USING THE GENETIC ALGORITHM TO OPTIMIZE LASER WELDING PARAMETERS FOR MARTENSITIC STAINLESS STEEL

International Research Journal of Computer Science (IRJCS) ISSN: 2393-9842
Issue 08, Volume 6 (September 2019) www.irjcs.com
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USING THE GENETIC ALGORITHM TO OPTIMIZE LASER
WELDING PARAMETERS FOR MARTENSITIC
STAINLESS STEEL
Long Nguyen-Nhut-Phi*
Faculty of Mechanical Engineering,
HCMC University of Technology and Education, Viet Nam
longnnp@hcmute.edu.vn
Son Nguyen-Hoai*
Faculty of Civil Engineering,
HCMC University of Technology and Education, Viet Nam
sonnh@hcmute.edu.vn
Manuscript History
Number: IRJCS/RS/Vol.06/Issue08/SPCS10084
Received: 04, September 2019
Final Correction: 20, September 2019
Final Accepted: 28, September 2019
Published: September 2019
Citation: Nhut-Phi, N. & Nguyen-Hoai (2019). Using the Genetic Algorithm to Optimize Laser Welding Parameters for
Martensitic Stainless Steel- IRJCS:: International Research Journal of Computer Science, Volume VI, 676-680.
doi://10.26562/IRJCS.2019.SPCS10084
Editor: Dr.A.Arul L.S, Chief Editor, IRJCS, AM Publications, India
Copyright: ©2019 This is an open access article distributed under the terms of the Creative Commons Attribution
License, Which Permits unrestricted use, distribution, and reproduction in any medium, provided the original author
and source are credited
Abstract— To achieve the pre-set welding size, this paper presents the optimization of the constrained overlap laser
welding input parameters for AISI 416 and AISI 440FSe stainless, thickness 0.5 mm. In this study, the proposed
optimization algorithm is the Genetic Algorithm (GA). After training 10 times for 30 NP (population size), each
training repeated 200 times, the results achieved as expected. The error is compared with the result of the
affirmation experiment not exceeding 5%.
Keywords—laser welding; optimization algorithm; AISI 416 and AISI 440FSe stainless; the Genetic Algorithm; error;
I. INTRODUCTION
During the welding process, the input parameters contribute to determining the quality of the weld: weld-bead
geometry, mechanical properties, etc. The research [1] presented the use of non-conventional techniques and the
Genetic Algorithm (GA) to determine near-optimal settings for the friction welding parameters for AISI 904L super
austenitic stainless steel. Through ANOVA analysis, optimization parameters are validated that have an impact on
fatigue strength, welding time and partially deformed zone. Based on predicted parameters, after the friction weld is
performed, the affected parameters are measured and compared with the original set of parameters. The error is
assessed to be quite small. The paper [2] shown the optimization of the input parameters (the plate thickness, pulse
frequency, wire feed rate, wire feed rate/travel speed ratio, and peak current) to achieve the desired bead
penetration depth by the Pulsed Gas Metal Arc welding technology through the use of the Genetic Algorithm. Optimal
results have been compared with a number of experimental results and yielded fairly high accuracy. Besides, the
Genetic Algorithm is also used in other research areas. The study [3] used fuzzy logic and the Genetic Algorithm to
optimize land and crop-related data to achieve high profit and maximum production. The project [4] used the
Genetic Algorithm (GA) to secure information through implementation and design on ASCII data because it is very
easy to convert binary data. The paper [5] presented and implemented the application of the Genetic Algorithm to
the Intrusion Detection System to support the effective detection of different ways of the network intrusion.

____________________________________________________________________________________________________________________________________
Based on the feasibility of the algorithm, the main objective of this study is to apply the Genetic Algorithm to
optimize the three input parameters of laser weld for AISI 416 and AISI 440FSe stainless in Khan's mathematical
model [6] to control the pre-set welding size.
II. PROBLEM FORMULATION
The mode laser welding is shown Figure 2.
Fig. 1 The weld bead characteristics (WZW: Weld Zone Width, WPD: Weld Penetration Depth)
In this study, the optimization problem model of the laser weld for AISI 416 and AISI 440FSe stainless thickness 0.5
mm is given by Khan [6]. Laser Power ‘LP’ (W), Welding Speed ‘WS’ (m/min), Fiber Diameter ‘FD’ (m) are process
parameters in Khan's mathematical model and Weld Zone Width ‘WZW’ (m), Weld Penetration Depth ‘WPD’ (m)
are output parameters. As follows:
 221.78917 0.26482 21.185 1.265WZ LP W FW S D       (1)
 
(891.94 213.06 250.69 93.61
73.75 26.94 30.97 ) 1 4
LP WS FD
LP W
WPD
S LP FD WS FD e
      
          
(2)
The desired weld size is the aim to be achieved. Two objective functions are shown in the equation (3):
1
2
ref
ref
f
f
WZW WZW
WPD WPD
 




(3)
Where  ,WZW WPD are the magnituded weld size and  ,ref refWZW WPD are the pre-set weld size.
The problem is to find the minimum value of the 1f and 2f functions. Alternatively, equation (3) is shown as follows:
( )
min max min max
1
;
ref reff WZW WZW WPD WPD
WZW WZW WZW WPD WPD WPD
l lìï = ´ - + - ´ -ïïí
ï £ £ £ £ïïî
(4)
Where ( )min max,WZW WZW and ( )min max,WPD WPD are limit of the weld zone width and the weld penetration
depth,  0 1   is optimally selected as to prioritize between the variance with the desired weld zone width
magnitude.
The algorithm diagram is shown in Figure 2
Fig. 2 The diagram of optimal algorithm

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III. THE GENETIC ALGORITHM
The nine steps of the Genetic Algorithm (GA) are as follows ([7]):
1. Set parameter CF and MF of GA
2. Initialize population of chromosomes, i.e., the solution X
3. Set iteration k = 1
4. Calculate the fitness of chromosomes ( ),k k
i iF f X i= " and find the index of the best chromosomes
{ }1,2,...,b NÎ
5. Perform a selection of chromosomes, crossover of parents and mutation of offsprings to form a new set of
chromosome 1
,k
iX i+
"
6. Evaluate fitness ( )1 1
,Xk k
i iF f i+ +
= " and identify the best chromosome 1b
7. If 1
1k k
b bF F+
< then 1b b=
8. If k Maxite< then 1k k= + and goto step 5 else goto step 9
9. The print optimum solution as k
bX
In is work, the parameters of GA are shown in Table 1 and the flowchart of the basic procedure is shown Figure 3.
TABLE I - THE PARAMETERS OF GA
Parameters Value
Mutation rate
Crossover rate
0.2
0.7
Fig. 3 The overall procedure flowchart
IV. RESULTS
The value of the desired weld in the proposed algorithm are as follows: 570 , 840ref refWZW m WPD m   , the
factor  used in the objective function (4) is optimally selected equal 0.1 and the three input parameters are limited
as given in Table 2.
TABLE II - THE LOWER AND UPPER LIMIT OF THE THREE INPUT PARAMETERS
Parameters Lower Limit Upper Limit
LP (W) 800 1100
WS (m/min) 4.5 7.0
FD (m) 300 400
The GA performed 10 different training times, with each training will repeat N = 200 times using the same
population size NP = 30 and the same number of variables D = 3.

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Table 3 shows the optimized and best target values for the target function of 10 runs of this algorithm.
Fig. 4 The mean value of fitness convergence f
TABLE III - THE OPTIMIZED AND BEST TARGET VALUES
Run
Parameters value Best fitness
value
f (m)
LP
(W)
WS
(m/min)
FD
(m)
1 908.99 6.11 335.46 0.2599
2 943.69 6.27 322.46 0.2599
3 967.60 6.10 314.57 0.8741
4 920.25 5.62 332.43 0.9060
5 917.90 5.61 333.35 0.9151
6 927.37 6.40 327.94 0.4590
7 941.15 6.49 322.80 0.3359
8 911.00 6.14 334.59 0.4152
9 981.12 6.66 308.76 0.0222
10 942.22 6.31 322.99 0.3915
The most optimal set of parameters of the GA for the functions (4) shown in the 9th run.
Table 5 presents the error of three optimal parameters with the result of the experiment I examined by Khan [6]
TABLE IV - THE ERROR BETWEEN THE RESULTS OF THIS STUDY AND THE KHAN’S EXPERIMENT I
WZWref =570 m and WPDref =840 m
LP (W) WS (m/min) FD (m)
Actual (Khan [6]) 1000 7.0 300
The result of this study 981.12 6.66 308.76
Error (%) -1.89 -4.80 2.92

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V. CONCLUSIONS
This paper presented the use of GA to optimize the input parameters (Laser Power ‘LP’ (W), Welding Speed ‘WS’
(m/min), Fiber Diameter ‘FD’ (m)) of the laser welding process to achieve the desired weld size: the Weld Zone
Width WZWref =570 m and the Weld Penetration Depth WPDref =840 m. The base material of the constrained
overlap weld is AISI 416 and AISI 440FSe stainless, thickness 0.5 mm. The results of the study were compared with
the Khan’s result of the affirmation experiment I with errors not exceeding 5%, are shown in detail in table 1.
Specifically, the error of the input parameters LP, WS, and FD, compared to the Khan’s values, respectively, were
1.89 %, 4.80 %, and 2.92 %.
REFERENCES
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