A comparative study on modelling material removal rate by ANFIS and polynomial methods in electrical discharge machining process

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(BQ) The study sheds light on the powerful learning capability of ANFIS models and its superiority over the conventional polynomial models in terms of modelling complex non-linear machining processes

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Nội dung Text: A comparative study on modelling material removal rate by ANFIS and polynomial methods in electrical discharge machining process

Computers & Industrial Engineering 79 (2015) 27–41 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie A comparative study on modelling material removal rate by ANFIS and polynomial methods in electrical discharge machining process Khalid Al-Ghamdi, Osman Taylan ⇑ King Abdulaziz University, Faculty of Engineering, Department of Industrial Engineering, P.O. Box 80204, Jeddah 21589, Saudi Arabia a r t i c l e i n f o Article history: Received 27 April 2013 Received in revised form 26 October 2014 Accepted 29 October 2014 Available online 7 November 2014 Keywords: EDM MRR Polynomial model Neuro-fuzzy model Non-conventional machining a b s t r a c t Due to the controversy associated with modelling Electrical Discharge Machining (EDM) processes based on physical laws; this task is predominantly accomplished using empirical modelling methods. The modelling studies reported in the literature deal predominantly with quantitative parameters i.e. ones with numerical levels. In fact, modelling categorical parameters has been devoted a scant attention. This study reports the results of an EDM experiment conducted on the Ti–6Al–4V alloy. Its aim was to model the relationship between the Material Removal Rate (MRR) and the parameters of the process, namely, current, pulse on-time and pulse off-time along with a categorical factor (electrode material). The modelling process was accomplished using adaptive neuro-fuzzy inference system (ANFIS) and polynomial modelling approaches. In fact, one purpose of this study was to compare the performance of these modelling approaches as no study was found contrasting their prediction capability in the literature. Regarding the polynomial model, two numerical parameters (current and pulse on-time) were declared signiﬁcant in the ANOVA together with the electrode material and its interaction with pulse on-time. Thus, they were all incorporated in the developed polynomial model. Furthermore, ﬁve ANFIS models with 6, 9, 19, 21 and 51 rules were developed utilizing the ﬁrst order Sugeno fuzzy approach by backpropagation neural networks training algorithm. Of these, the ANFIS model with 21 rules was the best. This model also outperformed the polynomial model remarkably in terms of predicting error, residuals range and the correlation coefﬁcient between the experimental and predicted MRR values. The study sheds light on the powerful learning capability of ANFIS models and its superiority over the conventional polynomial models in terms of modelling complex non-linear machining processes. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Recent years have witnessed remarkable increase in the demand for the titanium based alloys owing to their high strength-weight ratio, excellent fracture and corrosion resistance and superior mechanical properties at elevated temperature. An extensive utilization of these alloys has been observed in the aerospace industry (Armendia, Garay, Iriarte, & Arrazola, 2010; Moiseev, 2005). Indeed, many of the aero-engine components are produced using these alloys due, in no small part, to their relatively lightweight which helps to reduce the aircraft’s overall weight thereby moderating fuel consumption (Singh & Khamba, 2007). Moreover, titanium alloys are noticeably replacing the traditionally used materials in aerospace industry such as aluminium (Lütjering & Williams, 2007). They are also used increasingly in other indus⇑ Corresponding author. Tel.: +966 500031056; fax: +966 26952486. E-mail addresses: kaaalghamdi@kau.edu.sa (K. Al-Ghamdi), otaylan@kau.edu.sa (O. Taylan). http://dx.doi.org/10.1016/j.cie.2014.10.023 0360-8352/Ó 2014 Elsevier Ltd. All rights reserved. trial and commercial applications such as, chemical processing, pollution control, surgical implantation, nuclear waste storage, food processing and petroleum reﬁning. A major hindrance for the wider use of titanium alloys is the difﬁculties associated with machining them conventionally. Being chemically reactive to almost all tool materials, they tend to weld the cutting tools while machining thereby accelerating tool failure (Hartung, Kramer, & Von Turkovich, 1982). The damage to cutting tools is compounded by the fact that the heat generated at the tool-work-piece interface while machining is concentrated at the tool’s cutting edges. This heat cannot be transferred through the work-piece due to the poor thermal conductivity of titanium alloys. Moreover, a very high mechanical stress is accumulated on the immediate vicinity of the cutting edge as a result of high strength and hardness that these alloys retain at elevated temperature poses a further impediment to their machine-ability (Che-Haron & Jawaid, 2005; Trent & Wright, 2000). Ezugwu and Wang (1997) asserted that it was due to the limitations associated with machining these alloys that large companies such as Rolls-Royce and General Electric invested large 28 K. Al-Ghamdi, O. Taylan / Computers & Industrial Engineering 79 (2015) 27–41 sums of money in developing techniques to deal with them. Ezugwu, Bonney, Da Silva, and Cakir (2007) argued that, despite these limitations, machining will remain the favoured option for manufacturing complex titanium alloys at a competitive cost in the foreseeable future. Non-conventional machining processes provide effective alternatives to the conventional ones in dealing with the technical difﬁculties associated with machining titanium alloys. Of these, Electrical Discharge Machining (EDM) is the most widely known and used process for the manufacture of engineering components (Aspinwall, Soo, Berrisford, & Walder, 2008). In this process, the material removal takes place as a result of the discharge of energy between a tool and a work-piece, which are separated by a small gap ﬁlled with a dielectric ﬂuid. The process involves a succession of discrete discharge pulses initiated using a DC pulse generator for a certain duration followed by a similar period during which deionisation of the dielectric occurs and the gap is ﬂushed of debris (McGeough, 1988). A very high temperature is generated by the discharge energy at the point of the spark on the work-piece and the material is removed by melting and vaporization. The stability of the process is maintained by a servo-controlled mechanism whereby a constant gap between the tool and the work-piece is sustained whilst impressing the former pre-selected shape (Singh, Maheshwari, & Pandey, 2004). The EDM theory was postulated by two Soviet scientists in the middle of 1940s (Ho & Newman, 2003). Its process is very effective in machining materials of any hardness given that they conduct electricity (Abbas, Solomon, & Bahari, 2007; Yan, Chung, & Yuan Huang, 2005). A major advantage of the EDM process is its electro-thermal nature which eliminates the need for any direct contact between the electrode and work-piece during machining thereby eradicating the mechanical stress, chatter, tool deformation and vibration problems (Tsai & Masuzawa, 2004). A recent review of titanium alloys EDM is reported in (Kumar, Singh, Batish, & Singh, 2012). The scope of the current work is centred on the EDM of the Ti–6Al–4V alloy, which accounts for 50–60% of total titanium alloy production (Hood, Lechner, Aspinwall, & Voice, 2007). Material Removal Rate (MRR) is one of the key performance measures in EDM. The ability to rigorously understand its mechanism and accurately predict its values based on the well-known physical laws are still debatable (Markopoulos, Manolakos, & Vaxevanidis, 2008; Tsai & Wang, 2001a). In fact, the large number of parameters involved and their interdependence together with the stochastic mechanism of the EDM process appear to signiﬁcantly impair the ability to establish a scientiﬁcally admissible theory correlating the process variables with the main performance measures such as the MRR. Consequently, this task is predominantly accomplished by means of empirical or semiempirical modelling methods. Broadly, two approaches are adopted; namely, the use of conventional statistical models and the application of soft computing algorithm such as ANFIS. For instance, the second order (quadratic) polynomials, conventionally employed in response surface method, were used to relate the EDM process parameters with its key performance measures in the case of machining cobalt-bonded tungsten carbide (Puertas, Luis, & Alvarez, 2004), silicon carbide (Luis, Puertas, & Villa, 2005), Al–4Cu–6Si alloy–10 wt.% SiCP composites (Dhar, Purohit, Saini, Sharma, & Kumar, 2007) and DIN 1.2714 steel (Zarepour, Tehrani, Karimi, & Amini, 2007). Artiﬁcial neural network (ANN) techniques, on the other hand, were used to model and predict the main EDM performance characteristics in the case of machining aluminium and iron (Tsai & Wang, 2001b) and various steel grades (Panda & Bhoi, 2005; Pradhan & Biswas, 2010). The performance of ANN was compared with that of the ANFIS in two studies. In one of these (Puertas et al., 2004), the ANFIS method outper- formed the examined ANN techniques in predicting the performance measures whereas comparable performance of the two approaches was reported by (Pradhan & Biswas, 2010). Some gaps were noted in the current literature on modelling die-sinking EDM process. First, while some of the studies compared the performance of ANN with that of ANFIS, none of them contrasted the prediction capability of polynomial models with that of ANFIS. This paper attempts to ﬁll this void by comparing the performance of a polynomial model with a Neuro-Fuzzy model derived based on different number of rules and fuzzy inference systems. Second, the parameters examined in published modelling studies were, by and large, quantitative i.e. their levels were numerical. In fact, scant attention has been accorded to the case of correlating qualitative (categorical) parameters with the key performance measures of EDM, particularly when polynomial modelling was adopted. In this study, the relationship between three numerical parameters along with a categorical one and MRR was modelled using a polynomial function as well as a Neuro-Fuzzy system. The implications of incorporating a qualitative factor and the way in which it was dealt with are elaborated on. Third, in the context of machining Ti–6Al–4V, Caydas and Hascalik (2008) appears to be the only study that addressed the modelling of the EDM process of this alloy. The present work extends that of Caydas and Hascalik (2008) in two aspects. First, while Caydas and Hascalik (2008) examined the inﬂuence of three parameters; namely, pulse ontime, pulse off-time and current on the electrode wear and recast thickness, the current research assessed the impact of the same three parameters (at different levels) along with the effect of electrode material on the MRR, which was not examined in the above mentioned study. Second, although the response surface method was the only modelling approach adopted in Caydas and Hascalik (2008), this paper utilizes and compares the performance of two methods; namely, polynomial modelling and ANFIS, bearing in mind that, to date, the latter has not been applied to model the die-sinking EDM of Ti–6Al–4V. The methods adopted in the current study are ﬁrstly described. A discussion of the experimental design and procedures follows. The obtained results are then presented and discussed. After comparing the performance of the investigated modelling approaches, the paper culminates with the main conclusions. 2. Methodology Design of Experiments (DoE) is an effective and efﬁcient approach for exploring, understanding and empirically modelling the cause-and-effect relationship between the engineering processes’ parameters and their performance measures. An experimental investigation involves purposeful changes of the input variables of a process or system to explore and justify the changes that may occur in the output response (Montgomery, 2010). Generally a DOE study is performed in three stages: plan ning, conducting and analysis and interpretation (Antony, 2003). The planning stage involves recognizing the problem or the improvement opportunity, stating the objectives, selecting the performance measure(s) and the measurement system(s), determining the factors that may inﬂuence the chosen performance measure(s), choosing the levels for the factors, ﬁnding an appropriate design to vary the factor levels in accordance with and assigning the factors and interactions to the selected design. Having accomplished these tasks, the next stage is to carry out the experiment as planned. Finally, the obtained results should be analyzed and interpreted. In so doing, two approaches were adopted in this study; namely, the polynomial modelling approach and the ANFIS. 29 K. Al-Ghamdi, O. Taylan / Computers & Industrial Engineering 79 (2015) 27–41 2.1. Polynomial modelling approach Polynomial modelling is a major phase of the statistical analysis of experimental data which comprises four stages: estimation, hypothesis testing, modelling and identifying the best parameters setting. The estimation involves obtaining a number to quantify the impact of each of the studied parameters and their interactions on the investigated performance measure(s). To accomplish this task in the current study, a measure that was initially proposed by Kelley (1935) and labelled the Percentage Contribution (PC) by Ross (1996) was adopted. This was obtained using Eq. (1). PC ¼ SSP À ðdfpÞMSE Â 100 SStotal ð1Þ where SSp is the parameter’s Sum of Squares, dfp is its degrees of freedom and the MSE is the mean square error of the experiment. The PC gives the percentage each parameter contributes to the total performance measure’s variation, and is a measure of how much the performance could be improved if the parameter was controlled accurately. The quantities required for estimating the PC can be obtained from the Analysis of Variance (ANOVA) which is the main technique for accomplishing the hypothesis testing task (the process through which the statistical signiﬁcance of each of the examined parameter and interaction is tested). The ANOVA involves decomposing the observed total variance into components due to different sources of variation (factors, interactions and experimental error). Dividing the estimated variance for each parameter by that of error lends a random variable that follows an F-distribution and can be used to test the statistical signiﬁcance of the concerned parameter. However, when the experiment is not replicated, there will be no degrees of freedom to estimate the error variance. In such cases, it is necessary to identify the factors or interactions that can reasonably be pooled to provide an estimate of the error variance. A powerful tool for accomplishing this task is the Half Normal probability Plot (HNP) (Daniel, 1959) of which the use is conventionally conﬁned to analyzing unreplicated two-level experiments. Essentially, HNP can be constructed for any design provided that the plotted effect estimates are uncorrelated and have the same variance. For three-level designs, Wu and Hamada (2011) showed how HNP can be used in the case of decomposing the studied factors into single degree of freedom components with equal variance. Whitcomb and Oehlert (2007) proposed an alternative strategy for using the HNP that relaxed the condition of splitting the effects into single degree of freedom elements. In this strategy, the sums of squares are used as alternative measures of the factorial effects which are commonly estimated using the contrasts among the averages of response values associated with the levels of the studied factors. Furthermore, an iterative method that bears considerable resemblance with the stepwise variable selection procedure is adopted to estimate a provisional error variance. Dividing the sum of squares of a selected effect by this estimate renders a chi-square statistic for which a provisional p-value can be computed and translated in terms of a provisional z-score of a Half Normal distribution. The factors and interactions that pronounced signiﬁcant in the ANOVA are used to develop an empirical model correlating them with the response under study (Wu & Hamada, 2011). Polynomials are very powerful for empirically modelling the cause-and-effect relationship between the process parameters (X1, X2..Xm) and the performance measure of interest (Yi). Mathematically, this relationship is developed using Taylor series expansion of terms involving the studied factors and interactions. Generally, a polynomial model is said to be of order ‘N’ if this is the power of one or more of its factor terms or if ‘N’ is the sum of the powers of the factors involved in one of its interaction terms. Polynomials of second order are commonly used in modelling EDM (Puertas et al., 2004; Luis et al., 2005; Dhar et al., 2007; Zarepour et al., 2007). For ‘m’ factors, a model of this order comprises (m + 1)(m + 2)/2 terms and takes the form that is given in Eq. (2): ^ ^ y ¼ b0 þ m m m X X X ^ ^ ^ bi xi þ bii x2 þ bij xi xj i i¼1 i¼1 ð2Þ i150 ls), arcing was observed with all of the electrode materials. Consequently, the discharge efﬁciency was compromised rendering a noticeable decrease in MRR. A polynomial model was used to represent the relationship between the parameters and the interaction that were declared signiﬁcant in the ANOVA and the MRR. As a categorical factor, one way of dealing with the electrode material is to develop a separate model consisting only of the quantitative factors for each of its levels rendering three separate models. This approach was adopted by (Sahoo, Routara, & Bandyopadhyay, 2009) in examining the impact of different work-piece materials. Helpful though in terms of avoiding explicit modelling of categorical factors, this approach becomes quite cumbersome as the number of these factors and their levels increases. In fact, explicit modelling of categorical factors has the advantage of being more practical as it yields a single predication equation. Moreover, it renders one estimate of the experimental error variance and more residual degrees of freedom than ﬁtting several regression models. Therefore, this approach was adopted in this study. To model the process under study, a model matrix was constructed from the design array given in Table 2. This is a coded matrix that has a column for each term in the model to be developed. As three main effects and one interaction of three-level factors were found signiﬁcant, ten terms were needed. Of these four corresponded to the linear and quadratic components of the two quantitative factors: pulse on-time and current. The qualitative factor (electrode material) has two terms associated with its two degrees of freedom. Finally, the interaction between the electrode material and pulse on-time has four terms corresponding to the four possible combinations of the linear and quadratic elements of pulse on-time and the two components of the electrode material. To construct the model matrix, it was necessary to code the levels of the studied parameters so that they become dimensionless and can be used to estimate comparable model coefﬁcients. Coding also improves the precision with which the coefﬁcients are estimated (Montgomery, 2010). Linear main effects of the quantitative parameters were coded so that the highest and lowest levels of each factors become 1 and À1 respectively. Any value in between can be calculated so that its difference from 1 and À1 is proportional to the difference between the corresponding actual value and the actual highest and lowest values. The codes for the quadratic main effect can then be obtained by squaring the coded linear main effect levels. Using this system, a least squares linear main effect coefﬁcient is interpreted as the average change in the response variable per unit change in its factor. The quadratic main effect coefﬁcient, on the other hand, is a measure of how its factor changes when its own values are changed. The components of the electrode material factor can be coded by assigning one dummy variable for each of the three electrode types. For each variable, a value of one can be assigned to the runs where the appropriate electrode material was used while a value of zero should be written for the remaining runs. This entails adding three dummy variable columns of which the row-wise sum is one, rendering a column identical to the one that should be used to estimate the model intercept. Consequently, it will not be possible to estimate any of the model coefﬁcients as the model matrix will be singular. One way out of this problem is to drop one of the three dummy variables, in which case, each of the coefﬁcients of the remaining