ISSN 1854-6250 APEM journal Advances in Production Engineering & Management Volume 9 | Number 2 | June 2014 Pfl Published by PEI apem-journal.org University of Maribor Advances in Production Engineering & Management Identification Statement APEM ISSN 1854-6250 | Abbreviated key title: Adv produc engineer manag | Start year: 2006 ISSN 1855-6531 (on-line) Published quarterly by Production Engineering Institute (PEI), University of Maribor Smetanova ulica 17, SI - 2000 Maribor, Slovenia, European Union (EU) Phone: 00386 2 2207522,Fax: 00386 2 2207990 Language of text: English APEM homepage: apem-journal.org UniversityofMaribor University homePage: WWW.um.si APEM Editorial Editor-in-Chief Miran Brezocnik editor@apem-journal.org, info@apem-journal.org University of Maribor, Faculty of Mechanical Engineering Smetanova ulica 17, SI - 2000 Maribor, Slovenia, EU Desk Editors Tomaz Irgolic deski@apem-journal.org Matej Paulic desk2@apem-journal.org Website Master_ Lucija Brezocnik lucija.brezocnik@student.um.si Editorial Board Members Eberhard Abele, Technical University of Darmstadt, Germany Bojan Acko, University of Maribor, Slovenia Joze Balic, University of Maribor, Slovenia Agostino Bruzzone, University of Genoa, Italy Borut Buchmeister, University of Maribor, Slovenia Ludwig Cardon, Ghent University, Belgium Edward Chlebus, Wroclaw University of Technology, Poland Franci Cus, University of Maribor, Slovenia Igor Drstvensek, University of Maribor, Slovenia Illes Dudas, University of Miskolc, Hungary Mirko Ficko, University of Maribor, Slovenia Vlatka Hlupic, University of Westminster, UK David Hui, University of New Orleans, USA Pramod K. Jain, Indian Institute of Technology Roorkee, India Isak Karabegovic, University of Bihac, Bosnia and Herzegovina Janez Kopac, University of Ljubljana, Slovenia Iztok Palcic, University of Maribor, Slovenia Krsto Pandza, University of Leeds, UK Andrej Polajnar, University of Maribor, Slovenia Antonio Pouzada, University of Minho, Portugal Rajiv Kumar Sharma, National Institute of Technology, India Katica Simunovic, J.J. Strossmayer University of Osijek, Croatia Daizhong Su, Nottingham Trent University, UK Soemon Takakuwa, Nagoya University, Japan Nikos Tsourveloudis, Technical University of Crete, Greece Tomo Udiljak, University of Zagreb, Croatia Kanji Ueda, The University of Tokyo, Japan Ivica Veza, University of Split, Croatia Limited Permission to Photocopy: Permission is granted to photocopy portions of this publication for personal use and for the use of clients and students as allowed by national copyright laws. 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Copyright © 2014 PEI, University of Maribor. All rights reserved. APEM journal is indexed/abstracted in Inspec, EBSCO (Academic Search Alumni Edition, Academic Search Complete, Academic Search Elite, Academic Search Premier, Engineering Source, Sales & Marketing Source, TOC Premier), ProQuest (CSA Engineering Research Database -Cambridge Scientific Abstracts, Materials Business File, Materials Research Database, Mechanical & Transportation Engineering Abstracts, ProQuest SciTech Collection), and TEMA (DOMA). Listed in Ulrich's Periodicals Directory and Cabell's Directory. journal University of Maribor Production Engineering Institute (PEI) Advances in Production Engineering & Management Volume 9 | Number 2 | June 2014 | pp 55-106 Contents Scope and topics 58 Artificial neural network modeling for surface roughness prediction in cylindrical grinding 59 of Al-SiCp metal matrix composites and ANOVA analysis Chandrasekaran, M.; Devarasiddappa, D. Determining the optimal area-dependent blank holder forces in deep drawing 71 using the response surface method Volk, M.; Nardin, B.; Dolsak, B. Imprecise data envelopment analysis model for robust design 83 with multiple fuzzy quality responses Al-Refaie, A.; Li, M.-H.; Jarbo, M.; Yeh, C.-H.B.; Nour, B. Hybrid Taguchi method for optimizing flux cored arc weld parameters for mild steel 95 Satheesh, M.; Edwin Raja Dhas, J. Calendar of events 104 Notes for contributors 105 Journal homepage: apem-journal.org ISSN 1854-6250 ISSN 1855-6531 (on-line) ©2014 PEI, University of Maribor. All rights reserved. Scope and topics Advances in Production Engineering & Management (APEM journal) is an interdisciplinary refer-eed international academic journal published quarterly by the Production Engineering Institute at the University of Maribor. The main goal of the APEM journal is to present original, high quality, theoretical and application-oriented research developments in all areas of production engineering and production management to a broad audience of academics and practitioners. In order to bridge the gap between theory and practice, applications based on advanced theory and case studies are particularly welcome. For theoretical papers, their originality and research contributions are the main factors in the evaluation process. General approaches, formalisms, algorithms or techniques should be illustrated with significant applications that demonstrate their applicability to real-world problems. Although the APEM journal main goal is to publish original research papers, review articles and professional papers are occasionally published. Fields of interest include, but are not limited to: Additive Manufacturing Processes Advanced Production Technologies Artificial Intelligence Assembly Systems Automation Cutting and Forming Processes Decision Support Systems Discrete Systems and Methodology e-Manufacturing Fuzzy Systems Human Factor Engineering, Ergonomics Industrial Engineering Industrial Processes Industrial Robotics Intelligent Systems Inventory Management Joining Processes Knowledge Management Logistics Machine Tools Machining Systems Manufacturing Systems Mechanical Engineering Mechatronics Metrology Modelling and Simulation Numerical Techniques Operations Research Operations Planning, Scheduling and Control Optimisation Techniques Project Management Quality Management Queuing Systems Risk and Uncertainty Self-Organizing Systems Statistical Methods Supply Chain Management Virtual Reality Advances in Production Engineering & Management Volume 9 | Number 2 | June 2014 | pp 59-70 http://dx.doi.Org/10.14743/apem2014.2.176 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Artificial neural network modeling for surface roughness prediction in cylindrical grinding of Al-SiCp metal matrix composites and ANOVA analysis Chandrasekaran, M.a*, Devarasiddappa, D.b aMechanical Engineering Department, North Eastern Regional Institute of Science and Technology, Nirjuli, India bAutomobile Engineering Department, Rajiv Gandhi Government Polytechnic, Itanagar, India A B S T R A C T A R T I C L E I N F O In the present work, surface roughness prediction model in cylindrical grinding of LM25/SiC/4p metal matrix composites (MMC) was developed using artificial neural network (ANN) methodology. The independent input machining parameters considered in the modeling were wheel velocity, feed, work piece velocity and depth of cut. The neural network architecture 4-12-1 with logsig transfer function was found optimum with 94.20 % model accuracy. The analysis of variance (ANOVA) was carried to study influence of the machining parameters on surface roughness. The study revealed higher F-ratio for wheel velocity and it found to be the most influencing parameter in prediction of surface roughness. The percentage of contribution for wheel velocity was 32.47 %, feed was 26.50 % and work piece velocity was 25.08 %. The depth of cut was found to have least effect on surface roughness with 13.22 % contribution. The independent and combined effect of process parameters on predicted value of surface roughness was studied using two-dimensional graphs and surface plots. The study showed that surface roughness increases as feed increases while it decreases with increase in wheel velocity. It was also observed that minimum surface finish could be obtained at high wheel and work piece velocities, and low feed and depth of cut. © 2014 PEI, University of Maribor. All rights reserved. Keywords: Metal matrix composites Cylindrical grinding Surface roughness Artificial neural network Analysis of variance *Corresponding author: mchse1@yahoo.com (Chandrasekaran, M.) Article history: Received 18 November 2013 Revised 9 May 2014 Accepted 19 May 2014 1. Introduction Metal matrix composites (MMC) having aluminium (Al) in the matrix phase and silicon carbide particles (SiCp) in reinforcement phase, i.e. Al-SiCp type MMC, have gained popularity in the recent past In this competitive age, manufacturing industries strive to produce superior quality products at reasonable price. This is possible by achieving higher productivity while performing machining at optimum combinations of process variables. The low weight and high strength MMC are found suitable for variety of components demanding high performance, especially in the automotive, aerospace, military, and medical applications [1]. The MMC provide advantages of higher specific strength and modulus over monolithic metals (steels and aluminium). Though the MMC can be produced to net-near shape, subsequent machining is found essential to bring them to the desired shape and size with proper surface integrity [2]. This is achieved by either of the machining processes viz. turning, milling or grinding. However, due to the hard and abrasive reinforcement used, MMC exhibit poor machinability resulting in accelerated tool wear and in- creased manufacturing cost. Thus, higher machining cost has remained a major concern which has impeded significant use of MMC components [3, 4]. Surface roughness (Ra) is one of the main attributes of a machined component that characterizes surface topography. It is evidently influenced by cutting parameters, work-tool material, tool geometry and statistical variation during machining. Surface roughness predominantly describes the quality of finish and plays a crucial role in various engineering applications. Reasonable surface finish is always desirable to improve tribological aspects and aesthetic appearance where as excessive surface finish involves higher machining cost. Surface finish of a machined component is defined as the degree of smoothness of surface as a result of roughness, waviness and flaws generated due to machining. Among various methods available, center line average (CLA) method is most commonly used for the measurement of surface roughness. In this method, surface roughness is measured as the average deviation from the nominal surface and mathematically expressed as in Eq. 1. where, Ra is arithmetic average deviation from the mean line, L is sampling length, and Y is ordinate of the roughness profile. Modeling of surface roughness prediction has been attempted using multiple regression analysis, response surface methodology (RSM), fuzzy logic (FL), and artificial neural network (ANN). The study of influence of cutting parameters on surface roughness in MMC machining has been the focused area in academia. The soft computing techniques viz. ANN and FL found effective to model machining processes which are complex in nature. Among the gamut of soft computing techniques, ANN and FL are the two important methods effectively applied for modelling and optimization of machining processes. Number of researchers has used these tools to develop predictive models in various machining processes. In the area of machining, ANN modelling techniques have been commonly used for the prediction of surface roughness, cutting forces, tool wear, tool life and dimensional deviation [5]. Recently, gravitational search algorithm (GSA) was applied for modelling of a turning process with multiple responses (main cutting force, surface roughness and tool life) by Hrelja et al. [6]. The coefficients of the polynomial model for each of the responses were optimized iteratively using PSO algorithm. The optimized model for cutting force was reported to be most accurate with 1.75 % average error (maximum error: 6.3 %) followed by prediction model for surface roughness (average error: 5.85 %, maximum error: 43 %) and tool life (average error: 24.5 %, maximum error: 60 %). The higher values of error were attributed to fewer datasets used in the knowledge base during the learning phase. The ANN and FL techniques were used to develop knowledge based system for prediction of surface roughness in turning process [7]. The knowledge based system consisted of a ANN module which is used to generate large data set to form if-then rules of the fuzzy model. A methodology that requires small size data set for ANN modeling is presented by Kohli and Dixit [8]. Risbood et al. [9] developed a multilayer perceptron (MLP) model for prediction of multiple responses (surface roughness and dimensional deviation) in wet turning of steel with HSS tool with four input parameters. The error in surface roughness prediction was reported nearly 20 %. Routara et al. [10] applied RMS to develop the second order mathematical models for surface roughness prediction. The models were further optimized by genetic algorithm (GA) to find the optimum cutting parameters. Sonar et al. [11] used radial basis function neural network (RBFN) for prediction of surface roughness in turning process with same accuracy in shorter computational time. Contrarily, the surface roughness prediction using neural network (NN) model was found less accurate than FL and regression models in hard turning of AISI 4140 steel [12]. The RBFN found more accurate than multi variable regression analysis in the prediction of thrust force and surface roughness in drilling of carbon fiber reinforced polymer (CFRP) composite materials [13]. The NN and FL (1) 0 models reported to predict multiple responses, i.e. material removal rate, tool wear and radial over cut with agreeable accuracy (prediction error 4.94-16.22 %) in electrical discharge machining of AISI D2 steel [14]. Optimization of machining parameters using ANN was found effective in comparison with analysis of variance (ANOVA) by Muthukrishan and Davim [15] in turning of Al-SiCp MMC. The influence of machining parameters on surface roughness in drilling [16] and in end milling [17] of Al-SiCp MMC has been studied using RSM. The surface roughness is predominantly influenced by feed rate and cutting speed. The depth of cut reported to have least effect. Thiagarajan et al. [18] have carried out experimental investigation of surface integrity during cylindrical grinding of LM25/SiCp MMC and reported that wheel velocity, job velocity and feed are the main influencing factors. The NN prediction models based on two different training algorithms viz., scaled conjugate gradient (SCG) and Levenberg-Marquardt (LM) compared with multiple regression models in turning of AISI 1040 steel [19]. Both the NN models found better in prediction than regression model. A similar work was carried out by Pare et al. [20] for cutting force prediction in turning of titanium alloy. The ANN model prediction found superior to RSM. Edwin Raja Dhas and Somasundaram [21] found ANN technique and fuzzy logic to accurately predict weld residual stress. Devarasiddappa et al. [22] developed ANN model for predicting the surface roughness in end milling of Al-SiCp MMC using small set of experimental data sets. The predictive performance of the model was found highly encouraging with average error of 0.31 % as against 0.53 % for the RSM published result. Number of researchers has carried out the experimental study and modeling of different machining processes by employing both conventional and soft computing based methodology. Recently, ANN is used as popular and promising technique for prediction surface roughness in machining process. Though, a large number of research publications are available on MMC machining, few publications are available in MMC grinding. In this paper, development of ANN based model for prediction of surface roughness during cylindrical grinding of Al-SiCp MMC has been attempted. The various machining parameters and their influences on job surface roughness were studied. The development of ANN predictive model and analysis of process parameters is detailed out in subsequent sections. 2. Development of surface roughness prediction model In order to improve machining process, surface roughness prediction model is developed. There are four common techniques for the development of a prediction model: 1) multiple regressions, 2) physics based modeling, 3) ANN, and 4) FL based models. ANN is one of the most widely used artificial intelligent techniques and has been successfully employed by researchers. It has ability to learn the mapping between a set of input and output values. 2.1 Artificial neural network modeling The ANN is a data processing system consisting of a large number of simple and highly interconnected processing elements resembling biological neural system. It can be effectively used to determine the input-output relationship of a complex process and is considered as a tool in nonlinear statistical data modeling. A multilayer NN that works on back propagation learning algorithm was used in the present work. The ANN model was trained initially using experimental data so as to predict response variable(s) for unknown input datasets within reasonable accuracy. In the present work, ANN model was developed for predicting surface roughness in cylindrical grinding of Al-SiCp MMC (i.e., LM25/SiC/4p) using vitrified-bonded white aluminium oxide grinding wheel. The independent input machining parameters considered were (a) cutting speed of the grinding wheel, Vs (m/min), (b) cutting speed of the work piece, Vw (m/min), (c) feed,/(m/min), and (d) depth of cut, d (|im). For training the neural network, real life datasets obtained through machining experimentation from experimental result of Thiagarajan et al. [19] were used. The four process parameters at three different levels were considered for experimentation. The level of the parameters considered is given in Table 1. Table 1 Levels of parameters used for experimentation Parameters Level 1 Level 2 Level 3 Vs (m/min) 1414 2026 2639 Vw (m/min) 6.11 12.72 26.72 /(m/min) 0.06 0.09 0.17 d (|m) 10 20 30 2.2 Network architecture and training A typical multilayer ANN model consists of input, hidden and output layers. The ANN architecture consisting of an input layer with four neurons each representing one input variable, one hidden layer (12 neurons) and an output layer with one neuron having purelin processing function was employed in the present work. The model was trained using 20 experimental datasets given in Table 2 including corner datasets of each variable. The five datasets given in Table 3 were used for testing the model during training. The source code was written in MATLAB version 7.8. Table 2 Experimental datasets used for ANN model training Sl. No Vs Vw / d Ra (m/min) (m/min) (m/min) Om) Om) 1 1414 6.11 0.06 10 0.40 2 1414 6.11 0.06 30 0.58 3 1414 6.11 0.17 10 0.67 4 1414 12.72 0.06 10 0.34 5 1414 12.72 0.09 30 0.72 6 1414 12.72 0.17 20 0.78 7 1414 12.72 0.17 30 0.86 8 1414 26.72 0.06 10 0.25 9 2026 6.11 0.09 10 0.46 10 2026 6.11 0.17 30 0.80 11 2026 12.72 0.09 20 0.43 12 2026 26.72 0.06 10 0.19 13 2026 26.72 0.09 20 0.34 14 2026 26.72 0.17 30 0.42 15 2639 6.11 0.09 20 0.43 16 2639 6.11 0.17 30 0.52 17 2639 12.72 0.06 30 0.29 18 2639 26.72 0.06 10 0.18 19 2639 26.72 0.17 10 0.19 20 2639 26.72 0.17 30 0.38 The Fig. 1 depicts the two layer feed forward NN used in this work. The input layer consists of 4 neurons as wheel speed, workpiece speed, feed and depth of cut being the control parameters. The output layer consists of one neuron having purelin processing function. The NN training was performed for desired error goal of 0.0001 by varying hidden layer neurons from 5-20 for two different transfer functions - tansig and logsig. The number of neurons in the hidden layer plays a vital role in deciding the optimal architecture of the model. If less number of neurons are taken, the network may not be able learn the input-output relationship properly and the error in prediction will be higher. Increasing the number of neurons in the hidden layer gives more flexibility to the network because the network has more parameters it can optimize and hence learning can be more accurate. Table 3 Testing datasets used for ANN model development Sl. No Vs Vw F d Ra (m/min) (m/min) (m/min) Om) Om) 1 1414 6.11 0.09 20 0.69 2 1414 6.11 0.17 20 0.80 3 1414 12.72 0.06 30 0.48 4 1414 26.72 0.09 10 0.33 5 2639 26.72 0.06 30 0.23 Cutting speed of grinding w h til Cutting speed , (y^ i.f wurk pit'll' Feed rate Surface roughness Depth of cut Input layer Hidden layer Output layer Fig. 1 Typical two layer NN architecture used However, if the hidden layer neurons are too large, it might cause the problem to be under-characterized since the network has to optimize more parameters than there are data vectors to constrain these parameters. Thus the generalization capability of the network and hence its performance is compromised with large number of neurons in the hidden layer. The selection of suitable transfer function is also equally important. The transfer function is used to calculate the output from the input parameters. In the present work, the log sigmoid (logsig) transfer function found suitable for the hidden layer. The Eq. 2 and Eq. 3 represent logsig and purelin transfer functions, respectively, a = logsig (ri) = 1 + e~ (2) a = purelin (ri) = n (3) where n is net weighted input to the neuron. The neural network was trained with different number of neurons (varying from five to twenty) and different transfer functions in the hidden layer. The maximum number of epochs allowed in each run is 25000. The code was run five times at each network topology with different initial random weights. The network configurations giving average percentage error in training and testing data set within 15 % were recorded. A properly trained NN gives nearly equal training and testing error. A network having smaller training error exhibits poor generalization capability and thus predicts poorly for new datasets. The detail of training and testing error for different network topology is presented in Table 4 and its graphical representation is depicted in Fig. 2. Table 4 Network training result for different architectures Sl.No NN architecture Average percentage e^ror Effective error (%) Training_Testing 1 4-6-1 (tansig) 8.66 12.12 3.46 2 4-15-1 (logsig) 11.93 8.53 3.40 3 4-17-1 (tansig) 11.32 14.59 3.27 4 4-18-1 (logsig) 11.79 14.38 2.59 5 4-11-1 (tansig) 3.83 5.73 1.90 6 4-12-1 (logsig) 10.55 9.35 1.20 taroig 4-<5-l logs ig 4-15-1 Training eixor I I Testing eixor Effective error logsig 4-18-1 logsig 4-12-1 y 1 I 3 4 AISN architectire. Fig. 2 Selection of optimal NN architecture The NN was trained using trainbr (Bayesian regulation back propagation) training function which uses Bayesian regularization. The training datasets of the converged network are given in Table 2. The testing datasets of the converged network are presented in Table 3. The network was trained with a different data set (80 %) each time, which were randomly selected. The testing datasets (20 %) were also selected randomly. The network converged at 362nd iteration. The weights and biases as well as sum squared weights of converged network remains constant. The sum squared error (SSE) during testing recorded approximately 0.1311 and remained constant. The SSE during training was found to be 0.4269. The mean squared error in training and testing datasets of the converged NN model was found to be 0.0025 and 0.0031 respectively. The optimum number of neurons and the selected transfer function that produce minimum effective error found as best network architecture. The ANN architecture 4-12-1 with logsig transfer function giving effective error of 1.20 % was found optimum in this work. At optimum network, weights and bias were saved and used to predict surface roughness for unknown datasets. 2.3 Network prediction performance Accuracy of the NN predictive model was tested for 10 randomly selected experimental datasets. The model predicted Ra values were compared with experimental values and percentage error was calculated. The results are presented in Table 5. The maximum and minimum percentage error recorded as 14.71 % and 0.0 %, respectively. The average percentage error (APE) and mean squared error (MSE) was computed using Eq. 4 and Eq. 5, respectively, APE n =£ X í=I l¿¿ - y¿ ti x 100 (4) mse n =£ X«. ¿=i y¿)2 (5) where ti is target value for data set i, yi is predicted value for data set i, and n is the total number of data sets. Table 5 Validation result of neural network model L No. Vs (m/min) Vw (m/min) f (m/min) d Exp. ANN Procentage error Prediction accuracy 1 1414 6.11 0.06 20 0.54 0.51 5.56 94.44 2 1414 6.11 0.09 10 0.52 0.57 9.62 90.38 3 1414 6.11 0.17 30 0.88 0.89 1.14 98.86 4 1414 26.72 0.09 30 0.5 0.46 8.00 92.00 5 2026 12.72 0.06 20 0.34 0.31 8.82 91.18 6 2026 26.72 0.06 30 0.29 0.29 0.00 100.00 7 2026 26.72 0.09 30 0.34 0.39 14.71 85.29 8 2639 6.11 0.06 20 0.34 0.36 5.88 94.12 9 2639 12.72 0.17 30 0.52 0.51 1.92 98.08 10 2026 6.11 0.06 20 0.42 0.41 2.38 97.62 0.2 Expt Jfl Ii O.S I Ü.S n.4 2 4 6 8 10 Experiment No. Fig. 3 Validation result of NN model The average percentage error and MSE was found to be 5.80 % and 0.00091 respectively. The graphical representation of the NN prediction for validation data set is depicted in Fig. 3. Model accuracy (MA) was computed as the average of individual accuracy on confirmation data set [23]. It is expressed by Eq. 6. The model accuracy of the developed model based on its predictive capability was found to be 94.20 %. n J^-^Sr1)*100 (6) 3. Analysis of process parameters The NN predicted surface roughness values were analysed to study the effect of process parameters. ANOVA technique was used to determine the significant control parameters affecting surface roughness. 3.1 Analysis of variance ANOVA is a method of portioning variability into identifiable sources of variation and the associated degree of freedom in the model. Four control parameters were considered in the present study. Each factor affects the response to a varying degree. There were 3 levels (low, medium, and high) on four control parameters having 34 factorial designs of 81 experimental cutting conditions (datasets). The surface roughness for these datasets was predicted from the developed NN model. ANOVA is used to decompose the total variability to quantify the effect machining parameters on surface roughness. The percentage contribution of machining parameters was estimated based on the sum of squares of responses. The grand total sum of squares (SSgrand) was evaluated using the Eq. 7. 81 ss. 'grand = 1* ¿ = 1 The SSgrand is decomposed into sum of squares due to mean (SSm (SStoto/) using Eq. 8 and Eq. 9, respectively, (7) „) and total sum of squares ÇÇ _ 81 vD2 JJmean u± 11am 81 S^total ~^am)2 ¿=1 (8) (9) where Ram is mean of responses. The sum of squares due to a factor is equal to its total squared deviation from the overall mean. In the present study, there were 27 experiments for each factor at each level. The sum of squares due to factor A (SSa) was computed using the Eq. 10, SSA — 27(RaA1 —Ram)2 + 27(Ra¿2 — Ram)2 +27(Ra¿3 —Ram)2 (10) where, RaAi, RaA2, and RaA3 are the mean of Ra at the level 1, 2, and 3 of the factor A, respectively. The relative importance of factor A influencing the surface roughness was computed as the percentage contribution (PCA) using Eq. 11. PCA = „„ A x 100 SS, (11) total Similarly, the total sum of squares due to factor B (SSB), C (SSC) and D (SSD) and their respective percentage contribution PCb, PCc, and PCd were computed as detailed above. Table 6 shows the results of ANOVA for surface roughness. The degrees of freedom (DF), sum of squares (SS), mean of squares (MS), F-ratio and PC associated with each factor is also presented. This analysis was carried out at 5 % significance level, i.e. at 95 % confidence level. The calculated values of the F-ratio showed high influence of the wheel velocity, feed and work piece velocity on surface roughness. The contributions of all the control parameters including error are presented pictorially in the pie chart shown in Fig. 4. The cutting speed of the grinding wheel has the highest influence both in NN model as well as statistically on the surface roughness. Feed and cutting speed of work piece has almost equal influence on the surface roughness. However, the value of surface roughness is inversely proportional to work piece velocity but directly proportional to the feed. The error associated with the ANOVA analysis found minimum as 2.73 %. Table 6 Result of ANOVA Control factors DF SS MS F-ratio PC A: Wheel velocity 2 71.77 35.88 358.88 32.47 B: Job velocity 2 55.44 27.72 277.2 25.08 C: Feed 2 5858 29.29 292.9 26.50 D: Depth of cut 2 29.20 14.60 146.0 13.22 E: Error 72 6.03 0.1 2.73 Total 80 221.02 100.00 A: Cutting speed of grinding wheel B: Cutting speed of workpiece C: Feed D: Depth of cut E: Error E: 25.OS % ' Fig 4 Contribution of control parameters 3.2 Study on influence of process parameters The performance of the NN based predictive model for predicting the surface roughness was found very encouraging with 5.80 % average percentage error when compared with the experimental results. Based on model prediction, the influence of the process parameters on surface roughness was studied. The effect of these parameters was plotted graphically and is shown in Fig. 5a and Fig. 5b. The increase in wheel speed and workpiece speed improves the surface finish (i.e. surface roughness value reduces) of the job. The value of surface finish deteriorates as work feed increases. The surface finish improves at lower depth of cut as the cutting load lowers at low feed and low depth of cut. Vs - 2Ö3H m min i Vw = 26.11 m mill 1 i o.: (i - 30 mil d - 20 mu á = 10 |im ^o 0" Q" " Cr- - 0.1L 0.06 OOS 0.1 0.12 0.14 0.16 0.1S Feed, f(ni niin-1) b. Effect of/on Ra Fig 5 Effect of process parameters on surface roughness grinding wheel, Vs (m min-1) a. Surface plot of Ra with/and Vs b. Surface plot of Ra with d and/ Fig. 6 Surface plots for combined effect of process parameters on Ra The Fig. 6a shows the surface plot of surface roughness with feed and wheel velocity when work piece velocity and depth of cut are kept constant. The increase in wheel velocity reduces the surface roughness value. On the other hand, in case of feed, the value of surface roughness increases as feed increases. The plot shows the effect these parameters for the workpiece velocity of 12.72 m/min and depth of machining of 20 |j.m. The same effect was seen on work piece velocity and feed verses surface roughness. The minimum surface roughness was obtained at low depth of cut. The Fig. 6b depicts the surface plot of surface roughness with feed and depth of cut when wheel velocity and work piece velocity are held constant. The plot reveals that the minimum surface roughness value can be obtained at low feed and low depth of cut With the combination of all parameters improved surface finish was obtained at high wheel velocity and work piece velocity. However, in case of feed and depth cut, the improved surface finish obtained at low feed and depth of cut due to reduced cutting load. 4. Conclusion In the present work, the ANN model for prediction of surface roughness in cylindrical grinding of Al-SiCp MMC was developed. For NN modeling the datasets were obtained from experimental result presented in [18]. The surface roughness value for different combination of process parameters was obtained and analyzed. The wheel velocity, work piece velocity, feed and depth of cut were considered as process parameters. The ANN architecture 4-12-1 with logsig transfer function giving effective error of 1.20 % was found optimum in the present work. The predictive model was validated with confirmation datasets. Based on NN prediction model and analysis of the parameters, the following conclusions were drawn. • The proposed neural network modeling was found easy and promising technique to develop predictive model for mapping input and output parameters. The developed model predicted surface roughness accurately for unseen data with 94.20 % model accuracy. • The result of ANOVA showed highest F-ratio for wheel velocity and is the most significant influencing parameter for prediction of surface roughness. The percentage of contribution for wheel velocity was 32.47 %, feed was 26.50 %, and work piece velocity was 25.08 %. The depth of cut was found have least effect on surface roughness with 13.22 % contribution. • The investigations on this study indicate that the process parameters wheel velocity, work piece velocity, feed and depth of cut are the primary influencing factors which affect the surface roughness of ground MMC component. • The NN prediction revealed that better surface finish could be obtained at high wheel velocity and high work piece velocity. This is due to development of low grinding force at high speed of operation. The surface finish deteriorates at high feed and depth of cut as it increases the grinding load. The minimum surface finish was obtained with the combination of high wheel and workpiece velocity and low feed and depth of cut. The neural network predicted 0.16 |im being the minimum surface roughness at Vs = 2639 m/min, Vw = 26.72 m/min, f = 0.06 m/min and d = 10 |im. The proposed methodology could be effectively employed for prediction of responses in variety of machining processes on different material combinations. The detailed ANOVA presented in this paper could be extended to study the influence of input variables on the response(s) in any of the machining processes effectively. The modeling technique discussed can be integrated with optimization algorithms. Acknowledgement The authors acknowledge the financial support received from NERIST, Arunachal Pradesh in carrying out the research and preparation of the manuscript. Also the authors are thankful to the anonymous reviewers for their useful comments and suggestions to improve the quality of the manuscript. 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Advances in Production Engineering & Management Volume 9 | Number 2 | June 2014 | pp 71-82 http://dx.doi.Org/10.14743/apem2014.2.177 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Determining the optimal area-dependent blank holder forces in deep drawing using the response surface method Volk, M.a*, Nardin, B.a, Dolsak, B.b aGorenje Orodjarna, d.o.o., Velenje, Slovenia bUniversity of Maribor, Faculty of Mechanical Engineering, Maribor, Slovenia A B S T R A C T A R T I C L E I N F O Metal forming processes are often currently highly automated mass production processes for manufacturing a wide variety of metal parts from various industries. Maximizing product quality and consequently minimizing waste and production costs are major goals for those companies exploiting metal forming processes. On the other hand, sheet metal parts become more complex especially because of complex product designs and the usages of higher strength steels that have less formability. Therefore, metal forming processes need to be optimized. This research study demonstrates an optimization system for optimizing the sheet metal forming process using the Finite Element Method (FEM) combined with the Response Surface Method (RSM). The proposed optimization system was tested on an industrial example from the household appliances industry. In this study, it is described as to how to determine optimal area-dependent blank-holder forces in deep drawing process in order to obtain the best possible quality of the drawing part. The optimization system consists of three main steps: modeling, screening, and optimization. The results showed that with better preferences regarding the blankholder forces, better results can be achieved. Forming and spring-back criteria were taken into account. The number of required numerical simulations using the RSM combined with the Design of Experiment was not critical and was much smaller than using other conventional optimization methods. Therefore, reasonably accurate results can be achieved in a relativity short time, which is one of the main advantages of this method. © 2014 PEI, University of Maribor. All rights reserved. Keywords: Sheet metal forming Optimization Finite element method Response surface method *Corresponding author: mihael.volk@gorenje-orodjarna.si (Volk, M.) Article history: Received 6 December 2013 Revised 30 May 2014 Accepted 3 June 2014 1. Introduction Despite all of the new technologies and improvements in sheet metal forming processes, the forming tools for deep drawing have not significantly changed. The production tools and deep drawing processes are very rigid, therefore it is very hard to improve the quality of the products without extra expenses. On the other hand, deep drawn products become more complex, thus creating additional problems for the toolmakers. Basically, the only (and the most influenced) parameter which can be optimized without encroaching into the tool, and which can be controlled, is a blank holder force (BHF) [1]. Many researchers used BHF for improving the quality of the drawing parts [1-16] and most of them described BHF with the technological window (Fig. 1). An excessive value of BHF causes fracture, whilst an insufficient value of BHF will result in wrinkles [4, 5]. 2 FRACTURE LOCALIZATION LU £ OPTIMAL S SETTING 2 ACCEPTABLE >Tl¡¡¡ g PRODUCTS^-*"'' O T * WRINKLING SELECTED h DRAWING HEIGHT h (mm) OR DRAWING RATIO p {1)( Fig. 1 Technological window [4] Beside wrinkles and fractures, one of the most important problems is spring-back [10, 12] and the BHF has a large influence on it [9, 13]. Spring-back in sheet-metal forming can be described as the change in the sheet-metal's shape compared with the shapes of the tools after the forming process [8]. We differentiate the following types of spring-back when considering the geometry of a product: angular change, sidewall curl, and twist (Fig. 2). Because BHF seems to be one of the most important parameters in sheet metal forming, a new holding system with segment inserts was developed. This holding system is described in [9, 13] and belongs to holding systems which can provide variable BHFs to the sheet metal [5-8]. While using this holding system, the stamping process is more controlled, the processing window is wider, and the process is more stable [9]. However, finding the optimal configuration of blank holder forces is critical and requires several experimental tests when using conventional optimization methods [5, 9, 15, 16]. This research study presents a method for finding the optimal configuration of blank holder forces. The mathematical approximation algorithm called the response surface method (RSM) and results of finite element numerical simulations were used. Design Expert 8.0 and Pam-stamp 2011 software packages were also used in this research study. The presented method was tested on the deep drawing process but could be used for other applications as well. 2. Used methods In this research study, the response surface method (RSM) with the combination of finite element method results was used. The response surface methodology is a collection of mathematical and statistical techniques useful for the modeling and analysis of problems in which a response of interest is influenced by several variables, and the objective is to optimize this response [17]. SIDE CUF Fig. 2 Types of spring-back [10] \ # H Fig. 3 Mathematical optimization [17] In general, the optimization method could be described as a mathematical problem in which we are seeking to minimize or to maximize a certain function by systematically choosing the values of certain variables which are allowed to be adopted [18]. Figure 3 presents a function f that needs to be minimized by adopting the variable x. The results of mathematical optimization is the optimum Xu* where function f reaches minimum value. However, in many practical problems, certain restrictions g or unwanted areas (the shaded area in the Fig. 3) are present. If we also take into consideration those restrictions, then the optimum of the mathematical optimization is not at Xu* anymore, but at Xc*. The success of the prediction and optimization critically depends on the ability to develop a suitable approximation for the actual response f of the system. With the RSM the response f is predicted by polynomial models. A first order polynomial model is given by Eq. 1 [16] y = ßo+YJßixi + ' Í=1 (1) A second order polynomial model also called as quadratic model is given by Eq. 2 [17] k k y A, A, Í = 1 Í = 1 í 300 QJ I 0 0.1 0.2 0.3 0.4 0.3 0,6 0.7 0.3 Strain e[1] Fig. 10 Strain-stress curve The forming limit curve (FLC) in Fig. 11 was calculated by the predictive method [24]. The main advantage of this method is that it accurately predicts FLC with the help of mechanical properties A80 which are obtained with the uniaxial tensile test, the r-values and the sheet thickness. No other data is needed. TE ,*1 \ M m H -0.4 -0.2 0 0.2 0.4- 0.6 £2 Fig. 11 Forming limit diagram 5. Results and discussion The results were evaluated to suit the requirements of the selected design of experiments. All the numerical results were analysed through RSM. For this purpose, the quadratic models were mainly used to explain the mathematical relationship between input variables and objective functions. Quadratic polynomial equation for one objective function "thinning" was: Thinning = E~s x (18459 + 16.84 - 68.5B - 450C - 27.9D + 135.5E + 316.8F - 2.48AD + 2.48AF - f5) 2.96BC + 1.94CD + 2.99CE - 2.9CF + 1.5DE - 3.92DF + 1.9B2 + 6.26C2 + 4.04D2 - 1.89£2) f5) 5.1 ANOVA The results of ANOVA presented in this section are presented for only one objective function "thinning". The results for this objective function are shown in Table 4 and indicate that the predictability of the model for thinning is in 99% confidential interval. The predicted responses fit well with those of the numerically obtained results. The coefficients of determination (R2) values close to 1 indicate that polynomial approximation (Eq. 5) is highly reliable. F-value is greater than that of the tabular F0.01 [15] and p-value is low which suggest that the model influence on the objective function is statistically significant. Table 4 ANOVA result for the "thinning" objective function in reduced quadratic model Sum of squares Number of factors Standard deviation F-value p-value Model 0.032921 18 0.001829 21.6705 < 0.0001 A-BHF1 8.37E-06 1 8.37E-06 0.099115 0.7540 B-BHF2 0.000754 1 0.000754 8.939431 0.0041 C-BHF3 0.006624 1 0.006624 78.48896 < 0.0001 D-BHF8 0.008627 1 0.008627 102.221 < 0.0001 E-BHF9 0.000914 1 0.000914 10.83443 0.0017 F-BHF10 0.005354 1 0.005354 63.44184 < 0.0001 AD 0.000327 1 0.000327 3.875955 0.0538 AF 0.000159 1 0.000159 1.879241 0.1757 BC 0.000964 1 0.000964 11.4271 0.0013 CD 0.00034 1 0.00034 4.029295 0.0494 CE 0.000917 1 0.000917 10.86932 0.0017 CF 0.000436 1 0.000436 5.171731 0.0267 DE 0.000229 1 0.000229 2.709674 0.1052 DF 0.000785 1 0.000785 9.305206 0.0034 BA2 0.000254 1 0.000254 3.004378 0.0884 CA2 0.002791 1 0.002791 33.07372 < 0.0001 DA2 0.001108 1 0.001108 13.12282 0.0006 EA2 0.000225 1 0.000225 2.66841 0.1078 R2=0.870555665; Adj. R2=0.830383285; pred. R2=0.776865668_ 5.2 Optimization Optimization is made based on the results which are predicted by the polynomial. The optimization system predicts a set of solutions with different BHFs and belonging values of objective functions. All results can be presented graphically with the response surface (Fig. 12). This Figure presents results based on BHF4, BH6 and desirability which is a parameter describing the achievement of our goals. It is calculated by Eq. 2. The solution on the top of the surface presents the best solution with a highest value of D. All input parameters for these solutions are shown in Table 5. Table 5 Best solution chosen based on desirability Variable BHF1 BHF2 BHF3 BHF8 BHF9 BHF10 Value (kN) 43 54 35 48 60 30 D 1.000 j= 0.920 1.000 .Q CO 0 000 ■- 0.840 CO CD O » = F4 X2 - FB F1 = 43.32 F2 = &4-.3B F3 = 35.43 F5 - 60.00 0.760 Best solution D=0.913 10.313 Fig. 12 Response surface of all solutions 5.3 Comparing with FEM results At the end of this research study, we checked if the optimal solution is really better than the previous one. We checked this by comparing numerical results made with BHFs before and after this optimization. This comparison is described in Fig. 13 and in Table 6. The results showed a significant improvement of all quality parameters. This has proven the usefulness of the presented method, and its great potential for the optimization of sheet metal forming processes. Deviation (a) (b) Fig. 13 Comparison of the results before and after optimisation Table 6 Comparing numerical results before and after optimisation Objective function Wrinkling trend Crack Insufficient stretching Thinning Maximum deviation Before optimization 2.27 % 0.02 % 24.08 % 21.5 % 2.94 After optimization 0.42 % 0 % 0 % 20.9 % 1.33 Improvements +82 % - +100 % +3 % +55 % Fig 13. graphically shows improvement in the part quality. The upper two figures show that more area which represents safe area (FE nodes which lay in area IV on Fig 5.) is present on the right part. The lower two figures show deviations between FE nodes before and after springback. The right optimized part has fewer deviations. Even better improvements can be seen in Table 6. The improvements shown are significant. For the quality parameter "crack" the improvements in % is not calculated because the defect after optimization is 0 % and even before optimization the % was very low. Reported results show that by using this optimization system, reasonably good results and improvements can be achieved in a relatively short time. This optimization can be done during the development of the manufacturing method for the part, which could be a substantial benefit later in the production. The accuracy of the results strongly depends on the accuracy of the numerical models. However, numerical simulations are becoming increasingly reliable; therefore, this optimization system will become even more valuable. 6. Conclusion This research study presents the newly developed optimization system for optimising deep drawing parameters in order to get better part quality. The optimization system consists of three steps: modeling, screening and optimization. The methodology incorporates RSM and the results of FEM; the optimum area-dependent BHFs are determined with FEM and RSM by optimizing the objective function related with variables that are very difficult to determine during try-outs, as well as very time consuming. At the end of this research study, the optimization system was tested on the industrial example from the household appliances industry. It took into account the most important input variables and unwanted output properties (as objective functions) of the part. Results showed that with optimization of the process and area-dependent BHF, that it is possible to achieve the better part quality. The optimization system was developed for deep drawing optimization problems, but could also be used for other problems in various fields. Acknowledgement Operation part financed by the European Union, European Social Fund. References [1] Tisza, M. (2013). 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APEM jowatal Advances in Production Engineering & Management Volume 09 | Number 2 | June 2014 | pp 83-94 http://dx.doi.Org/10.14743/apem2014.2.178 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Imprecise data envelopment analysis model for robust design with multiple fuzzy quality responses Al-Refaie, A.a*, Li, M.-H.b, Jarbo, M.a, Yeh, C.-H.B.b, Nour, B.a department of Industrial Engineering, The University of Jordan, Amman, Jordan department of Industrial Engineering and Systems Management, Feng Chia University, Taichung, Taiwan A B S T R A C T A R T I C L E I N F O In this research, Imprecise Data Envelopment Analysis (IDEA) model was utilized to improve fuzzy multiple responses in robust design. The combination of process factor levels at each experiment was considered as a Decision Making Unit (DMU) with responses treated as inputs and outputs for all DMUs. The Fuzzy C-Means Clustering (FCMC) technique is used to fit the response fuzziness by clustering the average values, relative to each response, into a suitable number of clusters with triangular/trapezoidal membership functions. IDEA models were used to estimate the fuzzy triangular / trapezoidal efficiency values for each DMU. Finally, the preference degree-based ranking approach was used to discriminate between the fuzzy efficiency values and identifying the best combination of factors levels that would improve fuzzy multiple responses. Two case studies are utilized to illustrate the proposed approach, including optimizing wire electrical discharge machining and sputtering process parameters. The results showed that the proposed approach provides better anticipated improvements than the fuzzy multiple regression based approach. This approach would provide great assistant to process engineers in improving process performance with fuzzy multiple responses over a wide range of business applications. © 2014 PEI, University of Maribor. All rights reserved. Keywords: Imprecise data envelopment analysis Robust design Multi fuzzy quality response *Corresponding author: abbas.alrefai@ju.edu.jo (Al-Refaie, A.) Article history: Received 30 September 2013 Revised 23 April 2014 Accepted 5 May 2014 1. Introduction To survive in today's competitive markets, manufacturers produce their products considering multiple quality responses of main customer interest. Therefore, engineers aim to determine the best combination of process settings that reduces the variability of the quality responses and simultaneously shift the mean to the desired target [1]. For this reason, several approaches are proposed to optimize product/process performance with multiple responses [2-8]. In reality, dealing with response fuzziness becomes a challenging task for process engineers. The fuzzy responses are captured as an imprecise value rather than crisp one. The imprecise value could be interval, triangular, trapezoidal, or even linguistic. Conceptually, response fuzziness can be justified by four reasons [9, 10]. The first reason is the vague and complex process behaviour which may be explained by the nondiscretionary factors. The second is the inability to fix the process settings at precise values or in words the fuzziness inherent in the settings physical values. The third is the qualitative nature of the response itself. Finally, the fuzziness occurs due to customer preference. Several approaches are proposed to deal with response fuzziness problem in robust design [9-16]. The Taguchi method utilizes an orthogonal array to provide experimental format. Let DMUj denotes the combination of factor settings at each experiment in Taguchi's orthogonal array. For DMUj, the fuzzy inputs and outputs are denoted by ytj and yrj, respectively. In fuzzy goal programming (FGP), the fuzzy efficiency value, Ej, of each DMUj is calculated as follows. For a fuzzy triangular inputs, ytj, and outputs, yrj, values, the relative efficiency value of each DMUj is also considered as a fuzzy triangular value with three parameters, Ej1 , £^,and EjJ, which represent the lower, nominal, and the upper efficiency values, respectively. That is, Ej = (EjJ,Eji ,E") and is formulated as shown in Eq. 1: Xr=1 U-r y-rj v™ •¿■1=1 viyij Vs Z-ir=1 U-r y~r j v™ •¿■¿=1 vi yîj Vs ur (1) ym v- vL where s and m denote the number of outputs and inputs, respectively. Let the lower and upper inputs values are denoted by y^- and yjj, respectively. Also, the lower and upper outputs values are expressed as y^- and y^, respectively. For a DMU, DMUkej, under consideration, the upper desired efficiency value, i^, is calculated by using Model 1. Model 1 is: subject to Ejç - WICÍX ^^ TXy "y-ffc (2) r=l m ^¿yf*= 1 ¿=1 s m - ^ vi ytk <0 (3) (4) r=l o m - ^ Vi yj¡ < 0, V j * r=l i=1 ur,Vi >£,Vr,(Eq (5) (6) where ur, and v,, are the weights assigned to the outputs and inputs, and £ is the non-Archimedean value. In model 1, the objective function seeks to maximize the upper relative efficiency for each DMUk under the most favorable situation. The first constraint keeps the inputs weighted sum of the DMUk equals one. The second and the third constraints represent the most favorable condition for DMUk, where the highest score of the upper efficiency value is attained by settings the relative interval outputs at their upper bounds and the interval inputs at their lower bounds. Meanwhile, the outputs of all other DMUj^k reach their corresponding lower bounds and the interval inputs reach their corresponding upper bounds. The last constraint keeps the inputs and outputs weights larger than a small positive value. Similarly, the lower efficiency value E^, is calculated by using Model 2. Model 2 is: a = max ^ ur y^k (7) r=l subject to ill. = i (8) í=I ö m ^uryr¿fc- ^v¿y¿yfc<0 (9) r=l í=1 ytj ^0, Vj (10) r=1 ¿=1 ur,Vi >E ,Vr,i (11) In Model 2, the objective function seeks to maximize the lower relative efficiency Ek, for each DMUk under the least favorable situation. The first constraint keeps the upper weighted sum of the DMUk inputs equals one. The second and the third constraints represent the least favorable condition for DMUk, where the highest score of the relative efficiency value is attained by setting the relative interval outputs at their lower bounds and the interval inputs at the upper bounds, while the interval outputs of all other DMUj^k reach their relative upper bounds and the interval inputs reach their corresponding lower bounds. The last constraint keeps the inputs and outputs weights larger than a small positive value. Further, let the middle inputs and outputs values are denoted by yfj and , respectively. Then, for DMUk the nominal efficiency value, Ejf, is calculated by using Model 3 as follows: Model 3 is: s Ek =max ^ ur y'^lk (12) r=l subject to III. = i (13) í=I o m ^uryrMfc -^Vi y& ^0, ] = k (14) r=l i=l a ni. - ^ Vi ytj <0, Vj (15) r=1 ¿=1 ur,vt >£,Vr,iEq (16) The objective function in Model 3 seeks the optimal setting of outputs and inputs weights, Ur and vu that maximize the nominal efficiency value, Ejf, for each DMUk. The second and the third constraints keep the input weighted sum for each DMUk constant and at the same time the relative efficiency value less than one. The fourth constraint represents the nominal desired condition for each DMUk such that the nominal efficiency value is achieved when its relative outputs and inputs values reach their middle level, while the outputs reach their corresponding higher levels and the inputs reach their corresponding lower levels for DMUj^k. The last constraint keeps the values of the inputs and outputs weights more than a small non Archimedean variable. On the other hand, for a fuzzy trapezoidal inputs, ytj and outputs yrj, values the relative efficiency value of each DMUj have four parameters, Ej1 , Ej'M,Ej,M, and Ej1 which represent the lower, lower mid, upper mid, and the upper efficiency values, respectively. The fuzzy trapezoidal efficiency value of each DMUj can be written as Ej = (Ej',EjM,EjJM,£'j/) which is shown in Eq. 17. Xr=l ^r Vrj ym „ VU ZI¿ = 1 Jij Ej ys . .LM Z_ir=l "r Jrj Zi¿=i "i yt LM = < y s .. VUM Air=l "•r Jrj ym V.VUM Zi¿ = 1 Jij yr=i ur yrj yr=ivryLrj (17) Then, Model 1 and Model 2 are used to calculate the upper and lower relative efficiencies for ■j each DMUj, respectively. The lower mid efficiency value, Ej'M, is calculated as follows: Model 4 is: subject to a E¡¿m = max "Yjur (18) r=l m y/f = i (19) ¿=1 ö m ^y^-^y^íO, (20) r=l i=l o ut. rJri ~YJVi ^ "O, J (21) r=l i=l ur,Vi >£,Vr,iEq (22) In Model 4, the lower mid values of the inputs are set as y^, while the lower mid values of the outputs are set as y^f. The objective function seeks the optimal setting of outputs and inputs weights Ur, Vi that maximize the relative efficiency value, for each DMUk. The second and the third constraints keep the lower mid efficiency value for each DMUk less than one and the input weighted sum equal to one. The fourth constraint represents the lower mid desired condition for each DMUk such that the lower mid efficiency value is achieved when its relative outputs and inputs values are at their lower mid-level, while the outputs and inputs for DMUj^k are at their corresponding higher and lower relative levels respectively. The last constraint keeps the values of the inputs and outputs weights larger than a small non Archimedean variable [17]. By the same way, the upper mid efficiency value, E^M, is calculated by using Model 5 as follows. Model 5 is: s E%m = max ^ ur y™ (23) subject to r=1 y™ = i (24) ¿=1 s m ^ry^-^y™^0' (25) r=1 ¿=1 s m rJri ~YJVi ^ -0' J (26) r=1 ¿=1 ur,Vi >£'Vr,iEq (27) Utilizing the Models 1 to 5, the optimal factor settings can then be determined. Therefore, this research proposes an extension to ongoing research by proposing a procedure for solving the fuzzy multiple responses problem in robust design using DEA approaches. The remaining of this research including introduction is organized as follows. Section two presents the proposed approach. Section three illustrates the proposed approach using two cases. Section four compares the results. Finally, section four highlights the research conclusions. 2. The proposed approach In robust design method, several combinations of process factor levels are conducted to determine the best combination that improves multiple responses of main concern. The proposed approach for solving the multiple fuzzy quality characteristics is outlined in the following steps: Step 1: Letyqj denotes the value of the q-th response at the j experiment. Then, the combination of factor levels at each experiment is treated as a DMUj. Let yqj be the response average of the-smaller-the-better (STB), the-larger-the-better (LTB) response or the quality loss value for the-nominal-the-best (NTB) response to a number of triangular or trapezoidal membership functions. Step 2: The FCMC technique is used to cluster the average values of yqj into a number of classes, d, each is treated either as a triangular or trapezoidal membership function. The parameter of each membership function is determined such that, the class center, Cqd, for the triangular membership function is considered as the most likely value, y^. The upper, and lower, yqd, pa- rameters are determined by the centers of the neighbor classes or the DMU with least considerable membership value. For the trapezoidal membership function, the lower mid, y^f, and the upper mid, y^f, of each class are considered as the DMUs of the largest membership value relative to the same class. The upper and lower parameters and y^d, are determined by the centers of the neighbor classes or the DMU with least considerable membership value. Step 3: The fuzzy efficiency values are computed by using models 1 to 5. The upper mid values inputs are set as yjjM and the upper mid outputs are set y™ in Model 5, which has similar to that of Model 4 except the fourth constraint represents the upper mid desired condition for each DMUk where the upper mid efficiency value is achieved when its relative outputs and inputs values are at their upper mid-level, while the outputs and inputs reach their corresponding higher and lower levels respectively for DMUj^k- Step 4: The preference degree based ranking approach [18] is used for clear-cut discrimination among the DMUs. In this regard, the complete ranking order for n fuzzy efficiency values can be obtained as (1) the triangular efficiency values and (2) the trapezoidal efficiency values. (1) For the triangular efficiency values: In the preference degree based ranking approach, let Ek = (Ek,Ek ,Ek) and Ej^k = (Ej',Ej*,EjJ), are two fuzzy triangular efficiency values. According to fuzzy arithmetic, there are four possible relationships to compare Ek with Ej^k as shown in Eq. 28. P(Ek >E^k) = 1, 0, IF (Et > Ejik) IF (E» < ELk), = (5 y ,IF (E»> E^k)n(E™< ££fc), (Fu - Fl + Fm -FM^(FU -FL + FU -Fl (Ejik _ Ek) C5 u 'j^k Fl + F M 7M Et+E, ,IF(4< Ejik)n(E¡f> Efik). (28) The preference matrix Pkj is calculated as follows: Pkj = PkJ EJ=i Ej=k Ej=n EJ=1 0.5 Ej=k Pi,k 0.5 F- Pl,n Pk,n 0.5 (29) where P^ is the preference matrix for all DMUs. Find a row from the matrix, Pkj, whose elements except the diagonal are larger than or equal to 0.5. If this row corresponds to Ek, then DMUk is considered as the most efficient DMU and its relative settings are the best. The kth row is eliminated from the matrix. In the reduced matrix, if Eh^k stands out with the largest preference values compared to the remaining efficiency values, then Eh^k is ranked in the second place. Repeat this step until all of the fuzzy efficiency values are properly ranked. (2) For the trapezoidal efficiency values: Let Ek(Ek,Ej;M,E%M,E%) and Ej^Ej^Ef^E^E^) be two fuzzy trapezoidal efficiency values. According to fuzzy arithmetic, there are five possible relationships to compare Ek with Ej^k, which are stated in Eq. (30). P(4 >Ej*k) = 1, 0, (Fu - Fh +FML-FMU^(FU -FL yDk Dj*k Dk J\ k Dk pMU _p. ML k pMU _ pML (ßk ' pUM _ pLM \ Dk Dj*k) (Fu — Fl + Fmu — Fml + Fmu — Fml +Fu -Fl Y _j^k- Ej)2_ (Fu — Fl +Fml — Fmu~\(Fv — Fh +Fmv — Fml + Fmv — Fml +Fv —Fl Y IF (Et > Ejik) IF (E« < EjiJ (Et > £]î)n(£r < Ej») (E™ >E™)n(Et" < í-,™) (E¡? >£,™)n (Et < EJÏJ (30) The preference matrix, P j is calculated using Eq. (30): PkJ = Vk,j Ej=1 ËJ=i 0.5 Ej=k ... Ej=n ... Ej=k Pi,k 0.5 p. Pl,n Pk,n 0.5 (31) where Pk,j is the preference matrix for all DMUs. Repeat until all of the fuzzy efficiency values are properly ranked. Step 5: The anticipated improvements are calculated by using the proposed approach, then the improvements gained by the proposed approach are compared to fuzzy multiple regression approach (FMRA). 3. Two cases for illustration Two cases adopted in the literature are applied to illustrate the proposed approach. The first case deals with response fuzziness that is best fit by fuzzy triangular membership function, whereas the second case considers trapezoidal membership function as the best fit to response fuzziness. 3.1 Case I: Optimization of Inconel on machining of CNC WEDM process Al-Refaie et al. [8] conducted nine experiments utilizing Taguchi's L9 array to optimize the multi quality responses of Inconel 718 on machining of CNC WEDM process using fuzzy multiple regression approach (FMRA). The two quality responses are surface roughness (SR), yi, which is a STB type response and material removal rate (MRR), y2, which is a LTB type response. Table 1 shows the four process factors considered which are: pulse in time (A), delay time (B), wire feed speed (C), ignition current (D) as well as the corresponding levels. The combination of factor settings at each experiment is treated as DMUj, where the average values of SR, yl7-, are considered as inputs, while the average values of MRR, y2j, are the outputs for DMUs. Table 1 displays the experimental results. Table 1 Experimental data for WEDM process optimization DMUj Process factors Inputs Outputs A B C D yij Ï2i DMUi 1 1 1 1 3.15 46.00 DMU2 1 2 2 2 3.25 47.50 DMU3 1 3 3 3 3.30 41.50 DMU4 2 1 2 3 3.75 55.50 DMUs 2 2 3 1 3.45 49.50 DMU6 2 3 1 2 3.25 52.50 DMU7 3 1 3 2 4.10 70.50 DMU8 3 2 1 3 3.65 73.50 DMU9 3 3 2 1 3.35 64.00 Table 2 The center values for the three triangular membership functions . _Membership function center_ Class _cid_cM_ dl°w 3.15 47 ^medium 3.65 57 __4.00_67_ Then, the Fuzzy C-Means Clustering (FCMC) technique is used to determine the center values for the three triangular membership functions which are listed in Table 2. Each defined class is considered as a triangular membership function, whose parameters are tuned such that the center of the relative class is considered as the most likely parameter, y^, while the centers of the neighbor classes are considered as the upper, y^d, and lower, y^d, parameters. Consequently, the experiments results shown in Table 1 are transformed into the fuzzy triangular numbers shown in Table 3. Model 1 is used to calculate the upper efficiency values, EjJ for all DMUs. Similarly, Model 2 is used to calculate the lower efficiency values, Ej1 for all DMUs. Model 3 is used to calculate the nominal efficiency values, Ej1 for all DMUs. Models 1, 2, and 3 are solved and the fuzzy triangular relative efficiency values are shown in Table 3. Table 3 Fuzzy efficiency values for WEDM process optimization DMUj Vu V2i Ek DMUi 3.15 s = (3.15,3.15,3.65)low 46.0 a (40,47,57)l°w (0.460, 0.625, 1.000) DMU2 3.25 s = (3.15,3.15,3.65)^ 47.5 a (40,47,57)low (0.460, 0.625, 1.000) DMU3 3.30 s = (3.15,3.15,3.65)^ 41.5 a (40,47,57)l°w (0.460, 0.625, 1.000) DMU4 3.75 a ; (3.4,3.65,4.0)medium 55.5 a (47,57,67)medium (0.550, 0.640, 1.000) DMUs 3.45 s = (3.15,3.15,3.65)^ 49.5 a (40,47,57)l°w (0.460, 0.625, 1.000) DMU6 3.25 = (3.15,3.15,3.65)^ 52.5 a (47,57,67)medium (0.587, 0.731, 1.000) DMU7 4.1 s (3.65 ,4.2,4.2)hish 70.5 a (57,67,74)h«h (0.555, 0.565, 1.000) DMU8 3.65 a : (3.4,3.65,3.8)medium 73.5 a (57,67,74)h«h (0.606, 0.752, 1.000) DMU9 3.35 = (3.15,3.15,3.65)^ 64.0 a (57,67,74)h«h (0.636, 0.864, 1.000) Then, the preference degree based ranking approach is used for more clear-cut discrimination among the DMUs. Eq.(28) is used to calculate the preference matrix as shown in Table 4, where it is found that DMUj=9 has the largest value in each column. The minimum of these nine largest values is 0.609. Hence, it is the most preferred DMU. Table 4 Preference matrix for WEDM process optimization DMUj Preference value P(Ek > E*k) Rank 1 2 3 4 5 6 7 8 9 DMU1 0.500 0.500 0.500 0.461 0.500 0.357 0.458 0.306 0.227 5 DMU2 0.500 0.500 0.500 0.461 0.500 0.357 0.458 0.306 0.227 5 DMU3 0.500 0.500 0.500 0.461 0.500 0.357 0.458 0.306 0.227 5 DMU4 0.539 0.539 0.539 0.500 0.539 0.383 0.491 0.327 0.240 4 DMU5 0.500 0.500 0.500 0.461 0.500 0.357 0.458 0.306 0.227 5 DMU6 0.643 0.643 0.643 0.617 0.643 0.500 0.589 0.435 0.328 3 DMU7 0.542 0.542 0.542 0.509 0.542 0.411 0.500 0.359 0.359 4 DMU8 0.694 0.694 0.694 0.673 0.694 0.565 0.640 0.500 0.390 2 DMU9 0.773 0.773 0.773 0.759 0.773 0.672 0.719 0.609 0.500 1 3.2 Case II: Optimizing of the sputtering process parameters Al-Refaie et al. [8] conducted eighteen experiments utilizing L18 array to optimize sputtering process parameters using fuzzy multiple regression based method. Five process factors considered, including: the R.F. power (P), the sputtering pressure (Q), the deposition time (R), the substrate temperature (S), and the post-annealing temperature (T). Further, three quality responses were considered including the electrical resistivity (ER), y1, which is a STB type response, the deposition rate (DR),y2, which is also a STB type response and the optical transmittance (OT),y, which is a LTB type response. The experimental results are shown in Table 5 in term of the responses average values, yqj. In Table 5, the average values of ER quality response yx, are considered as inputs, while the outputs are considered as the average values of DR, y2, and OT, y3. The FCMC technique is employed to categorize each response average values into three clusters. The class center value, cqd with respect to each class are calculated and listed in Table 6. The trapezoidal membership functions for all responses are shown in Table 7. Further, the fuzzy trapezoidal efficiency values and preference degree matrix for sputtering process are listed in Tables 8 and 9, respectively. Table 5 Experimental data for sputtering process optimization Exp. No. Process factors Responses P Q R S T yi/ y2 1 y3/ 1 50.00 0.13 30.00 25.00 0.00 15.10 4.60 88.40 2 50.00 0.67 60.00 50.00 100.00 9.75 5.60 87.70 3 50.00 1.33 90.00 100.00 200.00 7.85 4.95 88.10 4 100.00 0.13 30.00 50.00 100.00 5.50 9.45 89.25 5 100.00 0.67 60.00 100.00 200.00 4.45 11.20 87.05 6 100.00 1.33 90.00 25.00 0.00 6.55 10.00 84.70 7 200.00 0.13 60.00 25.00 200.00 1.65 20.00 86.60 8 200.00 0.67 90.00 50.00 0.00 1.95 21.60 82.35 9 200.00 1.33 30.00 100.00 100.00 1.70 20.90 85.45 10 50.00 0.13 90.00 100.00 100.00 7.15 4.70 87.60 11 50.00 0.67 30.00 25.00 200.00 7.00 4.95 89.10 12 50.00 1.33 60.00 50.00 0.00 7.75 4.85 87.40 13 100.0 0.13 60.00 100.00 0.00 6.00 9.70 87.00 14 100.00 0.67 90.00 25.00 100.00 5.90 11.35 83.70 15 100.00 1.33 30.00 25.00 200.00 5.60 10.75 88.35 16 200.00 0.13 90.00 50.00 200.00 1.05 19.45 83.10 17 200.00 0.67 30.00 100.00 0.00 1.25 22.05 85.70 18 200.00 1.33 60.00 25.00 100.00 1.35 20.50 83.80 Table 6 The center values for the three triangular membership functions Class Membership function center _Cid_C2d_C3d Low (d>°w) 1.57 4.95 83.50 Medium (d™d>um) 6.70 10.50 86.50 High (dh'ai>)_14.80_21.00_88.40 Table 7 Fuzzy trapezoidal experimental data for sputtering process DMUj ?n ?2I ?3I DMUi 15.10 « (6.7,14.8,15.1,15.1)H 4.60 « (4.6,4.6,4.95,10.5)L 88.40 « (86.5,88.4,90,90)H DMU2 9.75 « (6.7,14.8,15.1,15.1)H 5.60 « (4.95,9.7,11.35,21)M 87.70 « (86.5,88.4,90,90)H DMU3 7.85 « 1.57,6,7.3,14.8)M 4.95 « (4.6,4.6,4.95,10.5)L 88.10 « (86.5,88.4,90,90)H DMU4 5.50 « 1.57,6,7.3,14.8)M 9.45 « (4.95,9.7,11.35,21)M 89.25 « (86.5,88.4,90,90)H DMUs 4.45 « 1.57,6,7.3,14.8)M 11.20 « (4.95,9.7,11.35,21)M 87.05 « (86.5,88.4,90,90)H DMUs 6.55 « 1.57,6,7.3,14.8)M 10.00 « (4.95,9.7,11.35,21)M 84.70 « (83.5,86,87,88.4)M DMU7 1.65 (1,1,1.95,5.5)L 20.00 « (10.5,19,22,22)H 86.60 « (83.5,86,87,88.4)M DMUe 1.95 « 1,1.57,1.95,6.7)L 21.60 « (12,19,22,22)H 82.35 « (82,82,83.5,86.5)L DMU9 1.70 « 1,1.57,1.95,6.7)L 20.90 « (10.5,19,22,22)H 85.45 « (83.5,86,87,88.4)M DMU10 7.15 « 1.57,6,7.3,14.8)M 4.70 « (4.6,4.6,4.95,10.5)L 87.6 = (83.5,86,87,88.4)M DMU11 7.00 « 1.57,6,7.3,14.8)M 4.95 « (4.6,4.6,4.95,10.5)L 89.1 s (86.5,88.5,90,90)H DMU12 7.75 « 1.57,6,7.3,14.8)M 4.85 « (4.6,4.6,4.95,10.5)L 87.4 s (86.5,88.4,90,90)H DMU13 6.00 « 1.57,6,7.3,14.8)M 9.70 « (4.95,9.7,11.35,21)M 87.00 « (83.5,86,87,88.4)M DMU14 5.90 « 1.57,6,7.3,14.8)M 11.35 « (4.95,9.7,11.35,21)M 83.70 « (82,82,83.5,86.5)L DMU15 5.60 « 1.57,6,7.3,14.8)M 10.75 « (4.95,9.7,11.35,21)M 88.35 « (86.5,88.5,90,90)H DMU16 1.05 « 1,1.57,1.95,6.7)L 19.45 « (10.5,19,22,22)H 83.10 « (82,82,83.5,86.5)L DMU17 1.25 « 1,1.57,1.95,6.7)L 22.05 « (10.5,19,22,22)H 85.70 « (83.5,86,87,88.4)M DMU18 1.35 « 1,1.57,1.95,6.7)L 20.50 « (10.5,19,22,22)H 83.80 « (82,82,83.5,86.5)L Table 8 Fuzzy trapezoidal efficiency values for sputtering process DMUj E, DMUi (0.070,0.073,0.073,0.619) DMU2 (0.117,0.121,0.123,1.000) DMU3 0.116,0.121,0.123,1.000) DMU4 (0.117,0.121,0.123,1.000) DMU5 (0.117,0.121,0.123,1.000) DMU6 (0.114,0.116,0.118,1.000) DMUy (0.229,0.235,0.244,1.000) DMUs (0.224,0.226,0.244,1.000) DMU9 (0.229,0.235,0.244,1.000) DMU10 (0.114,0.116,0.117,1.000) DMUii 0.116,0.121,0.123,1.000) DMU12 (0.116,0.121,0.123,1.000) DMU13 (0.114,0.116,0.118,1.000) DMU14 (0.112,0.112,0.114,1.000) DMU15 (0.117,0.121,0.123,1.000) DMU16 (0.224,0.226,0.244,1.000) DMU17 (0.229,0.235,0.244,1.000) DMU18 (0.224,0.226,0.244,1.000) Table 9 Preference degree matrix for the fuzzy trapezoidal efficiency values (columns 1 to 9) _Preference value P(Ek >Ej^k)_ DMUj Rank DMUk 1 2 3 4 5 6 7 8 9 DMU1 0.500 0.320 0.320 0.320 0.320 0.324 0.207 0.212 0.207 7 DMU2 0.680 0.500 0.500 0.500 0.500 0.504 0.403 0.407 0.403 2 DMU3 0.679 0.499 0.50 0.499 0.499 0.503 0.402 0.406 0.402 3 DMU4 0.680 0.500 0.500 0.500 0.500 0.504 0.403 0.407 0.403 2 DMU5 0.680 0.500 0.500 0.500 0.500 0.504 0.403 0.407 0.403 2 DMU6 0.676 0.495 0.495 0.495 0.495 0.500 0.400 0.404 0.400 4 DMU7 0.792 0.595 0.596 0.595 0.595 0.598 0.500 0.504 0.500 1 DMU8 0.641 0.393 0.394 0.393 0.393 0.398 0.495 0.500 0.495 6 DMU9 0.792 0.595 0.596 0.595 0.595 0.598 0.500 0.504 0.500 1 DMU10 0.676 0.495 0.495 0.495 0.495 0.500 0.400 0.404 0.400 4 DMU11 0.679 0.499 0.50 0.499 0.499 0.503 0.402 0.406 0.402 3 DMU12 0.679 0.499 0.50 0.499 0.499 0.503 0.402 0.406 0.402 3 DMU13 0.676 0.495 0.495 0.495 0.495 0.500 0.400 0.404 0.400 4 DMU14 0.672 0.492 0.492 0.492 0.492 0.495 0.398 0.401 0.398 5 DMU15 0.680 0.500 0.500 0.500 0.500 0.504 0.403 0.407 0.403 2 DMU16 0.641 0.393 0.394 0.393 0.393 0.398 0.495 0.500 0.495 6 DMU17 0.792 0.595 0.596 0.595 0.595 0.598 0.500 0.504 0.500 1 DMU18 0.641 0.393 0.394 0.393 0.393 0.398 0.495 0.500 0.495 6 Table 9 Preference degree matrix for the fuzzy trapezoidal efficiency values (continuation, columns 10 to 18) _Preference value P{Ek >Ej^k)_ DMUk 10 11 12 13 14 15 16 17 18 DMU1 0.324 0.320 0.320 0.324 0.327 0.320 0.212 0.207 0.212 7 DMU2 0.504 0.500 0.500 0.504 0.506 0.500 0.407 0.403 0.407 2 DMU3 0.503 0.500 0.500 0.503 0.503 0.499 0.406 0.402 0.406 3 DMU4 0.504 0.500 0.500 0.504 0.506 0.500 0.407 0.403 0.407 2 DMU5 0.504 0.500 0.500 0.504 0.506 0.500 0.407 0.403 0.407 2 DMU6 0.500 0.495 0.495 0.500 0.502 0.495 0.404 0.400 0.404 4 DMU7 0.598 0.596 0.596 0.598 0.601 0.595 0.792 0.595 0.596 1 DMU8 0.398 0.394 0.394 0.398 0.398 0.393 0.500 0.495 0.500 6 DMU9 0.598 0.596 0.596 0.598 0.601 0.595 0.792 0.595 0.596 1 DMU10 0.500 0.495 0.495 0.500 0.502 0.495 0.404 0.400 0.404 4 DMU11 0.503 0.500 0.500 0.503 0.503 0.499 0.406 0.402 0.406 3 DMU12 0.503 0.500 0.500 0.503 0.503 0.499 0.406 0.402 0.406 3 DMU13 0.500 0.495 0.495 0.500 0.502 0.495 0.404 0.400 0.404 4 DMU14 0.495 0.492 0.492 0.495 0.500 0.492 0.401 0.398 0.401 5 DMU15 0.504 0.500 0.500 0.504 0.506 0.500 0.407 0.403 0.407 2 DMU16 0.398 0.394 0.394 0.398 0.398 0.393 0.500 0.495 0.500 6 DMU17 0.598 0.596 0.596 0.598 0.601 0.595 0.792 0.595 0.596 1 DMU18 0.398 0.394 0.394 0.398 0.398 0.393 0.500 0.495 0.500 6 4. Research results and discussion 4.1 Results of case I For this case, Table 4 reveals that DMU9 is the most preferred DMU. Table 10 shows the results of the proposed approach against that of the fuzzy multiple regression approach (FMRA). Using the proposed approach, the MRR fuzzy response value, yx, which is a LTB type response improved from (56.4, 59.10, 62.46) to (57, 67, 74), where the y^ and yf* values are significantly increased. Also, the SR fuzzy response value, y2, which is a STB type response improves from (2.94, 3.32, 3.75) to (3.15, 3.15, 3.65). Note that the proposed approach provides smaller mean and upper bound value than FMRA. Therefore, to improve the performance of WEDM process, the best combination of factor settings is pulse in time A3, delay time B3, wire feed speed C2, ignition current D1. Table 10 Improvement comparison for case I Response ?! (LTB) (STB) Initial condition « (49.4,51.9,54.58) « (2.99,3.42,3.92) Fuzzy multiple regression approach (FMRA) « (56.4,59.10,62.46) « (2.94,3.32,3.75) Proposed approach results (IDEA) « (57,67,74) « (3.15,3.15,3.65) 4.2 Results for case II For case II, it is found that DMU9 is the best DMU, which corresponds as shown in Table 5. Table 11 displays the anticipated improvements using the proposed approach and FMRA. Using the proposed approach the fuzzy trapezoidal value of the ER, yr, which is a STB type response decreased from (1.39, 2.91, 3.19, 4.32) to (1.0, 1.57, 1.95, 6.7). Although the proposed approach increased the upper response value, yf it significantly decreased the lower mid and upper mid response values. For DR, y2, which is a LTB type response, the proposed approach enhances the response fuzzy trapezoidal value from (11.84, 12.26, 12.75 21.94) to (10.5, 19, 21, 22). Finally for OT, y3, which is a LTB type response, the proposed approach improves the upper response value from 87.7 to 88.5. Consequently, the best combination of factor settings for the sputtering process is the R.F. power P = 200, the sputtering pressure Q = 1.33, the deposition time R = 30, the substrate temperature S = 100, and the post-annealing temperature T = 100. Table 11 Improvement comparison for case II Methods FMRA results IDEA results Quality responses yi (STB, input)_ _y2 (LTB, output)__y3 (LTB, output) yi yML yUL y? V2 y2ML yU2L yi yk yML yïL y3u 1.39 2.91 3.19 4.32 11.84 12.26 12.75 21.94 86.4 86.5 87.6 87.7 1.0 1.57 1.95 6.7 10.5 19.0 21.0 22.0 83.5 86.0 87.0 88.5 5. Conclusions In this research, a fuzzy DEA based procedure is proposed to solve the fuzzy multiple responses problem in robust design. DEA models are utilized to calculate the fuzzy efficiencies. Then, the preference matrix is adopted to identify the best decision making unit. Two real case studies from previous literature are employed to illustrate the proposed approach including improving performance of the WEDM and sputtering processes, where the response fuzziness is fitted by a triangular and trapezoidal membership functions in the first and second case study, respectively. In both studies, the proposed approach efficiently identified the best combination of factor settings and provides better anticipated improvements than the fuzzy multiple regression based approach. In conclusion, the proposed approach may provide great assistant to process engineers in determining the best combination of factor settings that improves fuzzy multiple re- sponses in a wide range of business applications. Nevertheless, this approach ignores process factor settings and preferences on quality responses. Another limitation is its complexity when many fuzzy responses are considered simultaneously. Future research will consider these issues. 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APEM jowatal Advances in Production Engineering & Management Volume 9 | Number 2 | June 2014 | pp 95-103 http://dx.doi.Org/10.14743/apem2014.2.179 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Hybrid Taguchi method for optimizing flux cored arc weld parameters for mild steel Satheesh, M.a, Edwin Raja Dhas, J.b* department of Mechanical Engineering, Noorul Islam Centre for Higher Education, Kumaracoil, Thuckalay, India department of Automobile Engineering, Noorul Islam Centre for Higher Education, Kumaracoil, Thuckalay, India A B S T R A C T A R T I C L E I N F O Flux cored arc welding has been applied in manufacturing industries for more than fifteen years. The quality of weld mainly depends on the mechanical properties of the weld, which in turn relays on the interaction of the weld parameters. This paper discusses the multi response optimization of weld parameters using grey based Taguchi method. Grey relational analysis was carried out to convert multi objective criterion into equivalent single objective function; overall grey relational grade, which is optimized by the Taguchi technique. Experiments are conducted using Taguchi's L27 orthogonal array. The weld parameters used in this study were welding current, welding speed, and arc voltage with bead hardness and material deposition rate as responses. Taguchi's Signal-to-Noise (S/N) ratio is computed based on their performance characteristics. Grey relational grade was obtained using Signal-to-Noise ratio values of responses. Based on the grey relational grade, optimum levels of parameters have been identified. Significant contributions were estimated using Analysis of Variance (ANOVA). A confirmation test was conducted to validate the proposed method. This evaluation procedure could be used in decision-making to select process parameters for a welding operator. The proposed and developed method has good accuracy and competency with the predicted value enhancing automation and robotization. © 2014 PEI, University of Maribor. All rights reserved. Keywords: Flux cored arc welding Optimization Process parameters Grey based Taguchi method Orthogonal array *Corresponding author: edwinrajadhas@rediffmail.com (Edwin Raja Dhas, J.) Article history: Received 23 August 2013 Revised 24 May 2014 Accepted 2 June 2014 1. Introduction Generally, the quality of a weld joint is directly influenced by the welding input parameters during the welding process; therefore, welding can be considered as a multi-input multi-output process. Unfortunately, a common problem that has faced the manufacturer is the control of the process input parameters to obtain a good welded joint with the required bead geometry and weld quality with maximum deposition rate. Weld deposition rate is the weight (in kg) of weld metal deposited per unit of arc-on-time (usually one hour). The weight deposited is less than the weight of the filler metal used, because of various losses. The ratio of the weight of metal deposited in the weld to that of filler metal employed, expressed in percent, is called the deposition efficiency. Flux cored arc welding process is a fully automated process, in which the welding electrode is a tubular wire that is continuously fed to the weld area [1]. The flux materials are in the core of the tube. The outer shell of the tube conducts the electricity that forms the arc and then becomes the filler metal as it is consumed. Recent studies indicate that FCAW has a number of advantages over the common welding techniques available that use solid wires such as manual metal arc welding and gas metal arc welding [2]. Using FCAW in any repair technique can pro- vide better control over current and heat input that is necessary to carry out the temper bead repair. As a fully automatic process, FCAW should also have cost advantages over other commonly used processes. Flux cored arc welding is considered a high deposition rate welding process that adds the benefits of flux to the simplicity of metal inert gas welding [3]. Many research attempts have been made by researchers to establish flux cored arc welding process. Mathematical modeling [4], particle swarm optimization algorithm [5], simulated annealing algorithm [6], memetic algorithm [7], Taguchi method [8], were used to optimize the parameters of flux cored arc welding process. Traditional Taguchi method can optimize a single objective function whereas it cannot solve multi objective function [9]. This paper explores the development of grey based Taguchi method for multi response optimization of flux cored arc weld parameters. 2. Grey based Taguchi method To resolve the problems subjected to multiple quality characteristics, a decision maker should rely on the subjective experiences of engineers to attain a compromise. As a result, uncertainty will be increased during the process. Hence some researchers have concentrated on achieving multiple quality characteristic at a time as a function of different appropriate level of input parameter settings. Orthogonal array with principle component analysis and Taguchi method and response surface methodology applied [10, 11] to optimize multiple quality characteristics during laser cutting of different thin sheets. Fuzzy based desirability function is used to optimize parameters of weld [12]. Grey relational analysis aims to fulfil the crucial mathematical criteria for multiple quality characteristic problems [13]. It avoids the inherent shortcomings of conventional, statistical methods and requires a limited data to estimate the behavior of an uncertain system. It provides an efficient solution to the uncertain, multi-input and discrete data problem. The main function of Grey relational analysis is to indicate the relational degree between two sequences by using discrete measurement method the distance. It can be effectively recommended as a method for optimizing the complicated interrelationships among multiple performance characteristics. 2.1 Taguchi method The quality engineering methods of Taguchi, employing design of experiments provide an efficient and systematic way to optimize designs for performance, quality and cost It is one of the most important statistical tools for designing high quality systems at reduced cost [14, 15]. The use of Taguchi method simplifies the optimization procedure for determining the optimal welding parameters in the FCAW process. The Taguchi method is performed to reduce the sources of variation on the quality characteristics of product, and reach a target of process robustness. The control factors that may contribute to reduce variation (improved quality) can be quickly identified by looking at the amount of variation present as a response. Taguchi recommends the use of the loss function to measure the performance characteristic deviating from the desired value. The value of the loss function is then transformed into an S/N ratio. Usually, there are three categories [16] of performance characteristic in the analysis of the S/N ratio, i.e. lower-the-better, higher-the-better, and nominal-the-best The deposition rate and hardness are the higher the better performance characteristic. The S/N ratio nij for the ith performance characteristic in the jth experiment can be expressed as Eq. 1. The loss function Lj for higher-the-better performance characteristic is expressed in Eq. 2: Vij = -10lOg(iy) (1) (2) where n is the number of replication, k is the number of tests, yjk is experimental value of the ith performance characteristic in the jth experiment at the kth tests. For lower-the-better performance characteristic, Lij is expressed in Eq. 3. n k=1 For nominal-is-best performance characteristics, the S/N ratio is expressed in Eq. 4. ^■ = 10logg) (4) The S/N ratio for each level of process parameters is computed based on the S/N analysis. This S/N ratio value can be considered for the optimization of single response problems. However, optimization of multiple performance characteristics cannot be straightforward as in the optimization of a single performance characteristic. 2.2 Grey relational analysis The grey relational analysis is based on the grey system theory used to solve complicated interrelationship multiple performance characteristics problems effectively. A grey system has a level of information between black and white. Black represents having no information and white represents having all information. Grey based Taguchi method is successfully applied to optimize film coating process [17], drilling process [18], plasma arc weld parameters [19], bead geometry in SAW process, and wire electrical discharge machining process [20, 21]. Depending upon the characteristics of a data sequence, there are various methodologies of datapre-processingavailablefor this analysis. Experimentaldatayij isnormalized as Zj (0 < Zj < 1) for the ith performance characteristics in the jth experiment is expressed as: For S/N ratio with larger-the-better: __yij-min(yij,i = 1,2 ...,n)_ ¿ij ~ ( \ ■ ( - il A (5) max {yij,i = 1,2, ...,n) - min(yij,i = 1,2, ...,n) For S/N ratio with smaller-the-better: max{ytj,i = 1,2, ...,n) max{ytj,i = 1,2, ...,n) — m.in(yij,i = 1,2, ...,n) ^ = __..,.. .. ^ ...,.,.. .. ^ (6) For S/N ratio with nominal-the-best: z __{yg -Target)-rnm(|y0- -Target], i = 1,2, ...,n)__(7) 11 max{\ytj — Target], i = 1,2, ...,n) — min^y^ — Target], i = 1,2, ...,n) Then, the grey relational coefficients are calculated to express the relationship between the ideal and the actual experimental results. The grey relational co-efficient is expressed in Eq. 8: Amin +