## 3 Results
### Experimental Studies  
(1) Experimental platform  
A functional schematic diagram of the test platform is shown in Figure 7. Bearings 5 and 6 are tested bearings, and 4 and 7 are test bearings. The test bench uses an electric spindle as the driving force. The speed can be adjusted continuously, and the speed error does not exceed \(\pm\)1%. During the experiment, the electric spindle rotates and loads bearings 5 and 6 (the loading capacity is 0-500 kg, and the loading accuracy is \(\pm\)2%) to simulate the working environment of the bearing, while temperature sensor 3 collects the outside temperature of the bearing in real-time. Vibration sensors 10 and 11 collect the vibration acceleration signals of the tested bearing in real-time and transmit them to the acquisition card. The experimental platform consists of an experimental platform and a control system. Figure 8 shows a physical diagram of the experimental station, which consists mainly of a tested bearing, companion test bearing, test spindle, bearing outer ring fixture, drive unit, and loading system. \begin{table}
\begin{tabular}{c c c} \hline \hline
**CQMA** & **DB4** & **TKEO** \\ \hline
0.0286 & 0.0098 & 0.0186 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Characteristic frequency intensity values. Figure 7: Functional schematic diagram of the test platform. 1—electric spindle; 2—coupling; 3—temperature sensor; 4—accompanying bearing; 5—subject bearing; 6—subject bearing; 7—accompanying bearing; 8 and 9—loading system; 10 and 11—accelerometer. Four sets of bearings, which included two sets of tested bearingss and two sets of companion test bearingss for a group, were used during the test. Two sets of loading systems were applied to the tested bearings. The drive unit provided power for the whole experimental platform and provided radial force for the tested bearing via the loading system; thus, the spindle drove the bearing to rotate, and the vibration signal of the bearing was obtained through the vibration sensor. The range of bearing speeds that the drive unit could provide was 1000 rpm\(\sim\)20,000 rpm, and the bearing speed was continuously adjustable. The loading range of the loading system was 0-6 KN, and the loading accuracy was \(\pm\)2% and continuously adjustable. Since this test bench was a horizontal test bench, the sensor was placed above the bearing seat in the direction perpendicular to the ground and located in the Z axis direction of the bearing. This experimental acquisition system is a non-invasive acquisition system. Figure 9 shows the fault diagram of the inner ring of the experimental bearing. It can be seen that there are only initial traces caused by the friction of the rolling elements, and there are no faults, such as cracks, which belong to the category of early faults. In Tables 4 and 5, we present the test bearing parameters and the bearing failure characteristic frequency calculation formulas, respectively. The sampling frequency was 8192 Hz, and the data length was 4096 points. The bearing rotation speed was 3000 rpm. Based on Tables 4 and 5, the fault feature frequencies of the inner ring were calculated as 407 Hz, and in the envelope spectrum, the fault feature frequencies of the inner ring and outer ring were 408 Hz, 816 Hz, 1224 Hz, 1632 Hz, and 2040 Hz. to compare the three methods. As presented in Table 6, the orthogonality index of the method that is proposed in this paper is minimal; hence, the decomposition performance of this method has been improved effectively compared with that of CEEMDAN and ITD. Figure 11 shows the reconstructed error after signal decomposition. The reconstruction error of the method that is proposed in this paper is smaller than that of the other two methods; hence, the method that is proposed in this paper has a higher decomposition precision than the other methods.