# Incipient Fault Feature Enhancement of Rolling Bearings Based on CEEMDAN and MCKD
## 4 Simulation Signal Analysis
### Experimental Study under Constant Operating Conditions  
The method of this paper is used for rolling bearing fault feature enhancement and extraction. Firstly, the incipient fault data of bearing 3_4 in XJTU-SY was analyzed and a noise of \(-13\) dB was added to the signal to highlight the feature enhancement capability of the proposed method in the strong noise background. The bearing inner ring's time domain diagram during a fault is shown in Figure 8 and the inner ring fault signal's spectrum without noise addition is shown in Figure 9. The vibration signal has more high-frequency interference noise, as shown in the spectrum. Figure 10 presents the results of the signal's envelope analysis and illustrates the difficulties in  
CEEMDAN was used to break down the fault signal and 13 components were acquired, with the decomposition results displayed in Figure 11. This improves the SNR and increases the difference of fault characteristics. To select the modal components that contain the information on the inner ring fault features, the influence of noise is further reduced, and the impact components are enhanced. The correlation coefficient and kurtosis values of each IMF component are displayed in  
Figure 11: Time domain diagram of CEEMDAN signal decomposition components. Figure 10: Inner ring fault signal envelope. Table 2 after combining the kurtosis and correlation coefficient criteria to choose the IMF components to reconstruct the signal. The correlation coefficient's standard deviation serves as the threshold value, while 3 serves as the threshold value for kurtosis. This allows for the effect of keeping the fault information in the signal and effectively reducing the noise by taking into account both the impact features of each component and the correlation between each component and the original signal simultaneously in time. The IMF2, IMF3, IMF4, IMF5, and IMF6, which also meet the value of kurtosis greater than 3 and the value of correlation coefficient greater than 0.1632, were selected to reconstruct the signals. The time domain diagrams of the reconstructed signals and the results of the envelope analysis are shown in Figures 12 and 13. From Figure 12, it can be seen that the shock component in the signal is significantly increased, which indicates that the noise in the signal can be effectively removed by using the CEEMDAN method. Comparing Figures 10 and 13, it is found that the noise is better suppressed in the envelope of the reconstructed signal, but the fault feature frequency, as well as the multiplier \begin{table}
\begin{tabular}{c c c} \hline \hline
**IMF Component** & **Kurtosis** & **Correlation Coefficient** \\ \hline IMF1 & 2.0957 & 0.7370 \\ IMF2 & 3.6166 & 0.4661 \\ IMF3 & 3.4088 & 0.4249 \\ IMF4 & 3.1486 & 0.3420 \\ IMF5 & 3.2082 & 0.2770 \\ IMF6 & 4.5772 & 0.2068 \\ IMF7 & 2.7392 & 0.1573 \\ IMF8 & 3.4486 & 0.0816 \\ IMF9 & 2.5464 & 0.0719 \\ IMF10 & 2.8642 & 0.0612 \\ IMF11 & 2.1216 & 0.0261 \\ IMF12 & 2.6415 & 0.0253 \\ IMF13 & 2.8042 & 0.0274 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Kurtosis and correlation coefficient of each IMF component of the signal. Figure 12: Time domain diagram of the reconstructed signal. Figure 13: Reconstructing the envelope of the signal. frequency, are still masked. As a result, the signal is feature-enhanced using the method presented in this work. Firstly, the feature frequency of the bearing failure under this condition is calculated as 196.6 Hz according to the formula (19), then T, and then the particle swarm algorithm is used to perform a parameter search for the filter L and shift number M in MCKD. The initial parameters of the particle swarm parameter optimization method are set, the number of particle swarms is 30, the maximum number of iterations is 30, the inertia weight is 1, the acceleration factor is 2, the search range of L is [50; 700], and the M search range is [1; 7]. After optimization, the optimal set of parameters is L = 700 and M = 4.