# Preprocessing Acoustic Emission Signal of Broken Wires in Bridge Cables
## 3 Results
### Comprehensive Noise Analysis
#### 3.3.2 Frequency Domain Analysis  
The following analysis of the noise signal is performed in the frequency domain:  
1. Signal spectrum analysis  
The FFT method is used to transform the noise signal from the time domain to the frequency domain to obtain the characteristic distribution of the noise signal in the frequency domain. Nearly one hundred noise signals at each bridge cable were FFT transformed, and the representative noise signals of each bridge were selected randomly. The time and frequency domain plots of the signal are shown in Figures 19-21. Figure 19: Time domain and frequency domain waveform diagram of noise signal of Yangma Island Bridge. (**a**) Signal time domain diagram; (**b**) signal frequency domain diagram. Figure 18: Noise signal impact-vehicle counting correlation diagram at position 2 of Yellow River Bridge. From the above figures, we can learn that the spectral range of the noise signals of the three bridges are concentrated within 20 kHz. 2. Energy-average frequency correlation analysis  
Average frequency (AF) indicates the number of times the AE signal exceeds the threshold value. Thus, AF is defined as the ringing count divided by the duration. Compared with the AE signal of broken wires, the noise signal has a smaller ringing count and longer duration, i.e., smaller AF value. So, the AF value is an important discriminative parameter for the noise signal. Figures 22-24 illustrate the correlation analysis of the average frequency-energy of the noise signals of the three bridges. Figure 21: Time domain and frequency domain waveform diagram of noise signal of Caihong Bridge. (**a**) Signal time domain diagram; (**b**) signal frequency domain diagram. Figure 20: Time domain and frequency domain waveform diagram of noise signal of Yellow River Bridge. (**a**) Signal time domain diagram; (**b**) signal frequency domain diagram. From the above three average frequency-energy correlation plots, we find that the correlation between average frequency and energy is not obvious. This indicates that the activity of the AE source is relatively independent of the type of AE signal. The average frequency of high-energy noise signals is mainly concentrated in the range of 20 kHz. There are noise signals in the range of 20 kHz to 30 kHz, but the energy is low. The average frequency of the noise signal of Yangma Island Bridge is less than 20 kHz and has a proportion of 96.1%. The average frequency of the noise signal of Yellow River Bridge is also less than 20 kHz and has a proportion of 90.6%. The average frequency of the noise of Caihong Bridge is also less than 20 kHz and has a proportion of 91.7%. Therefore, the average frequency threshold of 20 kHz can filter out most of the high-energy noise signals. Figure 23: Average frequency-energy correlation diagram of noise signal of Yellow River Bridge. Figure 22: Average frequency-energy correlation diagram of noise signal of Yangma Island Bridge. AsL-centroid frequency correlation analysis  
The ASL of the signal represents the average signal amplitude in the time domain. The centroid frequency of the signal represents the location of the center of gravity of the signal frequency. The calculation is shown in Equation (4), where \(f_{x}\) is the centroid frequency and \(m_{i}\) is the amplitude at frequency \(f_{i}\). \[f_{x}=\frac{\sum m_{i}f_{i}}{\sum m_{i}} \tag{4}\]  
ASL is the characteristic parameter in the time domain and the centroid frequency is the characteristic parameter in the frequency domain, respectively. Figures 25-27 show their correlation analysis. Figure 24: Average frequency-energy correlation diagram of noise signal of Caihong Bridge. Figure 25: ASL-centroid frequency correlation diagram of Yangma Island Bridge. From the above figures, we find that the ASL of each bridge noise signal has a negative linear relationship with its centroid frequency. The larger the ASL, the smaller the centroid frequency. This indicates that the higher the amplitude level of the noise signal, the smaller the spectral distribution in the region.