Front. Mech. Eng. 2013, 8(4): 429–442 DOI 10.1007/s11465-013-0277-3
RESEARCH ARTICLE
Reza TEIMOURI, Hamed SOHRABPOOR
Application of adaptive neuro-fuzzy inference system and cuckoo optimization algorithm for analyzing electro chemical machining process
© Higher Education Press and Springer-Verlag Berlin Heidelberg 2013
Abstract Electrochemical machining process (ECM) is increasing its importance due to some of the specific advantages which can be exploited during machining operation. The process offers several special privileges such as higher machining rate, better accuracy and control, and wider range of materials that can be machined. Contribution of too many predominate parameters in the process, makes its prediction and selection of optimal values really complex, especially while the process is programmized for machining of hard materials. In the present work in order to investigate effects of electrolyte concentration, electrolyte flow rate, applied voltage and feed rate on material removal rate (MRR) and surface roughness (SR) the adaptive neuro-fuzzy inference systems (ANFIS) have been used for creation predictive models based on experimental observations. Then the ANFIS 3D surfaces have been plotted for analyzing effects of process parameters on MRR and SR. Finally, the cuckoo optimization algorithm (COA) was used for selection solutions in which the process reaches maximum material removal rate and minimum surface roughness simultaneously. Results indicated that the ANFIS technique has superiority in modeling of MRR and SR with high prediction accuracy. Also, results obtained while applying of COA have been compared with those derived from confirmatory experiments which validate the applicability and suitability of the proposed techniques in enhancing the performance of ECM process. Received April 29, 2013; accepted July 20, 2013
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Reza TEIMOURI ( ) Mechanical Engineering Department, Babol University of Technology, Babol, Iran E-mail:
[email protected] Hamed SOHRABPOOR Mechanical Engineering Department, Islamic Azad University of Dezful, Dezful, Iran
Keywords electrochemical machining process (ECM), modeling, adaptive neuro-fuzzy inference system (ANFIS), optimization, cuckoo optimization algorithm (COA)
1
Introduction
The cemented tungsten carbide is a hard and tough composite with noticeable wear resistance that satisfies growing demands of material with higher mechanical properties and lower weight. Due to high wear resistance and hardness of this material, it cannot be machine with conventional machining process. Among non-conventional machining methods electrochemical machining (ECM) is a potential process which is useful for machining such difficult-to-cut electrically conductive materials. ECM has been extensively used in machining of hard-tocut materials such as titanium, stainless steel, high-strength temperature resistant alloys, ceramics, refractories, fiberreinforced composites, super alloys and etc. which are not suitable to be machined by the conventional machining processes because of their high hardness, strength, brittleness, toughness and low machinability properties. Moreover, by application of ECM process, any kind of intricate shape can be generated with high accuracy and precision with minimum residual stress generation. However, the process is not exactly the substitutes of the conventional machining processes, but can only complement them [1,2]. The ECM has complex nature due to various complex physico-chemical and hydrodynamic phenomena that occur in the machining gap [3]. During the course of machining, the machining rate at any instant depends not only on the end gap, but also on other process parameters [4]. The electrolyte flow velocity plays an important role in surface formation [5]; moreover, the increment in gap resistance due to various causes, e.g., electrolyte heating, gas bubble generation sludge formation, etc., leads to an uneven current flow, causing overcut
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phenomena that result in poor dimensional control of the workpiece [6]. So, optimal quality of workpiece and economical aspects of ECM can be achieved through combinational control of various process parameters. According to above explanation, generation of a certain physical model which provides a precise prediction of ECM process is actually difficult especially when the process is characterized for machining of hard-to-cut materials. According to above explanations, in order to generate a model which can predict behavior of complex ECM process, researchers focused on developing comprehensive predictive model based on statistical analysis and artificial intelligence. Methods such as response surface methodology (RSM), artificial neural network (ANN), fuzzy inference system and etc. are most commonly used for modeling of the manufacturing processes. In the case of ECM, Bhattacharyya and Sorkhel [7] applied response surface methodology for investigation and modeling of electrochemical machining process. They developed mathematical models to correlate relationships between electrolytic concentration, electrolytic flow rate, applied voltage and inter-electrode gap as process inputs to material removal rate and overcut as responses. Senthilkumar et al. [8] used RSM to study effects of ECM parameters on MRR and SR. They showed that increasing in applied voltage and feed rate leads to higher MRR and lower surface roughness. Also, they indicated that increasing in electrolytic concentration and flow rate resulted in higher material removal rate and better surface finish. Moreover, they optimize the process for achieving higher MRR and lower Ra based on RSM. In the case of modified ECM, Baran Puri and Banerjee [9] studied effects of voltage and cutting speed on current density, material removal rate and surface finish in electrochemical grinding process. They applied regression analysis to develop a mathematical model for each response. Then, they utilized desirability approach and overlapping contour plots to optimize the process in the form of multiple responses problem. Furthermore, Taweel and Gouda [10] proposed wire electrochemical turning process and fulfilled a feasibility study to use wire as tool. They investigated effects of applied voltage, wire feed rate, wire diameter, workpiece rotational speed and overlap distance on material removal rate, surface roughness and roughness error. The experimental results were statistically analyzed and modeled through response surface methodology. Although there are numbers of publications that used RSM and statistical techniques in modeling of ECM process, there is not a certain work which uses the predictive methods based artificial intelligence for modeling the characteristics of ECM process. The superiority of intelligent method such as neural network rather than RSM has been verified by researchers [11–14]. However, the neural network is a potential method in modeling of manufacturing process rather than statistical models and
mathematical equations, but the main weakness of neural network is its dependency on large amount of data for a problem in which many inputs are contributed. Also, in the case of manufacturing processes with complex behavior the neural network cannot predict the process characteristics as well. It means that for a process with complex behavior some linguistic terms are needed to provide a precise prediction. Thus, application of fuzzy logic can be beneficial for modeling of complex behavior. But construction of an appropriate fuzzy membership function and fuzzy rules is really difficult and time consuming job. Thus, for modeling of a complex process with small amount of data in a short time, a method with both concepts of neural network and fuzzy logic is needed. Therefore, an adaptive neuro-fuzzy inference system (ANFIS) is proposed as a hybrid predictive approach that uses both meanings of neural network and fuzzy logic for modeling of complex processes in which many inputs are contributed and the amount of experimental data are small. According to the surveyed literatures, there is not a certain publication that uses the ANFIS for modeling of ECM process. Hence, application of this method in the present work is quite novel. However, there number of publications that used ANFIS for modeling characteristics of nontraditional machining process. In this case, Caydas et al. [15] used ANFIS for modeling white layer thickness in wire EDM process. Gill and Singh [16] applied ANFIS to predict depth of cut in stationary ultrasonic drilling of sillimanite ceramic. Maji and Pratihar [17] utilized ANFIS for forward and reverse mapping of MRR and SR in electrical discharge machining process. Pradhan and Biswas [18] applied ANFIS along with neural network for modeling various responses in EDM process. Non-traditional optimization algorithms have been widely used in the case of processes in which too many parameters affect performances. Genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO), artificial bee colony (ABC), imperialist competitive algorithm (ICA) and etc. have been utilized most commonly by researches for optimization of nontraditional machining process. In this case, Rao et al. [15] applied a particle swarm optimization (PSO)-based algorithm to find out the optimal process parameters for an electrochemical machining (ECM) process and compared its performance with that obtained by the other optimization methods. Dimensional accuracy, tool life and material removal rate of the ECM process were optimized subject to the constraints of temperature choking and passivity. Teimouri and Baseri [11] applied SA and PSO along with the ANFIS and ANN for generating smoother surface in magnetic abrasive finishing process. Teimouri et al. [12] used PSO to determine the optimal combination of process parameters for a wire electric discharge machining (WEDM) process. Teimouri and Baseri [13] associated artificial bee colony algorithm with neural network for optimization of dry EDM process in both cases of single-
Reza TEIMOURI et al. Application of adaptive neuro-fuzzy inference system and cuckoo optimization algorithm
objective and multi-objectives problem. In another attempt Teimouri et al. [14] used the ICA for minimizing springback in bending of CK45 sheets. Cuckoo optimization algorithm (COA) is a novel evolutionary algorithm, suitable for continuous nonlinear optimization problems [19]. This algorithm is inspired by the life of a bird family, called Cuckoo. Special lifestyle of these birds and their characteristics in egg laying and breeding has been the basic motivation for development of this new evolutionary optimization algorithm. In the present work, the main reason for choosing the COA to optimize the ECM process is its faster performance rather than other algorithms such as GA and PSO [19]. Due to existing special elitist mechanism in COA, the executing time is about five time shorter than one by GA or PSO. It means that in a problem with too many inputs the COA converges to a global optimum just after seven iterations. Hence, it is claimed that application of COA in the present work may lead to reduction of optimization time and the work is quite novel. By searching through conducted researches, it can be inferred that there is not a certain publication which used COA in optimization of manufacturing processes. There is only one publication which associated the cuckoo search algorithm with fuzzy logic to solve multi-objective scheduling problem [20]. Hence, association of this algorithm with ANFIS and their applications for analyzing ECM process is quite novel and it is innovative approach. The present work can be summarized as follows: 1) Designing and conducting experiments based on four factors-five levels central composite design 2) Creating predictive models of material removal rate and surface roughness using ANFIS technique 3) Plotting ANFIS 3D surfaces of MRR and SR for
Fig. 1
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analyzing effect of process parameters 4) Multi-objective optimization of the process using cuckoo algorithm 5) Comparing results obtained through COA with those derived by confirmatory experiments 6) Analyzing optimal results based on process physical behavior
2
Methodologies
2.1
Adaptive neuro-fuzzy inference system (ANFIS)
An adaptive neuro-fuzzy inference system is a hybrid predictive model which uses both of neural network and fuzzy logic to generate mapping relationship between inputs and outputs [21]. The structure of this model consists of five layers which each layer is constructed by several nodes. Such as a neural network, in an ANFIS structure the inputs of each layer are gained by the nodes from pervious layer. Figure 1 describes an ANFIS structure. It can be inferred from Fig. 1 that the network includes m inputs (X1,…,Xm), in which each one consists of n membership functions (MFs). Moreover, a layer with R fuzzy rules and also an output layer are contributed to construction of this model. Number of nodes in first layer can be calculated by product of m as number of inputs and n as number of MFs (N = m$n). Number of nodes in other layers (layers 2–4) relates to number of fuzzy rules (R). In the present work this technique is used to correlate mapping relationship between process inputs (e.g., electrolyte concentration, electrolyte flow rate, applied voltage and feed rate) and main outputs (material removal rate and
Basic structure of an ANFIS model [22]
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surface roughness). Thus, for each output a separate ANFIS structure can be defined. For example for MRR the first layer of ANFIS structure is input layer that contains four nodes (for four inputs). And the last layer (output layer) has one node that represents values of MRR. Figure 2a and 2b indicates the proposed ANFIS topography for MRR and SR, respectively. Further details about implementation of ANFIS network has been presented in literature [22]. The layers of ANFIS can be summarized as follows: First layer: fuzzification layer In this layer crisp inputs transforms to linguistic type Aij (such as bad, middle, good) by using of membership functions. The output of this layer can be expressed as: O1ij ¼ ij ðXi Þ, i ¼1,:::,m, j ¼1,:::,n,
(1)
where mij is the jth membership function for the input Xi. Several types of MFs are used, for example, triangular, trapezoidal and generalized bell function. In this study the Triangular and Gaussian functions has been selected for MRR and SR, respectively. The matematical equations for Triangular and Gaussian type of membership function are expressed as Eqs. (2 and 3), respectively. For Triangular type of MF, the mathematical equation is:
Fig. 2
8 0, > > > > > > > < xja , ðX ,a,b,cÞ ¼ bja > cjx > > > , > > > : cjb 0,
x
