## 3 Results
### Experimental Studies
To evaluate the performance of CQMA, wavelet transform is selected similarly, and the Teager-Kaiser energy operator (TKEO) is used to demodulate the reconstructed mode components that are obtained from the ICEITDAN method. The obtained demodulation results and their envelope spectra are shown in Figure 13. According to (a), the method that is proposed in this paper can clearly identify the fault frequency of the inner rolling bearing and its 7 th frequency. However, the wavelet analysis in (b) shows that the fault frequency of the bearing cone and its 5 th frequency are completely covered by noise and cannot be obtained. The envelope spectrum effect analysis by TKEO in (c) outperforms the wavelet analysis. However, its 7 th fault frequency was covered by noise. Therefore, the fault diagnosis results of the proposed method are the same as those of the analog signal. To evaluate the performance of the release method that is proposed in this article, an experiment was also conducted on the outer ring fault. Due to space limitations, this article only presents the envelope spectrum result of the outer ring fault. Figure 12 shows that the proposed method can accurately locate the outer ring and the characteristic frequency of loop failure. At the same time, it maintains a high superiority and practicality. Therefore, the proposed CQMA method outperforms the commonly used wavelet and Teager-Kaiser energy operator methods. The proposed CQMA method has higher bearing fault feature frequencies than ICEITDAN, which also demonstrates the superior performance and necessity of the proposed CQMA algorithm. Figure 11: Comparison of the reconstruction errors of three methods: CEEMDAN, ICEITDAN, and ITD. (**a**) CEEMDAN, (**b**) ICEITDAN, and (**c**) ITD. To evaluate the performance of the proposed CQMA method in practical application, the results of the three methods are compared using the characteristic frequency intensity coefficient index in actual operation. As shown in Table 8, the characteristic frequency intensity of the CQMA method is the largest. This also shows from another angle that the method can effectively diagnose the early weak fault of the bearing. According to previous studies, when the rolling body passes through local defects, its time domain acceleration signal will produce a double-pulse phenomenon [42]. The reason for this is that when the rolling body passes through a local defect, a double pulse will be excited. Moreover, the larger the local defect, the greater the signal amplitude. Compared with the other methods, the higher the local defect, the higher  
the uniform inner and outer ring distribution, the fundamental frequency of the bearing vibration acceleration response is the same under the non-uniform distribution, while the amplitude and peak frequency increase. To sum up, the proposed ICEITDAN-CQMA method not only achieves better results than the other methods in the feature extraction of analog signals, but also maintains the best results in the measured signals. This method has the advantages of small reconstruction error, low root mean square error, minimum orthogonality, shortest calculation time, and better extraction of feature frequency. It provides a good foundation for subsequent bearing fault diagnoses.