## 4 Results and Discussions
### Wind Turbine Gearbox Analysis  
The studied gearbox in this part contained 11 different types of bearings. Including the corresponding frequencies of the gears, more than 50 different frequencies of interest were available to analyse. In the present study only the result corresponding to the planetary stage of the gearbox and its bearing defect are shown.  
The vibration signal used to analyse the bearing defect at the planetary stage was obtained from the Radial sensor placed at the planetary stage of the gearbox.  
The damaged bearing was a cylindrical roller bearing with its characteristic frequencies listed in Table 3. Given the wind turbine working at full rated load, the planets were turning at around 1.07 Hz. The other frequency of interest in the planetary stage fault is the gear-mesh of the planets which was calculated to be 140.84 Hz. The next nearest calculated frequencies to this frequency were 99.1 Hz and 192.5 Hz belonging to the intermediate and high-speed shaft bearings.  
As it can be seen in the Figure 9a,b, the gear-mesh of the planets (140.8 Hz) are present in both spectra, indicating possible damage in the planetary gear. It is also evident that the cyclic spectral coherence of the first IMF of the signal is considerably less contaminated with noise originating from other gears.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Speed**} & \multicolumn{4}{c}{**Characteristic Frequency (Hz)**} \\ \hline
**PRM** & **Hz** & **FTF** & **BPFO** & **BPFI** & **BSF** \\ \hline
60 & 1.00 & 0.405 & 5.676 & 8.323 & 2.550 \\
64 & 1.07 & 0.433 & 6.057 & 8.881 & 2.721 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The unit characteristic frequencies and the operation characteristic frequencies of the bearing used for the planets in the monitored gearbox.  
Similarly in the Figure 9c,d, the Ball Passing Frequency of Inner race (BPFI) at 8.8 Hz is distinctly visible. The other closest present frequencies to this frequency are 7 Hz and 9.5 Hz corresponding to the sun gear defect and carrier bearing frequencies. Again, similar to the gear mesh analysis the cyclostationary analysis on the first IMF of the signal shown in Figure 9d shows less artefacts related to the other gears.  
For comparison purposes, the same signal recorded from the planetary stage was also analysed using FFT, Hilbert transform and Cepstrum that are commonly used in condition monitoring and fault detection. As it can be seen in Figure 10a,b the gear-mesh frequency is not detectable in the applied Cepstrum, FFT or Hilbert analysis while the cyclic spectral coherence enhanced with EEMD preconditioning was able to detect it. Similarly, Figure 10c,d show the same analysis applied to the signal to detect BPFI frequency. Similar to the gear mesh analysis, the BPFI frequency was not detected using either Cepstrum or FFT analysis. Although, the Hilbert transform analysis shows some peaks around the BPFI frequency, the amplitude of the peaks are not very significant which can lead to underestimation of the severity. Again, using the cyclic spectral coherence with EEMD the BPFI frequency was detected clearly reducing the likelihood of underestimation of the severity of the defect.  
Figure 9: Cyclic Spectral Coherence of vibration signal recorded from planetary gearbox of wind turbine. From left to right the top row shows analysis on the original signal and its first IMF showing the gear-mesh of the planets. Similarly, the bottom row is the analysis of the same signal (down sampled) and its first IMF showing the BPFI of the bearing of the planet.