# Incipient Fault Feature Enhancement of Rolling Bearings Based on CEEMDAN and MCKD
## 4 Simulation Signal Analysis
### Experimental Study under Variable Working Conditions  
Considering that the operation of the bearing is not constant, there will be some unpredictable working conditions; the load change of the system input and the change of speed and other factors with the system change of power input and load will change the operating conditions of the bearing. The vibration signals collected under variable working conditions are more complex. To enhance the features and realize the feature extraction for the incipient faults of rolling bearings under different rotational speeds, the fault signals of two different working conditions in XJTU-SY, namely, working condition 1 and working  
Figure 19: Rolling bearing inner ring fault signal enhancement before and after envelope: (**a**) original signal envelope; (**b**) the enhanced envelope. Figure 18: Rolling bearing inner ring failure signal and enhancement results of this study method. (**a**) Original signal. (**b**) Adding noise signal. (**c**) Signal after enhancement. condition 3, are selected to construct a fault signal of the outer ring of the bearing under variable working conditions. The data set in working condition 1 is Bearing1_1 and the data set in working condition 3 is Bearing3_1. The rotational speed of the rolling bearing in working condition 1 is 2100 r/min and the radial force is 12 kN, the rotational frequency of the rolling bearing is 35 Hz, and the theoretical value of the fault feature frequency is 107.94 Hz. The rotational frequency of the rolling bearing in working condition 3 is 40 Hz and the fault feature frequency of the outer ring is 123.94 Hz. The time domain diagram of the fault signal under the corresponding working condition is shown in Figure 20, in which 0.1 s data is intercepted under each working condition, and the sampling frequency is 25,600 Hz. The rolling bearing's vibration signal, which switches from working condition 1 to working condition 3 during operation, is built using the time domain waveforms of working conditions 1 and 3. Figure 21 displays the signal's time domain waveform. A total of \(-\)10 dB of noise is introduced to the signal in order to improve the impact component of the signal. The signal's envelope is analyzed and the results are displayed in Figure 22. According to Figure 22, the two prominent feature frequencies are 244.90 Hz and 494.08 Hz, which are the 2-fold and 4-fold frequencies of the outer ring fault feature frequency 123.36 Hz under working condition 3. However, no additional characteristic frequency information can be obtained, and the fault feature frequency under working condition 1 is not successfully obtained, so the signal is enhanced by CEEMDAN-MCKD. As shown in Figure 23, the signal is divided into 13 components using CEEMDAN. Following the resolution of the kurtosis and correlation coefficients for each component, Table 3 lists the values for the first eight components' kurtosis and correlation coefficients. Based on the correlation coefficient 0.171 and kurtosis 3 threshold values, the components IMF2, IMF3, IMF4, IMF5, and IMF6 are selected for reconstruction. The reconstructed signals are then obtained and the results of the envelope analysis of the reconstructed signals are shown in Figure 24. The fault feature frequencies of 124.95 Hz, 244.90 Hz of the second octave, and 494.08 Hz of the fourth octave under working condition 3 are highlighted after noise reduction by CEEMDAN decomposition, as can be seen in Figure 24,  
Figure 21: Time domain waveform of outer ring failure under variable working conditions. Figure 20: Time domain waveform of outer ring failure under different working conditions: **(a)** time domain diagram of outer ring failure under working condition 1; **(b)** time domain diagram of outer ring failure under working condition 3.