# Optimization of GMAW Process Parameters Using Particle Swarm Optimization

Authors: P. Sreeraj; T. Kannan; Subhashis Maji
Journal: ISRN Metallurgy
 (2013)

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## Abstract

To improve the corrosion-resistant properties of carbon steel cladding process is usually  used. It is a process of depositing a thick layer of corrosion resistant material-over carbon steel plate. Most of the engineering applications require high strength and corrosion resistant materials for long-term reliability and performance. By cladding, these properties can be achieved with minimum cost. The main problem faced in cladding is the selection of optimum combinations of process parameters for achieving quality clad and hence good clad bead geometry. This paper highlights an experimental study to optimize various input process parameters (welding current, welding speed, gun angle, contact tip to work distance, and pinch) to get optimum dilution in stainless steel cladding of low-carbon structural steel plates using gas metal arc welding (GMAW). Experiments were conducted based on central composite rotatable design with full-replication technique and mathematical models were developed using multiple regression method. The developed models have been checked for adequacy and significance. Using particle swarm optimization (PSO) the parameters were optimized to get minimal dilution.


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## Body

## 1. Introduction

Prevention of corrosion is a major problem in industries. Even though it cannot be eliminated completely, it can be reduced to some extent. A corrosion resistant protective layer is made over the less corrosion resistant substrate by a process called cladding. This technique is used to improve life of engineering components but also reduce their cost. This process is mainly used in industries such as chemical, textiles, nuclear, steam power plants, food processing, and petro-chemical industries [1].Most accepted method of employed in weld cladding is GMAW. It has got the following advantages.(i)
High reliability;(ii)
all position capability;(iii)
ease to use;(iv)
low cost;(v)
high productivity;(vi)
suitable for both ferrous and non ferrous metals;(vii)
high deposition rate;(viii)
absences of fluxes;(ix)
cleanliness and ease of mechanization.The mechanical strength of clad metal is highly influenced by the composition of metal but also by clad bead shape. This is an indication of bead geometry. Figure1 shows the clad bead geometry. It mainly depends on wire feed rate, welding speed, arc voltage, and so forth. Therefore it is necessary to study the relationship between in process parameters and bead parameters to study clad bead geometry. Using mathematical models it can be achieved.Figure 1
Clad bead geometry. Percentage dilution(D) = [B/(A+B)] × 100.This paper highlights the study carried out to develop mathematical and PSO models to optimize clad bead geometry, in stainless steel cladding deposited by GAMAW. The experiments were conducted based on four factor five level central composite rotatable designs with full replication technique [2]. The developed models have been checked for their adequacy and significance. Again using PSO, the bead parameters were optimized.


## 2.   Experimental Procedure

The following machines and consumables were used for the purpose of conducting experiments.(1)
A constant current gas metal arc welding machine (Invrtee V 350-PRO advanced processer with 5–425 amps output range);(2)
welding manipulator;(3)
wire feeder (LF-74 Model);(4)
filler material Stainless Steel wire of 1.2 mm diameter (ER-308 L).;(5)
gas cylinder containing a mixture of 98% argon and 2% of oxygen;(6)
mild steel plate (grade IS-2062).Test plates of size 300 × 200 × 20 mm were cut from mild steel plate of grade IS-2062 and one of the surfaces is cleaned to remove oxide and dirt before cladding. ER-308 L stainless steel wire of 1.2 mm diameter was used for depositing the clad beads through the feeder. Argon gas at a constant flow rate of 16 litres per minute was used for shielding. The properties of base metal and filler wire are shown in Table1. The important and most difficult parameter found from trial run is wire feed rate. The wire feed rate is proportional to current [3].Table 1
Chemical composition of base metal and filler wire.
Materials
Elements wt%
C
SI
Mn
P
S
Al
Cr
Mo
Ni
IS 2062
0.150
0.160
0.870
0.015
0.016
0.031
—
—
—
ER 308L
0.03
0.57
1.76
0.021
0.008
—
19.52
0.75
10.02Wire feed rate must be greater than critical wire feed rate to achieve pulsed metal transfer. The relationship found from trial run is shown in (1). The formula derived is shown in Figure 2:
(1)wirefeedrate=0.96742857*current+79.1.
The selection of the welding electrode wire based on the matching the mechanical properties and physical characteristics of the base metal, weld size, and existing electrode inventory. A candidate material for cladding which has excellent corrosion resistance and weldability is stainless steel. These have chloride stress corrosion cracking resistance and strength significantly greater than other materials. These have good surface appearance, good radiographic standard quality, and minimum electrode wastage. Experimental design procedure used for this study is shown in Figure 3 and important steps are briefly explained.Figure 2
Relationship between current and wire feed rate.Figure 3
Experimental design procedures.


## 3. Plan of Investigation

The research work was planned to be carried out in the following steps.(1)
Identification of factors and responses.(2)
Finding limits of process variables.(3)
Development of design matrix.(4)
Conducting experiments as per design matrix.(5)
Recording the responses.(6)
Development of mathematical models.(7)
Checking the adequacy of developed models.(8)
Conducting conformity tests.


## 4. Prediction of Clad Bead Geometry Using Regression Equation

The following independently controllable process parameters were found to be affecting output parameters. These are wire feed rate (W), welding speed (S), welding gun angle (T), contact tip to work to distance (N) and pinch (Ac), the responses chosen were clad bead width (W), height of reinforcement (R), depth of Penetration (P), and percentage of dilution (D). The responses were chosen based on the impact of parameters on final composite model.The basic difference between welding and cladding is the percentage of dilution. The properties of the cladding is the significantly influenced by dilution obtained. Hence control of dilution is important in cladding where a low dilution is highly desirable. When dilution is quite low, the final deposit composition will be closer to that of filler material and hence corrosion resistant properties of cladding will be greatly improved. The chosen factors have been selected on the basis to get minimal dilution and optimal clad bead geometry [4].Few significant research works have been conducted in these areas using these process parameters and so these parameters were used for experimental study. Working ranges of all selected factors are fixed by conducting trial runs. This was carried out by varying one of the factors while keeping the rest of them as constant values. Working range of each process parameters was decided upon by inspecting the bead for smooth appearance without any visible defects. The upper limit of given factor was coded as −2. The coded value of intermediate values were calculated using(2)Xi=2[2x-(xmax+xmin)][(xmax-xmin)],
where Xi is the required coded value of parameter X is any value of parameter from Xmin-Xmax. Xminis the lower limit of parameters and Xmax is the upper limit parameters. The chosen level of the parameters with their units and notation are given in Table 2.Table 2
Welding parameters and their levels.
Parameters
Unit
Notation
Factor levels
−2
−1
0
1
2
Welding current
A
I
200
225
250
275
300
Welding speed
mm/min
S
150
158
166
174
182
Contact tip to work distance
mm
N
10
14
18
22
26
Welding gun angle
Degree
T
70
80
90
100
110
Pinch
—
Ac
−10
−5
0
5
10Design matrix chosen to conduct the experiments was central composite rotatable design. The design matrix comprises of full replication of 25(= 32), Factorial designs. All welding parameters in the intermediate levels (o) constitute the central points and combination of each welding parameters at either is highest value (+2) or lowest value (−2) with other parameters of intermediate levels (0) constitute star points. 32 experimental trails were conducted that make the estimation of linear quadratic and two way interactive effects of process parameters on clad geometry [5].The experiments were conducted at SVS College of Engineering, Coimbatore, India. In this work thirty-two experimental runs were allowed for the estimation of linear quadratic and two-way interactive effects of corresponding each treatment combination of parameters on bead geometry as shown Table3 at random. At each run settings for all parameters were disturbed and reset for next deposit. This is very essential to introduce variability caused by errors in experimental set up.Table 3
Design matrix.
Trial number
Design matrix
I
S
N
T
Ac
1
−1
−1
−1
−1
1
2
1
−1
−1
−1
−1
3
−1
1
−1
−1
−1
4
1
1
−1
−1
1
5
−1
−1
1
−1
−1
6
1
−1
1
−1
1
7
−1
1
1
−1
1
8
1
1
1
−1
−1
9
−1
−1
−1
1
−1
10
1
−1
−1
1
1
11
−1
1
−1
1
1
12
1
1
−1
1
−1
13
−1
−1
1
1
1
14
1
−1
1
1
−1
15
−1
1
1
1
−1
16
1
1
1
1
1
17
−2
0
0
0
0
18
2
0
0
0
0
19
0
−2
0
0
0
20
0
2
0
0
0
21
0
0
−2
0
0
22
0
0
2
0
0
23
0
0
0
−2
0
24
0
0
0
2
0
25
0
0
0
0
−2
26
0
0
0
0
2
27
0
0
0
0
0
28
0
0
0
0
0
29
0
0
0
0
0
30
0
0
0
0
0
31
0
0
0
0
0
32
0
0
0
0
0
I: welding current; S: welding speed; N: contact tip to work distance; T: welding gun angle; Ac: pinch.In order to measure clad bead geometry of transverse section of each weld overlays were cut using band saw from mid length [6]. Position of the weld and end faces were machined and grinded. The specimen and faces were polished and etched using a 5% nital solution to display bead dimensions. The clad bead profiles were traced using a reflective type optical profile projector at a magnification of ×10, in M/s Roots Industries Ltd. Coimbatore. Then the bead dimension such as depth of penetration height of reinforcement and clad bead width were measured. The traced bead profiles were scanned in order to find various clad parameters and the percentage of dilution with help of AUTO CAD software. This is shown in Figure 4 [7].Figure 4
Traced Profiles (Specimen no. 2). 02A represents profile of the specimen (front side) and 02B represents profile of the specimen (rear side).The measured clad bead dimension and percentage of dilution is shown in Table4. Cladding deposited at optimal conditions is shown in Figure 5.Table 4
Design matrix and observed values of clad bead geometry.
Trial no.
Design matrix
Bead parameters
I
S
N
T
Ac
W (mm)
P (mm)
R (mm)
D (%)
1
−1
−1
−1
−1
1
6.9743
1.67345
6.0262
10.72091
2
1
−1
−1
−1
−1
7.6549
1.9715
5.88735
12.16746
3
−1
1
−1
−1
−1
6.3456
1.6986
5.4519
12.74552
4
1
1
−1
−1
1
7.7635
1.739615
6.0684
10.61078
5
−1
−1
1
−1
−1
7.2683
2.443
5.72055
16.67303
6
1
−1
1
−1
1
9.4383
2.4905
5.9169
15.96692
7
−1
1
1
−1
−1
6.0823
2.4672
5.49205
16.5894
8
1
1
1
−1
−1
8.4666
2.07365
5.9467
14.98494
9
−1
−1
−1
1
−1
6.3029
1.5809
5.9059
10.2749
10
1
−1
−1
1
1
7.0136
1.5662
5.9833
9.707297
11
−1
1
−1
1
1
6.2956
1.58605
5.5105
11.11693
12
1
1
−1
1
−1
7.741
1.8466
5.8752
11.4273
13
−1
−1
1
1
1
7.3231
2.16475
5.72095
15.29097
14
1
−1
1
1
−1
9.6171
2.69495
6.37445
18.54077
15
−1
1
1
1
−1
6.6335
2.3089
5.554
17.23138
16
1
1
1
1
1
10.514
2.7298
5.4645
20.8755
17
−2
0
0
0
0
6.5557
1.99045
5.80585
13.65762
18
2
0
0
0
0
7.4772
2.5737
6.65505
15.74121
19
0
−2
0
0
0
7.5886
2.50455
6.4069
15.77816
20
0
2
0
0
0
7.5014
2.1842
5.6782
16.82349
21
0
0
−2
0
0
6.1421
1.3752
6.0976
8.941799
22
0
0
2
0
0
8.5647
3.18536
5.63655
22.94721
23
0
0
0
−2
0
7.9575
2.2018
5.8281
15.74941
24
0
0
0
2
0
7.7085
1.85885
6.07515
13.27285
25
0
0
0
0
−2
7.8365
2.3577
5.74915
16.63287
26
0
0
0
0
2
8.2082
2.3658
5.99005
16.38043
27
0
0
0
0
0
7.9371
2.1362
6.0153
15.18374
28
0
0
0
0
0
8.4371
2.17145
5.69895
14.82758
29
0
0
0
0
0
9.323
3.1425
5.57595
22.8432
30
0
0
0
0
0
9.2205
3.2872
5.61485
23.6334
31
0
0
0
0
0
10.059
2.86605
5.62095
21.55264
32
0
0
0
0
0
8.9953
2.72068
5.7052
19.60811
W: width; P: penetration; R: reinforcement; D: dilution %.Figure 5
Clad deposited at optimal conditions.


## 5. Development of Mathematical Models

The response function representing any of the clad bead geometry can be expressed as [8],
(3)Y=f(A,B,C,D,E),whereY= response variable, A = welding current (I) in amps, B= welding speed (S) in mm/min, C = contact tip to work distance (N) in mm, D = welding gun angle (T) in degrees,E= pinch (Ac).The second order surface response model equals can be expressed as below [9]. 						(4)Y=β0+β1A+β2B+β3C+β4D+β5E+β11A2+β22B2+β33C2+β44D2+β55E2+β12AB+β13AC+β14AD+β15AE+β23BC+β24BD+β25BE+β34CD+β35CE+β45DE,
where β0 is the free term of the regression equation, the coefficients β1, β2, β3, β4 and β5 are linear terms, the coefficients β11, β22, β33, β44 and β55 quadratic terms, and the coefficients   β12, β13, β14, β15, and so forth are the interaction terms. The coefficients were calculated using Quality America six sigma software (DOE-PC IV). After determining the coefficients, the mathematical models were developed. The developed mathematical models are given as follows.
(5)CladBeadWidth(W),mm:=8.923+0.701A+0.388B+0.587C+0.040D+0.088E-0.423A2-0.291B2-0.338C2-0.219D2-0.171E2+0.205AB+0.405AC+0.105AD+0.070AE-0.134BC+0.225BD+0.098BE+0.26CD+0.086CE+0.012DE.(6)DepthofPenetration(P),mm:=2.735+0.098A-0.032B+0.389C-0.032D-0.008E-0.124A2-0.109B2-0.125C2-0.187D2-0.104E2-0.33AB+0.001AC+0.075AD+0.005AE-0.018BC+0.066BD+0.087BE+0.058CD+0.054CE-0.036DE.(7)HeightofReinforcement(R),mm:=5.752+0.160A-0.151B-0.060C+0.016D-0.002E+0.084A2+0.037B2-0.0006C2+0.015D2-0.006E2+0.035AB+0.018AC-0.008AD-0.048AE-0.024BC-0.062BD-0.003BE+0.012CD-0.092CE-0.095DE.(8)PercentageDilution(D):=19.705+0.325A+0.347B+3.141C-0.039D-0.153E-1.324A2-0.923B2-1.012C2-1.371D2-0.872E2-0.200AB+0.346AC+0.602AD+0.203AE+0.011BC+0.465BD+0.548BE+0.715CD+0.360CE+0.137DE.


## 6. Checking Adequacy of the Developed Models

The adequacy of the developed model was tested using the analysis of variance (ANOVA) technique. As per this technique, if theF-ratio values of the developed models do not exceed the standard tabulated values for a desired level of confidence (95%) and the calculated R-ratio values of the developed model exceed the standard values for a desired level of confidence (95%) then the models are said to be adequate within the confidence limit [10]. These conditions were satisfied for the developed models. The values are shown in  Table 5.Table 5
Analysis of variance for testing adequacy of the model.
Parameter
1st order terms
2nd order terms
Lack of fit
Error terms
F-ratio
R-ratio
Whether model is adequate
SS
DF
SS
DF
SS
DF
SS
DF
W
36.889
20
6.233
11
3.513
6
2.721
5
1.076
3.390
Adequate
P
7.810
20
0.404
11
0.142
6
0.261
5
0.454
7.472
Adequate
R
1.921
20
0.572
11
0.444
6
0.128
5
2.885
3.747
Adequate
D
506.074
20
21.739
11
6.289
6
15.45
5
0.339
8.189
Adequate
SS: sum of squares; DF: degree of freedom;F ratio (6, 5, 0.5) = 3.40451; R ratio (20, 5, 0.05) = 3.20665.


## 7. Optimization of GMAW Process Parameters by PSO

Heuristic technique PSO is proposed to optimize clad bead geometry of stainless steel cladding deposited by GMAW. This is for achieving good cladding. The optimization procedure is shown in Figure6. Initial populations is the possible number of solutions (particles) of the optimization problem and each possible solution is called an individual. In this study possible number of solutions is formed by the values of welding current, welding speed, contact tip to work distance, welding gun angle, and pinch. The objective of this study is to minimize percentage of dilution taken from (8).Figure 6
Procedure for proposed PSO to optimize GMAW process parameters.Initial population is created using the cladding parameters (welding current, welding speed, contact tip to work distance, welding gun angle, and pinch) and for the current populations using objective function. The best fitness value is stored as Pbest from history. From all random solutions reobtained for percentage of dilution. Fitness function values for each individual (particles) are calculated particles choose the best fitness value called Gbest [11].  For each particle, calculate the velocity of the particle by Velocity[] = wVelocity[] + C1rand1(Pbest[] − present[]) + C2xrand2(Gbest[] − present[]).Particle position is updated byPresent[]=Present[]+velocity[].rand1 and rand2 are two random functions in the range[0,1] where C1 and C2 are two positive constants named learning factors taken as 2 and “w” is the inertial weight taken as 0.5.The parameters used for PSO optimization are shown in Table 6.Table 6
Parameters for PSO optimization.
Population size
30
Dimension size
5
Inertia weight
0.4–0.9
Velocity factorsC1, C2
1.4
Number of iteration allowed
100


### 7.1. Method for Developing PSO Model

(i)
Initiate each particle.
(ii)
Calculate fitness value of each particle. If the fitness value is better than the best fitness value (Pbest) in history. Set the current value as new Pbest.
(iii)
Calculate Gbest.
(iv)
For each particle calculate the particle velocity.


### 7.2. Numerical Illustration for Developed PSO Model

The numerical illustration for the developed model to find optimal parameters for percentage of dilution as summarised in below.Welding currentI=Imin+ (Imax-Imin) − rand()Welding speedS=Smin + (Smax-Smin) −  rand()Contact tip to work distanceN=Nmin + (Nmax-Nmin) − rand()Welding gun angleT=Tmin + (Tmax-Tmin) − rand()PinchP=Pmin+ (Pmax-Pmin) − rand()These values are substituted in (8) and dilution is obtained Consider.X(1) = A = Welding current (I) in Amps,X(2) = B = Welding Speed (S) in mm/min,X(3) = C= Contact to work piece distance (N) in mm,X(4) = D= Welding gun angle (T) in degree,X(5) = E= Pinch (Ac).Objective function for percentage of dilution which must be minimized was derived from 5–8. The constants of welding parameters are given Table2 [12].Subjected to bounds:(9)200≤X(1)≤300,150≤X(2)≤182,10≤X(3)≤26,70≤X(4)≤110,-10≤X(5)≤10.


### 7.3. Objective Function

(10)
f
(
x
)
=
19.75
+
0.325
*
x
(
1
)
+
0.347
*
x
(
2
)
+
3.141
*
x
(
3
)
-
0.039
*
x
(
4
)
-
0.153
*
x
(
5
)
-
1.324
*
x
(
1
)
2
-
0.923
*
x
(
2
)
2
-
1.012
*
x
(
3
)
2
-
1.371
*
x
(
4
)
2
-
0.872
*
x
(
5
)
2
-
0.200
*
x
(
1
)
*
x
(
2
)
+
0.346
*
x
(
1
)
*
x
(
3
)
+
0.602
*
x
(
1
)
*
x
(
4
)
+
0.203
*
x
(
1
)
*
x
(
5
)
+
0
.
011
*
x
(
2
)
*
x
(
3
)
+
0.465
*
x
(
2
)
*
x
(
4
)
+
0.548
*
x
(
2
)
*
x
(
5
)
+
0.715
*
x
(
3
)
*
x
(
4
)
+
0.360
*
x
(
3
)
*
x
(
5
)
+
0.137
*
x
(
4
)
*
x
(
5
)
.This is the percentage of dilution.


### 7.4. Constraint Equations

(11)
W
=
(
8.923
+
0.701
*
x
(
1
)
+
0.388
*
x
(
2
)
+
0.587
*
x
(
3
)
+
0.040
*
x
(
4
)
+
0.088
*
x
(
5
)
-
0.423
*
x
(
1
)
2
-
0.291
*
x
(
2
)
2
-
0.338
*
x
(
3
)
2
-
0.219
*
x
(
4
)
2
-
0.171
*
x
(
5
)
2
+
0.205
*
x
(
1
)
*
x
(
2
)
+
0.405
*
x
(
1
)
*
x
(
3
)
+
0.105
*
x
(
1
)
*
x
(
4
)
+
0.070
*
x
(
1
)
*
x
(
5
)
-
0.134
*
x
(
2
)
*
x
(
3
)
+
0.2225
*
x
(
2
)
*
x
(
4
)
+
0.098
*
x
(
2
)
*
x
(
5
)
+
0.26
*
x
(
3
)
*
x
(
4
)
+
0.086
*
x
(
3
)
*
x
(
5
)
+
0.12
*
x
(
4
)
*
x
(
5
)
)
-
3
.(Clad bead width (W) mm lower limit)
(12)P=(2.735+0.098*x(1)-0.032*x(2)+0.389*x(3)-0.032*x(4)-0.008*x(5)-0.124*x(1)2-0.109*x(2)2-0.125*x(3)2-0.187*x(4)2-0.104*x(5)2-0.33*x(1)*x(2)+0.001*x(1)*x(3)+0.075*x(1)*x(4)+0.005*x(1)*x(5)-0.018*x(2)*x(3)+0.066*x(2)*x(4)+0.087*x(2)*x(5)+0.058*x(3)*x(4)+0.054*x(3)*x(5)-0.036*x(4)*x(5))-3.(Depth of penetration(P) upper limit),
(13)P=(2.735+0.098*x(1)-0.032*x(2)+0.389*x(3)-0.032*x(4)-0.008*x(5)-0.124*x(1)2-0.109*x(2)2-0.125*x(3)2-0.187*x(4)2-0.104*x(5)2-0.33*x(1)*x(2)+0.001*x(1)*x(3)+0.075*x(1)*x(4)+0.005*x(1)*x(5)-0.018*x(2)*x(3)+0.066*x(2)*x(4)+0.087*x(2)*x(5)+0.058*x(3)*x(4)+0.054*x(3)*x(5)-0.036*x(4)*x(5))+2.(Depth of penetration(P) lower limit),
(14)W=(8.923+0.701*x(1)+0.388*x(2)+0.587*x(3)+0.040*x(4)+0.088*x(5)-0.423*x(1)2-0.291*x(2)2-0.338*x(3)2-0.219*x(4)2-0.171*x(5)2+0.205*x(1)*x(2)+0.405*x(1)*x(3)+0.105*x(1)*x(4)+0.070*x(1)*x(5)-0.134*x(2)*x(3)+0.225*x(2)*x(4)+0.098*x(2)*x(5)+0.26*x(3)*x(4)+0.086*x(3)*x(5)+0.012*x(4)*x(5))-10.(Clad bead width(W) upper limit),
(15)R=(5.752+0.160*x(1)-0.151*x(2)-0.060*x(3)+0.016*x(4)-0.002*x(5)+0.084*x(1)2+0.037*x(2)2-0.0006*x(3)2+0.015*x(4)2-0.006*x(5)2+0.035*x(1)*x(2)+0.018*x(1)*x(3)-0.008*x(1)*x(4)-0.048*x(1)*x(5)-0.024*x(2)*x(3)-0.062*x(2)*x(4)-0.003*x(2)*x(5)+0.012*x(3)*x(4)-0.092*x(3)*x(5)-0.095*x(4)*x(5))-6.(Height of reinforcement(R) lower limit),
(16)R=(5.752+0.160*x(1)-0.151*x(2)-0.060*x(3)+0.016*x(4)-0.002*x(5)+0.084*x(1)2+0.037*x(2)2-0.0006*x(3)2+0.015*x(4)2-0.006*x(5)2+0.035*x(1)*x(2)+0.018*x(1)*x(3)-0.008*x(1)*x(4)-0.048*x(1)*x(5)-0.024*x(2)*x(3)-0.062*x(2)*x(4)-0.003*x(2)*x(5)+0.012*x(3)*x(4)-0.092*x(3)*x(5)-0.095*x(4)*x(5))+6.(Heights of reinforcement(R) upper limit),
(17)f(x)-23-f(x)+8.(Dilution Upper and lower limit),(18)x(1),x(2),x(3),x(4),x(5)≤2,x(1),x(2),x(3),x(4),x(5)≥-2.


### 7.5. Calculation of Pbest Value

The minimum percentage of dilution for each individual solution is considered as Pbest value. This is the best value for the particular solution only [13, 14].


### 7.6. Calculation of Gbest Value

The minimum dilution for initial solution or the whole iteration is considered as Gbest value. Table7 shows Pbest values and Table 8 shows velocity of particle. A program on MATLAB 7 is created and run to get optimal dilution. Figure 7 shows convergence of PSO for optimal dilution.Table 7
pbest value.
I
S
T
N
AC
0.6241
1.1490
−1.9241
−0.3936
−0.5707
0.6213
1.1414
−1.9139
−0.4406
−0.5562
−0.7617
1.2651
−1.8204
−0.3466
−0.5956
1.1993
0.4661
−1.4140
0.4173
−0.1746
0.6213
1.1368
−1.9224
−0.4496
−0.5725
1.2525
1.5234
−0.1270
−0.9208
0.6041
0.6188
1.1379
−1.9242
−0.4524
−0.5750
0.6196
1.1364
−1.9284
−0.4547
−0.5780
0.6230
1.1385
−1.9187
0.4487
−0.5717
0.6223
1.1368
−1.9227
−0.4507
−0.5761
0.6182
1.1378
−1.9227
−0.4507
−0.5761
0.6182
1.1378
−1.9221
−0.4511
−0.5754
0.6256
1.1393
−1.9129
−0.4459
−0.5675
0.6230
1.1385
−1.9187
−0.4487
−0.5717Table 8
Velocity of particles.
I
S
T
N
Ac
−0.0766
−0.0000
0.0000
0.0000
0.0000
−0.0737
−0.0000
0.0000
0.0000
0.0000
−0.0278
−0.0953
−0.0960
−0.3871
−0.3927
0.0369
−0.0000
−0.6304
−0.5643
−0.6966
−0.611
−0.1051
−0.1121
−0.4074
−0.4324
−0.0732
−0.0000
0.0000
0.0000
0.0000
−0.0000
−0.0000
0.0000
0.0000
0.0000
−0.0195
−0.0000
0.0000
0.0000
0.0000
−0.0517
−0.0940
−0.1307
−0.3794
−0.4224
−0.0296
−0.0000
0.0000
0.0000
0.0000
−0.0344
−0.0000
0.0000
0.0000
0.0000
−0.0766
−0.1135
−0.0974
−0.4006
−0.4197
−0.0211
−0.0000
0.0000
0.0000
0.0000Table 9
Optimal process parameters.
Parameters
Range (coded value)
Actual
Welding current (I)
0.6196
265 A
Welding speed (S)
−1.1364
174 mm/min
Contact tip to work distance (N)
−1.9284
10 mm
Welding gun angle (T)
−0.4547
88 degree
Pinch (Ac)
−0.5780
−6
Dilution obtained is 8.5% and optimal process parameters shown in Table9Figure 7
Convergence of PSO for optimal dilution.


## 7.1. Method for Developing PSO Model

(i)
Initiate each particle.
(ii)
Calculate fitness value of each particle. If the fitness value is better than the best fitness value (Pbest) in history. Set the current value as new Pbest.
(iii)
Calculate Gbest.
(iv)
For each particle calculate the particle velocity.


## 7.2. Numerical Illustration for Developed PSO Model

The numerical illustration for the developed model to find optimal parameters for percentage of dilution as summarised in below.Welding currentI=Imin+ (Imax-Imin) − rand()Welding speedS=Smin + (Smax-Smin) −  rand()Contact tip to work distanceN=Nmin + (Nmax-Nmin) − rand()Welding gun angleT=Tmin + (Tmax-Tmin) − rand()PinchP=Pmin+ (Pmax-Pmin) − rand()These values are substituted in (8) and dilution is obtained Consider.X(1) = A = Welding current (I) in Amps,X(2) = B = Welding Speed (S) in mm/min,X(3) = C= Contact to work piece distance (N) in mm,X(4) = D= Welding gun angle (T) in degree,X(5) = E= Pinch (Ac).Objective function for percentage of dilution which must be minimized was derived from 5–8. The constants of welding parameters are given Table2 [12].Subjected to bounds:(9)200≤X(1)≤300,150≤X(2)≤182,10≤X(3)≤26,70≤X(4)≤110,-10≤X(5)≤10.


## 7.3. Objective Function

(10)
f
(
x
)
=
19.75
+
0.325
*
x
(
1
)
+
0.347
*
x
(
2
)
+
3.141
*
x
(
3
)
-
0.039
*
x
(
4
)
-
0.153
*
x
(
5
)
-
1.324
*
x
(
1
)
2
-
0.923
*
x
(
2
)
2
-
1.012
*
x
(
3
)
2
-
1.371
*
x
(
4
)
2
-
0.872
*
x
(
5
)
2
-
0.200
*
x
(
1
)
*
x
(
2
)
+
0.346
*
x
(
1
)
*
x
(
3
)
+
0.602
*
x
(
1
)
*
x
(
4
)
+
0.203
*
x
(
1
)
*
x
(
5
)
+
0
.
011
*
x
(
2
)
*
x
(
3
)
+
0.465
*
x
(
2
)
*
x
(
4
)
+
0.548
*
x
(
2
)
*
x
(
5
)
+
0.715
*
x
(
3
)
*
x
(
4
)
+
0.360
*
x
(
3
)
*
x
(
5
)
+
0.137
*
x
(
4
)
*
x
(
5
)
.This is the percentage of dilution.


## 7.4. Constraint Equations

(11)
W
=
(
8.923
+
0.701
*
x
(
1
)
+
0.388
*
x
(
2
)
+
0.587
*
x
(
3
)
+
0.040
*
x
(
4
)
+
0.088
*
x
(
5
)
-
0.423
*
x
(
1
)
2
-
0.291
*
x
(
2
)
2
-
0.338
*
x
(
3
)
2
-
0.219
*
x
(
4
)
2
-
0.171
*
x
(
5
)
2
+
0.205
*
x
(
1
)
*
x
(
2
)
+
0.405
*
x
(
1
)
*
x
(
3
)
+
0.105
*
x
(
1
)
*
x
(
4
)
+
0.070
*
x
(
1
)
*
x
(
5
)
-
0.134
*
x
(
2
)
*
x
(
3
)
+
0.2225
*
x
(
2
)
*
x
(
4
)
+
0.098
*
x
(
2
)
*
x
(
5
)
+
0.26
*
x
(
3
)
*
x
(
4
)
+
0.086
*
x
(
3
)
*
x
(
5
)
+
0.12
*
x
(
4
)
*
x
(
5
)
)
-
3
.(Clad bead width (W) mm lower limit)
(12)P=(2.735+0.098*x(1)-0.032*x(2)+0.389*x(3)-0.032*x(4)-0.008*x(5)-0.124*x(1)2-0.109*x(2)2-0.125*x(3)2-0.187*x(4)2-0.104*x(5)2-0.33*x(1)*x(2)+0.001*x(1)*x(3)+0.075*x(1)*x(4)+0.005*x(1)*x(5)-0.018*x(2)*x(3)+0.066*x(2)*x(4)+0.087*x(2)*x(5)+0.058*x(3)*x(4)+0.054*x(3)*x(5)-0.036*x(4)*x(5))-3.(Depth of penetration(P) upper limit),
(13)P=(2.735+0.098*x(1)-0.032*x(2)+0.389*x(3)-0.032*x(4)-0.008*x(5)-0.124*x(1)2-0.109*x(2)2-0.125*x(3)2-0.187*x(4)2-0.104*x(5)2-0.33*x(1)*x(2)+0.001*x(1)*x(3)+0.075*x(1)*x(4)+0.005*x(1)*x(5)-0.018*x(2)*x(3)+0.066*x(2)*x(4)+0.087*x(2)*x(5)+0.058*x(3)*x(4)+0.054*x(3)*x(5)-0.036*x(4)*x(5))+2.(Depth of penetration(P) lower limit),
(14)W=(8.923+0.701*x(1)+0.388*x(2)+0.587*x(3)+0.040*x(4)+0.088*x(5)-0.423*x(1)2-0.291*x(2)2-0.338*x(3)2-0.219*x(4)2-0.171*x(5)2+0.205*x(1)*x(2)+0.405*x(1)*x(3)+0.105*x(1)*x(4)+0.070*x(1)*x(5)-0.134*x(2)*x(3)+0.225*x(2)*x(4)+0.098*x(2)*x(5)+0.26*x(3)*x(4)+0.086*x(3)*x(5)+0.012*x(4)*x(5))-10.(Clad bead width(W) upper limit),
(15)R=(5.752+0.160*x(1)-0.151*x(2)-0.060*x(3)+0.016*x(4)-0.002*x(5)+0.084*x(1)2+0.037*x(2)2-0.0006*x(3)2+0.015*x(4)2-0.006*x(5)2+0.035*x(1)*x(2)+0.018*x(1)*x(3)-0.008*x(1)*x(4)-0.048*x(1)*x(5)-0.024*x(2)*x(3)-0.062*x(2)*x(4)-0.003*x(2)*x(5)+0.012*x(3)*x(4)-0.092*x(3)*x(5)-0.095*x(4)*x(5))-6.(Height of reinforcement(R) lower limit),
(16)R=(5.752+0.160*x(1)-0.151*x(2)-0.060*x(3)+0.016*x(4)-0.002*x(5)+0.084*x(1)2+0.037*x(2)2-0.0006*x(3)2+0.015*x(4)2-0.006*x(5)2+0.035*x(1)*x(2)+0.018*x(1)*x(3)-0.008*x(1)*x(4)-0.048*x(1)*x(5)-0.024*x(2)*x(3)-0.062*x(2)*x(4)-0.003*x(2)*x(5)+0.012*x(3)*x(4)-0.092*x(3)*x(5)-0.095*x(4)*x(5))+6.(Heights of reinforcement(R) upper limit),
(17)f(x)-23-f(x)+8.(Dilution Upper and lower limit),(18)x(1),x(2),x(3),x(4),x(5)≤2,x(1),x(2),x(3),x(4),x(5)≥-2.


## 7.5. Calculation of Pbest Value

The minimum percentage of dilution for each individual solution is considered as Pbest value. This is the best value for the particular solution only [13, 14].


## 7.6. Calculation of Gbest Value

The minimum dilution for initial solution or the whole iteration is considered as Gbest value. Table7 shows Pbest values and Table 8 shows velocity of particle. A program on MATLAB 7 is created and run to get optimal dilution. Figure 7 shows convergence of PSO for optimal dilution.Table 7
pbest value.
I
S
T
N
AC
0.6241
1.1490
−1.9241
−0.3936
−0.5707
0.6213
1.1414
−1.9139
−0.4406
−0.5562
−0.7617
1.2651
−1.8204
−0.3466
−0.5956
1.1993
0.4661
−1.4140
0.4173
−0.1746
0.6213
1.1368
−1.9224
−0.4496
−0.5725
1.2525
1.5234
−0.1270
−0.9208
0.6041
0.6188
1.1379
−1.9242
−0.4524
−0.5750
0.6196
1.1364
−1.9284
−0.4547
−0.5780
0.6230
1.1385
−1.9187
0.4487
−0.5717
0.6223
1.1368
−1.9227
−0.4507
−0.5761
0.6182
1.1378
−1.9227
−0.4507
−0.5761
0.6182
1.1378
−1.9221
−0.4511
−0.5754
0.6256
1.1393
−1.9129
−0.4459
−0.5675
0.6230
1.1385
−1.9187
−0.4487
−0.5717Table 8
Velocity of particles.
I
S
T
N
Ac
−0.0766
−0.0000
0.0000
0.0000
0.0000
−0.0737
−0.0000
0.0000
0.0000
0.0000
−0.0278
−0.0953
−0.0960
−0.3871
−0.3927
0.0369
−0.0000
−0.6304
−0.5643
−0.6966
−0.611
−0.1051
−0.1121
−0.4074
−0.4324
−0.0732
−0.0000
0.0000
0.0000
0.0000
−0.0000
−0.0000
0.0000
0.0000
0.0000
−0.0195
−0.0000
0.0000
0.0000
0.0000
−0.0517
−0.0940
−0.1307
−0.3794
−0.4224
−0.0296
−0.0000
0.0000
0.0000
0.0000
−0.0344
−0.0000
0.0000
0.0000
0.0000
−0.0766
−0.1135
−0.0974
−0.4006
−0.4197
−0.0211
−0.0000
0.0000
0.0000
0.0000Table 9
Optimal process parameters.
Parameters
Range (coded value)
Actual
Welding current (I)
0.6196
265 A
Welding speed (S)
−1.1364
174 mm/min
Contact tip to work distance (N)
−1.9284
10 mm
Welding gun angle (T)
−0.4547
88 degree
Pinch (Ac)
−0.5780
−6
Dilution obtained is 8.5% and optimal process parameters shown in Table9Figure 7
Convergence of PSO for optimal dilution.


## 8.  Results and Discussions

Experiments were conducted using GMAW to produce cladding of austenitic stainless steel material. From the experimental results a mathematical model was developed using regression model. Further to enhance scope of work PSO model was developed to optimize clad bead geometry.In this study, a PSO model to optimize clad bead geometry was developed. To ensure accuracy of model developed evolutionary computing technique PSO invoked to optimize the parameters of GMAW, for optimal weld quality. Convergence of developed model for optimal dilution is shown in Figure7. From the figure it is evident that dilution is increasing up to 15th iteration then it is constant up to 92 and iterations and decreasing and then constant.PSO maintains internal memory to store the Gbest and Pbest solutions. Each individual in the population will try to emulate the Gbest and Pbest solutions in the memory through updating PSO equations. Hence effectiveness of finding the global solutions is s very effective.It can be see that PSO models can be effectively used to model cladding parameters. These optimized values can be directly used in automatic cladding in the forms of programs and for real time quality control and for the entire cladding process control application to improve bead geometry.


## 9. Conclusions

(i)
A PSO model has been developed from the experimental data to achieve desired clad bead geometry. PSO models are capable of making optimization of clad bead geometry with reasonable accuracy.
(ii)
The developed models are able to optimize process parameters required to achieve the desired clad bead geometry of stainless steel cladding deposited by GMAW with reasonable accuracy.
(iii)
In this study, the following steps were applied for prediction of stainless steel clad bead geometry using GMAW: (a) data collection using experimental studies,(b) analysing and processing of data, (c) prediction using regression equation, (d) development of PSO model, and (e) optimizing using PSO algorithm.
(iv)
The results showed that PSO models can be used as an alternative tool according to the present conventional calculation methods.



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*Source: 460651-2013-01-22.xml*