# Incipient Fault Feature Enhancement of Rolling Bearings Based on CEEMDAN and MCKD
## 4 Simulation Signal Analysis
### Experimental Study under Constant Operating Conditions
Combined with the parameters T, the optimal set of parameters is formed and inputted into the MCKD algorithm to enhance the signal and then perform envelope analysis. The time domain signal plot after enhancement is shown in Figure 14, where it can be observed that the fault pulse characteristics have been greatly improved while the majority of the noise has been eliminated. The envelope of the signal after enhancement is shown in Figure 15; it is clear that the pulse characteristics at frequencies of 199.96 Hz, 349.92 Hz, 589.88 Hz, 789.8 Hz, and 984.80 Hz are noticeable. These results almost exactly match the 196.6 Hz fault feature frequency computed theoretically and the multiplier frequency, demonstrating the applicability of the approach for the diagnosis of incipient bearing problems. To prove the necessity of combining the CEEMDAN algorithm and the PSO optimized MCKD algorithm, the fault signal is not preprocessed with CEEMDAN, and the simulated signal is analyzed based on the PSO optimized MCKD, setting the L and T seeking ranges to [50; 700] and [1; 7]. The envelope analysis is used after the MCKD feature enhancement, and the analysis results are shown in Figure 16.  
Figure 14: The signal after MCKD enhancement. Figure 15: Envelope spectrum of CEEMDAN-MCKD processed signal. As can be seen in Figure 16, the shock component is enhanced when the fault features in the signal are enhanced using only the PSO-MKCD method, but there is more interference in the envelope, and it is more difficult to observe the fault feature frequencies from the envelope where the periodic trend exists. There is also more interference near the peak 194.96 Hz and 394.92 Hz. This demonstrates that the noise may be mistaken for the impact component to increase the signal by the MKCD method, lowering the accuracy of feature extraction. The results of the envelope analysis of the fault signal processed by CEEMDAN-MED are shown in Figure 17. From the figure, it can be seen that the two spectral peaks closest to the theoretical value of 196.6 Hz of the inner ring fault frequency are 189.96 Hz and 209.96 Hz, which are far from 196.6 Hz. As a result, the results of the envelope analysis cannot be used to determine whether the bearing's inner ring is defective. In contrast, the method of CEEMDAN-MCKD is more effective in extracting features for incipient faults in the inner ring. With regard to the second set of data, Figure 18a demonstrates that the shock component in the signal exhibits periodicity and that noise of \(-\)7 dB is added to the signal. Figure 18b displays the temporal domain diagram of the signal following the addition of the noise. Applying this technique to the signal results in an improvement, as shown in Figure 18c, and when compared to Figure 18a, the signal's shock component has undergone a considerable enhancement. The envelope spectrum before and after the enhancement is acquired to further confirm the enhancement effect. The actual fault signal envelope appears in Figure 19a, although, while having a more prominent feature frequency in the envelope, there is a significant disparity between it and the fault feature frequency, making it challenging to directly extract the fault features. The envelope spectrum after enhancement is shown in Figure 19b, from which the rolling bearing's fault feature frequency  
Figure 16: Envelope spectrum of direct PSO-MCKD processing. Figure 17: CEEMDAN-MED processed signal envelope. and multiplier frequency can be seen. The prominent frequency is 50 Hz, which is nearly identical to the inner ring fault feature frequency of 49.6 Hz under this working condition, indicating that the method has good effects in the feature enhancement. The aforementioned experimental investigation demonstrates the viability and efficiency of the CEEMDAN-MCKD method, which is helpful for accurately extracting the fault features.