## 4 Methodology
### Data Analysis  
#### 4.2.1 Feature Extraction  
The reliability of the prediction of output variables such as tool wear, process parameters, or component quality depends on the quality of the extracted features [8]. The vast majority of research already conducted extracts features using spectral analysis [16; 25; 27]. Extraction from time signals is also used [8; 25; 34; 35]. An overview of the features used in the aforementioned works can be seen in Table 2. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Time Domain** & \multicolumn{2}{c}{**Frequency Domain**} \\ \hline \(\bullet\) & Mean value of the amplitudes & \(\bullet\) & Mean value of the amplitudes of a frequency band \\ \(\bullet\) & RMS value of the amplitudes & \(\bullet\) & RMS value of the amplitudes of a frequency band \\ \(\bullet\) & Maximum/minimum of the amplitudes & \(\bullet\) & Signal energy of a frequency band \\ \(\bullet\) & Signal energy & \(\bullet\) & Maximum/minimum amplitude \\ \(\bullet\) & Sum of all amplitudes & \(\bullet\) & Frequency of maximum/minimum amplitude \\ \(\bullet\) & Span between maximum and minimum amplitudes & \(\bullet\) & Percentile \\ \(\bullet\) & Mean value of the envelopes of all amplitudes & \(\bullet\) & Mean value of the 1 st derivative of the signal \\ \(\bullet\) & Skewness & \\ \(\bullet\) & Kurtosis & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selection of possible features in the time and frequency domain according to [PERSON] [32], [PERSON] [25], [PERSON] et al. [8], and [PERSON] et al. [34]. Figure 7: Visualization of the overall transmission error (OTE). [PERSON] [25] extracted features from both the time and frequency domains using the short-time Fourier transform (STFT) and the wavelet transform (WT). Since the features extracted using STFT and from the time domain carry more relevant information, they are selected more frequently than the WT features in the feature selection discussed below. [PERSON] et al. [34] also extracted statistical features such as the RMS value, mean, standard deviation, and maximum values from the spectrum using the wavelet packet transform (WPT). The feature types used here can be seen in Table 3. These are chosen due to their good results in the literature. Features of the recorded structure-borne sound signals are extracted both from the raw signal itself and from the time-frequency spectra of various spectral analyses. In addition to the short-time Fourier transform, the best-known spectral transform, various types of wavelet transforms are used here for feature extraction. Compared to STFT, these have the advantage that the resolution is not constant in the time-frequency domain. This results in a fine-frequency resolution at low frequencies, which becomes coarser as the frequency increases. With the wavelet packet transform (WPT) the resolution can even be adapted to the signal under consideration. For theoretical background, the reader is referred to Puente Leon 2019 [36]. For feature extraction, the time-frequency spectra STFT, a continuous wavelet transform (CWT), a discrete wavelet transform (DWT), and the WPT with two different resolutions (15 and 128 coefficients), are used here. Features can be extracted from the complete time series as well as from single intervals. [PERSON] and [PERSON] [16] analyze the spectrum of effective cutting times at which the tooth of the tool is engaged. As a result, less data has to be transformed into the time-frequency domain, which increases the efficiency of feature extraction. A time interval of either the raw signal or a spectrum is used here to determine a feature. Four time intervals are defined for feature extraction. Time interval one covers the entire hobbing process, while time intervals two to four cover only partial sections. The division into different time intervals allows the individual phases of the process to be considered separately and their characteristics to be examined individually. In this way, characteristics that only occur in one of the process steps become visible.