## 2 Materials and Methods
### Features Generation in the Time Domain  
Feature extraction in the time domain is a crucial aspect of signal analysis, particularly for applications such as tool condition monitoring in milling processes. In this study, we extracted 11 distinct time-domain features from the signal data for every 11 signals. These features include the following: mean (\(\mu\)), RMS (root mean square), standard deviation (\(\sigma\)), shape factor, SNR (signal-to-noise) ratio, THD (total harmonic distortion), SINAD (signal-to-noise and distortion) ratio, peak value (\(x_{peak}\)), crest factor, clearance factor, and impulse factor [20]. These features provide a comprehensive insight into the characteristics of the signal, facilitating an effective analysis of tool conditions. The feature extraction process involved computing these mathematical formulas for each signal captured, thereby enabling a detailed examination of the signal's properties. In this study, a total of 11 features were generated for each of the 11 signals, resulting in 121 features from the time domain. Below, we detail these features along with their mathematical formulations [20, 21, 22]:  
1. Mean (\(\mu\)): The average value of the signal; providing a measure of the signal's central tendency. \[\mu=\frac{1}{N}\sum_{i=1}^{N}x_{i}\] (1)
2. RMS (Root Mean Square): Represents the square root of the mean of the squares of all values in the signal, indicating its overall energy. \[RMS=\sqrt{\frac{1}{N}\sum_{i=1}^{N}x_{i}^{2}}\] (2) \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset Name** & **Measured Parameter** & **Trial Duration** & \
\begin{tabular}{c} **Sampling Rate** \\ **(Hz)** \\ \end{tabular} &
\begin{tabular}{c} **Observation** \\ **Time (s)** \\ \end{tabular} \\ \hline HighData & Acoustic Emission & 27,999,960 & 5,000,000 & 5.59 \\ LowData & \(X\)-axis Force & 700,000 & 200,000 & 3.50 \\ LowData & \(Y\)-axis Force & 700,000 & 200,000 & 3.50 \\ LowData & Noise & 700,000 & 200,000 & 3.50 \\ LowData & Vibration & 700,000 & 200,000 & 3.50 \\ CurrentData & Device Current & 30,000 & 50,000 & 0.60 \\ CurrentData & Device Voltage & 30,000 & 50,000 & 0.60 \\ CurrentData & Head Current & 30,000 & 50,000 & 0.60 \\ CurrentData & Head Voltage & 30,000 & 50,000 & 0.60 \\ CurrentData & Servo Current & 30,000 & 50,000 & 0.60 \\ CurrentData & Servo Voltage & 30,000 & 50,000 & 0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of variable configuration within datasets. Standard Deviation (\(\sigma\)): Measures the amount of variation or dispersion from the average signal value. \[\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\mu)^{2}}\] (3)
4. Shape Factor: Describes the shape of the signal's waveform by comparing it with an ideal shape. \[Shape\ Factor=\frac{RMS}{\frac{1}{N}\sum_{i=1}^{N}|x_{i}|}\] (4)
5. SNR (Signal-to-Noise Ratio): Compares the level of the desired signal to the level of background noise. \[SNR=10\log_{10}\left(\frac{P_{signal}}{P_{noise}}\right)\] (5)
6. THD (Total Harmonic Distortion): Indicates the distortion of the signal by measuring the harmonics. \[THD=\frac{\sqrt{\sum_{n=2}^{N}P_{n}}}{P_{1}}\] (6)
7. SINAD (Signal-to-Noise and Distortion ratio): Represents the ratio of the total power of the signal to the undesired signal's power (noise plus distortion). \[SINAD=10\log_{10}\left(\frac{P_{signal}}{P_{noise}+P_{distortion}}\right)\] (7)
8. Peak Value (\(x_{peak}\)): The maximum absolute value of the signal, showing its amplitude. \[x_{peak}=\max(|x_{i}|)\] (8)
9. Crest Factor: The ratio of the peak value of the signal to its RMS value; used to assess signal peaks. \[Crest\ Factor=\frac{x_{peak}}{RMS}\] (9)
10. Clearance Factor: A measure that evaluates the signal's peaks in relation to the RMS value; similar to the crest factor but emphasizes the extreme peaks more. \[Clearance\ Factor=\frac{x_{peak}^{3/2}}{\sqrt{\frac{1}{N}\sum_{i=1}^{N}|x_{i}|^{3 /2}}}\] (10)
11. Impulse Factor: The ratio of the peak value to the mean value of the signal; indicates the impulsiveness of the signal.