variation of FSW 
parameters. The impacts of welding conditions on 
the costs and grain size will be explored in future 
works.
5. Practically, the weights reflect the importance of 
each response in relation to other performances. 
Therefore, the weight should be objectively 
determined based on experimental data, instead 
subjective chosen of the decisive maker to 
generate reliable optimal outcomes.  
5  ACKNOWLEDGEMENTS
This research is funded by Vietnam National 
Foundation for Science and Technology Development 
(NAFOSTED) under grant number 107.04-2020.02.
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