## 3 Experiment and Analysis
### Extraction of Time  
_Frequency Image Features_  
The vibrational raw signal of bearing 1_1, during its whole lifetime, is shown in Figure 5. In the time domain vibration signal, the horizontal and vertical axes represent time and amplitude, respectively. The unit g, representing the acceleration of gravity, is usually used to define the amplitude. Here, 1 g is equivalent to 9.81 m/s2. The amplitude of the vibration signal increased gradually over time, indicating that the signal had abundant information for diagnostics and bearing prognostics. High-quality features of the vibration signal contain useful information about degradation and effectively filter out unnecessary information. However, the traditional fault diagnosis features, based on frequency domain analysis, did not work efficiently, because the vibration of bearings was nonstationary and nonlinear. Additionally, the frequency resolution was too low for detailed analysis [7]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Operational Conditions** & **Speed (rpm)** & **Load (N)** & **Training Dataset** & & **Testing Dataset** \\ \hline \multirow{2}{*}{Condition1} & \multirow{2}{*}{1800} & \multirow{2}{*}{4000} & Bearing1\_1 & \multirow{2}{*}{Bearing1\_3} & Bearing1\_4 & \multirow{2}{*}{Bearing1\_5} \\  & & & Bearing2\_2 & & Bearing1\_6 & & Bearing1\_7 \\ \hline \multirow{2}{*}{Condition2} & \multirow{2}{*}{1650} & \multirow{2}{*}{4200} & Bearing2\_1 & \multirow{2}{*}{Bearing2\_3} & \multirow{2}{*}{Bearing2\_4} \\  & & & Bearing2\_2 & & Bearing2\_6 & & Bearing2\_7 \\ \hline \multirow{2}{*}{Condition3} & \multirow{2}{*}{1500} & \multirow{2}{*}{5000} & Bearing3\_1 & \multirow{2}{*}{Bearing3\_3} & \multirow{2}{*}{Bearing3\_3} \\  & & & Bearing3\_2 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Bearing dataset with operational conditions. Figure 4: Overview of PRONOSTIA [31] experimental platform. In this study, we used the Morlet-based CWT to extract image features from the raw vibration signal. The basic principle of determining a wavelet function is to select a shape similar to the vibration signal generated by a mechanical fault. The vibration signals from a failed bearing contain periodic impulses, and the shape of the signal is known to be similar to the Morlet wavelet. In addition, the previous studies have proven superior performance of fault classification using CNN with the Morlet-based CWT [28,29]. Therefore, the Morlet wavelet was chosen in this study. Figure 6 depicts the raw vibration signal and contour plot of wavelet power spectrum generated by the Morlet-based CWT. The vibration signal sampled for 0.1 s at frequencies of 25.6 kHz has 2560 data points. Figure 6a shows a normal vibration signal and Figure 6c shows a fault vibration signal. When the bearing is in a fault condition, the amplitude of the signal is about \(-30\) g to 30 g, which is larger than in the normal condition. In the wavelet power spectrum, the horizontal axis and vertical axis represent time and frequency, respectively. The color of each point indicates the magnitude of the wavelet coefficients on the time-frequency grid. The red color means that the energy level is high. In Figure 6b, when the bearing is operating in normal condition, the most of the energy is concentrated around 4 kHz. There is no clear periodicity in the energy distribution. On the other hand, Figure 6d shows energy bursts in the frequency range from about 0.25 kHz to over 8 kHz. The impacts occur in the frequency band between 0.25 kHz and 1 kHz at regular interval. When high energy is observed in the low frequency band, it notices that the bearing is heading to the defect [25]. Figure 7 shows image features during the run-to-failure experiment of the training bearings. They show the energy distribution of vibration signals according to the degree of progression of defects in the time-frequency domain. The fault progress is calculated as a percentage of the operation time over the lifetime of the bearing.