## 4 Methodology
### Artificial Neural Network (Modeling and Analysis)  
The artificial neural network model adopted for this study is shown in Figure 4. The model consists of three layers; the input layer, the hidden layer, and the output layer. The input parameters to the ANN model consist of the cutting parameters studied during the numerical simulations, and the outputs are the corresponding cutting reaction force and tool-chip interface temperature. The four input parameters consist of cutting force (\(V\) in m/min), cutting feed (\(C\) in 0.4 mm), contact friction (\(F\)), cutting reaction force (\(RF\) in Newtons), tool rake angle (\(R\) in degree), and the temperature at tool chip interface (\(T\) in \({}^{\circ}\)C). The output layer consists of two neurons: the cutting reaction force \(RF\) (N) and tool-chip interface temperature \(T\) (\({}^{\circ}\)C). The MATLAB (R2013, The MathWorks, Natick, MA, USA, 2013), neural network toolbox was used for training and testing of the simulations data. Training of the network was accomplished by considering the 64 numerical simulations. The output (cutting reaction force and tool-chip interface temperature) and the corresponding input parameters of these simulations are given in Table 3. Design of the numerical experiments could also be accomplished with some standard technique (such as Taguchi's configuration). In this research, different combinations of the input parameters were selected by considering the range of each parameter used in actual machining experiments. With four input parameters, all the possible combinations result into 4 \(\times\) 4 \(\times\) 2 \(\times\) 2 = 64 design of numerical experiments. \begin{table}
\begin{tabular}{  
Considering the available experimental data [42], the Abaqus simulations run at serial 13, 14, 16, 57, 58, and 60 were used for validation of the ANN model. The input parameters of these simulations are similar to the corresponding cutting conditions in actual experiments. The standard feedforward backpropagation neural network was studied by considering the Log-Sigmoid transfer function (LOGSIG). The Log-sigmoid transfer function is used for training the data in multi-layer networks with back-propagation algorithm [54; 55; 56]. The selection of optimal number of hidden layers is a difficult task. The optimal numbers of hidden layers are determined by training several networks and estimating the error. A few hidden layers may cause a high training error due to under-fitting and too many hidden layers may cause a high generalization error due to over-fitting. Selection also depends upon the numbers of input and output layers, learning function, the ANN architecture, the activation function, and the training algorithm. For the proposed ANN architecture, the numbers of neurons in the hidden layers were determined through a trial-and-error method. The best configuration was observed with two hidden layers and 10 neurons in each layer. The ANNs predicted outcomes and properties were evaluated by considering the mean-square-error and regression analysis. The predicted outcomes were validated with the published experimental results [42]. Details of the machining experiments, testing scheme, and the measurement techniques are described in the published article. The ANN parameters for training and testing are given in Table 4.  
The default Levenberg-Marquardt algorithm was used for training the network. The maximum validation checks (max_fail) function was taken as 6. This parameter (max_fail) serves as a training function parameter and ensures the maximum number of validation checks before the training is stopped. Therefore, it must be a positive integer. The validation fails are total successive iterations that the validation performance fails to decrease or when the validation MSE (mean-square-error) increases the max_fail value. This criterion can be changed by setting the parameter net.trainParam.max_fail. A large number of trainings show the over training and Matlab tries to stop the training after 6 failed in a row.