Pipeline network leakage detection and location method based on variational mode decomposition and neural network

Abstract

The present invention discloses a method for detecting and locating pipe network leakage based on variational mode decomposition and neural network, which includes dividing the pipe network into regions, collecting and fusing multiple signals in each region, then reconstructing the signal and using continuous wavelet transform to obtain the time-frequency diagram of the pipe network signal, constructing a deep separable convolutional neural network model to detect the leakage of the pipe network, and finally using pressure wave and sound wave positioning methods to complete the leakage positioning. The present invention can effectively avoid the problems of mode aliasing and boundary effect caused by empirical mode decomposition and local mean decomposition, reduce the number of parameters and the number of operations of the neural network model, improve the accuracy of leakage point positioning and reduce the false alarm rate of detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of leakage detection and positioning of pipe network systems, and in particular relates to a pipe network leakage detection and positioning method based on variational mode decomposition and neural network. Background Art

[0002] Due to the continuous expansion of the pipeline network and the aging of the pipelines, the amount of water loss in the water supply pipeline network is increasing. In addition to causing direct economic losses and waste of water resources, the leakage of the water supply pipeline network will also increase the operating costs of the water plant, cause the pollution of drinking water in the pipeline, and sometimes cause more serious disasters such as road collapse. It can be seen that the leakage of the water supply pipeline network is not only a cost issue, but also an environmental sanitation and public safety issue. Therefore, it is of great practical significance to study efficient water supply pipeline network leakage detection and positioning technology.

[0003] In recent years, with the use of SCADA systems and GIS systems in water supply networks, it has become possible to obtain real-time data on the operation of the network, so data-driven leak detection and location methods have become a hot topic of research. The basic idea of ​​data-driven leak detection and location methods is to obtain data through various sensors, then convert the data into images, and use classification and pattern recognition technology to detect and locate leaks. Therefore, how to effectively reduce the noise of the monitoring signal and achieve fast and accurate pipeline network leak detection and location has always been the focus of data-driven leak detection and location methods.

[0004] In terms of pipeline monitoring signal processing, in recent years, adaptive signal analysis methods represented by empirical mode decomposition have demonstrated their advantages in filtering noise reduction, information representation, signal analysis, etc., and have been applied in the fields of pipeline leakage detection and pipeline signal analysis. However, in the problem of signal time-frequency expression where instantaneous frequency traces and instantaneous frequency trajectories intersect, empirical mode decomposition has problems such as mode aliasing, over-envelope, under-envelope, and boundary effects, making it difficult to accurately identify the time-frequency structure of the signal.

[0005] In terms of intelligent identification of pipeline networks, deep network models represented by convolutional neural networks have been applied to pipeline leakage detection due to their advantages in classification and object detection. However, the convolutional layer calculation of traditional convolutional neural networks contains a huge number of parameters and operations, which reduces the training and identification efficiency of the entire network. Summary of the invention

[0006] The purpose of the present invention is to provide a pipeline leakage detection and positioning method based on variational mode decomposition and neural network, aiming to improve the current pipeline leakage detection level from the two aspects of signal analysis and intelligent identification. This method can effectively avoid the problems of mode aliasing, over-envelope, under-envelope, boundary effect, etc. that appear in the noise reduction process of empirical mode decomposition, reduce the number of parameters and the number of operations of the traditional convolutional neural network model, and improve the accuracy and efficiency of pipeline leakage detection and positioning.

[0007] The technical solution adopted by the present invention is: a pipeline network leakage detection and positioning method based on variational mode decomposition and neural network, comprising the following steps:

[0008] Step 1: divide the urban water supply network into several independent and non-overlapping network areas, each area contains several monitoring points for real-time monitoring of pressure, flow, sound waves and other signals of the network;

[0009] Step 2, respectively collect and fuse the pressure, flow, sound wave and other signals of each monitoring point in each area under the conditions of no pipeline leakage, different leakage positions and different leakage apertures;

[0010] Step 3, performing variational modal decomposition on the fused signal to obtain the decomposed modal components;

[0011] Step 4: reconstruct the signal using the modal components after modal decomposition to obtain the fused signal after noise reduction in each region;

[0012] Step 5, using continuous wavelet transform to transform the reconstructed fusion signal into an image, and obtaining a training image set, a verification image set and a test image set of the neural network;

[0013] Step 6, using the obtained training image set as input, training the deep separable convolutional neural network, building a deep separable convolutional neural network model, and using the verification image set to test the model;

[0014] Step 7, using the constructed convolutional neural network to perform leakage detection on the test image set to determine whether leakage occurs and the area where the leakage occurs;

[0015] Step 8: Use the pressure and sound wave data of the upstream and downstream monitoring points near the leakage area to accurately locate the leakage point.

[0016] The present invention is also characterized in that:

[0017] The process of dividing the network into different areas in step 1 is as follows: through investigation and evaluation of the water supply pattern, network characteristics, operating status and leakage status of the water supply network, appropriate zoning metering management implementation routes are selected, an overall design plan is formulated, and the water supply zoning level, regional boundaries, and the number and installation locations of metering and other monitoring equipment are determined.

[0018] In step 2, the fusion is weighted data fusion, and the formula of the fusion method is as follows:

[0019]

[0020] in, represents the fused signal data, f j (t) represents the jth signal data before fusion, w j is the weight coefficient of the jth signal, satisfying

[0021] The variational mode decomposition calculation process in step 3 is as follows:

[0022] The original fusion signal Decomposed into K modal components u k (t)(k=1,…,K), for each mode u k (t), calculate the corresponding analytical signal through Hilbert transform and obtain the single-sided spectrum

[0023]

[0024] Where δ(t) is the Dirac function, * is the convolution operator, and t is time.

[0025] By tuning to the respective estimated center frequency index Mixing, moving the spectrum of the mode to baseband

[0026]

[0027] The gradient of the demodulated signal in the above equation is L 2 The signal bandwidth of each mode is obtained by square operation of the norm. The constrained variational problem is as follows:

[0028]

[0029] Among them, {u k}={u1,…,u K} represents the intrinsic mode function (IMF) component obtained by decomposition, {ω k}={ω1,…,ω K} represents the frequency density center of each modal component.

[0030] In order to solve this constrained optimization problem, the quadratic penalty parameter α and the Lagrange multiplier λ(t) are introduced to transform the constrained optimization problem into an unconstrained optimization problem. The quadratic penalty parameter α is introduced to improve the signal-to-noise ratio of the reconstructed signal, and the Lagrange multiplier λ(t) is introduced to add constraints to the objective function to ensure strict execution of the constraints. Therefore, we can get the augmented Lagrangian formula as follows:

[0031]

[0032] The alternating direction multiplier method (ADMM) is used to solve the augmented Lagrangian formula above. The solution process is to update alternately λ n+1 To iterate and obtain the saddle point of the augmented Lagrangian formula, that is, the solution to the original constrained optimization problem. The specific solution process of using the alternating direction multiplier method to solve equation (5) is as follows:

[0033] ① Initialization λ 1 , the maximum number of iterations N and the accuracy convergence criterion parameter ε;

[0034] ② Assign the number of iterations n to 1;

[0035] ③ Update using the following formula ω k ,

[0036]

[0037]

[0038]

[0039] in, They are u i (t) The Fourier transform of λ(t), γ is the noise tolerance, and ω is the frequency. From formula (6), we can see that The result is actually a Wiener filter.

[0040] ④If n<N, perform iterative accuracy determination, otherwise proceed to ⑥.

[0041] ⑤Accuracy convergence criterion ε>0, if satisfied Then proceed to step ⑥, otherwise execute n=n+1 and return to step ③ to continue iterating until the accuracy requirement is met or the maximum number of iterations is exceeded, and then proceed to step ⑥.

[0042] ⑥ Output the final and ω k .

[0043] In step 4, the eigenmode function u obtained by variational mode decomposition is k (t) Use summation to reconstruct the signal, the formula is as follows

[0044]

[0045] in, is the reconstructed signal, and K is the number of decomposed intrinsic mode functions.

[0046] In step 5, the continuous wavelet transform is: given a signal Its continuous wavelet transform is

[0047]

[0048] Among them, WT x (a,τ) is the transformed function, a is the scale factor, satisfying a>0, τ is the translation factor, ψ * (t) is the basic wavelet function.

[0049] In step 6, the convolution calculation layer of the deep separable convolutional neural network mainly includes two parts: channel-by-channel convolution and point-by-point convolution. The model is tested using the validation image set. The process is as follows:

[0050] First, the time-frequency image obtained by wavelet transform is segmented into n*n (n∈[3,256]) pixel, three-channel images, and then the segmented images are used as input for channel-by-channel convolution. In the channel-by-channel convolution process, the number of convolution kernels is the same as the number of channels in the previous layer, and each convolution kernel is responsible for only one channel. Therefore, if the size of the convolution kernel is W*H (W≤n,H≤n), W is the width of the convolution kernel, and H is the height of the convolution kernel, then the number of channels of the feature map generated after channel-by-channel convolution is consistent with the number of input channels, and the size of the feature map is (n-W+1)*(n-H+1).

[0051] Then, the feature map generated by the channel-by-channel convolution is convolved point by point, with a size of (n-W+1)*(n-H+1) and a number equal to the number of output channels of the channel-by-channel convolution. In the point-by-point convolution process, the size of the convolution kernel is 1×1×P, where P is the number of channels in the previous layer and the number of convolution kernels Q is the number of output channels. After the point-by-point convolution, the new feature map is generated with a size of (n-W+1)*(n-W+1) and a number equal to the number of output channels Q. At this point, a depth-wise separable convolution process is completed.

[0052] Using a deep separable convolutional neural network can effectively reduce the number of model parameters, reduce the amount of floating-point calculations during the convolution process, and improve the efficiency of the entire neural network.

[0053] The leakage location process of the pipe network in step 8 is as follows: determine whether the pipe network leaks and the area where the leakage occurs according to the result of the leakage detection in step 7, then select the pressure and sound wave data of the upstream and downstream monitoring points near the leakage area, and use the two positioning methods of negative pressure wave and sound wave for precise positioning; the negative pressure wave positioning method can realize the positioning of pipe burst and large flow leakage, while the sound wave positioning can realize the positioning of small leakage. By using the two positioning means of negative pressure wave and sound wave, the detection range of the leakage volume is expanded, and the two positioning methods can also complement and verify each other, improve the accuracy of leakage point positioning, and reduce the false alarm rate; the principles of the two positioning methods are as follows:

[0054] Assume that t1 and t2 are the time (s) when the negative pressure wave of the sound wave is captured by the upstream and downstream monitoring points of the pipeline, v is the propagation speed of the negative pressure wave of the sound wave in the pipeline (m / s), u is the flow rate of the fluid in the pipeline (m / s), L is the distance between the upstream and downstream monitoring points of the pipeline (m), and x is the distance from the leakage point to the upstream monitoring point of the pipeline (m), then we can get

[0055]

[0056] According to t1-t2=Δt, the negative pressure wave (sound wave) positioning formula is:

[0057]

[0058] If the fluid flow velocity u in the pipe and the propagation velocity v of the negative pressure wave of the sound wave satisfy: u<<v, then formula (12) can be simplified to:

[0059]

[0060] The propagation velocity of the negative pressure wave in the pipeline is calculated using the following formula:

[0061]

[0062] Among them, K is the volume elastic coefficient of water, ρ is the density of water, E is the elastic modulus of the pipe, D is the pipe diameter, e is the pipe wall thickness, and C1 is the correction factor related to the pipe constraint.

[0063] The propagation velocity of the sound wave in the pipeline is calculated using the following formula:

[0064]

[0065] Where K is the volume elastic coefficient and ρ is the density of the medium.

[0066] The beneficial effects of the present invention are:

[0067] (1) Signal fusion technology is used in the signal acquisition process to ensure data integrity, improve data accuracy and the transmission rate of effective data. The present invention can effectively avoid problems such as mode aliasing and boundary effects that occur in empirical mode decomposition and local mean decomposition, reduce the number of parameters and the number of operations of the neural network model, improve the accuracy of leak point positioning and reduce the false alarm rate of detection.

[0068] (2) The variational mode decomposition method is used. This method does not use a screening process during the decomposition process, which makes this method superior in solving the mode mixing problem and can effectively avoid the problems of mode aliasing, over-envelope, under-envelope, boundary effect, etc. that appear in the empirical mode decomposition. The algorithm has the advantages of a strong theoretical basis and good robustness to noise and sampling.

[0069] (3) Introducing a deep separable convolutional neural network for pipeline network leakage identification can effectively reduce the number of parameters and the number of operations of the neural network model, improve the model calculation efficiency, and save hardware resources.

[0070] (4) The negative pressure wave positioning method can locate burst pipes and large-flow leaks, while the sound wave positioning method can locate small leaks. By using both negative pressure waves and sound waves as positioning methods, the detection range of leaks can be expanded. Moreover, the two positioning methods can complement and verify each other, thereby improving the accuracy of leak point positioning and reducing the false alarm rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a flow chart of the method for detecting and locating pipe network leakage based on variational mode decomposition and neural network of the present invention;

[0072] Figure 2 It is a flow chart of the pipe network area division in the present invention;

[0073] Figure 3 This is a flow chart of using the alternating direction multiplier method to solve the augmented Lagrangian formula in the present invention;

[0074] Figure 4 This is a structural diagram of the deep separable convolutional neural network used in the present invention;

[0075] Figure 5 A schematic diagram of convolution calculation in a deep separable convolutional neural network of the present invention;

[0076] Figure 6 It is a schematic diagram of the principle of pipe network leakage location in the present invention. DETAILED DESCRIPTION

[0077] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] The present invention provides a pipeline network leakage detection and positioning method based on variational mode decomposition and neural network. The specific process is as follows: Figure 1 As shown, it includes pipe network area division, signal acquisition and fusion, variational mode decomposition, signal reconstruction, wavelet transform, construction of deep separable convolutional neural network, pipe network leakage detection and leakage location. The specific implementation plan is as follows:

[0079] (1) Pipeline network area division

[0080] The water supply network is divided into regions to facilitate the management of regional metering. Figure 2 As shown, it mainly includes three steps:

[0081] First, it is necessary to investigate and evaluate the current status of the water supply network, mainly including the water supply pattern, network characteristics, operating status, leakage status, etc. Understand the location of the water plant, topography, water supply range, water supply method, water supply scale, network topology, network material, user water consumption spatial distribution, flow rate, network leakage rate and the layout of existing monitoring points in the network, etc., to provide a working basis for the subsequent regional division of the network.

[0082] Then, determine the implementation route of the network zoning. Generally speaking, for a network with relatively complete basic data, simple topological relationships, and water main line leakage, it is advisable to give priority to the top-down zoning route. For a network with incomplete basic data, complex topological relationships, and water branch line leakage, it is advisable to give priority to the bottom-up zoning route. It is also possible to adopt a combination of the above two zoning routes based on actual conditions.

[0083] Finally, according to the selected implementation route, the fuzzy clustering method is used to divide the pipe network area, determine the water supply zoning level, boundary division, and the number and installation location of metering and other monitoring equipment.

[0084] (2) Signal acquisition and fusion

[0085] Various types of sensors are used to obtain the flow, pressure and acoustic wave signals at the monitoring points in each area of ​​the pipeline network, and then the signals are fused using the following formula to obtain the fused signal

[0086]

[0087] in, represents the fused signal data, f j (t) represents the jth signal data before fusion, w j is the weight coefficient of the jth signal, satisfying

[0088] (3) Variational mode decomposition

[0089] The original fusion signal Decomposed into K modal components u k (t)(k=1,…,K), for each mode u k (t), calculate the corresponding analytical signal through Hilbert transform and obtain the single-sided spectrum

[0090]

[0091] Where δ(t) is the Dirac function, * is the convolution operator, and t is time.

[0092] By tuning to the respective estimated center frequency index Mixing, moving the spectrum of the mode to baseband

[0093]

[0094] The gradient of the demodulated signal in the above equation is L 2 The signal bandwidth of each mode is obtained by square operation of the norm. The constrained variational problem is as follows:

[0095]

[0096] Among them, {u k}={u1,…,u K} represents the intrinsic mode function (IMF) component obtained by decomposition, {ω k}={ω1,…,ω K} represents the frequency density center of each modal component.

[0097] In order to solve this constrained optimization problem, the quadratic penalty parameter α and the Lagrange multiplier λ(t) are introduced to transform the constrained optimization problem into an unconstrained optimization problem. The quadratic penalty parameter α is introduced to improve the signal-to-noise ratio of the reconstructed signal, and the Lagrange multiplier λ(t) is introduced to add constraints to the objective function to ensure strict execution of the constraints. Therefore, we can get the augmented Lagrangian formula as follows:

[0098]

[0099] The alternating direction multiplier method (ADMM) is used to solve the augmented Lagrangian formula above. The solution process is to update alternately λ n+1 The saddle point of the augmented Lagrangian formula is obtained by iteration, which is the solution to the original constrained optimization problem. The flowchart of the process of solving the augmented Lagrangian formula using the alternating direction multiplier method is as follows: Figure 3 As shown, the specific solution process is as follows:

[0100] ① Initialization λ1 , the maximum number of iterations N and the accuracy convergence criterion parameter ε;

[0101] ② Assign the number of iterations n to 1;

[0102] ③ Update using the following formula ω k

[0103]

[0104]

[0105]

[0106] in, They are u i (t) The Fourier transform of λ(t), γ is the noise tolerance, and ω is the frequency. From formula (6), we can see that The result is actually a Wiener filter.

[0107] ④If n<N, perform iterative accuracy determination, otherwise proceed to ⑥.

[0108] ⑤Accuracy convergence criterion ε>0, if satisfied Then proceed to step ⑥, otherwise execute n=n+1 and return to step ③ to continue iterating until the accuracy requirement is met or the maximum number of iterations is exceeded, and then proceed to step ⑥.

[0109] ⑥ Output the final and ω k .

[0110] (4) Signal reconstruction

[0111] The variational mode decomposition is obtained Perform inverse Fourier transform to get u k (t)(k=1,2,…K), the signal is reconstructed using the following formula

[0112]

[0113] Get the fused signal after noise reduction Where K is the number of decomposed intrinsic mode functions.

[0114] (5) Wavelet transform

[0115] The reconstructed signal The time-frequency diagram is obtained by wavelet transform using the following formula:

[0116]

[0117] Among them, WT x (a,τ) is the transformed function, a is the scale factor, satisfying a>0, τ is the translation factor, ψ * (t) is the basic wavelet function.

[0118] The obtained time-frequency maps with no leakage, different leakage locations, and different leakage sizes are divided into training sets, validation sets, and test sets for training and establishing a deep separable convolutional network.

[0119] (6) Constructing a deep separable convolutional neural network

[0120] First, the time-frequency graphs in the training set are segmented into n*n (n∈[3,256]) pixel, three-channel images and input into the deep separable convolutional neural network. Figure 4 The structure diagram of the deep separable convolutional neural network is shown, which includes the input layer, convolution layer, pooling layer, fully connected layer and Softmax layer.

[0121] Then, the first layer of convolution operation is performed. The convolution operation of the deep separable convolutional neural network is different from that of the traditional convolutional neural network. The schematic diagram of the deep separable convolution operation process is as follows: Figure 5 As shown, it includes two parts: channel-by-channel convolution and point-by-point convolution.

[0122] The convolution kernel size of the channel-by-channel convolution is W*H*3, where W is the width of the convolution kernel, H is the height of the convolution kernel, and 3 is the number of convolution kernels. The number of convolution kernels in the channel-by-channel convolution is the same as the number of channels in the input image. After the channel-by-channel convolution, 3 features of size (n-W+1)*(n-H+1) are generated. Figure 1 .

[0123] Features generated by channel-by-channel convolution Figure 1 Perform point-by-point convolution. The size of the convolution kernel is 1×1×P, where P=3 is the number of channels in the previous layer. The number of convolution kernels Q is the same as the number of output channels. After point-by-point convolution, Q features of size (n-W+1)*(n-H+1) are generated. Figure 2 .

[0124] The calculation of the second convolution layer is similar to that of the first convolution layer. The calculation of other steps, such as the pooling layer and the fully connected layer, are the same as those of the traditional convolutional neural network. Finally, the classification result of the image is output, and a deep separable convolutional neural network model is obtained.

[0125] Finally, the convolutional neural network is validated using the images in the validation set to ensure the accuracy of the model.

[0126] (7) Pipeline network leakage detection

[0127] The images to be detected in the test set are input into the constructed deep separable convolutional neural network for leak detection, and the classification results are output to determine whether a leak occurs in the pipeline network and the area where the leak occurs.

[0128] (8) Leak location

[0129] According to the leak detection results in step 7, select the pressure and sound wave data of the upstream and downstream monitoring points near the leak area, and use the two positioning methods of negative pressure wave and sound wave for accurate positioning. The positioning principles of negative pressure wave and sound wave are basically the same. Figure 6 The schematic diagram for positioning of the two methods is as follows:

[0130] Assume that t1 and t2 are the time (s) when the negative pressure wave of the sound wave is captured by the upstream and downstream monitoring points of the pipeline, v is the propagation speed of the negative pressure wave of the sound wave in the pipeline (m / s), u is the flow rate of the fluid in the pipeline (m / s), L is the distance between the upstream and downstream monitoring points of the pipeline (m), and x is the distance from the leakage point to the upstream monitoring point of the pipeline (m), then we can get

[0131]

[0132] According to t1-t2=Δt, the negative pressure wave (sound wave) positioning formula is:

[0133]

[0134] If the fluid flow velocity u in the pipe and the propagation velocity v of the negative pressure wave of the sound wave satisfy: u<<v, then formula (12) can be simplified to:

[0135]

[0136] The propagation velocity of the negative pressure wave in the pipeline is calculated using the following formula:

[0137]

[0138] Among them, K is the volume elastic coefficient of water, ρ is the density of water, E is the elastic modulus of the pipe, D is the pipe diameter, e is the pipe wall thickness, and C1 is the correction factor related to the pipe constraint.

[0139] The propagation velocity of the sound wave in the pipeline is calculated using the following formula:

[0140]

[0141] Where K is the volume elastic coefficient and ρ is the density of the medium.

Claims

1. A pipeline network leakage detection and location method based on variational mode decomposition and neural network, characterized in that: The following steps are involved: Step 1: divide the urban water supply network into a number of independent and non-overlapping network areas, each area containing a number of monitoring points for real-time monitoring of the pressure, flow, and acoustic wave signals of the network; Step 2, respectively collect and fuse the pressure, flow rate, and acoustic wave signals of each monitoring point in each area under the conditions of no pipeline leakage, different leakage positions, and different leakage apertures; Step 3, performing variational modal decomposition on the fused signal to obtain the decomposed modal components; Step 4: reconstruct the signal using the modal components after modal decomposition to obtain the fused signal after noise reduction in each region; Step 5, using continuous wavelet transform to transform the reconstructed fusion signal into an image, and obtaining a training image set, a verification image set and a test image set of the neural network; Step 6, using the obtained training image set as input to train the deep separable convolutional neural network, building a deep separable convolutional neural network model, and using the verification image set to test the model; Step 7, using the constructed convolutional neural network to perform leakage detection on the test image set to determine whether leakage occurs and the area where the leakage occurs; Step 8: Use the pressure and sound wave data of the upstream and downstream monitoring points near the leakage area to accurately locate the leakage point; The fusion in step 2 is weighted data fusion, and the formula of the fusion method is as follows: in, represents the fused signal data, f j (t) represents the jth signal data before fusion, w j is the weight coefficient of the jth signal, satisfying 2. The method for detecting and locating pipe network leakage based on variational mode decomposition and neural network according to claim 1, characterized in that: The process of dividing the pipe network area in step 1 is: by investigating and evaluating the water supply pattern, pipe network characteristics, operating status and leakage status of the water supply network, the water supply zoning level, regional boundaries, and the number and installation locations of metering and monitoring equipment are determined.

3. The method for detecting and locating pipe network leakage based on variational mode decomposition and neural network according to claim 1, characterized in that: The calculation process of variational mode decomposition in step 3 is as follows: The original fusion signal Decomposed into K modal components u k (t)(k=1,…,K), for each mode u k (t), calculate the corresponding analytical signal through Hilbert transform and obtain the single-sided spectrum Where δ(t) is the Dirac function, * is the convolution operator, and t is time; By tuning to the respective estimated center frequency index Mixing, moving the spectrum of the mode to baseband The gradient of the demodulated signal in the above equation is L 2 The square operation of the norm gives the signal bandwidth of each mode, from which the constrained variational problem is as follows: Among them, {u k }={u1,…,u K } represents the intrinsic mode function (IMF) component obtained by decomposition, {ω k }={ω1,…,ω K } represents the frequency density center of each modal component; In order to solve the constrained optimization problem, the quadratic penalty parameter α and the Lagrangian multiplier λ(t) are introduced to transform the constrained optimization problem into an unconstrained optimization problem. The augmented Lagrangian formula is as follows: The augmented Lagrangian formula above is solved using the alternating direction multiplier method ADMM, and the solution process is alternating update λ n+1 To iterate and obtain the saddle point of the augmented Lagrangian formula, that is, the solution to the original constrained optimization problem; the specific solution process of using the alternating direction multiplier method to solve equation (5) is as follows: ① Initialization The maximum number of iterations N and the accuracy convergence criterion parameter ε; ② Assign the number of iterations n to 1; ③ Update using the following formula ω k , in, They are u i (t) The Fourier transform of λ(t), γ is the noise tolerance, ω is the frequency, and is obtained from formula (6): The result is actually a Wiener filter; ④If n<N, then perform iterative accuracy determination, otherwise proceed to ⑥; ⑤Accuracy convergence criterion ε>0, if satisfied Then proceed to step ⑥, otherwise execute n=n+1 and return to step ③ to continue iterating until the accuracy requirement is met or the maximum number of iterations is exceeded, and then proceed to step ⑥; ⑥ Output the final and ω k .

4. The method for detecting and locating pipe network leakage based on variational mode decomposition and neural network according to claim 3, characterized in that: In step 4, the eigenmode function u is obtained by summing the variational mode decomposition. k (t) Signal reconstruction is performed, and the formula is as follows: in, is the reconstructed signal, and K is the number of decomposed intrinsic mode functions.

5. The method for detecting and locating pipe network leakage based on variational mode decomposition and neural network according to claim 4, characterized in that: In step 5, continuous wavelet transform is used to transform the signal into an image. The formula of wavelet transform is as follows: Among them, WT x (a,τ) is the transformed function, a is the scale factor, satisfying a>0, τ is the translation factor, ψ * (t) is the basic wavelet function.

6. The method for detecting and locating pipe network leakage based on variational mode decomposition and neural network according to claim 1, characterized in that: In step 6, the model is tested using the validation image set, and the process is as follows: First, the time-frequency image obtained by wavelet transform is divided into n*n pixel, three-channel images, where n∈[3.256], and then the segmented image is used as input for channel-by-channel convolution. In the channel-by-channel convolution process, the number of convolution kernels is the same as the number of channels in the previous layer, and each convolution kernel is responsible for only one channel. Therefore, if the size of the convolution kernel is W*H (W≤n,H≤n), W is the width of the convolution kernel, and H is the height of the convolution kernel, then the number of channels of the feature map generated after channel-by-channel convolution is consistent with the number of input channels, and the size of the feature map is (n-W+1)*(n-H+1); Then, the feature map with a size of (n-W+1)*(n-H+1) and the number of output channels of the channel-by-channel convolution generated by the channel-by-channel convolution is convolved point by point. In the point-by-point convolution process, the size of the convolution kernel is 1×1×P, P is the number of channels in the previous layer, and the number of convolution kernels Q is the number of output channels. After the point-by-point convolution, the new feature map with a size of (n-W+1)*(n-W+1) is generated, and the number is the number of output channels Q. At this point, a depth-wise separable convolution process is completed.

7. The method for detecting and locating pipe network leakage based on variational mode decomposition and neural network according to claim 1, characterized in that: The leakage location process of the pipe network in step 8 is as follows: determine whether the pipe network has leakage and the area where the leakage occurs according to the leakage detection result in step 7, then select the pressure and sound wave data of the upstream and downstream monitoring points near the leakage area, and use the negative pressure wave and sound wave positioning methods for accurate positioning; the principles of the two positioning methods are as follows: Assume that t1, t2 are the time s when the upstream and downstream monitoring points of the pipeline capture the arrival of the negative pressure wave of the sound wave, v is the propagation speed of the negative pressure wave of the sound wave in the pipeline, u is the flow rate of the fluid in the pipeline, L is the distance between the upstream and downstream monitoring points of the pipeline, and x is the distance from the leakage point to the upstream monitoring point of the pipeline, then we can get According to t1-t2=Δt, the negative pressure wave positioning formula is: If the fluid flow velocity u in the pipe and the propagation velocity v of the negative pressure wave of the sound wave satisfy: uv, then formula (12) is simplified to: The propagation velocity of negative pressure waves in the pipeline is calculated using the following formula: Among them, K f is the volume elastic coefficient of water, ρ is the density of water, E is the elastic modulus of the pipe, D is the pipe diameter, e is the pipe wall thickness, and C1 is the correction factor related to the pipe constraint; The propagation velocity of the pipe sound wave is calculated using the following formula: Where K is the volume elastic coefficient and ρ is the density of the medium.

Images