## 3 Results
### Numerical Simulation
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline ICEITDAN & GPR1 & GPR2 & GPR3 & GPR4 & GPR5 \\ \cline{2-6}  & **0.5595** & 0.0319 & 0.0044 & \(-\)0.0014 & \(-\)0.0012 \\ \cline{2-6}  & GPR6 & GPR7 & GPR8 & GPR9 & Mean value \\  & \(-\)0.0014 & \(-\)0.0012 & 0.0003 & 0.0153 & 0.0674 \\ \hline \multirow{6}{*}{CEEMDAN} & IMF1 & IMF2 & IMF3 & IMF4 & IMF5 \\  & **0.563998** & **0.142603** & 0.034035 & 0.016968 & 0.011412 \\ \cline{2-6}  & IMF6 & IMF7 & IMF8 & IMF9 & IMF10 \\  & 0.008603 & 0.002923 & \(-\)0.0002 & \(-\)0.00137 & \(-\)0.00158 \\ \cline{2-6}  & IMF11 & IMF12 & Mean value & & \\  & \(-\)0.00025 & 0.013288 & 0.065869 & & \\ \hline \multirow{6}{*}{ITD} & PR1 & PR2 & PR3 & PR4 & PR5 \\  & **0.536236** & 0.044549 & 0.005468 & \(-\)0.00154 & -0.00093 \\ \cline{2-6}  & PR6 & Mean value & & & \\ \cline{2-6}  & \(-\)0.00043 & 0.097226 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PMGI values of different methods. Figure 5: Comparison chart of envelope spectrum results of the three methods: CEEMDAN, ICEITDAN, and ITD. (**a**) ITD, (**b**) ICEITDAN, and (**c**) CEEMDAN. the mean PMGI value. Therefore, it is concluded that this mode component contains periodic pulse information; hence, GPR1 is selected as the main component for further analysis. With the objective of evaluating the performance of CQMA, the traditional demodulation method--namely, wavelet transform--and Teager-Kaiser energy operator (TKEO) are used to demodulate the reconstructed signal that is obtained through PMGI parameters after decomposition by the ICEITDAN method. The envelope spectrum of the obtained demodulation result is shown in Figure 6. By observing the fault frequency and harmonic wave in the three demodulation methods, it is found that fault feature frequency and the 16 harmonics behind it can be identified clearly in the frequency spectrum that has been demodulated by the CQMA method. However, the fault feature frequency and the harmonic wave are not easy to identify in the spectra that are obtained using wavelet transform and the TKEO method; thus, the method that is proposed in this paper outperforms the others in terms of signal demodulation. To further evaluate the performance of the proposed CQMA method, we use the characteristic frequency intensity value as an index [43], and the feature frequency intensity coefficient represents the apparent degree of the frequency amplitude of the fault feature in the spectrogram. It is defined as follows:  
\[A_{s}=\sum_{i=1}^{n}AF_{i}/\sum_{j=1}^{M}A_{j}, \tag{42}\]  
Figure 6: Comparison chart of the envelope spectrum results of the composite quantum morphology analysis (CQMA), DB4, and Teager–Kaiser energy operator (TKEO) methods: (**a**) CQMA, (**b**) DB4 wavelet, and (**c**) TKEO. where \(A_{s}\) is the characteristic frequency intensity coefficient, \(AF_{i}\) is the amplitude value that corresponds to the fault feature frequency and the frequency doubling of the rolling bearing, and \(A_{j}\) is the amplitude value of all frequencies in the envelope spectrum graph. The characteristic frequency intensity value reflects the frequency ratio of the fault feature frequency in the spectrum diagram and reflects the effects of signal decomposition. The larger \(A_{s}\) is, the better the signal decomposition effect and the more clearly the effects on the fault type are reflected in the envelope spectrum. The fault of bearings during diagnosis is unknown in practice. All faults of the bearing inner ring, outer ring, and rolling element must be calculated in advance. At this point, the characteristic frequency intensity coefficient is the ratio of the sum of the amplitudes that correspond to each fault and its frequency doubling to the sum of all frequency amplitudes. Therefore, as presented in Table 3, the characteristic frequency intensity value for the method that is proposed in this paper is maximal, which further demonstrates the effectiveness of this method in signal demodulation.