# Application Research of Negative Pressure Wave Signal Denoising Method Based on VMD
## 3 Results and Discussion
### The Laboratory Experiments
#### 3.1.2 Leak Signal Denoising  
The original NPW signal is shown in Figure 3. As can be seen, the original NPW signal is greatly disturbed by noise, which makes it very difficult to extract the inflection point of the pressure drop. According to the noise reduction process in Section 2.2, the leak signal is denoised. The signal information entropy of different decomposition layers is shown in Figure 4.  
According to the results in Figure 4, when \(k\) is 4, the information entropy is the minimum. At this time, the \(k\) value is the optimal, and the denoising effect is the optimal. Similarly, the optimal denoising signal under the condition of no leakage can be obtained.  
The denoising results of our method are compared with the low-pass filter, wavelet denoising, and EMD-based method. The cut-off frequency of the low-pass filter is 20 Hz. A 'Sym4' wavelet with four-layer decomposition is used when applying wavelet denoising [26].  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Pipeline Inner Diameter (D)** & **0.08 m** \\ \hline Density of the water (\(\rho\)) & 998.203 kg/m\({}^{3}\) \\ Tube thickness (\(e\)) & 0.003 m \\ Bulk modulus of water (\(K\)) & 2.1 \(\times\) 10\({}^{8}\) Pa \\ Young’s modulus of pipe material (\(E\)) & 2.1 \(\times\) 10\({}^{11}\) Pa \\ Sampling rate (\(f\)) & 2 kHz \\ Pressure of the pipeline & 0.16–0.21 MPa \\ \hline \hline \end{tabular}
\end{table}
Table 2: The physical parameters of the test pipeline.  
Figure 4: Information entropy calculation results.  
Figure 3: Original negative pressure wave signal.  
EMD uses the IMF components selection method as described in Section 2.2.3. Figure 5 shows the denoising results of the above methods.  
In Figure 5, the green curve is the original NPW signal collected by the sensor, and the black curve shows the denoising results obtained using the above method. The position of the inflection point of the NPW is partially enlarged, as shown in the rectangular box. By analyzing the characteristics of the original NPW signal, we can see that it is difficult to accurately extract the inflection point of NPW caused by leakage due to the influence of noise, and the leakage localization cannot be carried out. The figure (above left) shows the denoising effect of the NPW signal produced by the low-pass filtering method. As can be seen from the enlarged details in the above left figure, although the noise in the original signal has been removed, there are still a large number of \"burrs\" in the inflection point part, indicating that the inflection point features are disturbed by noise, which is not conducive to accurately extracting the inflection point information. This will seriously affect the positioning effect. The figure on the right shows the denoising effect using the wavelet method. The denoising effect of the wavelet is very similar to that observed with the low-pass filter method. The inflection point signal is still strongly interfered with by noise. The lower left figure shows the denoising effect of EMD. For EMD, although the small noise is eliminated and a smooth signal is obtained, the signal is distorted due to excessive smoothing of the original signal. Similarly, the inflection point of NPW is also difficult to extract. The bottom figure on the right shows the denoising effect of our method. After the signal is denoised by our method, not only is a smooth signal obtained, but also the inflection point is obvious. This is because the correlation coefficient is used to determine the IMF component of VMD, which makes the inflection point feature extraction induced by negative pressure waves more accurate. The accurate extraction of the inflection point will obviously greatly help to improve the positioning accuracy of the leakage point.