## 4 Experimental Results
### Results and Discussion  
(1) From the planetary gearbox fault detections, it can be seen that multiwavelet denoising methods can effectively eliminate noise and improve the signal-to-noise ratio so as to outstand the fault features. Besides, the denoising methods using customized multiwavelets [shown in Figures 11(b) and 16(a)] have a better result than the denoising methods using GHM multiwavelet. However, only the proposed method using the customized multiwavelets and the improved neighboring coefficients [shown in Figures 11(a) and 15] could effectively enhance the fault features. Thus, the appropriate multiwavelet functions for feature separation and the optimal threshold and length of neighbors for denoising are both important, neither of them could be dispensed with in planetary gearbox fault detections.  
(2) The computing times of these methods in planetary gearbox fault detections are listed in Table 3. All the tests of time consumption are carried out and recorded in Matlab software with the same computer platform of Intel Pentium Dual CPU E5200 @2.5 GHz and DDR2 memory 2 G. As it is known that every coin has two sides, the optimization of the customized multiwavelets has to take some time for the effective planetary gearbox fault detections. For example, a signal of length 4096 has to take about 2 minutes using the proposed method. In practice, the customized multiwavelets are suitable for a certain kind of fault. For example, the customized multiwavelets proposed in this paper are effective for detecting the pitting faults of other gears in planetary gearboxes, without constructing customized multiwavelets again. Therefore, the calculation efficiency of the proposed method is similar to other denoising methods using standard multiwavelets after the customized multiwavelets have been constructed.  
(3) As shown in Figure 14, the denoising result in time domain could accurately represent the shock impulses caused by the pittings of the sun gear. Its Fourier spectrum is shown in Figure 19, the frequency components mainly distribute at 1,000-3,000 Hz. The rotating frequency or the meshing  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Time in healthy** & **Time in defective** \\
**Method** & **planetary gearbox (s)** & **planetary gearbox (s)** \\  & **(Signal length 5760)** & **(Signal length 5760)** \\ \hline Customized multiwavelets with INC & 156.05 (_150.81_) & 156.05 (_150.81_) \\ Customized multiwavelet with NC & 155.18 (_150.81_) & 155.18 (_150.81_) \\ GHM multiwavelet with INC & 3.79 & 3.79 \\ GHM multiwavelet with NC & 3.71 & 3.71 \\ \hline \hline \end{tabular} The time in italics represents the cost for the optimization of the customized multiwavelets.  
\end{table}
Table 3: The computing time of the methods in planetary gearbox fault detections.  
frequency and their harmonics of the planetary gearbox cannot be detected in the spectrum. The spectrum is not so distinct as the denoising result in the time domain of Figure 14. Besides, the spectrums of denoising results using other methods are similar to the spectrum in Figure 19. Therefore, FFT is not effective to detect the pittings of the sun gear in the planetary gearbox.