# Acoustic Emission Based Fault Detection of Substation Power Transformer
## 3 Methods  
### Feature Extraction  
Joint time-frequency representation is the most common technique used in the AE signals signal process. The effective signals are transferred into a time-frequency representation to yield [23]:  
\[X_{n}\left(e^{i\omega}\right)=\sum_{m=-\infty}^{\infty}x(m)\omega(n-m)e^{-i \omega m} \tag{2}\]  
where \(x(n)\) is the signal received after endpoint detection and \(\omega(n)\) is the window function, which shifts the AE signals signal by one step length on the time axis. As one of the joint time-frequency representations, the spectrogram, has demonstrated its good prospects for the information in the signals. The spectrogram representation \(X\) can be calculated as,  
\[X=\left|X_{n}\left(e^{i\omega}\right)\right|^{2} \tag{3}\]  
For acquiring the spectrogram of each segment, the 1.0 s segment is subdivided into overlapping sub-segments of 50 ms duration (800 samples) with a progression of 25 ms (400 samples). Each sub-segment is multiplied with a hamming window and padded with zeros to obtain a frame of 1024 samples. After doing so, we can obtain a 512 \(\times\) 39 spectrogram of the 1-s signal as shown in Figure 1. Figure 1 also demonstrates that the energy of the AE signals is mainly concentrated in the low-frequency region, whether in the normal state or the discharging state, and the distribution of the energy becomes sparse with the increase of the frequency. Due to uneven resolution of the human auditory system to frequency domain [24], for example, the human ear is more sensitive to low frequency, Mel-scale is often used in the speech and audio process. Although there is a well-defined Mel-scale frequency band division formula, we find that the division effect will be better after properly adjust. Here the frequency band is divided into 8 sub-bands (1-60, 61-125, 126-180, 181-240, 241-300, 301-365, 366-425, 426-512). Considering the entire difference of different patterns, the energy of the sub-segment calculated as an energy term was appended to form a feature vector with nine feature parameters for each sub-segment. Therefore, every one-second segment has a total of 9 \(\times\) 39 feature vectors such as Figure 2. Compared with Figure 1, the differences of the spectrograms between the normal operating state (Figure 2a) and the discharged state (Figure 2b) become more evident. Furthermore,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **AE Signals** \\ **Type** \\ \end{tabular} } & \multicolumn{4}{c}{**Normal**} & \multicolumn{4}{c}{**Fault**} \\ \cline{2-9}  & **Normal** & **Normal with** & **Normal with** & **Normal with** & **Normal with** & **Discharge** & **Mechanical** \\  & **Clean (A)** & **Bird Call (B)** & **Wind (C)** & **Rain (D)** & **Voice (E)** & **Signals (F)** & **Signals (G)** \\ \hline Total samples & 4000 & 1200 & 4000 & 4000 & 2000 & 160 & 160 \\ \hline
\begin{tabular}{c} Testing \\ samples \\ \end{tabular} & 400 & 120 & 400 & 400 & 200 & 16 & 16 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Sample distribution in the seven different types of AE signals and division of normal and fault samples in binary classification.  
the burr that appears in the spectrogram (Figure 1b) is also significantly attenuated in the 9 \(\times\) 39 feature vector (Figure 2b).