## 3 Results
### Experimental Studies
Similarly, we calculate the root mean square error (RMSE) and computation time of each of the three methods and present the results in Table 6. The obtained parameter values show that the method that is proposed in this paper has substantial advantages over the other two methods. Next, PMGI values are calculated for each mode component, and mode components that exceed the average values for reconstruction and envelope spectrum conversion are selected for use in extracting fault feature frequencies and identifying frequency doubling; the result is shown in Figure 12. By adopting the CEEMDAN and ITD methods, only four harmonics of the fault feature frequency can be clearly identified. The method that is proposed in this paper yields two more peaks of the fault feature frequency compared with these two methods. Therefore, the proposed method outperforms the others in terms of practical fault feature extraction. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ball Number N** & **Pitch Diameter D** & **Roller Diameter d** & **Contact Angle** \\ \hline
14 & 46 & 7.5 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Bearing parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Bearing Fault** & **Equation** \\ \hline Bearing cage (FTF) & \(\frac{1}{2}f_{r}[1-(d/D)\cos\alpha]\) \\ Bearing roller (BSF) & \(\frac{1}{2}f\Big{\{}1-\left[(d/D)^{2}\cos^{2}\alpha\right]\Big{\}}D/d\) \\ Bearing outer race (BPSO) & \((N/2)f_{r}[1-(d/D)\cos\alpha]\) \\ Bearing inner race (BPFL) & \((N/2)f_{r}[1+(d/D)\cos\alpha]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Bearing failure characteristic frequency calculation formulas. Figure 9: Failure diagram of the experimental bearing inner ring. The envelope spectrum of the ICEITDAN results still contains strong noise, but the method that is proposed in this paper can effectively detect the early failure of the bearing inner ring. The reason is that the white noise that is added in the CEITDAN method can only be used to offset the white noise part of the signal, and the noise reduction in colored noise remains insufficient. This also verifies the packet that was extracted from the analog signal with only white noise added. The network spectrum does not contain noise interference. In addition, to better extract fault features, we must use the CQMA method for further analysis and demodulation. When extracting the fault feature frequency after decomposition, the CQMA method that is proposed in this paper can extract more fault feature frequencies of bearings than ICEITDAN, which explains the reliability, necessity, and the noise reduction in the noise reduction. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Decomposition Method** & **IO** & **RMSE** & **Time (s)** \\ \hline ICEITDAN & 0.0216 & \(4.1305\times 10^{-16}\) & 21.59 \\ CEEMDAN & 0.1241 & \(4.8015\times 10^{-15}\) & 78.54 \\ ITD & 0.0262 & 0.0082 & 0.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison indicators for the three methods. Figure 10: Comparison chart of the decomposition results of three methods: CEEMDAN, ICEITDAN, and ITD. (**a**) CEEMDAN, (**b**) ICEITDAN, and (**c**) ITD. and foresight of the method that is proposed in this paper. In the envelope spectrum after CQMA demodulation, the influence of noise is reduced; thus, the technical solution that is proposed in this article can effectively solve the problem of difficult feature frequency extraction, due to excessive noise in the early failure and reduce noise better than the other methods. According to the comparison above, the proposed ICEITDAN decomposition method outperforms CEEMDAN and ITD. Therefore, in the next step, we will focus on the demodulation and analysis of ICEITDAN-CQMA on signals. As presented earlier in Table 7, there are three mode components that exceed the mean PMGI value for the method that is proposed in this paper; hence, they are selected as signals for further analysis, and the signal is also reconstructed.