*Author for correspondence E-mail: deeproymech@gmail.com
An approach for solving multi characteristics optimization of submerged arc welding process parameters by using grey based genetic algorithm
Joydeep roy1, Arindam majumder, J. D. Barma, R. N. Rai and S. C. Saha Department of Mechanical Engineering, National Institute Technology, Agartala Received 04 September 2012; revised 12 December 2012; accepted 29 March 2013
The quality of a weld joint is directly influenced by the welding input parameters during welding and the joint quality can be defined in terms of properties like weld-bead geometry, mechanical properties and distortion. In this paper, an attempt has been made to find the optimal process parameters for achieving good quality welded joint by using multi objective function genetic algorithms (GA). Taguchi design of experiment (DOE) was used for conducting the experiment and these experimental data used to develop regression model for correlating mechanical properties with the process parameters. Grey relational analysis has been introduced to convert the multi objective function into single objective one, which will be the objective function in genetic algorithm.
Keywords: Genetic algorithms, relational analysis, arc welding, Taguchi method, regression analysis.
Introduction
Submerged arc welding (SAW) is employed as one of the major fabrication processes in industry due to its inherent advantages of deep penetration, smooth bead, superior quality and high efficiency1, 2. Therefore, SAW process is still widely used in the nuclear plant, power generation, shipbuilding, offshore and construction industries. To overcome this problem, various optimization techniques can be applied to define the desired output variables through developing different mathematical model between process parameters and response parameters. Taguchi method is powerful design of experiments (DOE), which is a simple, efficient and systematic approach for optimizing joint quality, performance and cost3. Tarng, Y. S. et al. applied grey- based Taguchi methods for optimization of Submerged Arc Welding process parameters in hard facing with multiple performance characteristics4. An orthogonal arra y, the signal-to-noise r atio, multi-response performance index and Analysis of Variance (ANOVA) were employed to study the performance characteristics in the submerged arc welding process. Serdar Karaog lu et.al. focused on the sensitivity analysis of parameters and fine tuning requirements of the parameters for
optimum weld bead geometry5. A widely used method to determine the welding process model is to use experimental design and regression analysis. Fractional factorial techniques were used to predict dimensions of the weld bead in automatic SAW6. Taguchi method and regression analysis also can be applied for optimization of welding process parameters in submerged arc welding.
Lee. et.al. has been applied multiple regression analysis to predict the process parameters of gas metal arc welding7, 8. They revealed that these are limited in application due to difficulties in modeling, time consuming and cumbersome. Toyofumi et al. investigated on optimization of welding materials and welding conditions for high speed submerged arc welding of spiral pipes9. Gunaraj and Murugan have highlighted the use of response surface methodology (RSM) to develop mathematical models and contour plots relating important process parameters namely the open-circuit voltage, wire feed-rate, welding speed and nozzle-to-plate distance to some responses namely, the penetration, reinforcement, width and percentage dilution of the weld bead in SAW of pipes10. Gunaraj and Murugan also studied the effect of SAW parameters on the heat input and the area of heat affected zone (HAZ) for low-carbon steel with two joint types, bead-on- plate and bead-on-joint, using mathematical models developed by RSM11. Benyounis et al. have applied RSM to investigate the effect of laser
welding parameters (laser power, welding speed and focal point position) based on four responses (heat input, penetration, bead width and width of HAZ) in CO2 laser butt-welding of medium carbon steel plates12. Tsai et al.
optimized submerged arc welding process parameters in hardfacing13. Colak et al. predicted surface roughness using evolutionary programming methods14. The data for cutting speed, feed and depth of cut of end milling operations are collected for predicting surface roughness and a linear equation is predicted for surface roughness related to experimental study. Datta et al.applied principle component analysis (PCA) and grey relational based Taguchi method for solving multi criterion optimization problem in submerged arc welding process15,16.
Genetic algorithm is effective tool in finding near- optimal conditions17. It does not need derivatives of objective functions, but needs only the values of objectives for optimization. Kim et al. have used genetic algorithm (GA) and RSM to determine the optimal welding conditions in GMAW process, the base metal was mild steel with a thickness of 5.8 mm18. First, the near-optimal conditions were determined through a GA, and then the optimal conditions were determined over a relatively small region by using RSM. A comparison between GA and RSM in the optimization of the GMAW process when welding of 9.5 mm thick mild steel with a square-groove butt joint was carried out by Correia et al19. Their results indicated that both methods are capable of finding the optimum conditions. It is shown that GA has the capability to determine the optimal setting to achieve a good welded joint by estimating various sets of welding process parameters that can all produce good mechanical properties. The present work aims at developing a grey based genetic algorithm to determine the optimal welding conditions of SAW process. In the present investigation three process variables viz. Wire feed rate (Wf), stick out (So) and traverse speed (Tr) have been considered as input factors and the response parameters are hardness (H), ultimate tensile load (Ts), toughness (Is).
Grey relational method
In Grey relational analysis, experimental data i.e., measured features of quality characteristics are first normalized ranging from zero to one. This process is known as Grey relational generation. Next, based on normalized experimental data, Grey relational coefficient is calculated to represent the correlation between the desired and actual experimental data. Then overall Grey
relational grade is determined by averaging the Grey relational coefficient corresponding to selected responses.
The overall performance characteristic of the multiple response process depends on the calculated Grey relational grade. This approach converts a multiple response process optimization problem into a single response optimization situation with the objective function is overall Grey relational grade. The optimal parametric combination is then evaluated which would result highest Grey relational grade. In Grey relational generation, lower-the-better (LB) criterion can be expressed as:
) ( min ) ( max
) ( ) ( (k) max
xi
k y k
y
k y k y
i i
i k
-
= - … (1)
And larger- the- better (HB) criterion can be expressed as:
) ( min ) ( max
) ( min ) ) (
( y k y k
k y k
k y x
i i
i i
i -
= - … (2)
Where Xi (k) is the value after the Grey relational generation, min yi(k) is the smallest value of yi(k) for the kth response, and max yi(k) is the largest value of yi(k) for the kth response. An ideal sequence is x0(k) (k=1, 2, 3..., 16) for the responses. The definition of Grey relational grade in the course of Grey relational analysis is to reveal the degree of relation between the 16 sequences [x0(k) and xi(k), i=1, 2, 3...,]. The Grey relational coefficient ξi(k) can be calculated as,
) max ( min ψ )
( D +YD
D +
= D oi k k mix
xi … (3)
Where Doi = xo(k)-xi(k) = difference of the absolute value x0(k) and xi (k); is the distinguishing coefficieno£ψ£1;Dmin =Îi"kmin xo(k)-xj(k) = the smallest value of Doi. and
) ( )
max (
max
max ="kj Îi"k xo k -xj k
D = lar gest
value of Doi . After averaging the Grey relational coefficients, the relational grade gi
)
1 (
1 n k
k i
n
i =
å
=x
g
… (4)Where n= number of response parameters. The higher value of Grey relational grade corresponds to intense relational degree between the reference sequence x0(k)
and the given sequence xi (k). The reference sequence x0(k) represents the best process sequence; therefore, higher Grey relational grade means that the corresponding parameter combination is closer to the optimal.
Experimental design and procedure
Submerged arc welding was completed on mild steel plates (200 mm × 100 mm× 10 mm) by forming a bead- on–plate according to the Taguchi’s L16 orthogonal array (OA) design matrix with sixteen combinations of wire feed rate (Wf), stickout (So), and traverse speed (Ts).
The chemical composition of base plate is (wt %) C- 0.163, Mn- 0.419, Si- 0.15, S- 0.013, P- 0.019 and copper coated electrode wire of 3.15 mm diameter (AWS A/S 5.17: EL 8, IS 7280). Chemical composition of the wire (wt %) is C- 0.04, Mn- 0.4, Si- 0.05.The mechanical properties of the test plates viz. Ultimate tensile load ,Ultimate stress and Vickers Hardness at HV10 are 29.27 KN, 909.86 N/mm2 and 156 respectively. Flux used in this experiment was fused type silicon product with grain size 0.2 to 1.6 mm with basicity index 1.6 having following chemical compositions, SiO2+TiO2=30%,CaO+ MgO
=10%, Al2O3 + MnO= 45%, CaF2= 15%. Welding has
been carried out on the SAW automatic welding machine (Make: ADOR WELDING LIMITED, INDIA; Model- MAESTRO 1200 (F)). The welding parameters and their associated levels are chosen on the basis of trial and error method by varying one factor at a time. Based on that result, wire feed rate, traverse speed and stickout was identified as the process control factors and the levels of the factors have been decided shown in Table 1. After welding test plates were visually inspected for detection of any defect or irregularity of weldment and then cut by hydraulic power saw across the welding. Transverse section of the welded joint was polished by using standard metallographic procedure and finally polished specimens were etched with mixture of 2% natal solution. Hardness of the welded zone was tested at constant load of 10kg in semi-vickers hardness tester. Tensile specimen was prepared as per ASTM E8 standard and tested in universal testing machine. Izod v-notch test was carried out to find the relative toughness of the welded structure in an impact testing machine at room temperature. Results obtained from experiment were provided in tabular form in Table 2.
Table 1—Welding Process control parameters and their levels
Parameters Units Notation Level Level Level Level
1 2 3 4
Wire feed mm/min Wf 105 140 175 210
rate
Stick out mm So 15 20 25 30
Traverse m/min Ts 0.75 0.9 1.15 1.2
speed
Table 2—L16 Design matrix with the experimental values of the mechanical performance tests.
Expt. No. Wf So Ts Hardness in weld ultimate tensile Toughness
zone (HV10) load (KN) (J)
1. 1 1 1 182 28.57 107.5
2. 1 2 2 183 30.47 114.5
3. 1 3 3 208 30.21 91
4. 1 4 4 198 30.87 73.5
5. 2 1 2 169 29.70 94.5
6. 2 2 1 160 30.44 101
7. 2 3 4 189 30.82 69
8. 2 4 3 179 31.45 67.5
9. 3 1 3 177 32.38 101.5
10. 3 2 4 173 33.87 85.5
11. 3 3 1 175 31.13 68
12. 3 4 2 172 32.42 96
13. 4 1 4 174 32.13 101.5
14. 4 2 3 169 33.57 62
15. 4 3 2 177 31.49 120
16. 4 4 1 163 31.52 76.5
Result and Discussion
The methodology applied for optimization of submerged arc welding process parameters is based on grey relational analysis and genetic algorithm model.
Using the observed experimental data, initially three different models were developed by multiple regression analysis to correlate welding process parameters like wire feed rate, stickout and traverse speed with weldment mechanical properties like hardness, ultimate tensile load and toughness. Then these models were incorporated in GA through grey relational analysis, and hence, the GA code was developed to optimize the welding process parameters to achieve desired welded joint mechanical properties.
Development of regression models
The statistical method multiple regression analysis (MRA) was used to develop the mathematical models using experimental data listed in table 2. In this study wire feed rate, stickout and traverse speed are the independent parameters and hardness, ultimate tensile load and toughness are the dependent parameters. The range of input variables shown in table 1 (min= level 1 and max= level 4). Regression equations of three responses are given below and related ANOVA table 3 and relationship between predicted and actual value are also given below.
16 0 180 2 00
1 60 1 80 2 00
Predicted
A ctu a l
2 8 3 0 3 2 3 4
2 8 3 0 3 2 3 4
Predicted
A ctu a l
6 0 8 0 1 0 0 1 2 0
6 0 8 0 1 0 0 1 2 0
Predicted
A c tu a l
Fig. 1—Plot between predicted and actual values of response parameters, (a) hardness; (b) ultimate tensile load; and (c) toughness.
Table 3—ANOVA tables of hardness, ultimate tensile load and toughness
Source Sum ofsquares df Mean square F value p- value prob> f R –squared Adj R squared
Hardness model 1802.94 6 300.49 5.29 0.0134 0.7792 0.6319
ultimate tensile load model 21.68 6 3.61 5.53 0.0117 0.7866 0.6443
Toughness model 2725.31 6 454.22 10.31 0.0013 0.8730 0.7883
(a) (b)
(c)
H = 188.59195-1.16964 * Wf +3.09250* So +78.08295*
Ts +3.11224E-003 * Wf ^2 -0.057500* So ^2 -23.85722
Ts ^ 2 (1)
Ts = +13.45237 +0.077075 * Wf +0.29907* So +10.35241* Ts -1.68878E-004* Wf ^2 -6.02500E-003 *
So ^2 -3.55033 * Ts ^2 (2)
Is = -130.91801-1.07071* Wf -2.11500*So +757.98857 * Ts +3.26531E-003* Wf ^2 +0.015000* So ^2 -402.20853
* Ts ^2 (3) From the ANOVA table, it was found that calculated F- ratios were larger than the tabulated values at a 95%
confidence level which means the models are significant.
The validity of regression model was further tested by drawing scatter diagrams shown in fig.1 (a,b,c) hardness, ultimate tensile load and toughness respectively. The predicted values and observed values of the responses
are scattered close to 45· line, which indicating an almost perfect fit of the developed models20.
Development of GA code
The code for the genetic algorithm was developed in MATLAB version 7.9.0 for optimising the SAW process parameters. The flow chart describing the various steps involved in execution of the genetic algorithm is given in Fig. 2, in which the Search Space defines the range of the input parameters, (Table 1), i.e the minimum and maximum values of the input parameters.
Development of objective function through grey relational analysis
To obtain the optimal setting for submerged arc welding process parameters GA code should be made to converge for solutions. To ease the multiobjective function and to converge the solutions with less iterations grey relational analysis is used as the objective function. The objective function is to maximize the joint strength in terms of hardness, ultimate tensile load and toughness, therefore grey relational larger- the-better criterion has been used.
By using eqns. 2, 3 and 4 overall grey relational grade can be evaluated which will be the objective function of GA. Though the objective function is minimized, the GA code works towards maximizing the solution. Hence, a fitness index defined as 1/1+objy is assigned to each solution such that the lower value of the objective function corresponds to the higher fitness values for the solution.
ovj Y = (ZH+ZTs+ZIs)/n=3 … (5)
Where, ovj Y is the objective function, ZH, ZTs and ZIs are the grey relational coefficient equations for hardness, ultimate tensile load and toughness respectively. n = 3, number of responses. y= 0.5, distinguishing coefficient.
Selection of GA parameters
Several parameters are involved in a GA like the population size, number of generations, type of selection, crossover type, crossover rate and mutation rate. The best combination of GA parameters leads to faster convergence of the solution. In GA procedure, Population size, crossover rate and mutation rate are important factors which determine the performance of the algorithm. Large population size or a higher crossover rate allows exploration of solution space and reduces the chances of settling for poor solution. The range of each welding process parameters like wire feed rate,
start
R ange of input variables
Initial population (Wf ,So and Tr)
Fitness evaluation and
R anking
Selection
Crossover
M utation
New population
Validation
Fig.2—Flowchart of GA to optimize SAW process parameters
stickout and traverse speed were specified. The initial population is randomly selected within the specified values for the iteration process. Each individual in the initial population represents each welding process parameters. Genetic operators (selection, crossover and mutation) are employed to produce the next generation of the new population.
Selection: To select the best chromosomes from the population roulette wheel selection is used. In this method, the parents are selected based on their fitness index values. The better chromosomes have the more chances to select21-23. The members of each individual were encoded in binary format, with the length of 100 individuals being selected as the initial population. The individuals selected from the roulette technique selection process are stored in a matting pool and the algorithm will until it has generated the entire population for the next generations.
Crossover: After selection, multipoint crossover was carried out in these selected chromosomes.
This method takes two parent strings from the matting pool and performs an exchange at some positions between them to form a new string.
First, two parent strings are selected randomly from the matting pool. Second, an arbitrary location (called crossover site) in both strings is chosen randomly. Finally, the portions of the strings
following the crossover site are exchanged between two parent strings to form two offspring strings. This crossover does not occur with all strings, but is limited by the crossover rate. Here the crossover rate was fixed at 0.80, which implies that crossover was carried out only on 80 chromosomes among the 100 chromosomes, and the remaining were added to the next generations without crossover.
Mutation: Mutation probability rate is set at a low value of 0.01 to avoid losing good strings. Mutation was carried out on the offsprings in which one allele of the gene is randomly replaced by another to produce a new genetic st ructure. The offsprings then are decoded into real values. Then the objective function is evaluated for this new set of chromosomes, and they are ranked based on their fitness index values. From this mix of parents and offsprings, the 100 best chromosomes are selected based on their fitness ranking. Then these newly selected chromosomes were reinserted for the next iteration. Similar iterations continue until no more changes take place in the value of the optimized process parameters.
Convergence of the developed GA model is shown in Fig 3. From the figure it is apparent that the maximum joint strength is obtained at the 46th iteration. Then the joint strength is constant for further iterations. The optimal
Fig. 3—convergence of GA model
process parameters obtained from the GA model are wire feed rate at 105.008, stickout at 15, and traverse speed at 0.953.
Confirmatory test
In this present work, to validate the computational model based on GA code a confirmatory has been carried out. Using the optimal condition of the process parameters i.e Wf 105.008, So 15 and Tr 0.953 another three welding run has been done. But submerged arc welding machine has the limitation to set these value due to fractional value so, process parameters have been set at the nearest possible value. Table 4 shows the comparison of results predicted by GA model with experimental results.
Conclusion
From the above discussions, the following conclusions can be drawn:
· Regr ession model correlating weldment mechanical properties, viz. hardness, ultimate tensile load and toughness with SAW process parameters, viz. wire feed rate, stickout and traverse speed, have been developed for the individual objective function in genetic algorithm. Close agreement was found between predicted and observed value.
· Grey relational analysis method is very useful to solve multiobjective functions. The overall grey relational grade has been used as the objective function in genetic algorithm to maximize the joint strength.
· The optimal process parametric combination optimized by genetic algorithms are wire feed rate at 105.008, stickout at 15, and traverse speed at 0.953. Confirmatory test validate the accuracy of the genetic algorithm model.
Acknowledgement
The author offers his sincere thanks to the Head and all other faculty members of Mechanical Engineering
Department. He also acknowledges the facilities rendered by the st aff members of Mechanical Engineering Department and Workshop Instructors of Workshop, NIT, Agartala for their valuable help in finishing this work.
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