# Construction of a Cutting-Tool Wear Prediction Model through Ensemble Learning
## 3 Approach Methods and Procedures
### Data Processing  
In the experiments, \(x\), \(y\), and \(z\)-axis cutting force signals were sampled, as shown in Figure 7. The raw cutting force signals include three portions, i.e., before cutting-tool engagement, the milling process, and after cutting-tool engagement. The signals before and after the cutting-tool engagement portions, highlighted by the red dashed boxes, are removed, while only the stable cutting force signals during the milling process, as indicated by the green dashed box, are reserved for use. In a study investigating the relationship between cutting forces and cutting-tool wear [25], it was found that by performing a Fourier transform on the cutting force signals, changes in the amplitudes of rotational speed frequency, tooth passing frequency, and their harmonics were observed due to cutting-tool wear. Following this research, this study applied a Fourier transform to the cleaned cutting force signals to analyze them in the frequency domain, as shown in Figure 8. From the graph, it can be observed that the dominant frequencies are low-frequency signals, with a frequency of 166 Hz, associated with a spindle speed of 10,000 rpm and a frequency of 664 Hz, associated with the 4-flute end mill. The other frequencies are harmonics of spindle speed or tooth passing frequencies. Since the cutting force signals are predominantly low-frequency signals, a low-pass filter was applied to complete the data cleaning process. The cutting force signals contain various environmental noises and, therefore, it is essential to extract significant features that reflect cutting-tool wear during the cutting  
Figure 8: Three cutting force components exhibited in frequency domain. Figure 7: Three cutting force component signals sampled from experiments. processes. As cutting-tool wear progresses, it affects the geometrical shape of the cutting edges of the end mill, which, in turn, impacts the contact area between the cutting-tool and the workpiece, resulting in increased cutting forces. Therefore, analyzing variations in cutting forces in the time domain can provide valuable insights into cutting-tool wear [26]. Moreover, variations in cutting forces also lead to variations in the frequency domain. Extracting features on frequency domain can also be used to assess the cutting-tool wear conditions [27]. Therefore, extracting features from different domains in the raw signals can effectively increase the relevance to cutting-tool wear [28; 29]. In this study, feature extraction was performed on the cleaned cutting force signals, with their expressions, as indicated in Table 4. The sampling frequency for the cutting forces in this study was set at 50 kHz. Thus, each cleaned cutting force signal for one component contains approximately 200,000 data points. The relevant details are stated as follows:  
1. For the \(x\), \(y\), and \(z\) axes, 9 features in the time domain and 4 features in the frequency domain were extracted from the cutting force signals. 2. For the \(x\), \(y\), and \(z\) axes, the cutting force signals were divided into 10 windows, with each window containing around 20,000 data points, as shown in Figure 9. Nine features in the time domain were then extracted for each window. 3. For the \(x\), \(y\), and \(z\) axes, the cutting force signals were transformed into the frequency domain using a Fourier transform. The frequencies of spindle speed at 10,000 rpm and 4-flute tooth passing in the experiments were approximately 166 Hz and 644 Hz, respectively. Therefore, these frequencies within \(\pm\)5 Hz were extracted, and their amplitudes were used as features. After completing the data feature extraction, the dataset is randomly split into a training set and a test set, with an 80% and 20% ratio, respectively. Subsequently, data standardization is performed. Features from different domains may have varying scales or range differences. Standardizing the data ensures that all feature magnitudes are within the same range, facilitating better model training and evaluation.