# A Novel Feature Selection Based on VMD and Information Gain for Pipe Blockages
## 4 Experimental Results and Analyses  
### Data Pre-Processing  
In signal processing, the aim is to maximize the extraction of valuable information from the signals. For physical systems such as buried pipelines, the sound pulse or frequency response is a characteristic quantity that contains detailed information, including the system geometry, sound velocity, and boundary conditions. Any changes in the properties of the physical system are reflected in the variations of sound pulse or relevant frequency response. During propagation in the pipe, acoustic signals collide with the pipe wall, blockages, and lateral connections to cause reflection, refraction, and diffraction. To investigate the frequency content of measured sound pressure signals, these time-domain signals were transformed from the time domain to the frequency domain via the Fourier transform. In Figure 3, the time-domain and frequency-domain waveforms of the acoustic signals are illustrated in the typical pipe conditions. \begin{table}
\begin{tabular}{c c c c} \hline
**No** & **State** & **Pipe Condition** & **Training Samples** & **Testing Samples** \\ \hline
1 & normally & Clean & 200 & 100 \\
2 & & Lateral Connection (LC) & 200 & 100 \\
3 & & a 20 mm blockage & 200 & 100 \\
4 & single blockage & a 40 mm blockage & 200 & 100 \\
5 & & a 50 mm blockage & 200 & 100 \\
6 & & a 40 mm blockage and a LC & 200 & 100 \\
7 & & a 55 mm blockage and a LC & 200 & 100 \\
8 & & a 40 mm blockage and a 55 mm blockage & 200 & 100 \\
9 & & a 40 mm blockage, a 55 mm blockage, and LC & 200 & 100 \\ \hline \end{tabular}
\end{table} 
Table 1: Pipe conditions information. In Figure 3a, the \"Distance\" of abscissa is the propagation distance of sound waves in the pipe, which facilitates the positional identification of pipe tail end, blockages, and lateral connections in the time-frequency domain diagrams. In the present paper, the propagation distance equals the propagation time multiplied by the sound propagation velocity in the air (approximately 340 m/s). The reasons are that in the drainage pipe, the water flow accounts for 20% of the cross-sectional pipeline area, and the sounds are transmitted mostly in the air. Figure 3a depicts the time-domain waveforms of original response signals. With the increasing propagation distance of sound waves in the pipeline, the energy of sound wave propagation was attenuated continuously, which was manifested as the decreasing signal amplitude with increasing distance in the sound pressure graphs. Nevertheless, the sound pressure waveforms in the three pipe conditions exhibit no distinct differences in the time domain, thus that it is difficult to distinguish the position and size of blockages in the time-domain waveforms, which are even hardly distinguishable from the pipe fittings (lateral connections). This is attributed mainly to the presence of environmental noise and the varying responses among objects to the frequency bands in different ranges. As is clear from Figure 3b, the frequencies in the three pipe conditions are concentrated primarily in [0-6000 Hz] in the spectrograms, while the components in other frequency bands are weak. Hence, the Butterworth filter was utilized to denoise the acoustic signals. Given the difficulty of identifying the pipe operational status based on the analysis of conventional time-domain waveforms and spectrograms for sound pressure signals, further analysis, and processing of these signals were needed. The time-frequency map reflects the information that the frequency of acoustic signal changes with time. The time-frequency map reflects the energy carried by each frequency component of the signal through the cold and warm color. The warmer the color, the greater the energy. The common time-frequency transformation methods include short-time Fourier transform, Wigner distribution, and wavelet transform. Compared with the first two, wavelet transform has adaptive time-frequency resolution and a faster algorithm.