A System Development for the Design and Optimization of ... - NOPR

Journal of Scientific & Industrial Research Vol. 73, April 2014, pp. 219-224

A System Development for the Design and Optimization of Metallurgical Experiments by Using Genetic Algorithms and Taguchi Methods Barış Gökçe*1 and Süleyman Taşgetiren2 1

* Afyon Kocatepe University, Faculty of Technology, Department of Mechatronic Engineering ANS Campus 03100 Afyonkarahisar/TURKEY 2 Afyon Kocatepe University, Faculty of Engineering, Department of Bio-Medical Engineering ANS Campus 03100 Afyonkarahisar/URKEY Received 24 July 2012; revised 03 September 2013; accepted 16 November 2013 There are two major types of research in science such qualitative and quantitative research. Experiments are parts of research and used by researchers to define and understand a system or a specific process in science. Time, cost are important elements of any research design. The minimum completion time of experimental design and the evaluation of outcome are important parameters in experimental studies for any researcher. The purpose of this study is to develop a multi objective software tool which will enable researchers to design their experiments at the beginning of their tests and determine the parameters affecting the test results, thereby finding effective levels of these parameters. The experimental results can also be optimized using GA which allows the use of data of an experimental study without considering the experimental design techniques. Keywords: Taguchi Method, Genetic Algorithm, Experimental Design, Software Tool

Introduction An experiment is an observation and analysis of outputs by making changes in the inputs of a system1. The interaction between parameters is often ruled out in experimental studies conducted with traditional methods, which can adversely affect the results2. The aim in experimental studies is to determine the conditions under which an experiment is to be conducted in order to maximize or minimize the accuracy with which the results are obtained3. Design of experiment provides a reliable basis for decisionmaking but requiring only a limited number of experiments4. Taguchi experimental design, the most widely accepted of experimental design models, is more suitable for the first aim5. A wide array of statistical methods and artificial intelligence techniques has been developed6. The technique known as analysis of variance (ANOVA) uses test results based on variance ratios to determine whether or not significant differences exist among the means of several groups of observations, where each group follows a normal distribution7. One of the most important aims of design of experiment is to reduce the errors to a minimum8. Voss and Dean stated that a control list is _______________ *Author for correspondence Email: [email protected]

needed for the design, and each step in control list is not independent from each other. Sometimes, some steps can be turned back for revision9. Two types of methods are used to avoid errors and deviations during the experiment. They are randomizing experiments and feeding back at each error and deviation10. There are some steps to perform for the design and analysis of experiment by using Taguchi method. Each step of the procedure must be repeated as required11. Taguchi experimental design is used to investigate the influence of parameters12-15, to optimize the process16-18, to determine optimal experimental conditions19 and optimal working conditions20, to measure the performance21, and to select the criteria22. GA is techniques relying on parameter encoding and seeking a solution by using random search techniques23. GA is a method that has a computation loop depending on number of generation or fitness function24. GA does not require a mathematical model. Input data and corresponding output data are used instead of complex algebraic calculations. Thus, GA has been in use in effectively handling complex problems25-26. Many studies about parameter estimation and optimization have been made possible with GAs and many are still underway such as efficient parameter estimation of large kinetic models27, Retrieval parameter optimization28, urban

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drainage model parameter optimization29, function optimization30, optimization of cutting parameters in turning processes31, parameter optimization for growth model of greenhouse crop32, parameter optimization of linear quadratic controller33. Materials and Methods In this study, a software tool was developed by using C# programming language and SQL Server database software tool. This software tool uses Taguchi technique to find the most suitable parameter and levels to get the desired target and GA technique either to find the optimum values according to the experiments or to guess the result in the points that has not been experienced. For the Taguchi technique the software create an experimental receipt by means of orthogonal arrays. After the researcher completes the experiment according to the design which is produced and logs in the system, program carries out the variance analysis of experimental results according to S/N ratio and mean. Six different levels in entering the parameters to the system were offered to the user: User Defined Levels: The levels from two to five can be entered to the system as user-defined parameters, being entirely determined by users. Parameters and levels do not necessarily mean numerical values for Taguchi experimental design. Linear Variation of Levels: If the scale of observation is linear, then the first and last values of parameters are defined as linear level. The software tool itself defines three intermediate levels linearly. Logarithmic Variation of Levels: Logarithmic level definition is a level which is decimal based logarithmic difference of two values entered. In this level, when the first and last values of a level are entered, three intermediate levels are generated logarithmically. a) Parabolic Variation of Levels contains three levels with minimum and maximum values and the midpoint of these two values. b) Exponential Variation of Levels 1 contains four levels. The minimum and maximum levels are entered by user. The rest of the levels, automatically created by the tool as exponential, are accumulated in the first half or in the second half. Another optimization technique in the system is the level and parameter optimization by using Genetic algorithm. A fully factorial or user defined experimental design is defined for GAs optimization in the developed system. Two to fifteen parameters can be

defined in user defined design, but it is limited to five parameters for fully factorial experimental design. There are two types of equations such as quadratic and exponential which can be selected by the user to analyze the results. Without knowing the background of the GA and Taguchi techniques is very difficult to use current software by scientists working in the field of metallurgy technique, Because, the background of these techniques relies on statistical analysis and evolutionary algorithms such inheritance, mutation, selection and crossover. Validation Study With a specially designed device, Başak34 applied surface hardening through ball burnishing process over the surface of brass plates by using a CNC milling machine. Ball diameter, pressing force, speed and feed rates were taken into consideration as parameters. Surface roughness and Brinell hardness numbers were measured under these parameters. Experimental design was performed as a fully factorial design by the researcher. Parameter names and experimental data were saved in the system for GA optimization. Levels of parameters were also entered and saved; fully factorial experiment expansion was created with levels of combinations. 192 tests were performed and surface hardness of the brass was measured in Brinell hardness by Başak34. All data were entered and saved in the system. Application of GAs

The data of the aforementioned study which was done by Başak34 was used to ensure effectiveness of the developed experimental design system. Firstly, the data were analyzed using the GAs, and an analysis called “Surface hardness” was defined to the system. Data input and results of the analysis were also entered and saved. Both equations were tried for the modeling of the experimental results of Başak34. The First equation (eq. 1) was defined as “exponential equation”, and the second one (eq. 2) as “quadratic equation”. Researchers can choose either equation as well as both while using the developed software tool.

f ( P)  w1  w2 P1w3  w4 P2 w5  w6 P3 w7  w8 P4 w9  w10 ( P1 P2 ) w11  w12 ( P1 P3 ) w13  w14 ( P1 P4 ) w15  w16 ( P2 P3 ) w17  w18 ( P2 P4 ) w19  w20 ( P3 P4 ) w21

… (1)

GOKCE & TASGETIREN: A SYSTEM DEVELOPMENT FOR METALLURGICAL EXPERTS

f ( P)  w1  w2 P1  w3 P2  w4 P3  w5 P4  w6 P12  w7 P2 2  w8 P32  w9 P4 2  w10 P1 P2  w11 P1 P3  w12 P1 P4  w13 P2 P3  w14 P2 P4  w15 P3 P4

… (2)

After choosing the type of the equation, parameters of genetic operators were defined and optimization was started. When the optimization reached to the specified generation, it was automatically stopped by the system and the results were examined. Results of the exponential and quadratic equations obtained by the software tool are given in Figures 1 and 2, respectively. While maximum error appeared 9% in

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exponential equation, it was 16% in quadratic equation. No number of points appeared over 10% within lower and upper boundaries in exponential equation, but there were 3 points in quadratic equation. It can be inferred that results of exponential equation proved to be better than quadratic equation. Weight factors (Wi) created by GAs can be seen in Table 1 for both equations. Maximum surface hardness was searched with the obtained weight factors. If required, intervals can also be estimated. However, minimum and maximum levels of parameters for penalty approach can also be used for such interrogation. When levels of parameters which cause maximum surface hardness were searched, a new GAs optimization was performed in the new window of the software tool labeled as “Optimal Levels”. Optimal levels of parameters for maximum surface hardness were achieved by both equations. Estimated optimum levels of exponential equation are ball diameter: 11.112 mm, press force: 400N, speed: 300rpm and feed rate: 0.15 mm/min. Estimated result by using exponential equation is 92 HBN. Real experimental result under these levels was 92.5 HBN. The deviation between estimated and measured values is 0.5 HBN. Given the maximum error (9%) of the equation, the result is highly effective. Table 1Weight factor values of exponential and quadratic equations

Fig. 1Correlation distribution diagram of exponential solution

Fig. 2Correlation distribution diagram of quadratic solution

Exponential solutions W1 0.42696 W2 -0.18566 W3 0.04944 W4 0.99999 W5 0.99968 W6 0.05777 W7 0.29062 W8 -0.17215 W9 -0.51268 W10 0.22483 W11 -0.40767 W12 0.03073 W13 0.54516 W14 0.37556 W15 -0.70042 W16 0.28849 W17 0.88182 W18 0.28391 W19 -0.1238 W20 -0.48444 W21 0.51105

Quadratic solutions W1 -0.21235 W2 0.13484 W3 0.77136 W4 0.19847 W5 0.13541 W6 -0.0046 W7 0.97890 W8 -0.00207 W9 -0.49883 W10 -0.04567 W11 -0.01972 W12 -0.00539 W13 -0.20236 W14 0.074852 W15 0.440737

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Application of Taguchi Method

The experiments conducted by Basak34 could be designed by using Taguchi Method. His main goal was to obtain the optimum effective levels and parameters. Thus, the experimental results were analyzed by means of the developed software tool based on Taguchi method besides GAs. Initially, an experiment with required number of data was defined to the system. Four parameters of the experiment and their levels were manually attributed as user defined. There was no interaction between parameters. Basak34 performed P14xP23xP34xP44 = 192 tests as a fully factorial experiment design. When all these parameters and their levels were entered to the system, a L4-16 orthogonal array was automatically prompted by the system to the user. The experiment receipt L4-16 Orthogonal array created by the system. Taguchi suggests that 16 tests would be adequate to estimate the best results instead of 192 tests. The results of the receipt were taken from fully factorial experimental results. F values of parameters A (pressing force) and D (ball diameter) are higher than the value of 4.191 for 90% trusted level. The other two parameters have lower values. As for the percentage of effective parameters, parameter D (ball diameter) has 10% while parameter A (pressing force) has 77-78% effect. Other parameters do not have any considerable effect. One key result regarding this study is the fact that total error is about 6%, which is a very favorable output. The lower the total errors on the experiment, the more reliable the experiment is. After calculating analysis of variance, effective level of parameters was determined by using column effect method. In this method, the sum of values of each level should be compared with each parameter. The level having the maximum value is the most effective level for the selected parameter. Table 2 shows the most effective levels of parameters according to mean and S/N ratio results. Both results turned out to be the same; pressing force: level 4 (400 N), speed: level 1 (100 rpm), feed rate: level 2

(0.25 mm/min) and ball diameter: level 1 (11.112 mm). The anticipated experimental result from fully factorial results at these level combinations was 91.5 HBN. Such combination did not exist in L4-16 orthogonal array but was offered by the software tool. Those level combinations should be performed later by users. The combination of levels given maximum HBN is A4B2C1D1 in fully factorial experiment and the corresponding result was 92.5 HB. The difference between A4B2C1D2 from Taguchi and A4B2C1D1 from fully factorial design was 1 HBN. This 1 HBN deviation was under 6% error margin, but pressing force (parameter A) and ball diameter (parameter D) had the same levels of error margins for both Taguchi and fully factorial design. They are important for effectiveness of the experiment. Corresponding results of level combinations given by the system should be in a confident interval. Therefore, expected mean of mass should be calculated: Expected value= A4+B1+C2+D1 - (P-1)*mean Expected value = (85.3125+ 76.9375+ 77.625+79.375) –(4-1)*75.78125=91.9HBN This can’t be considered a certain value to be obtained from level combinations. CI (Confident Interval) should be added to that value by using equations (3) and (4). A tolerance value between minimum and maximum intervals to be obtained from the test result was calculated and prompted to the user.

CI  F ;1;ve Ve 1/ neff   1/ r 

… (3)

Table 2Effective levels for mean and S/N ratio Levels

A(Pressing B(Speed) C (Movement) D (Ball Force) diameter)

MEAN

Estimated optimum levels of quadratic equation are ball diameter: 12.2 mm, press force: 400N, speed: 100 rpm and feed rate: 0.15 mm/min. Estimated value of hardness under these levels is 90HBN, which is slightly lower than the measured value. This result does not mean that exponential equation always proves to be better than quadratic one. It should be evaluated for each analysis separately.

1 2 3 4 Effective Level

72 69.4375 76.375 85.3125 4

S/N RATIO

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76.9375 74.3125 74.9375

1 2 3 4 Effective Level

37.12943 37.68779 36.81725 37.33620 37.63750 37.46214 38.58972 4 1

1

76.125 77.625 74.8125 74.5625 2

79.375 75.625 75.5 72.625 1

37.58193 37.77161 37.40544 37.41493 2

37.92939 37.54005 37.51796 37.18650 1

GOKCE & TASGETIREN: A SYSTEM DEVELOPMENT FOR METALLURGICAL EXPERTS

neff 

N 1  VT 

… (4)

CI was found 3.75 and the test result was between 91.9±3.75. The mean real test result under A4+B1+C2+D1 level combination appeared to be 91.5 HBN, and S/N ratio of 39.2 db. A conclusion can be drawn following the discussion of results for this experimental study. 16 experiments would be sufficient to obtain the nearest value for the best result instead of 192 fully factorial experiments. It was considerably easier to obtain the best results owing to low error rate of the experiment. The effect of each parameter on the experimental results was also determined. Conclusion GAs and Taguchi methods can be effectively employed to control the number of experiments prior to the actual testing and thus it reduces the cost and time of experiments. By employing the software tool which is developed based on these two methods under this study, researchers would be able to design their experiments with ease and cost-effectiveness, save time, and reliably analyze the results. Following benefits are provided to the researchers: The number of experiments can be determined as function of parameters and levels, the effect of uncontrolled factors can be determined, the best results can be extracted from fully factorial tests and the optimization of the results are reliably carried out. References

1 Montgomery D C, Design and analysis of experiments, 5th edn, (John Wiley & Sons Inc, Arizona) 2001, 1-18. 2 Breyfogle F W, Implementing Six Sigma: Smarter Solutions Using Statistical Methods, 2nd edn, (John Wiley & Sons Inc, USA) 2003, 555-585. 3 Emery A F & Nenarokomov A V, Optimal Experiment Design, Meas Sci Technol, 9(6) (1998) 864-876. 4 Eriksson L, Johansson E, Kettaneh-Wold N, Wikström C & Wold S, Design of experiments: principles and applications (MKS Umetrics AB, Umea) 2008, 7-99 5 Gökçe B, Design of metallurgical experiments by using Taguchi and GAs, PhD Thesis, University of Afyon Kocatepe, Afyonkarahisar, Turkey, 2009. 6 Gökçe B & Taşgetiren S, Design of experiment for quality, Technol Res: EJMT 1 (2009) 71-83. 7 Lazic´ Z R, Design of experiments in chemical engineering: a practical guide. (Wiley-VCH, USA) 2004, 157-165. 8 Hinkelmann K & Kempthorne O, Design and analysis of experiments volume 2: advanced experimental design (A John Wiley & Sons Inc. Publication, New Jersey) 2005, 312-350.

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9 Dean A & Voss D, Design and analysis of experiments (Springer, Ohio) 1999, 193-243. 10 Cox D R & Reid N, The theory of the design of experiments, (Chapman & Hall/CRC Press, USA) 2000, 269-275. 11 Ross P J, Taguchi techniques for quality engineering, 2nd edn. (McGraw-Hill Professional, New York) 1995, 43-65. 12 Basavarajappa S, Chandramohan G & Davim, J P, Some studies on drilling of hybrid metal matrix composites based on Taguchi techniques, J. Mat. Proc. Tech. 1(3) (2008) 332-338. 13 Hsu W H, Chao C K, Hsu H C, Lin J & Hsu C C, Parametric study on the interface pullout strength of the vertebral body replacement cage using FEM-based Taguchi methods, Med Eng Phys. 31(3) (2009) 287-294. 14 Lin Y C, Chen Y F, Wang D A & Lee H S, Optimization of machining parameters in magnetic force assisted EDM based on Taguchi method, J Mat Proc Tech 7 (2009) 3374-3383. 15 Mahapatra S S, Patnaik A & Satapathy A, Taguchi method applied to parametric appraisal of erosion behavior of GFreinforced polyester composites. Wear 1(2) (2008) 214-222. 16 Chiang M Y & Hsieh H H, The use of the Taguchi method with grey relational analysis to optimize the thin-film sputtering process with multiple quality characteristic in color filter manufacturing, Comput Ind Eng 2 (2009) 648661. 17 Davidson M J, Balasubramanian K & Tagore G R N, Experimental investigation on flow-forming of AA6061 alloys a Taguchi approach, J. Mat. Proc. Tech. 1(3) (2008) 283-287. 18 Keleş O, An Optimization study on the cementation of silver with copper in nitrate solutions by Taguchi design. Hydrometallurgy 95 (2009) 333–336. 19 Chou C S, Ho C Y & Huang C I, The optimum conditions for combination of magnetic particles driven by a rotating magnetic field using the Taguchi method, Adv Powder Technol 20 (1) (2009) 55-61. 20 Comakli K, Simsek F, Comakli O & Sahin B, Determination of optimum working conditions R22 and R404A refrigerant mixtures in heat-pumps using Taguchi method. Appl Energ 86 (11) (2009) 2451–2458. 21 Ganapathy T, Murugesan K & Gakkhar R P, Performance optimization of Jatropha biodiesel engine model using Taguchi approach, Appl Energ 86(11) (2009) 2476–2486. 22 Mahalakshmi P, & Ganesan K, Mahalanobis Taguchi system based criteria selection for shrimp aquaculture development, Comput Electron Agr 65 (2) (2009) 192-197. 23 Goldberg D E, Genetic algorithms in search, optimization, and machine learning, (Addison Wesley Longman, Boston) 1989, 1-25. 24 Michalewics Z, Heuristic methods for evolutionary computation techniques. J Heuristic 1(2) (1995) 1-36. 25 Alli H & Kaya M, A study on the definition of PID control parameters by GAs, Sci Eng J Univ Fırat 13(2) (2001) 1-8. 26 De Jong KA, An analysis of the behavior of class of genetic adaptive systems, Ph D Thesis, University of Michigan, Michigan, 1975. 27 Katare S, Bhan A, Caruthers J M, Delgass W N & Venkatasubramanian V, A hybrid genetic algorithm for efficient parameter estimation of large kinetic models, Comput Chem Eng, 28(12) (2004) 2569–2581.

224

J SCI IND RES VOL 73 APRIL 2014

28 Fujita S, Retrieval parameter optimization using genetic algorithms, Inform Process Manag 45(6)(2009)664–682. 29 Siriwardene N R & Perera B J C, Selection of genetic algorithm operators for urban drainage model parameter optimization, Math Comput Model, 44 (2006) 415–429 30 Hwang S & He R S, A hybrid real-parameter genetic algorithm for function optimization, Adv Eng Inform 20(1) (2006) 7-21. 31 Sardiñas R Q, Santana M R & Brindis E A, Genetic algorithm-based multi-objective optimization of cutting parameters in turning processes, Eng Appl Artif Intel 19(2) (2006) 127–133.

32 Dai C, Yao M, Xie Z, Chen C & Liu J, Parameter optimization for growth model of greenhouse crop using genetic algorithms. Appl Soft Comput 9(1) (2009) 13–19. 33 Li J, Shang C & Zou M, Parameter Optimization of Linear Quadratic Controller Based on Genetic Algorithm, Tsinghua Sci Technol 12(1) (2007) 208-211. 34 Başak H, Surface finish by ball burnishing: effect of burnishing on surface roughness, hardness and strength, Final report of project supported by TUBITAK (the Scientific and Technological Research Council of Turkey) Turkey, 2008.