# Study on EEMD-Based KICA and Its Application in Fault-Feature Extraction of Rotating Machinery
## 4 Application and Validation
### Experimental Analysis of a Faulty Shift  
A faulty-shaft experimental analysis is applied to verify the effectiveness of the proposed method. The schematic diagram of the test system is shown in Figure 16, and the test rig and signal acquisition system are shown in Figure 17. The test system includes a sensor, shaft test-bed, shaft speed controller, dynamic signal acquisition instrument, computer and analysis software. The sensor sends a radial vibration signal of the shaft into the dynamic signal acquisition instrument, and then converts the analog signal into a digital signal. Finally, the digital signal will be uploaded to analysis software of the computer to realize various analyses required by the user.  
In this experimental analysis, the artificial imbalance fault and rub-impact fault are created. Only one eddy current displacement sensor is used to collect the mixed vibration signal of the faulty shaft. The sampling frequency is 1000 Hz and the number of sampling points is 10,000. The motor speed is 2000 rpm, that is, the rotation frequency \(f_{r}=33.3\) Hz. From experience, the feature of an imbalance fault causes the frequency \(f_{r}\) alone in the frequency-domain. The feature of a rub-impact fault causes the frequency \(f_{r}\) and \(1/n\) of \(f_{r}\), where \(n\) is equal to 2, 3, 4 or 5. The time-domain waveform of the collected signal is shown in Figure 18, and the amplitude spectra of the collected signal obtained with FFT is shown in Figure 19.  
Figure 16: The schematic diagram of the test system.  
Figure 17: The test rig and signal acquisition system of a faulty shaft.  
As can be seen in Figure 18, none of the periodic amplitude can be seen in the time domain. The frequency of 33.45 Hz, which is very close to \(f_{r}\), can be seen in Figure 19, but the amplitude of other frequencies is very high and the noise energy is high.  
In the proposed method, firstly, the collected single-channel vibration signal is decomposed with EEMD, and then the number of fault signals can be estimated with SVD. The ratios of neighboring singular values are shown in Table 3.  
As shown in Table 3, the sequence number of the maximum NSVR is 2. Therefore, the number of fault signals is 2. Finally, high-correlation IMFs are selected to reconstruct a new observation signal, and then fault signals can be extracted with KICA. The Hilbert envelope spectra of the extracted fault signals are shown in Figure 20.  
Both the frequencies of 33.45 Hz and 6.836 Hz can be found in Figure 20a, which can be considered the features of a rub-impact fault. Figure 20b only has the frequency of 33.45 Hz, which can be considered as the feature of an imbalance fault. Furthermore, the fault features are significantly  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Sequence Number** & **NSVR** \\ \hline
1 & 1.926 \\
2 & 22.568 \\
3 & 3.448 \\
4 & 2.962 \\
5 & 1.979 \\
6 & 1.038 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The ratios of neighboring singular values.  
Figure 19: The amplitude spectra of the collected signal.  
Figure 18: The time-domain waveform of the collected signal.  
obvious. It demonstrates that the proposed method has a good performance of fault-feature extraction of a faulty shaft with both the imbalance fault and the rub-impact fault.