## 3 Results and Discussions  
Extracting features using the signal decomposition method with the Hilbert transform helps to provide detailed and useful information on each signal buffer produced by different classes of tools and workpiece conditions, and thus to optimize manufacturing. This implies that the condition of the tool and workpiece can accurately be determined during production while avoiding machine downtime, meeting job requirements, and reducing scraps due to product damage (i.e., surface quality exceeding the required standards). Due to the non-linear and non-stationary characteristics of the signal captured at the machining station, it is advantageous to use the signal decomposition function to identify the varying condition of the cutting tool during the machining operation. In a review, [PERSON], [PERSON] [59] showed that 80% of the most recent analyses of non-stationary and non-linear wind turbine signals adopted EMD for signal analysis for the prediction models. Compared to other decomposition methods, EMD generates relatively stationary subseries (IMFs) that are easily modeled [60]. Furthermore, IMFs developed with EMD eliminate stochastic volatility and, therefore, improve the prediction results [61]. The vibration signals captured during the machining operation were decomposed using the EMD method to extract the IMFs, as indicated in Equation (11):  
\[[IMFs,\ res]=emd(data); \tag{11}\]  
Six IMFs and one residual were obtained after the decomposition of the signals, as indicated in Figure 4. The iterative decomposition was stopped using the stopping criterion indicated in Equation (4). The instantaneous properties of the signals were obtained by applying the Hilbert transform (HHT) to the IMFs. The obtained feature vectors comprised 12 features. These included the instantaneous frequencies, amplitude, and energy of the IMFs. These features were fed into the ML algorithm to classify the varying signals from each tool type. The feature vectors were first trained using a feed-forward neural network model with a scaled conjugate gradient (SCG) algorithm. The model had four (4) features, while the hidden layer had eighteen (18) nodes, and four (4) output classes were used. The label for the data to be trained had one (1) column and a thousand (1000) samples. The network trained the data set using 44 iterations and the confusion matrix was used to evaluate the performance of the network. The best validation performance, as shown in Figure 5, was 0.047349 at epoch 103. The histogram of the error of the neural network with the SCG algorithm indicates the classification prediction error after training the feed-forward backprop neural network. It shows how the prediction class differs from the target class in a training example. This is very important in determining the accuracy of the trained network in classifying new samples of data. The error histogram has 20 bins, which indicate that the range of error bars on the histogram is divided into 20 samples, as shown in Figure 6. This is evaluated from Equation (12):  
\[Bin\ Width=\frac{Right\ limit-lower\ limit}{20} \tag{12}\]  
The bin width from Figure 6 can be evaluated to be 0.08882. Although the classification algorithm performs very well according to the error histogram, there are other error distributions to the left and right of the zero-error line. The confusion matrix in Figure 7 shows that the accuracy of the classification algorithm is 89.2%. To further determine the accuracy of the classification algorithm, other ML classification algorithms were considered for classifying the conditions of the cutting tool during machining operation from extracted vibration signals. The SVM is a powerful technique used in data classification and regression analysis, and it has become one of the most used classification methods due to its good theoretical foundations and good generalization capacity [62].