Forward and Reverse Mapping for WEDM Process using Artificial Neural Networks

Article history: Received October 29, 2014 Received in revised format: March 28, 2015 Accepted April 24, 2015 Available online April 27 2015 Suitable selection of various machining parameters for wire electrical discharge machining (WEDM) process heavily relies on the operator’s experience and manufacturer’s technologies because of their numerous and diverse operating ranges. Artificial neural networks have been introduced as an effective tool to predict values of responses and input parameters of different machining processes through forward and reverse modeling approaches respectively. This paper mainly focuses on predicting values of some machining responses, like machining rate, surface roughness, dimensional deviation and wire wear ratio using feed forward back propagation artificial neural network based on six WEDM process parameters, such as pulse on time, pulse off time, peak current, spark gap voltage, wire feed and wire tension. The corresponding reverse model is also developed to recommend the optimal settings of WEDM process parameters for achieving the desired responses according to the requirements of the end users. These modeling approaches are quite efficient to predict the values of machining responses as well as process parameter settings with reduced time and effort which otherwise have to be determined experimentally based on trial and error method. The predicted results are found to be in well congruence with the previously obtained experimental observations.


Introduction
Wire electrical discharge machining (WEDM) is a non-traditional material removal process mainly used to cut hard or difficult-to-cut materials, where the application of a mere traditional machining process is not at all convenient.WEDM is a special form of electrical discharge machining process in which the electrode is a continuously moving electrically conductive wire (made of thin copper, brass or tungsten of diameter 0.05-0.3mm) (Mukherjee et al., 2012).The movement of this wire is numerically controlled to achieve the desired three-dimensional shape and accuracy of the workpiece.The wire is kept in tension using a mechanical device reducing the tendency of producing inaccurate shapes.The mechanism of material removal in WEDM process involves a complex erosion effect by rapid, repetitive and discrete spark discharges between the wire tool and the job immersed in a liquid dielectric (kerosene/deionized water) medium.These electrical discharges melt and vaporize minute amounts of work material, which are ejected and flushed away by the dielectric, leaving small craters on the workpiece (Scott et al., 1991; Spedding & Wang, 1997 a ; Spedding & Wang, 1997 b ; Ho et al.,  2004).WEDM process offers several special advantages including higher machining rate, better precision and control, higher surface finish, and the capability to machine a wider range of workpiece materials.In general, it is perceived to be an extremely actuate process and there are various reasons behind this perception.In WEDM process, no direct contact takes place between the wire tool (electrode) and the workpiece; as a result, the adverse effects, such as mechanical stresses, chatter and vibration normally present in conventional machining processes are thus eliminated.The wire used as a tool has high mechanical properties and small diameter that can produce very fine, precise and clean cuts (Saha et al., 2008;Shandilya et al., 2013).Apart from tool and die, mold, and metalworking industries, WEDM process is also being widely used to machine a wide variety of miniature and microparts in metals, alloys, sintered materials, cemented carbides, ceramics and silicon.Being a competitive and economical machining process, it can thus fulfill the demanding machining requirements of short product development cycle and high surface finish (Ghodsisyeh et al., 2013).
The accuracy and success of WEDM process mainly depends on a large number of process parameters which influence the machining process significantly (Kumar et al., 2013 a ; Ugrasen et al., 2014).Thus, it is always suggested to determine the optimal operational settings of various WEDM process parameters for achieving enhanced machining performance.For having those optimal WEDM process parameter settings, the machine operator has to often rely on the manufacturer's handbook or take the help of machining experts.In this paper, an attempt is made to develop an intelligent system to establish the input-output relationship of a WEDM process while utilizing forward and reverse mappings of artificial neural networks (ANNs).In forward mapping, machining rate, surface roughness, dimensional deviation and wire wear ratio values are predicted from a known set of six WEDM process parameters, such as pulse on time, pulse off time, peak current, spark gap voltage, wire feed and wire tension.An attempt is also made to develop the corresponding reverse model to predict the recommended process parameter settings for achieving the desired responses to meet the end user's requirements.In this direction, a back propagation neural network (BPNN)-based approach is applied to develop the related ANN models.The batch mode of training is employed for both the supervised learning networks which requires a large set of training data.This requirement for having a large set of training data is fulfilled by artificially generating the necessary data with the help of simulation based on the real time experimental observations of the earlier researchers.The performance of BPNN is also validated against the past experimental data to show its effectiveness and suitability in advanced machining applications in selecting the settings of the most influential process parameters to achieve the desired responses.

Data mining and artificial neural networks
Data mining, popularly known as knowledge discovery in databases (KDD), refers to the non-trivial extraction of implicit, previously unknown and potentially useful information from data in databases.While data mining and KDD are frequently treated as synonyms, data mining is actually a part of the knowledge discovery process.Various techniques of data mining have been successfully applied in diverse areas, such as computers and information technology, medical sciences, database management systems and manufacturing sciences for creating intelligent systems for prediction purposes.
On the other hand, an ANN is a mathematical or computational model that is inspired by the structure and/or functional aspects of biological neural networks.A neural network consists of an interconnected group of artificial neurons, and it processes information using a connectionist approach to computation.These are powerful data mining tools for modeling, especially when the underlying data relationship is unknown.The ANNs can identify and learn correlated patterns between input data sets and the corresponding target values.After proper training, the ANNs can be used to predict the outcome of new independent input data.A feed forward neural network is a biologically inspired classification algorithm.It consists of a (possibly large) number of simple neuron-like processing units, organized in layers.Every unit in a layer is connected with all the units in the previous layer.These connections are not all equal, each connection may have a different strength or weight.The weights on these connections encode the knowledge of a network.Often the units in a neural network are also called nodes.Data enters at the inputs and passes through the network, layer by layer, until it arrives at the outputs.During normal operation, that is when it acts as a classifier, there is no feedback between layers.This is why it is called as feed forward neural network.Thus, feed forward neural networks are one class of ANNs.Back propagation refers to a common method by which these networks can be trained.Training is the process by which the weight matrix of a neural network is adjusted automatically to produce the desired results.A back propagation network usually learns by examples.This algorithm takes datasets as inputs and tries to learn the hidden pattern from these inputs.It changes or adjusts the network's weights according to the learning capability so that when the training is completed, it can provide the required output for a particular input.Back propagation neural networks are ideal for simple pattern recognition and mapping tasks (Sivanandam, 2003;Samarasinghe, 2006).Kumar et al. (2013) conducted 54 experiments on a four-axis CNC type WEDM (Electronica Sprintcut 734) setup and investigated the effects of six WEDM process parameters, i.e. pulse on time (Ton) , pulse off time (Toff), peak current (Ip), spark gap voltage (SV), wire feed (WF) and wire tension (WT) on four process responses, i.e. machining rate (M/c rate) (in mm/min), surface roughness (Ra) (in µm), dimensional deviation (Dd) (in µm) and wire wear ratio (WWR).Each of the six WEDM process parameters was set at three different levels, i.e.Ton at 112 µs, 116 µs and 120 µs; Toff at 44 µs, 50 µs and 56 µs; Ip at 120 A, 160 A and 200 A; SV at 40 V, 50 V and 60 V; WF at 4 m/min, 7 m/min and 10 m/min; and WT at 500 g, 950 g and 1400 g.A work material of pure titanium in the form of a square plate and a brass wire electrode with 0.25 mm diameter were taken for the experimentation work.The detailed experimental plan along with the observed responses is given in Table 1.The related ANNbased model to predict the responses for a given set of input parameters for the WEDM process is developed in Matlab utilizing the experimental data of Table 1.

ANN-based model development for WEDM process
Selection of the optimal ANN architecture to be used for prediction is usually decided by hit and trial method, choosing the one which gives the lowest value of mean square error (MSE).The variation of MSE value with changing number of nodes in the hidden layer is exhibited in Fig. 1.Amongst several ANN architectures tried, it is found that the 6-5-4 architecture, as shown in Fig. 2, provides the minimum MSE value.The supervised learning process of an ANN generally requires a large set of training data.In actual practice, this requirement of huge data is fulfilled by generating artificial datasets through simulation.In this case, based on the experimentation data of Table 1, 5000 new datasets are generated for the training purpose.This training data is then linear normalized to achieve better training and prediction results.The details of the developed ANN model for predicting the responses for a given set of WEDM process parameters in forward mapping are given as below.   1 2 3 4 5 6 7 8 9  After the training phase using the new 5000 datasets, the developed ANN is employed for forward and backward prediction purposes (Chandrashekarappa et al., 2014).Forward mapping deals with predicting the responses/outputs of the WEDM process for known sets of input conditions.It thus fulfils the end user's requirements of achieving the desired responses for varying values of WEDM process parameters.In forward mapping, the end user may also obtain the tentative response values for an unknown set of WEDM process parameters.Table 2 exhibits the experimentally observed and ANN predicted WEDM response values along with the estimated prediction error for the considered WEDM process based on the experimental data of Table 1.In forward mapping, it is also observed that for a new combination of WEDM process parameter settings (not considered in the actual experimental plan) of Ton = 112 µs, Toff = 50 µs, Ip = 170 A, SV = 50 V, WF = 7 m/min and WT = 950 g, the responses are predicted as M/c rate = 0.565 mm/min, Ra = 2.51 µm, Dd = 150.84µm and WWR = 0.07.In WEDM process, machining rate is a desirable response characteristic and it should be as maximum as possible to have the least machining cycle time leading to increased productivity (Saha et al., 2007).The most widely used surface quality indicator is the center line average (Ra) value.It plays a crucial role in evaluating and measuring the quality of a machined part.The ability of a machined part to withstand stresses, temperature, friction and corrosion is greatly affected by its roughness.In addition, roughness has also an impact on other properties, like wear resistance, light reflection and coating.The difficulty in controlling surface roughness is mainly due to the intrinsic complexity of the phenomenon that generates its formation (Pontes et al., 2009).For these reasons, surface modeling has become not just an especially defying issue but an area of great interest for research.Dimensional deviation is the difference between the observed and the target dimensional values, and it is a measure of accuracy of a machining process (Kumar et al., 2013 b ).Wire wear ratio is normally defined as the ratio of the weight loss of wire after the WEDM process to the initial wire weight.Many researchers (Prasad et al., 2014;Goswami & Kumar, 2014)   An ANN model is also developed for reverse mapping of the considered WEDM process based on a 4-5-6 ANN architecture.This model for reverse mapping is also trained using the simulated data and is subsequently used for prediction of the tentative settings of the WEDM process parameters based on a set of desired response characteristics.It can also be treated as an advisory system which in absence of human experts, can predict the settings of various process parameters in a WEDM set-up in order to achieve the desired responses according to the requirements of the end users.Table 3 provides a set of 40 simulated data as used for training of the developed ANN for reverse mapping.The predicted values of various WEDM process parameters for the given set of responses are shown in Table 4. From this table, it is observed that the average prediction errors for the six WEDM process parameters, i.e.Ton, Toff, Ip, SV, WF and WT are 2.21%, 4.33%, 3.66%, 4.59%, 3.63% and 4.49% respectively.Figs.7-12 respectively compare the simulated and ANN predicted values of all the six WEDM process parameters.This reverse model is now specifically applied for a single input dataset which can be thought of as the requirement of the end user, and it successfully predicts the necessary WEDM process parameter settings to achieve those desired response values.For the response values of M/c rate = 1.5 mm/min, Ra = 2.00 µm, Dd = 150 µm and WWR = 0.1, the corresponding WEDM process parameters are to be set at Ton = 116 µs, Toff = 53 µs, Ip = 174 A, SV = 37 V, WF = 2 m/min and WT = 876 g.For the considered WEDM process, it is thus recommended to set the neighborhood process settings at Ton = 116 µs, Toff = 50/56 µs, Ip = 160 A, SV = 40 V, WF = 4 m/min and WT = 950 g in order to achieve the desired responses.Wire wear ratio (Experimental) Wire wear ratio (ANN)

Wire wear ratio
The pulse on time represents the duration of machining time in micro seconds during which the current is flowing in each cycle.During this time, the voltage is applied across the electrodes.The single pulse discharge energy increases with increasing pulse on time, resulting in higher machining rate.With higher values of pulse on time, however, surface roughness tends to be higher.The higher value of discharge energy may also cause wire breakage.The pulse off time represents the duration of time in micro seconds between two simultaneous sparks.
The voltage is absent during this part of the cycle.With a lower value of pulse off time, there are more number of discharges in a given time, resulting in increase in sparking efficiency.As a result, the machining rate also increases.Using very low values of pulse off time, however, may cause wire breakage which in turn reduces the machining efficiency.As and when the discharge conditions become unstable, the pulse off time can be increased.This will allow lower pulse duty factor and will reduce the average gap current.From Fig. 7 and Fig. 8, it is observed that the predicted values of pulse on and pulse off times match well with the simulated dataset values.There are some small deviations between the simulated and predicted values which can be minimized further using more accurate training data.
The peak current is the maximum value of the current passing through the electrodes for a given pulse.
An increase in peak current will increase the pulse discharge energy which in turn can improve the machining rate further.For higher values of peak current, gap conditions may become unstable with improper combination of other process parameter settings.Wire feed is the rate at which the wire electrode travels along the wire guide path and is fed continuously for sparking.It is always desirable to set the wire feed to be maximum.This will result in less wire breakage, better machining stability and slightly more cutting speed.Both the process parameters, i.e. peak current and wire feed are considered to be critical in WEDM process.It can be confirmed from Fig. 9 and Fig. 10 that the developed reverse ANN model is quite successful in predicting both these process parameters.The spark gap voltage is a reference voltage for the actual gap between the workpiece and the wire used for the machining operation.On the other hand, wire tension determines how much the wire needs to be stretched between the upper and lower wire guides.This is a gram equivalent load with which the continuously fed wire is kept under tension so that it remains straight between the wire guides.More the thickness of the workpiece, more is the wire tension

Wire tension (grams)
Data sets

Fig. 1 .Fig. 2 .
Fig. 1.Variation of MSE with changing number of nodes in hidden layer Fig. 2. Optimal ANN architecture for forward mapping

Fig. 7 Fig. 8
Fig. 7 Comparison of simulated and ANN predicted pulse on time values

Table 1
Experimental data for forward mapping(Kumar et al., 2013 a ) 1011121314151617181920

Table 2
ANN predicted results and prediction error for forward mapping have investigated the effects of different WEDM process parameters on WWR, and have experimentally observed that increasing values of pulse duration and open circuit voltage would cause an increment in WWR, whereas, increasing wire speed and dielectric fluid pressure would decrease it.Figs.3-6 compare the experimental and ANN predicted values of M/c rate, Ra, Dd and WWR respectively for the considered WEDM process, and it is interesting to observe that for all the four responses, the ANN predicted responses closely match with those obtained experimentally.It is also observed that the average prediction errors for M/c rate, Ra, Dd and WWR are only 3.17%, 2.30%, 1.01% and 4.35% respectively which confirm the developed ANN model to almost accurately predict the output responses for a given set of WEDM process parameters.

Pulse off time (µs) Data set required
. Improper setting of tension may result in job inaccuracies as well as wire breakage.The developed reverse ANN model is also capable to successfully predict the spark gap voltage and wire tension which can be validated fromFig.11 and Fig. 12.

Table 4
ANN predicted results in reverse mapping