# Wind Turbine Gearbox Fault Diagnosis Based on Improved EEMD and Hilbert Square Demodulation
## 4 The Proposed Method for Gearbox Fault Diagnosis of a Wind Turbine
### Bearing Experimental Evaluation  
An experimental study on the fault diagnosis of a rolling bearing was firstly employed to show how the proposed method worked and to validate its effectiveness and suitability. The experimental dataset by the Case Western Reserve University (CWRU) Bearing Data Center [24] has become a standard reference in the bearing diagnostics field. The proposed method was applied to the CWRU dataset. The basic layout of the test rig is shown in Figure 5. It consisted of a 2-hp motor (left), a torque transducer (center), a dynamometer (right) and control electronics (not shown). Two bearings were installed in the motor-driven mechanical system, one at the drive end of the motor and the other at the fan end. In both bearings, three types of faults (outer race, inner race and ball faults) and various levels of fault severity (7-28 mils) were introduced using electro-discharge machining. Each bearing was tested under four different loads, 0-3 hp. The motor rotational speed was varied between 1730 and 1797 RPM depending on the load. Data was collected at 12,000 samples per second and at 48,000  
Figure 4: The flow chart of the proposed method. HSD, Hilbert square demodulation. samples per second for drive end bearing experiments. All fan end bearing data were collected at 12,000 samples per second. A more detailed description of the experimental setup and the apparatus involved can be found at the Case Western Reserve University's website [24]. In this study, we employed the drive end bearing data collected at 1719 RPM (\(f_{r}=28.5\) Hz) using an accelerometer. The sampling frequency \(f_{8}\) was 48 kHz. The fault was seeded at the outer race with a 21 mils fault diameter. Fault characteristic frequency was the multiple of the rotating frequency, the coefficient of the driven end bearing outer ring and the coefficient of the drive end bearing and is listed in Table 1[24]. Therefore, the fault characteristic frequency could be obtained by Equation (18):  
\[f_{ep}=\frac{1719}{60}\times 3.5848=102.7\ \mathrm{Hz} \tag{18}\]  
The time domain waveform of the experimental vibration signal and its FFT spectrum are shown in Figure 6, from which the fault characteristic frequency cannot be identified. The proposed method was applied to this vibration signal. As show in Figure 6a, the vibration signal presented a periodic change with the increasing of experiment times. Spectrum analysis has been made, and the result is shown in Figure 6b. However, it is difficult to find out any obvious fault information, for the feature with gear fault information is drawn in the background vibration signals. \begin{table}
\begin{tabular}{c c c c} \hline
**Inner Ring** & **Outer Ring** & **Cage Train** & **Rolling Element** \\ \hline
5.4152 & 3.5848 & 0.39828 & 4.7135 \\ \hline \end{tabular}
\end{table} 
Table 1: Coefficient of drive end bearing: 6205-2 RS JEM SKF, deep groove ball bearing. Figure 5: Bearing test rig. The proposed method in this article is then introduced to analyze the vibration signal. According to the resample criterion presented in Section 3.2, if we subtract 12-times the maximum frequency from sampling frequency, the value of the result was bigger than the maximum frequency. Therefore, the resample should be taken to improve the accuracy and computational efficiency of EEMD. \[f_{e}=f_{s}-f_{r}=48000-12\times 3293=8484\;\mathrm{Hz}\geq 3293\;\mathrm{Hz} \tag{19}\]  
The resample was first applied on the vibration signal with a frequency of 39,516 Hz. The first eight IMFs of the resample signal are shown in Figure 7a. The IMF1 was selected for further analysis because it had the highest kurtosis value compared with the other IMFs. The demodulation spectrum obtained from applying the HSD on IMF1 is illustrated in Figure 7b, which shows that the identified frequency matched the calculated fault frequency \(f_{ep}=102.7\;\mathrm{Hz}\). The side-bands' frequencies were also clearly identified. Figure 6: Experimental bearing vibration signal and its spectrum.