# Application Research of Negative Pressure Wave Signal Denoising Method Based on VMD
## 3 Results and Discussion
### The Real Pipeline Tests  
In order to verify the effectiveness of the algorithm, we conducted a verification experiment on a real pipeline in Shanghai. In this field test, high-frequency dynamic pressure sensors were installed in valve well J15 and valve well J23 to detect the water pressure in the pipeline. As shown in Figure 11, valve well J22 is located between J15 and J23. The pipeline leakage condition is simulated by opening the drain valve in valve well J22 as shown in Figure 12. Wireless communication is adopted for signal transmission. The installations  
The drain valve is the butterfly valve with a fully open diameter of about 200 mm. The different areas of leakage are simulated through the use of different openings (\(11^{\circ}\), \(20^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(67.5^{\circ}\), and \(90^{\circ}\)). Firstly, the original leakage signals are denoised using the method proposed, and Figure 15a shows the denoised leakage signal under three different openings (\(11^{\circ}\), \(20^{\circ}\), and \(30^{\circ}\)). It can be seen that when the valve is opened at \(11^{\circ}\), \(20^{\circ}\), and \(30^{\circ}\), it is difficult to determine the location of the leakage. However, under the conditions of \(45^{\circ}\), \(67.5^{\circ}\), and \(90^{\circ}\), as shown in Figure 15b, the recovery process of leakage curve is relatively slow, and the pressure drops caused by leakage are more obvious. In the actual operation of the water supply pipeline, the interference noise is much stronger than the signal noise collected in the laboratory test, due to the influence of pump adjustment, load fluctuation and unforeseeable pressure fluctuation. In the case of a small leakage area, the inflection point characteristics of NPW pressure drop caused by leakage are very similar to the pressure fluctuation in the real pipeline. This presents a great challenge to our method of identifying inflection points. When the valve opening angle is higher than \(45^{\circ}\), the method proposed in this paper shows a better extraction effect of the inflection point, and the introduction of correlation coefficient improves the recognition of real signals and the removal effect of noise signals. These results lay a foundation for the engineering application of our method.  
Figure 14: GPS installation location and main pipe.  
Figure 13: The physical picture of acquisition equipment installation.  
We calculate the negative pressure wave velocity, which is 976.45 m/s in this experiment. Table 4 lists the results of leak location experiments. As shown in Table 4, leakage point positioning errors are within 10% at valve openings of 90\({}^{\circ}\), 67.5\({}^{\circ}\), and 45\({}^{\circ}\). The minimum relative positioning error used by our method is 0.41%, and the maximum is 9.52%. Under other conditions of small opening angles, the positioning error of the leakage point is too large, and we consider the positioning failure. Obviously, the size of the leakage port area will affect the positioning effect. For a leakage with a small area in particular, the pressure change after leakage is not obvious. Therefore, it is difficult to find the inflection point of the negative pressure wave, and thus impossible to calculate \(\Delta t\), which makes it harder to locate the leakage point. These results provide strong support for the application of the negative pressure wave denoising and leak location methods based on the VMD algorithm in practical engineering.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test Number** & **Valve Opening** & **Error (\%)** & **Absolute Error (m)** \\ \hline
1 & 90 & 8.87 & 522.79 \\
2 & 90 & 7.04 & 414.59 \\
3 & 90 & 0.57 & 33.77 \\
4 & 67.5 & 4.88 & 287.65 \\
5 & 67.5 & 0.41 & 24.01 \\
6 & 67.5 & 8.05 & 473.97 \\
7 & 45 & 1.91 & 112.69 \\
8 & 45 & 0.9 & 53.30 \\
9 & 45 & 9.52 & 561.06 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Field test results.  
Figure 15: Noise reduction leakage signal of valve under different opening angles.