## 4 Results and Discussion
### ANN, SVR and RF  
In order to verify the scientificity of the ANFIS material removal model we developed, three other regression models (ANN, SVR and RF) were tested with the same data. The model parameters for ANN, SVR and RF were carefully chosen to obtain the best accuracy, giving objective and unbiased comparative results. In this study, the model was trained using 70% of the data set, and tested using the remaining 30% of the data set. The architecture and training process of an ANN model affects its accuracy. One neuron is employed in the output layer to represent MRD, whereas three neurons in the ANN input layer represent the three input parameters. In regard to ANN, nonlinear structures between input and output are built using back-propagation neural networks. First, the network's weights were modified at the output neurons during the learning phase. Second, the weights were inversely adjusted at the hidden layer throughout the training process, up till the predicted error was obtained. Finally, the modeling results were produced using the ANN toolbox in the MATLAB software and the hyperbolic tangent sigmoid transfer function. The back-propagation method used by ANN was Bayesian regularization and the remaining data was used for model verification. For SVR, first it is necessary to define the datasets and predictors. Then, the kernel function is fitted to be Gaussian and an ideal model chosen to train the predictor and  
Figure 12: The control surface of the fuzzy model shows the interdependence between (**a**) MRD, Force (N), and Speed (m/min); (**b**) MRD, Force (N), and Mesh; (**c**) MRD, Speed (m/min), and Mesh. Figure 13: Comparison between experimental grinding depth and ANFIS prediction. response of the input data [31]. Moreover, the Bayesian optimization model was used to train the model in the MATLAB environment. Finally, the test set was used to validate the model. The random forest regression algorithm's fundamental tenet is to construct a data sample with a sample size of \(N\), having a retrieval of \(N\) times, and then to create a sample set \((x_{1},x_{2}...x_{n})\). There are \(M\) attributes for the sample \(x_{i}\). When the decision tree needs to be split at each node, \(m\) attributes are chosen at random from the \(M\) attributes, where \(m\ll M\). The split attribute of the node is then chosen using information obtained from among \(m\) attributes. Each node must be divided until it can no longer be divided as part of the decision tree construction process. After creating a substantial number of decision trees, a random forest is created. Finally, the mean absolute percentage error (\(MAPE\)) was used to assess the accuracy of the ANFIS, ANN, SVR, and RF models in comparison. Table 6 shows the partial prediction data and error percentage of the four models. \(MAPE\) is defined as:  
\[MAPE=\frac{100\%}{n}\sum_{k=1}^{n}\mid\frac{M_{k}-P_{k}}{M_{k}}\mid \tag{10}\]  
where \(M_{k}\) and \(P_{k}\) are the measured and predicted grinding quantities and \(n\) is the total number of samples used [32]. The \(MAPE\) of ANFIS, ANN, SVR, and RF were 3.976%, 5.713%, 12.717%, and 16.635%, respectively. Notice that ANN was close to the prediction result of ANFIS and that the RF performance was relatively poor [21]. The absolute percentage error (APE) of the four models is shown in Figure 14.