## 3 Experiments and Analysis
### Experiment 1: Case Western Reserve University (CWRU) Bearing Dataset
#### 3.1.2 Spectral Characteristic Analysis and IMFs Screening  
Before processing, the raw signal was analyzed preliminarily. The rotating frequency of the shaft is 29.5 Hz. According to the bearing parameters and the shaft rotating frequency, the fault characteristic frequencies of each part can be calculated [40]. The characteristic frequencies of IRF, ORF and BF are \(f_{\mathrm{f}}=159.9\) Hz, \(f_{\mathrm{O}}=105.8\) Hz and \(f_{\mathrm{B}}=139.2\), respectively. The time domain signals of four different conditions and their spectra figures are shown in Figure 7. It can be seen the main frequency components of normal condition are concentrated within 2000 Hz, and main characteristic frequencies are 87.89 Hz, 1066 Hz and 2104 Hz, which are 3, 36 and 71 times of the frequency conversion respectively. The main frequency components of ORF are concentrated, and 2449 Hz, 2602 Hz, 2707 Hz, 2871 Hz and 3357 Hz are the main frequency components, and only 2449 Hz is the frequency doubling of the shaft rotating frequency and its characteristic frequency. The main frequency components are  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & **Outside** & **Inside** & **Thickness** & **Ball** & **Pitch** & **Number of** \\
**Diameter** & **Diameter** & **Diameter** & **Diameter** & **Diameter** & **Balls** \\ \hline
6205-2 RS & & & & & \\ JEM SKF & 52 & 25 & 15 & 7.94 & 39 & 9 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The employed drive end (DE) bearing parameters (mm) in Experiment 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fault Type** & **Fault Diameter** & **Training** & **Testing** & **Sample Length** & **Sample Label** \\
**(mm)** & **Samples** & **Samples** & **Samples** & **Sample Length** & **Sample Label** \\ \hline N & 0 & 100 & 50 & 1 \\ ORF & 0.18/0.36/0.54 & 100/100/100 & 50/50/50 & 2048 & 2 \\ BF & 0.18/0.36/0.54 & 100/100/100 & 50/50/50 & 3 \\ IRF & 0.18/0.36/0.54 & 100/100/100 & 50/50/50 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Training and testing samples of the bearing dataset in Experiment 1.  
Figure 6: Bearing test ring. A = fan end bearing; B = electronic motor; C = drive end bearing; D = torque transducer; E = dynamometer.  
also concentrated in BF spectrum, 3217 Hz and 3480 Hz are the frequency doubling of the rotating frequency and its characteristic frequency. The main frequency components of IRF are multiple and scattered, and only 2742 Hz and 3539 Hz are the frequency doubling of the rotating frequency and its characteristic frequency. From the above spectrum analysis, it can be seen that only a few of the main frequency components in each state are frequency conversion and frequency doubling of their fault characteristic frequencies, and there are many interference frequencies.  
The signal samples were initially preprocessed with EEMD. Figure 8 shows IMFs of a BF signal sample. As can be deduced from the IMF waveform, the first five-order IMFs contain sufficient frequency components, and IMF6-IMF8 may be low-frequency false components. As shown in Figure 9, (a) is spectrogram of a BF sample, and (b) are the spectrogram of its eight-order IMFs. It can be seen that IMF1 to IMF5 contain the main characteristic frequency components of the raw signal from high frequency to low frequency, respectively. IMF5 is followed by low-frequency false components. So the first five-order IMFs were selected for the subsequent feature extraction.  
Figure 7: Time domain waveform and spectrogram of the four health conditions. (**a**) Normal condition (N); (**b**) Outer race fault (ORF); (**c**) Ball fault (BF); (**d**) Inter race fault (IRF).  
Figure 8: Eight-order IMFs of a BF signal decomposed by ensemble empirical mode decomposition (EEMD).  
Figure 9: Spectrogram of a BF signal and its IMFss. (**a**) Spectrogram of a BF signal sample; (**b**) Spectrogram of the eight-order IMFs.