At present, the leakage rate of the water distribution network in China is still high, and the waste of water resources caused by water distribution network leakage is quite serious every year. Therefore, the location of pipeline leakage is of great significance for saving water resources and reducing economic losses. Acoustic emission technology is the most widely used pipeline leak location technology. The traditional non-stationary random signal de-noising method mainly relies on the estimation of noise parameters, ignoring periodic noise and components unrelated to pipeline leakage. Aiming at the above problems, this paper proposes a leak location method for water supply pipelines based on a multivariate variational mode decomposition algorithm. This method combines the two parameters of the energy loss coefficient and the correlation coefficient between adjacent modes, and adaptively determines the decomposition mode number K according to the characteristics of the signal itself. According to the correlation coefficient, the effective component is selected to reconstruct the signal and the cross-correlation time delay is estimated to determine the location of the pipeline leakage point. The experimental results show that this method has higher accuracy than the cross-correlation method based on VMD and the cross-correlation method based on EMD, and the average relative positioning error is less than 2.2%.

Pipeline transportation is currently the most important transportation method for water resources, and it plays a huge role in urban water supply systems [

At present, some scholars have proposed many effective algorithms for the leak location of water supply pipelines [

In recent years, with the development of related technologies, EMD, WT and other technologies are often used in non-stationary signal analysis [

In summary, this paper proposes a leak location method for water supply pipelines based on Multivariate Variational Mode Decomposition (MVMD) combined with correlation coefficients. The MVMD algorithm expands the traditional VMD algorithm from one-dimensional to multi-dimensional, and this method can ensure that the obtained component frequencies remain consistent when processing multi-channel data, which facilitates the extraction of effective components. Collect the vibration signals during normal operation and leakage of the pipe network for time-frequency domain analysis to determine the characteristic frequency band of the leakage signal. This method combines the two parameters of the energy loss coefficient and the correlation coefficient between adjacent modes, and adaptively determines the decomposition mode number K according to the characteristics of the signal itself. According to the correlation coefficient, the effective component is selected to reconstruct the signal, and perform cross-correlation analysis on the reconstructed signal to achieve water supply precise positioning of the pipeline.

VMD is a new time-frequency analysis method proposed in 2014, which has been widely used in recent years, which can effectively eliminate the phenomenon of modal aliasing in the process of signal decomposition [

Step 1. The number of multivariate modulation oscillations is preset as K, then,

MVMD decomposition is completed when the following two conditions are met:

Minimum sum of mode bandwidth

The sum of modes can restore the original signal

Step 2. Hilbert transform

Step 3. The solving process of the above problems is complex, so it is convenient to construct an augmented Lagrange for solving:

Step 4. Wu et al. [

Through the above introduction of MVMD algorithm, it can be seen that when using MVMD algorithm to decompose the signal, the decomposition number K needs to be set, and the selection of K value affects the accuracy of signal decomposition. In previous studies, Liu et al. [_{1} is set to 0.01). At the same time, set the initial value of the number of modes to K = 2, and calculate the energy loss coefficient according to _{1}, it is considered that the K value at this time is the number of modes. If it is greater than the set threshold μ_{1}. Make K = K + 1 and recalculate the energy loss coefficient until the energy loss coefficient is less than the set threshold μ_{1}. However, for some signals, this method may have over decomposition, resulting in poor signal preprocessing effect. Therefore, this paper uses the correlation coefficient of adjacent modes to detect whether MVMD is over decomposed.

In the above equation, E stands for mathematical expectation and D stands for variance operation _{2}. According to reference [_{2} is set to 0.2. If _{2}, let K = K − 1, decompose and calculate again _{2} is small, then the K value currently is the number of final modes.

The schematic diagram of leak location is shown in

According to _{w} is the propagation velocity of acoustic signal in water, and α is the average radius of the pipe, B is the bulk modulus of water in the pipeline E is the young's modulus of the pipe, and h is the wall thickness of the pipe.

Combined with the principle of leak location introduced in

Step 1. Perform time-frequency analysis on the collected leakage signals x_{1}(k), x_{2}(k) and no leakage signals x_{11}(k), x_{22}(k) to determine the characteristic frequency band of the leakage signal

Step 2. Decompose the leakage signals x_{1}(k), x_{2}(k) by MVMD algorithm to obtain K IMF components, initialize the number of decomposition modes K = 2, and set the penalty parameter α = 2000, and the energy loss coefficient

Step 3. If _{1}, preliminarily determine the number of decomposition modes K, if _{1}, make K = K + 1 and repeat Step 2 until _{1};

Step 4. Calculate the correlation coefficient of adjacent IMF components _{2}, K at this time is deemed to be the number of final decomposition modes, if _{2}, make K = K − 1 to perform MVMD decomposition again and calculate the correlation coefficient of adjacent IMF components _{2};

Step 5. Calculate the correlation coefficient between each IMF component and the characteristic band signal of the leakage signal ρ, the IMF component with correlation coefficient greater than

Step 6. Similarly, carry out Steps 2∼5 for x_{2}(t) to obtain the reconstructed signal

The experimental platform includes two parts: water distribution network and acoustic emission detection system. The pipe is an overhead steel pipe with a diameter of 42 mm and a wall thickness of 4.8 mm. A water pump is installed at the beginning of the pipe network. The start and stop of the water pump can be controlled manually or automatically to control the operation state of the pipe network. In this experiment, the pressure in the pipe network is controlled at about 0.2 MPa. The valve is installed on the pipe network. When the valve is opened, the real leakage of the pipe network is simulated. The acoustic emission detection system includes IEPE acceleration sensor, data acquisition card and host computer. The real water supply platform is shown in

Experimental environment | Diameter (mm) | Tube thickness (mm) | Young's modulus (N/m^{2}) |
Density of pipe (Kg/m^{3}) |
---|---|---|---|---|

Numerical value | 42 | 4.5 | 2.1 × 10^{11} |
7900 |

S_{1} sensor is placed 3 m upstream of the leakage point, S_{2} sensor is placed 3.6 m downstream of the leakage point, and the pressure in the pipe network is 0.2 MPa. The duration of data acquisition is 10 s, and the middle stable 3 s is selected for analysis. Suppose the signal collected by sensor S_{1} is x_{1}(t), the signal collected by sensor S_{2} is x_{2}(t), and

Calculate the energy loss coefficient of MVMD decomposition under different K values according to _{1}(t) signal decomposition under different K values. It is easy to see from _{1}, and when K continues to increase to 8, the energy loss coefficient _{1}. Therefore, it is preliminarily determined that the decomposition mode number K is 8. _{1}(t) signal. It can be seen from _{2}, it is considered that the decomposition is excessive under the K value at this time, and when the value of K decreases to 6, the maximum correlation coefficient of adjacent components _{2}, so the final mode decomposition number determined is 6.

K | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|

0.3424 | 0.1906 | 0.1308 | 0.0547 | 0.0368 | 0.0191 | 0.0081 | 0.0058 |

K | 8 | 7 | 6 |
---|---|---|---|

0.2241 | 0.2028 | 0.1601 |

After determining the pre decomposition scale K, carry out MVMD decomposition for x_{1}(t) and x_{2}(t). _{1}(t) signal. The correlation coefficient between each IMF component and the signal in the characteristic frequency band is shown in _{2}(t) is decomposed and reconstructed to obtain

The delay time between upstream and downstream sensors is calculated by MVMD and correlation coefficient combined positioning method, VMD and correlation coefficient combined positioning method, EMD and correlation coefficient combined positioning method and direct cross-correlation positioning method. The results are shown in

Analyzing _{1}(t) and x_{2}(t) will produce multiple different peaks, and it is difficult to accurately obtain the delay time of the two leakage signals. Since EMD decomposition has problems such as modal aliasing and false components, it is difficult to accurately extract the leakage signal of the original signal, and the resulting positioning error is relatively large. However, the VMD combined with the correlation coefficient method has low recognition for signals with small differences, and the reconstructed signal will contain some noise. The method proposed in this paper can effectively reduce the influence of noise and extract the leakage signal contained in the original signal to the greatest extent, improve the accuracy of the leak location of the water supply pipeline.

According to the direct cross-correlation positioning method, the combination of EMD and correlation coefficient, the combination of VMD and correlation coefficient and the positioning method proposed in this paper, the relative positioning errors are 25.5%, 6.38%, 3.33% and 1.67%, respectively.

The results of a single experiment are accidental and unrepresentative, based on the above experimental platform, 10 groups of data are collected respectively when the position of two sensors on 42 mm pipeline and 32 mm pipeline remains unchanged and the leakage size changes, and 10 groups of data are collected respectively when the position of two sensors on 42 mm pipeline and 32 mm pipeline changes and the leakage size changes, a total of 40 groups of data, The experiments of MVMD and correlation coefficient combined positioning (Algorithm 1), VMD and correlation coefficient combined positioning (Algorithm 2), EMD correlation coefficient combined positioning (Algorithm 3) and direct cross-correlation positioning (Algorithm 4) are carried out and the results are compared. Among them, 1–6 groups of data are collected from the same position of the pipeline with an outer diameter of 42 mm, and 7–12 groups of data are collected from different positions of the pipeline with an outer diameter of 42 mm, 13–18 groups of data are collected from the same position of the pipe with an outer diameter of 32 mm, and 19–24 groups of data are collected from different positions of the pipe with an outer diameter of 32 mm. The statistics of leak location error of water supply pipeline based on four different methods are shown in

Data group number | Relative positioning error (%) | |||
---|---|---|---|---|

Algorithm 1 | Algorithm 2 | Algorithm 3 | Algorithm 4 | |

1–6 | 2.80 | 4.12 | 7.52 | 23.84 |

7–12 | 1.55 | 2.45 | 5.42 | 23.92 |

13–18 | 2.17 | 4.03 | 6.96 | 24.46 |

19–24 | 2.02 | 3.46 | 5.43 | 22.01 |

1–24 | 2.13 | 3.51 | 6.33 | 23.55 |

It can be seen from

The traditional non-stationary random signal de-noising method mainly depends on the estimation of noise parameters, ignoring the periodic noise and components unrelated to pipeline leakage. To solve the above problems, this paper proposes a solution based on MVMD. The decomposition mode number k is determined according to the steps in this paper, and the effective component is selected according to the correlation coefficient to reconstruct the signal for cross-correlation time delay estimation to determine the location of pipeline leakage point. The experimental verification is carried out through multiple groups of data collected by the established water supply system experimental platform. The experimental results show that this method has higher accuracy than the other three methods, and the average relative positioning error is less than 2.2%.

This article is an experiment based on the situation that there is only a single leakage point between the two sensors. The influence of multiple leakage points on the experiment is not considered. This can be used as a further research direction.