## 3 Audio Characterization and Recognition Tests
### Data Analysis
#### 3.1.3 Frequency Band Energy Share and Harmonic Component  
To analyze the frequency energy share of the three types of audio in different frequency bands, the frequency band vectors T of A1-C4 were calculated and compared, as seen in Figure 6. A1, A3, A4, and B1-B3 have similar energy shares, with the largest energy share at 0-1 kHz, rapidly decreasing to less than 10% at 0-5 kHz, and stabilizing after 5 kHz. A2, B4, and C1-C4 have similar energy shares, with the energy share in each band not exceeding 15%. Unlike the previous decreasing trend, the energy share of these audios after 5 kHz shows an increasing and then decreasing trend. In addition, the energy share of C2 and C4 shows another increasing trend after 10 kHz. The spectra of A2, B4 and C1-C4 were further analyzed, and it was found that A2 has high frequencies only part of the time within a frame-length window, while B4 and C1-C4 have continuous high frequencies throughout the window. This analysis showed that most of background noise and mechanical vibration were distributed in the low frequency band of 0-5 kHz, and the energy share of different frequency bands decreased with the increase in frequency, while the energy share of PD in 0-16 kHz was balanced, and the energy was more concentrated in the high frequency band of 5 kHz-16 kHz. However, some background noise and mechanical vibrations were also distributed in the frequency band above 5 kHz, with a similar energy share as PD,  
Figure 5: Time domain waveform of PD. Figure 6: Energy share of different frequency bands for a typical frame. with the difference being that the high frequency duration of the background noise was short. Although PD has a higher frequency distribution and can be used to distinguish between background noise and mechanical vibrations, the limited microphone performance of smartphones restricts the acquisition of PD signals above the 16 kHz band. Therefore, the accuracy of identifying the three types of audio captured with smartphones from the band energy alone may not be high. In Figure 7, the maximum amplitude values of background noise A1-A4 appear at 203 Hz, 52 Hz, 60 Hz, and 78 Hz, respectively, with neither a fundamental frequency nor significant harmonic component. In Figure 8, the maximum amplitude values of mechanical vibration B1-B4 all appear at the fundamental frequency of 100 Hz, but the harmonic components are different. B1 has no harmonic component, and the harmonic components of B2 are mainly distributed at 300 Hz, 600 Hz, and 800 Hz, while the B3 is distributed at 200 Hz, 600 Hz, and B4 is distributed at 200 Hz. In addition, B4 still has 100 Hz harmonic component in the frequency band of 5 kHz-8 kHz. In Figure 9, there is no harmonic in C3, whereas harmonic components appear in C1, C2, and C4. The fundamental frequency of C4 is 100 Hz, but C1 and C2 are 50 Hz. In addition, the frequency of the maximum magnitude does not coincide with the fundamental frequency. The maximum magnitude of C1, C2, and C4 are 100 Hz, 800 Hz, and 54 Hz, respectively. This analysis shows that there was no fundamental frequency and harmonic component in the frequency domain spectrum of the background noise, and if there was a fundamental frequency, it was not 50 Hz or 100 Hz. The four sets of mechanical vibrations in the paper came from different vibration types from the switchgear. Although the fundamental frequency was 100 Hz and the fundamental values were all equal to the maximum magnitude, the harmonic components were different. The harmonic component of abnormal vibration was large, but there was almost no harmonic component to the normal vibration. Therefore, the difference in harmonic components can be used as a feature for smartphones to recognize different mechanical vibrations in the switchgear.