Comparison of Regression Model with Multi-layer Perceptron Model While Optimising Cutting Force Using Genetic Algorithm

Various process parameters and machining performance (responses) are captured during machining process. In order to understand the relation and predict future responses, mathematical modelling is used. Mathematical models are usually developed based on experimental data using conventional methods like regression technique [1] used response surface methodology to predict the surface roughness in grinding operation and concluded that the model is adequate in estimating the response.  Fratila and Caizar [2] in their paper stated that regression models are suitable for finding the relation between input variables and output responses. Lazir et al. [3] predicted the tool life in terms of both first order and second order models. Though both the models are valid in predicting the response, second order models have less average percentage error in prediction. Cakir et al. [4] in their paper developed linear model, second order model and exponential order model for surface roughness. The authors concluded that second order models are best in predicting the response with small errors compared to linear models. Linear regression models do not accurately reflect the non-linear relationship between the parameters and responses, leading to increased error in prediction. In these scenarios, non-conventional approaches like Artificial Neural Network (ANN) are also being used to predict responses where the conventional mathematical models are not effective in predicting the response accurately. ANN is a computer-based modelling technique based on statistical approach, and being increasingly used in many fields of engineering for modelling complex relationships between input parameters and output responses. Abbas et al. [5] developed a surface roughness model using ANN with a prediction accuracy of 1.35%. Ezugwu et al. [6] developed ANN model for various responses and build a relation between input parameters and responses. Zain et al. [7] developed regression and ANN model for predicting surface roughness and reduced the surface roughness by 1.57% and 1.05% respectively. Thus the authors concluded that regression model is better than ANN. Zerti et al. [8] developed 3 different models (L₂₇, RSM and ANN) for surface roughness and showed that ANN models are better in prediction followed by RSM and Taguchi techniques. Abbas et al. [9] proposed a new optimisation method edge worth- pareto to optimise surface roughness while developing a model with ANN. Mukherjee and Ray [10] made a review on different mathematical models and suggested a systematic approach to optimise the process parameters in metal cutting operation.

Cutting fluids are an important part of machining process, where they reduce friction, improve the surface finish and prolong the tool-life [11]. However, the cutting fluids add to the cost, and are difficult to dispose due to environmental hazards and statutory regulation. For this reason, traditional wet lubrication is increasingly being replaced with minimum quantity lubrication (MQL). In MQL, a cutting fluid is converted to a fine mist using highly pressurized air. Various researchers conducted the study on MQL and concluded that MQL machining is the most efficient machining in reducing the cutting forces, surface roughness and to increase the tool life [12-17]. More recently, nano-particle based cutting fluids are gaining importance due to their superior properties over conventional fluids. Nano-fluids have been shown to improve surface finish, tool-life and thermal conductivity, while reducing cutting forces [18-22]. There are various parameters related to a nano-fluid that can be modelled and optimised for a specific machining operation. Some of the parameters are the size of the nano particles, type of nano particles and the volume concentration (%) of the nano-particles in a base fluid.

Though research is conducted using ANN technique less work is carried in comparison of regression and ANN techniques. The novelty of the work lies in application of genetic algorithm for regression and ANN models under nano MQL systems.

In this study, both regression technique and ANN technique were used to develop models for an experimental data set using nano-fluids in machining through minimum quantity lubrication (MQL). The predicted responses were optimised using genetic algorithm, and results from both techniques are compared.

The regression equation for cutting force (N) is obtained from the coefficient values and is given in Eq. (1):

CF=253.496+18.772*Flowrate+71.610*Speed+39.768*feed+86.876*DOC          (1)

Eq. (1) is used to predict the values of the cutting force (F_z). The percentage error is obtained between the experimental values and predicted values which are tabulated in Table 5.

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Figure 2. Experiment vs Predicted values for cutting force

From Table 5 it is clear that the errors in predicting the cutting force are within the acceptable range. The same conclusion can be drawn from the line graph of experimental and predicted values of cutting force in Figure 2.

3.2 Computation of ANN model

Artificial neural networks (ANN) are computer models developed based on principles similar to how animal/human brains work. An ANN is modelled as a collection of artificial neurons (or) nodes, that are connected with other nodes with edges. Each node and edge have associated weights, which determine the output as a non-linear function of the inputs and weights. These weights are adjusted based on a training set of data (input and actual output). After the network is trained, the model can be used to predict the output for unknown inputs. There are multiple factors that are used / can be varied in development of ANN models for specific applications. Some of the most important factors are the network architecture or topology, activation functions used by the neurons, and the learning algorithm which is used to find the optimal values of weights. There are two types of network architecture, namely feedforward, and feedback neural networks. Feed forward neural networks are more popular. Signals travel only in one direction, i.e., from input to output. There are no cycles in the directed acyclic graphs [24]. Whereas, in the feedback network, the signals can also traverse from output to input, leading to cycles in the directed acyclic graphs [25].

The data should be normalized in order to get the best accurate network. Normalization of data was done using Eq. (2) [26]:

$X_{i}=\frac{\max y_{i}-y_{i}}{\max y_{i}-\min y_{i}}$         (2)

where, X_i is the normalised data for ith experiment. max(y_i) and min(y_i) are the maximum and minimum values of y_ipresent in the data set. The normalised values were calculated using Eq. (2) and used as target values while creating the network.

Initially several networks were build based on trial and error method for finding the best parameter settings to form a suitable network. The criteria for selecting the best network is to obtain the least Mean Square Error (MSE). The best network is obtained while using the Levenberg-Marquadt (LM) algorithm for training the network. The network was designed as a feed forward network with 6 neurons in the hidden layer for 5 input parameters and 1 output response. The network architecture is shown in Figure 3.

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Figure 3. ANN with 6 neurons in hidden layer

At first, the optimum number of neurons required was determined based on Mean Square Error (MSE). Options of 5, 6 and 7 neurons were tried and a size of 6 neurons was found to be optimal with low MSE. The overall R value which represents the correlation between training data and predicted values for network were 0.92427, 0.97265 and 0.89647 respectively for 5, 6 and 7 neurons. The performance graphs of the networks with 5,6 and 7 neurons indicating the MSE are shown in Figure 4.

From Figure 4 it is clear that network with 6 neurons in hidden layer has the least mean square error of 0.0056962 and hence are considered as the optimum number of neurons for constructing the network.

The input data from experiments can be divided into 3 different groups training, validation and testing. Training datasets are used for training the model. Validation datasets are used to measure network generalization and to halt training if the generalization stops improving. Testing datasets are used to check the predicted values and error in prediction based on actual data. These samples don’t have any effect on training. To check the efficiency of the network by improving the generalisation of network, 3 different percentages of validation data were considered as shown in Table 6. The mean square error and R values for 3 networks are shown in Figure 5 and Figure 6 respectively.

Table 6. Percentage of data used for training, validation and testing

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(a) 5 neurons

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(b) 6 neurons

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(c) 7 neurons

Figure 4. Performance of ANN

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(a) 10% validation data

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(b) 15% validation data

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(c) 20% validation data

Figure 5. Performance graphs

From Figure 5 it can be noticed that as the percentage of validation data increases the mean square error increases. The reason might be less data available for training. If validation and testing data are 20% each (total 8) then the no. of samples in training data will be only 10 (60%) which is very small. In this case least mean square value 0.000972 is obtained while validating and testing 10% data and training 80% data.

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(a) 10% validation data 

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(b) 15% validation data

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(c) 20% validation data

Figure 6. R values

From Figure 6 it can be noticed that all the 3 networks have good R values for training, validation, testing and overall data. Highest overall R value (0.98336) which is close to 1 is obtained for the network with 10% validation and testing data and 80% training data.

Hence the network having 6 neurons in hidden layer and with 10% validation and testing data and 80% training data is considered as the optimum network. The predicted values from this network and the percentage error in predicting the values from the experimental values are presented in Table 7.

Table 7. Percentage error for Experimental Vs prediction through ANN

From Table 7 it is observed that the average error percentage in predicting the response from ANN is only 3.8%.

(1) Equations are developed for cutting force for both L18 model and multi-layer perceptron model.

(2) Multi-layer perceptron model with 6 neurons in the hidden layer is considered as the best network.

(3) The percentage error in predicting the response for regression and MLP models are 7.58 and 3.78 respectively.

(4) Optimum cutting force obtained for regression and MLP models is 36.47N and 33.62N after application of GA.

(5) MLP model is better in predicting the response with less error and also to obtain the optimum cutting force compared to regression model.

(6) MLP model reduced the cutting force by 7.814% compared to L18 model.