# Research on Leakage Location of Pipeline Based on Module Maximum Denoising
## 3 Results
### Leakage Location  
Wavelets have the role of a \"mathematical microscope\", which can make the characteristics of abnormal information of the pressure abrupt point, caused by pipeline leakage, more clear. According to the experiment, we found that the number of wavelet decomposition layer is 7, as shown Figure 8. S is the NPW signal after denoising, and a7 is the low-frequency signal part after decomposition. The high frequency part d is the description of the signal change. The more the signal changes, the greater the value of d, and vice versa. At that position, it can be seen from Figure 8 that when the number of decomposition layers is 7, the pressure drop inflection point of NPW can be well captured. In the NPW signal, the low frequency part describes the details of the signal, and the high frequency part describes the change of the signal. The more drastic the signal change, the greater the value of the decomposition layer, and vice versa. In the position of the signal mutation, the coefficient after the wavelet transformation has a module maximum. Therefore, the wavelet detail feature is similar to the first-order differential, which is called the differential feature of the wavelet detail. Figure 9 shows the results of using wavelet decomposition to find the inflection point of NPW, collected by two sensors. Figure 9a shows the inflection point extraction result of the NPW signal of sensor A, and Figure 9b corresponds to the result of sensor B. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Denoising Algorithm** & **SNR1** & **SNR2** & **SNR3** \\ \hline VMD & 1.77 & 18.33 & 35.45 \\ Wavelet & 0.42 & 19.11 & 38.16 \\ module maximum & 1.43 & 30.24 & 48.21 \\ Improved module maximum & 1.96 & 35.55 & 51.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average SNR calculation results. Figure 8: Wavelet decomposition of the signal after denoising. In Figure 9, the maximum modulus of the wavelet method is between 8000 and 10,000, corresponding to the burst interference of the NPW signal. There are a lot of small fluctuations in the signal after noise reduction. Despite the interference of these small noises, the method in this paper still obtains a clear maximum peak value, and the correct inflection point of NPW can be easily extracted. Assume that the inflection point of the NPW collected by sensor A is n\({}_{1}\) and that of the NPW collected by sensor B is n\({}_{2}\). The Formula (15) can be used to calculate the location of the leakage point. In order to verify the stability of the proposed method, several sets of experiments were conducted to verify the method, and the results of leakage location are shown in Table 3.  
Figure 9: Negative pressure wave inflection point identification. (**a**) Extraction of inflection point after noise reduction (Sensor A); (**b**) Extraction of inflection point after noise reduction (Sensor B). In Table 3, \(L\) is the distance between two sensors, \(La\) is the distance between the leakage point and sensor A. As can be seen from the experimental results in Table 3, the positioning accuracy of the leakage point is also related to the simulated leakage area. The larger the leakage area, the more accurate the positioning accuracy. At the same time, it can be known that the leakage point positioning accuracy of the proposed method is higher than that of the other three methods under any leakage area condition. Compared with VMD, the localization accuracy of the proposed method is improved by 0.5 to 3.9 percentage points when the water valve is open at 45\({}^{\circ}\), and by 0.6 to 3.4 percentage points when the water valve is open at 90\({}^{\circ}\). Compared with the wavelet threshold method, the localization accuracy of the proposed method is improved by 1.0 to 1.5 percentage points when the water valve is open at 45\({}^{\circ}\), and by 1.3 to 2.1 percentage points when the water valve is open at 90\({}^{\circ}\).