## 3 Results
### Vibration Signal Analysis  
In this experiment, a motor was artificially set to 15% inter-turn short circuit fault of a single phase. The vibration signal was analyzed to extract the fault features. The time-domain waveforms of vibration signals are shown in Figure 6. It could be seen from Figure 6 that the amplitude of the fault motor vibration signal was much larger than that of normal motor, and that the vibration signal oscillated periodically. Figure 7 shows the results of the power spectrum of the two vibration signals. In Figure 7, the fundamental frequency of the vibration signal, which was 100 Hz, was two times of the current signal, which was 50 Hz. Compared with the frequency spectrum of the normal motor, the amplitude of the fault motor was obviously increased at the fundamental frequency, which was 2 _fs_ = 100 Hz. In addition, several high frequency harmonic components appeared in the vibration signal, located at the frequencies of 3 _fs_ = 150 Hz, 4 _fs_ = 200 Hz, 6 _fs_ = 300 Hz, and 8 _fs_ = 400 Hz. The above is all that we could obtain from the Fourier Transform analysis in frequency domain. However, since the vibration signal was a time-varying signal, the STFT method could get more information from its spectrogram. Figure 6: Time domain waveforms of the vibration signal of the two motors: (**a**) the normal motor; (**b**) the fault motor. Figure 7: The spectrums of the vibration signal of the two motors: (**a**) the normal motor; (**b**) the fault motor. Figure 8 is the STFT spectrogram of the fault motor, obtained by MATLAB. The spectrogram drawn by an embedded device, based on the proposed SMSG algorithm is shown in Figure 9. It could be seen from Figures 8 and 9 that the two results were very similar, which means that the proposed SMSG algorithm was correct. From the front view of the spectrogram, it could be clearly seen that the amplitude of the 100 Hz frequency was very large, but the other Time-Frequency Distribution (TFD) components behind the 100 Hz frequency were invisible. Therefore, in order to observe the TFD more comprehensively, the back view spectrogram was needed. The back view of the spectrograms of the fault motor and the normal motor are shown in Figures 10 and 11, respectively. Since the amplitude of the normal motor was smaller than that of the fault motor, its spectrogram has been zoomed in for easy observation. It could be seen from the 3D time-frequency spectrogram that the motors' frequency components are very abundant, and the appearances of the spectrograms of the two motors, were distinct. If the stator winding of a motor broke down, it would cause magnetic field distortions in the air gap, which  
Figure 8: Spectrogram of the fault vibration signal obtained by MATLAB. Figure 9: Spectrogram of fault vibration signal, generated by an embedded device. would generate electromagnetic forces and would finally lead to the radial vibration of the stator and the rotor. So, the characteristic of the motor vibrations would appear to be very different. From Figure 10 of the fault motor, we can see that the amplitude of two frequency components, that is, 100 Hz and 200 Hz, exhibited a very significant periodic variation. However, the same frequency components of the normal motor, as shown in Figure 11, did not show this feature. This indicated that the two frequency components of 100 Hz and 200 Hz are varied with time, by a periodic shock, only in the fault state. It can be seen from Figure 10 that the period of this shock was approximately equal to 0.5 s, which meant that the changing frequency of the two frequency components was nearly 2 Hz. According to the parameters of the motor, the speed of the revolution could be calculated by the following formula:  
\[ \begin{array}{l}n=\frac{60f_{z}}{p}=\frac{60\times 50}{26}\mathrm{r/min}\\ \approx 115.4\mathrm{r/min}\approx 2\mathrm{r/s}\end{array}