CN114245337A

CN114245337A - Water supply pipe network leakage positioning sensor arrangement method based on graph convolution network

Info

Publication number: CN114245337A
Application number: CN202111550865.1A
Authority: CN
Inventors: 杨晓萍; 张卫东; 李娟�; 卢长刚
Original assignee: Jilin University
Current assignee: Jilin University
Priority date: 2021-12-17
Filing date: 2021-12-17
Publication date: 2022-03-25

Abstract

The invention discloses a water supply pipe network leakage positioning sensor arrangement method based on a graph convolution network, which comprises the following steps: step one, establishing a data set of a water supply pipe network by using three-dimensional data; step two, clustering data into K classes by using a K-means clustering algorithm, selecting a sample point of each class, which is closest to the center of the class, as a node for constructing a pseudo label, and attaching labels from 0 to K; thirdly, dividing monitoring areas of all sample points in the data set through a graph convolution network; and step four, traversing the sample points in each monitoring area by using a cross-correlation function algorithm until all the nodes are traversed once, and selecting one most representative sample point in each monitoring area as an optimal sensor arrangement node. According to the invention, the problem of optimal arrangement of the sensors for leakage detection is solved by combining the graphic analysis with the topological structure information of the water supply distribution network for the first time, and the influence caused by the leakage event of each node in the actual water supply network is practically considered.

Description

Water supply pipe network leakage positioning sensor arrangement method based on graph convolution network

Technical Field

The invention relates to the technical field of water supply distribution networks, in particular to a water supply network leakage positioning sensor arrangement method based on a graph convolution network.

Background

The water distribution network is used as an infrastructure system, and the factors influencing the service quality of the water distribution network are many, wherein the most important factor is leakage. However, with the increasing population of the world and the impact of some natural disasters, many countries are facing the problem of severe shortages of water resources. In addition, there are many important factors that exacerbate the shortage of water resources, such as the aging of water supply pipelines, the incompleteness of construction facilities, and the lack of measures for regular maintenance management. Thus, water loss in the water distribution network is as high as 30% of the total water usage. In order to reduce the loss of water resources and reduce the expensive operation cost of a tap water company, it is important to develop an effective anomaly detection method.

Currently, some methods of leak detection and location are based on data collected by sensors installed in the water supply network. Therefore, the field of research on the optimal sensor arrangement for water supply network leak detection is very worthy of research, and aims to effectively control, efficiently manage and continuously maintain the water supply network. Therefore, leak detection and an optimal sensor arrangement should be put together to study, the optimal sensor arrangement providing indispensable data for leak detection, the results of which prompt continuous optimization of the optimal sensor arrangement.

In reality, the water supply and distribution network is very large, and a large amount of operation expenses and maintenance costs are required every year, so that it is important to arrange a limited number of data acquisition sensors in the very large water supply and distribution network without affecting the monitoring of the whole water supply and distribution network.

For a water distribution network with known leak locations, the leak locations may be of significant concern, referred to as under supervised conditions. Typically, leaks in water distribution networks are unknown, i.e. sensor locations are arranged for leak detection under unsupervised conditions. Also, for some methods, some nodes in the complete supply water distribution network are often discarded, for example, in prior studies nodes near the water tank and pump are not considered. In a real situation, each node in the water supply distribution network needs to be taken into account. In addition, there is a lack of research into the optimal sensor placement method for leak detection that combines graphical analysis with water distribution network topology information.

Disclosure of Invention

The invention aims to design and develop a water supply network leakage positioning sensor arrangement method based on a graph convolution network, combine graph analysis and water supply distribution network topological structure information for solving the problem of sensor optimal arrangement of leakage detection, combine the influence brought by the occurrence of leakage events of all nodes in the actual water supply and distribution network, and improve the accuracy of sensor arrangement.

The technical scheme provided by the invention is as follows:

a water supply pipe network leakage positioning sensor arrangement method based on a graph convolution network comprises the following steps:

the method comprises the following steps of firstly, acquiring three-dimensional data to create a data set of a water supply network;

step two, clustering the data into K classes by using a K-means clustering algorithm, respectively selecting a sample point of each class, which is closest to the center of the class, as a node for constructing a pseudo label, and labeling from 0 to K;

thirdly, dividing monitoring areas of all sample points in the data set through a graph convolution network;

and step four, traversing the sample points in each monitoring area by using a cross-correlation function algorithm until all the sample points are traversed once, and selecting one sample point with the maximum correlation sum with other sample points in the monitoring area as an optimal sensor arrangement node.

Preferably, the three-dimensional data includes:

the first dimension data is a value of pressure difference of each node under the condition that a leakage event and a leakage simulation time point of each node are determined;

the second dimension data is the condition that the value of each node pressure difference changes along with the starting and stopping time of the leakage simulation under the condition of the leakage event of the designated node;

the third dimension data is the case of a change in the value of the pressure difference corresponding to each node at different leak simulation times in the case of a leak event at different nodes.

Preferably, the first step further includes sequentially performing noise processing and normalization processing on the data set, where the noise processing is:

the data set is divided into a training data set and a testing data set, the training data set randomly adds noise with a probability of 50%, the testing data set randomly adds noise with a probability of 100%, and the signal-to-noise ratio of the noise is 30db to 40 db.

Preferably, the normalization process satisfies:

in the formula (I), the compound is shown in the specification,

for the noise-added and normalized data set, S is the raw unprocessed data set, μ_SIs the mean, σ, of the original data set_SIs the standard deviation, σ, of the original data set_nIs the mean standard deviation of the noise.

Preferably, the K-means clustering algorithm in the second step specifically includes the following steps:

step 1, dividing the data set into K types randomly according to the number of the arranged positioning sensors, randomly selecting an initialization area, and calculating the clustering center of each type;

wherein the cluster center satisfies:

in the formula, K_iNumber of sample points included for class i, w_ijFor the jth sample point in the ith class, th

Is the average of the i class centers;

step 2, respectively calculating the distances from all sample points to K clustering centers, and classifying the sample points into the clustering center category with the minimum distance;

step 3, when the distance between the sample point and the clustering center does not belong to the minimum value, moving the sample point to the clustering center class with the minimum distance, and recalculating the clustering center for the class migrated from the sample point and the class migrated to the sample point;

step 4, stopping clustering when the square error reaches the minimum value;

wherein the square error is:

wherein, is₁,C₂,…,C_KAnd j is the data set divided into K classes, K is the number of classes, and i is the number of class objects.

Preferably, the graph convolution network satisfies:

in the formula, g_θ(Λ) is an eigenvalue function of the Laplace matrix, Λ is a diagonal matrix of eigenvalues, x is a vector representation of the node attributes in the graph, θ is the Chebyshev coefficient,

is a matrix of the degrees, and the degree matrix,

is a self-circulating adjacency matrix;

wherein the degree matrix satisfies:

in the formula (I), the compound is shown in the specification,

a self-circulation matrix of the current node i;

the self-circulating adjacency matrix satisfies:

wherein A is an adjacent matrix, I_NIs an identity matrix.

Preferably, the cross-correlation function algorithm in the fourth step satisfies:

in the formula (I), the compound is shown in the specification,

is the sample cross-covariance function and s is the sample standard deviation of the process.

Preferably, the method further comprises the following steps:

step five, evaluating the optimal sensor arrangement node by a bidirectional long-short term memory network;

the evaluation comprises accuracy, average topological distance and root mean square error of the average topological distance;

the accuracy satisfies:

where ACC is precision, Γ_a,aThe number of times node a is correctly predicted to leak, N is the number of nodes in the water supply network, Γ_a,jIdentifying a number of times the leak in node a is identified as a leak in node j;

the average topological distance satisfies:

wherein ATD is the average topological distance, D_a,jIs the distance between node a and node j;

the root mean square error of the average topological distance satisfies:

where RMSE is the root mean square error of the mean topological distance.

Preferably, the storage unit of the bidirectional long and short term memory network is composed of an input gate, a forgetting gate and an output gate, and specifically includes the following processes:

and (3) transferring the operation result of the previous output and the current input to the next storage unit through a forgetting gate, and determining whether the previous information is reserved or cleared by the forgetting gate:

f_t＝σ(W_f·(h_t-1,x_t)+b_f)；

in the formula (f)_tFor forgetting gate vectors, σ (-) is a sigmoid activation function, W_fWeight matrix for forgetting gate, h_t-1For the previous output, x_tAs current input, b_fAn offset value for a forget gate;

deciding whether the temporary new state updates the current cell state by inputting the gate vector:

i_t＝σ(W_i·(h_t-1,x_t)+b_i)；

in the formula i_tFor inputting the gate vector, W_iAs a weight matrix of the input gates, b_iTo input the offset value of the gate,

is a temporary new state, W_cWeight matrix modified for cell state, b_cOffset value modified for cell state, C_tFor the current cell state, tanh (-) represents the activation of the function by tanh;

the current output satisfies:

o_t＝σ(W_o·(h_t-1,x_t)+b_o)；

h_t＝tanh(C_t)×o_t；

in the formula o_tTo output the gate vector, h_tFor the current output, W_oWeight matrix representing output gates, b_oThe offset value of the output gate is indicated.

The invention has the following beneficial effects:

(1) the invention discloses a water supply network leakage positioning sensor arrangement method based on a graph convolution network, which is designed and developed by the invention, firstly combines the graphic analysis and the water supply distribution network topological structure information to solve the problem of sensor optimal arrangement of leakage detection, and practically considers the influence brought by the occurrence of each node leakage event in the actual water supply distribution network.

(2) The invention relates to a water supply network leakage positioning sensor arrangement method based on a graph convolution network, which is designed and developed by the invention, converts the sensor optimization arrangement problem into a semi-supervised graph convolution network node classification problem and a maximum correlation problem between nodes, obtains pseudo label nodes based on a criterion of minimum error square sum between each sample and each center by using an unsupervised K-Means clustering algorithm, only obtains one pseudo label node for each type of sample, divides the water supply distribution network into a plurality of areas after training the semi-supervised graph convolution network combining graph analysis and network topology structure, selects the most representative node in the area through the maximum correlation of each area node, and arranges the sensors to monitor the whole water supply distribution network, thereby improving the effectiveness and superiority of sensor arrangement.

Drawings

Fig. 1 is a schematic flow chart of a water supply network leakage positioning sensor arrangement method based on a graph convolution network according to the invention.

Fig. 2 is a schematic diagram of the format of the data set according to the present invention.

FIG. 3 is a schematic diagram of a bidirectional long/short term memory network according to the present invention.

FIG. 4 is a schematic diagram of a memory cell structure of the bidirectional long-term and short-term memory network according to the present invention.

Fig. 5 is a schematic diagram of an Anytown network structure according to the present invention.

Fig. 6 is a column diagram of the hourly node demand coefficients of all nodes in Anytown according to the present invention.

FIG. 7 is a diagram illustrating the results of k-means clustering and pseudo-labeled nodes in Anytown according to the present invention.

Fig. 8 is a diagram illustrating a classification result of Anytown by the graph convolution network according to the present invention.

Fig. 9 is a schematic diagram of a monitoring node selected by the proposed method 2 in Anytown according to the present invention.

Fig. 10 is a schematic diagram of a monitoring node selected by the method 1 in Anytown according to the present invention.

Fig. 11 is a schematic network layout diagram of the complex network Net3 according to the present invention.

Fig. 12 is a bar chart of hourly node demand coefficients for all nodes in the Net3 according to the present invention.

FIG. 13 is a diagram showing the results of k-means clustering and pseudo label nodes in the Net3 according to the present invention.

Fig. 14 is a diagram illustrating the classification result of the graph convolution network of Net3 according to the present invention.

Fig. 15 is a schematic diagram of monitoring nodes selected by the method of the present invention in Net3 according to the present invention.

Fig. 16 is a schematic diagram of a monitoring node selected by the new semi-supervised method in Net3 according to the present invention.

Fig. 17 is a schematic diagram of a monitoring node selected by a conventional semi-supervised method in Net3 according to the present invention.

Detailed Description

The present invention is described in further detail below in order to enable those skilled in the art to practice the invention with reference to the description.

As shown in fig. 1, the method for arranging leakage positioning sensors in a water supply network based on a graph convolution network provided by the invention converts the problem of optimal arrangement of sensors in the water supply network under an unsupervised condition into the problem of regional division and node selection under a semi-supervised condition, and assumes that only three sensors are arranged in the water supply network, and comprises the following steps:

step one, creating a data set:

1. generation of the data set:

if real pipeline leakage data of a municipal water supply network is required to be acquired, pipeline nodes in certain areas of the water supply network need to be artificially damaged to acquire the data. Obviously, this practice has a serious impact on the personal life of the entire urban population. Therefore, the invention obtains the complete leakage data of the city through a hydraulic simulator. However, EPANET python wrapper WNTR version 0.3.1 would be used as the hydraulic simulator kit of the present invention to acquire complete leak data. WNTR contains EpanetSimulator and WNTRSimulator, which are used in the present invention. The simulator evaluates a specific water supply network leakage scenario by establishing a transient model. Since the simulator adds the leak to the water supply network by building a transient model, there is no need to adjust the transmitter coefficients to control the magnitude of the leak. The WNTRS simulator is used for modeling the leakage of the pipe network, outputting normal pressure P through the normal demand d of a water supply pipeline, and generating the leakage demand d after the leakage point is added into the water supply pipeline_lThereby generating an abnormal pressure-P_lGenerating a value Δ P of the pressure difference as a sum of the normal pressure and the abnormal pressure;

wherein the mass flow of fluid through the holes in the water supply network is represented as follows:

wherein d is_lTo leakage demand, C_dIn the case of the flow coefficient, α is an index relating to the leakage characteristic, i.e., a flow-rate-related index, p is the water pressure in the water supply pipe, ρ is the density of the fluid, and a is the area of the leakage mesh.

The area of the leakage mesh satisfies:

where D is the diameter of the leakage mesh.

If the water flow is turbulent and the steel pipe has a large amount of leakage, taking C_dFurther simplifying the above formula, α is 0.75 and α is 0.5, the indenter is defined as follows:

wherein H is the pressure head, p is the water pressure in the pipe, ρ is the density of the fluid, and g is the gravitational acceleration.

From the above two equations, an expression of the magnitude of the leakage flow can be derived and expressed as follows:

by using the data set established by the transient model, the establishment of the data set needs to be completed in two steps, including setting the position of the simulated leakage, the time of leakage simulation and the area of the leakage, and simulating the influence of the leakage amount on the pressure data through the established transient model. If a correct simulated leakage position is desired, first the pipe in the water supply network that simulates the leakage needs to be found; then, acquiring a starting node and an ending node of the pipeline through a WNTR tool packet, finding a leakage position to be simulated on the pipeline according to a set leakage position, adding nodes, connecting the nodes added to a water supply pipeline with a new pipeline, accessing the new pipeline into a network, controlling the size of leakage amount by setting the size of a simulated leakage area after determining the position of simulated leakage, and setting the time for the node to simulate leakage by using the WNTR tool packet after determining the leakage position and the leakage size; and finally, simulating the node to generate leakage through the established transient model, and running simulation.

In order to make the data generated by the simulated leakage more similar to the data under the actual pipeline leakage, and to eliminate the bad influence on data acquisition caused by different placement positions of the sensors for acquiring data, further processing needs to be performed on the data, including noise addition and standardization processing.

The data set is divided into a training data set and a testing data set, in order to simulate the situation in actual leakage, noise is randomly added to the training data set at a probability of 50%, noise is randomly added to the testing data set at a probability of 100%, and noise with a signal-to-noise ratio of 30db to 40db is added to both the training data set and the testing data set.

After the noise addition, the training data set and the test data set are normalized in the same way, which is expressed as follows:

in the formula (I), the compound is shown in the specification,

As shown in fig. 2, the created data sets (including the training set, the validation set, and the test set) are all generated in the above manner, and the generated data sets are all consistent in format, and are three-dimensional data, each dimension representing a different meaning:

the first dimension data represents values of pressure differences at each node with both leak events at the node and leak simulation time points determined;

the second dimension data represents the condition that the value of each node pressure difference changes along with the starting and stopping time of the leakage simulation in the case of the leakage event of the designated node;

the third dimension data represents the change of the pressure difference value corresponding to each node in different leakage simulation time under the leakage events of different nodes.

The size of the data set is determined by the self configuration (the number of nodes and the number of pipelines) of the water supply network, the time for simulating leakage and the size of the simulated leakage amount, when the data set is generated, the starting and ending time points of the simulated leakage and the leakage area of the simulated leakage are set by traversing all nodes with water supply requirements in a certain water supply network, and the pressure difference value of each node in the network is collected until a simulated leakage scene of the complete network is generated and is stored in the data set.

Step two, creating a pseudo label:

in real life, the leakage of a real water supply network is a situation where it is not known in advance, that is, for the network, the leakage label can not be known, in the invention, if the simulation of the leakage of the actual pipe network also does not know where the leakage occurs, i.e., the data set is free of leak signatures, however, to accomplish the task of optimal sensor placement in a water supply network, the data set must have at least one signature, therefore, all nodes (except a water tank, a water pump and a water storage tank) in a water supply network are gathered into K types (K represents the number of the arranged sensors) by using a K-means clustering algorithm, the node of each type closest to the clustering center of the type is respectively selected as the node for constructing the pseudo label, and the label is attached from 0 to K, so that the unsupervised problem is converted into a semi-supervised problem for further processing.

The K-means clustering algorithm is an unsupervised clustering algorithm, has good clustering effect and is simple to realize, so thatWidely used, this method is based on an optimized clustering criterion function F, which generally depends on the database C₁,C₂,...,C_kThe current area of the element is found using the sum of the distances between each element and its nearest cluster center as a clustering criterion, sometimes referred to as the square error criterion, and thus can be expressed by the following formula:

wherein, is₁,C₂,…,C_KIs a data set divided into K classes, K being the number of classes, K_iFor the number of sample points contained in the ith class, i is the number of class objects, w_ijIs the jth sample point in the ith class, w_iCentroid for class i, defined as:

in the formula (I)

Is the average of the i class centers;

the steps of the K-means clustering algorithm are as follows:

step 1: class K { C provided in a database₁,C₂,...,C_kSelecting an initialization area in a random mode, and calculating the clustering center (mass center) of each class;

step 2: and calculating the distance from any sample point to K cluster centers, and classifying the sample point into the cluster center class with the minimum distance.

And 3, step 3: sample w_iReassigned to its nearest cluster center, 1,2, …, K, j ≠ s for all j, if

Then w_i∈C_sFrom C_sMove to C_tThen recalculate the cluster center C_sAnd C_t；

And 4, step 4: until the squared error cannot be further reduced, and then stopping; otherwise, returning to the step 3.

Step three, division of monitoring areas:

the range of variation in pressure difference between adjacent nodes in a water supply network is generally similar. The graph convolution network is used as a characteristic extractor of the graph network, so that the characteristics among all nodes in the water supply network can be well extracted, the nodes are classified (namely all sample points are classified into K types), a data set with pseudo labels attached is input into the two layers of graph convolution networks for proper training, and the obtained output result is used as the basis for dividing the monitoring area of the water supply network;

convolutional Neural Networks (CNN) are applied to deal with regular networks, however, most of the data are presented in irregular forms, such as social networks, and therefore, Graph Convolutional Networks (GCN) are proposed, and graph data in the water supply network node classification task studied by the present invention are presented in irregular forms.

There are two approaches to graph convolution networks: spectroscopy and spatial methods. The basic idea of the graph convolution network based on the spectrum method is to realize graph convolution through a filter from the view point of graph signal processing; graph convolution networks based on spatial methods act on graphs using direct relationships between spatial nodes.

The graph convolution network operation based on spectroscopy is represented as follows:

g_θ(Λ)*x＝Ug_θ(Λ)U^Tx；

wherein x is vector representation of node attribute in the graph, and U is normalized graph Laplacian L ═ UΛ U^TΛ is a diagonal matrix of eigenvalues λ, U^TGraphic Fourier transform with x as x, g_θ(Λ) is a function of the eigenvalues of L.

Complexity of multiplication of eigenvalue function and eigenvector matrix for large graphsVery high, about o (N)²) Second, therefore, to simplify the operation, g_θ(Λ) may be represented by a K-order chebyshev polynomial

By a truncated expansion approach of, wherein

λ_maxIs the maximum eigenvalue of L, I_NIs an identity matrix, i.e.

Where θ' is ∈ R^KThe K-order Chebyshev coefficient vector is represented, so that the graph convolution network operation can be restated as;

wherein the content of the first and second substances,

since this expression is a polynomial of degree K, it is a local optimization that relies on the K neighborhood of the central node, which is linear in edge number, as can be seen from the above equation, on the basis of which K is 1 and λ_maxThe graph convolution network model is further simplified by 2, and a fast approximation expression is proposed:

is a matrix of the degrees, and the degree matrix,

is a self-circulating adjacency matrix;

wherein the degree matrix satisfies:

in the formula (I), the compound is shown in the specification,

a self-circulation matrix of the current node i;

the self-circulating adjacency matrix satisfies:

wherein A is an adjacent matrix, I_NIs an identity matrix.

And applying the formula to the graph G data with the attribute matrix X to perform multilayer graph convolution operation and perform layer-by-layer propagation.

Step four, selecting a representative node:

after the division of the monitoring area of the water supply network is completed, the node in each area can be the most representative node of the area, the nodes in each area are traversed through the algorithm of the cross-correlation function until all the nodes of the area are traversed once, and finally, one node which is most representative of the area is selected. And respectively traversing each region until all regions are traversed. The most representative nodes selected in each area are used as the nodes for arranging the sensors, that is, the selected most representative nodes are the nodes for arranging the sensors optimally.

The most representative node is the sample point with the maximum correlation sum with other sample points in the monitoring area where the node is located.

The cross-correlation function may reflect the degree of similarity, i.e. a measure of similarity, between two functions or data sets at different relative positions. The cross-correlation function is calculated differently for the continuous function and the discrete function.

Assuming f and g are two continuous functions, the cross-correlation function is defined as follows, given a time lag τ:

wherein f is^*(t) is the complex conjugate function of f (t);

assuming f and g are two discrete functions, the cross-correlation function is defined as follows, given a time lag τ:

thus, as can be seen from the above two equations, the cross-correlation function can measure the degree of similarity of the functions f (t) and g (t + τ).

Suppose (X)_t,Y_t) Representing a pair of stationary time series, the cross-correlation function of the two stationary time series is then as follows:

wherein, γ_X,Y(τ)＝E(X_t-μ_X)(Y_t+τ-μ_Y) Mu is the mean of the stationary time series and sigma is the standard deviation of the stationary time series as a cross-covariance function.

Suppose (X)_t,Y_t) Two stationary processes are represented, the cross-correlation function of which is as follows:

wherein the content of the first and second substances,

In the invention, a random stable process is performed among the nodes in the data set.

Step five, result evaluation:

the invention uses a simple built BilSTM neural network to complete the task of positioning the leakage of the water supply network. The trained classifier needs an index to measure how well it is trained, and the confusion matrix is used as a result of the classifier for verifying the test data set. The confusion matrix is typically a square matrix with equal number of rows and columns, equal to the number of nodes in the network (nodes used for leakage simulation). Ideally, the confusion matrix should be a diagonal matrix, i.e. the predicted values and the true values are identical, where each coefficient Γ on the diagonal is identical_a,aIndicating the number of times node a is correctly predicted to leak. In fact, non-zero values may appear on the off-diagonal of the confusion matrix, i.e. the prediction values are not the same as the true values, and prediction errors occur, where Γ_a,jIndicating the number of times the leak in node a is identified as a leak in node j. As can be seen from the above, the present invention,

indicating the number of times node a is mispredicted, where N indicates the number of nodes in the network. Therefore, the accuracy ACC of the classifier is used as an important indicator of the result evaluation, and its expression is as follows:

from the above, it is far from sufficient to use the accuracy as the evaluation index, because the accuracy is used to judge the classification effect of the classifier and cannot explain the quality of the leak location. Therefore, the Average Topological Distance (ATD) is used as the second evaluation index. ATD refers to the average topological distance between a real leaking node and a predicted leaking node. The expression is as follows:

wherein D is_a,jThe distance between the node a and the node j is expressed as the number of two-node connecting pipelines in the network.

In general, an important indicator for evaluating the error of the experimental result is the root mean square error, which is defined as follows:

the index can indicate the error of the average topological distance between the real leakage node and the predicted leakage node, so that the quality of the prediction result is further illustrated, and the index has important significance.

A Recurrent Neural Network (RNN) is a network in the context of data time. However, this structure has problems such as disappearance of the gradient and explosion of the gradient. Thus, Long Short Term Memory (LSTM) networks solve the RNN gradient vanishing or gradient explosion problem by adding a gate mechanism in each cell. The LSTM network may remember previous state information with the ability to predict sequence data. However, the LSTM network can memorize only the previous state information, and cannot memorize the subsequent state information. In the art, a bidirectional long short term memory (BilSTM) network has been proposed to solve this problem. The structure of the BiLSTM network is shown in fig. 3. The output of the current state is determined by the past state and the future state. Such as the last layer cell output y_nIs a function of the forward layer output and the backward layer output. The forward layer output is from the current input layer x_nPast forward layer output

And previous layer cell state

And (4) determining. Similarly, the backward layer output is from the current inputLayer x_nFuture backward layer output

And the next level cell state

And (4) determining.

Each memory cell serves as the core part of the BiLSTM network, wherein the structure of one memory cell of the BiLSTM is shown in fig. 4. Each memory cell is mainly composed of three control gates, including an input gate (middle dotted line portion), a forgetting gate (left dotted line portion) and an output gate (right dotted line portion). The operations in each control gate mainly include addition, multiplication, sigmoid, and tanh. Wherein sigmoid and tanh are two different activation functions, respectively expressed as follows:

the functional implementation of each memory cell is represented as follows:

firstly, the previous output h is output through a forgetting gate_t-1And the current input x_tPasses the result of the operation to the next memory location, and the forgetting gate determines whether the previous information is retained or cleared:

f_t＝σ(W_f·(h_t-1,x_t)+b_f)；

second, by inputting the gate vector i_tDetermining a temporary New State C_tFor current cell state C_tUpdating:

i_t＝σ(W_i·(h_t-1,x_t)+b_i)；

finally, the current output h_tBy outputting the gate vector o_tAnd current cell state C_tThe determined:

o_t＝σ(W_o·(h_t-1,x_t)+b_o)；

h_t＝tanh(C_t)×o_t；

The invention provides two embodiments, all experiments were run on a desktop computer using INTEL CORE i5-10400F CPU @2.90 GHz, 8 GB of RAM memory as well as a Windows 10Home 64bits OS. At the same time, Python 3.8 software was applied.

Example 1

As shown in fig. 5, the network consists of 16 nodes, 40 pipes, 1 water pump, 2 storage tanks and 1 reservoir. Table 1 gives the node attributes of the Anytown network; the pipe properties are listed in table 2; the pipe diameter is between 200 mm and 400 mm and the daily average demand is about 457.08 l/s. Different nodes are assigned different daily demand patterns. The hourly node demand coefficients for all nodes in Anytown are shown in fig. 6.

Table 1 node attributes for Anytown networks

TABLE 2 pipeline characteristics of an anytime network

Although there is no actual standard for water supply network leakage, it must be satisfied that the abnormal change in the node pressure caused by leakage is different from the normal pressure at the node when there is no leakage. In this case the simulated water flow to the surface is set to 7.88% of the daily average demand, i.e. the leakage is 36 litres/second for all nodes of the water supply network. The time sample for each leak event (each node leak) is 9 hours. The input to the present invention is a pressure differential matrix of size 19 x 171, where 19 represents the number of leak events and 171 represents the product of the time sample and the number of nodes for each leak event. Subsequently, the WDN (water supply network) is divided into several regions according to a K-Means clustering algorithm and the clustering center position of each region is calculated. As the value of K increases, the number of clusters increases from 1 to 4. No matter how many areas Anytown is divided, the clustering result can be conveniently obtained. And then finding the node closest to the position of the clustering center in each divided region by utilizing an Euclidean distance method to construct a pseudo label. In the present invention, the Anytown network in fig. 5 is divided into 2 areas and 1 pseudo tag is constructed in each area (see fig. 7). The pseudo-labeled data is then input into a 2-layer graph convolution neural network, and the training results are shown in fig. 8. Anytown is divided into 2 areas, consisting of 9 and 10 nodes. Each zone is composed of several adjacent nodes with similar pressure change laws. And finally, selecting monitoring nodes by utilizing the correlation of the nodes in each divided region, wherein the final aim of the sensor optimization arrangement problem is to deploy pressure sensors on the most representative nodes. A semi-supervised method and a deep learning method are adopted to select monitoring nodes. The monitoring nodes selected by the two methods are shown in fig. 9 and 10. Method one represents the deep learning method and method two represents the method proposed herein. As can be seen from fig. 9 and 10, the set of nodes selected by method 1 is {80, 110} and the set of nodes selected by method 2 is {140, 150 }. Different node sets are selected based on the two methods shown in fig. 9 and 10. As can be seen from fig. 8 and fig. 9 and 10, in an alternative method, the monitoring pressure sensors are respectively distributed at the edge portions of the divided regions. However, the monitoring pressure sensors selected by the second method are distributed more dispersedly among the divided regions than the distribution of the first method. In contrast to method one, method two can detect almost all leakage situations. The first method does not consider the correlation and redundancy between all nodes of the divided region. However, method two takes into account the correlation and redundancy between all nodes of each partitioned area in the water supply network. Therefore, compared with the first method, the second method is better for processing the problem of optimal arrangement of the sensors in the wireless communication network. Finally, the selected monitoring pressure sensor combination is subjected to leakage detection through a simple BilSTM neural network, so that the practicability of the two methods is verified. It should be noted that the size of the leak should be distributed as widely as possible under reasonable conditions, that is, the size of the leak should be distributed from small to large leaks within a reasonable range. Otherwise, the actual scene of pipeline leakage in the actual life cannot be met. In this case, the average water demand for the flow to surface simulation is in the range of 23 liters/second to 47 liters/second, and is added to all nodes of the water supply network at randomly sized intervals, and the leak conditions generated by each node of the training and test sets satisfy 4: 1, each node in the training set generates 120 leakage cases, and each node in the test set generates 30 leakage cases. The results of the BilSTM neural network are not particularly stable due to a series of data preprocessing of the training set. To overcome this problem, the data of the training set were preprocessed separately, for a total of 10 times. Accuracy, average topological distance, and RMSE were applied to evaluate the performance indicators of the two methods and are summarized in tables 3 and 4.

TABLE 3 ACC, ATD and RMSE results for Anytown based on method 1

TABLE 4 ACC, ATD and RMSE results for Anytown based on method 2

Data set	ACC	ATD	RMSE
					1	0.92	0.144	0.533
2	0.93	0.116	0.463
				3	0.92	0.137	0.509
4	0.92	0.135	0.518
				5	0.91	0.158	0.565
6	0.92	0.129	0.513
				7	0.91	0.149	0.538
8	0.92	0.146	0.541
				9	0.90	0.175	0.601
10	0.91	0.159	0.567
				Average	0.92	0.145	0.535

As can be seen from tables 3 and 4, the LSTM neural network leak detection result based on method 2 is more accurate than method 1, and is about 1.07 times higher. The value of ATD for method 1 is 1.84 times that of method 2, and the value of RMSE for method 1 is 1.46 times that of method 2. This means that, according to the experimental results of the above two methods, the longer the Average Topological Distance (ATD) between the predicted leak location and the actual leak location, the lower the stability of the predicted leak location.

Example 2

As shown in fig. 11, the network consists of 92 nodes, 117 pipes, 2 pumps, 3 tanks and 2 reservoirs. It is noted that in the prior art, some nodes are considered too close to the reservoir, tank or pump, such as the node set {10, 20, 40, 50, 60, 61, 601}, and therefore leakage from these nodes is not considered. However, in practical situations, a water supply network leak may also occur in close proximity to the reservoir, tank or pump. Therefore, all nodes in the water supply network should be taken into account. The daily average traffic of the network is approximately 3048.11L/s. The hourly node demand coefficients for all nodes in Net3 are shown in fig. 12.

The simulated water flow to the surface was set at 3.94% of the daily average demand, i.e. leakage was 120 l/s at all nodes of the water supply network. The time sample for each leak event (each node leak) is 640 hours. That is, the input pressure difference matrix size is 92 x 58880, where 92 represents the number of leak events and 58880 represents the product of the time sample and the number of nodes for each leak event. Subsequently, the Net3 water supply pipe network was divided into 4 regions according to the K-Means clustering algorithm and the cluster center position for each region was calculated. And then finding the node closest to the position of the clustering center in each divided region by utilizing an Euclidean distance method to construct a pseudo label. The Net3 network in fig. 11 is divided into 4 regions and 1 pseudo label is constructed in each region (as in fig. 13). The pseudo-labeled data is then input into a 2-layer graph convolution neural network, and the training results are shown in fig. 14. In fig. 14, adjacent nodes are respectively allocated to the same area. Furthermore, adjacent nodes share a common feature, that is, the pressure difference matrix is approximately the same.

And finally, selecting the monitoring node by utilizing the correlation of the nodes in each divided region. The selected combination of all nodes is as follows:

wherein N is_cFor all selected combinations of nodes, n_fFor the number of all nodes, n_sIs the number of nodes to be selected.

This is clearly not practical if several nodes are to be selected for pressure sensor placement using correlation from a water supply network having hundreds or thousands of nodes. For example, in Net3, n_f＝92，n _s4, then N_c2794155. However, only a small number of combinations of such many selected nodes are reasonably predictive of the occurrence of a leak. Therefore, it is very necessary to find the most representative node of each region using correlation among the divided regions. It can be found through experiments that each area can find a node which can represent all nodes in the area, that is, the discovered node has the greatest correlation with the rest nodes in the area. Therefore, as shown in fig. 15, the last selected node set of the proposed method is {105, 237, 169, 151 }. In addition adopt a novel halfThe supervised method and a conventional semi-supervised method select the set of nodes as {109, 119, 184, 229} and {109, 119, 149, 229} respectively, as shown in FIGS. 16 and 17.

For the 3 methods, the method provided by the invention can well cover all nodes of the whole water supply network, and realizes full coverage of the area. However, the conventional semi-supervised method has a regional monitoring dead zone, that is, there is no monitoring node in a certain region, which means that there is no node in a certain region that can represent all nodes in the region. As shown in fig. 17, there are no monitoring nodes in the 2 nd cluster area, and instead there are 2 monitoring nodes in the 3 rd cluster area to monitor the area, which may cause waste of resources. Although the new semi-supervised approach may enable monitoring of each area, the monitoring nodes in each area are distributed at the boundaries of the area, which may result in that an efficient monitoring cannot be achieved in a certain area. As shown in fig. 16, the monitoring nodes of the 0 th cluster area, the 2 nd cluster area and the 3 rd cluster area are all distributed on the boundary of the area, which may cause the invalidity of area monitoring.

To verify the utility of these 3 methods, the pressure difference matrix of the monitoring nodes was input to a simple LSTM neural network for leak detection. The average water demand for the flow direction surface simulation is in the range of 63 liters/second to 630 liters/second, and is added to all nodes of the water supply network at random sized intervals, and the leakage condition generated by each node of the training set and the test set meets 4: 1, each node in the training set generates 120 leakage cases, and each node in the test set generates 30 leakage cases. As in case one, the data from the training set was preprocessed separately for a total of 10 times. Accuracy, average topological distance, and RMSE were applied to evaluate the performance metrics of these 3 methods and are summarized in tables 5, 6, and 7.

ACC, ATD and RMSE results based on the novel semi-supervised method in Table 5 Net3

Results for ACC, ATD and RMSE based on the proposed methods in Table 6 Net3

Results for ACC, ATD and RMSE based on conventional semi-supervised methods in Table 7 Net3

As can be seen from tables 5, 6 and 7, the accuracy of the new semi-supervised method is 0.70, the average topological distance is 1.269 and the RMSE is 3.671. The accuracy of the traditional semi-supervised approach is 0.66, the average topological distance is 1.439 and the RMSE is 3.655. The accuracy of the proposed method is 0.72, the average topological distance is 0.892 and the RMSE is 2.601. It follows that the complexity of the water supply network Net3 is much higher than that of Anytown, which is the main reason for the reduced accuracy and the increased average topological distance and RMSE values.

The invention relates to a water supply network leakage positioning sensor arrangement method based on a graph convolution network, which is used for positioning leakage of nodes in a water supply network. In this method, a K-means clustering algorithm is applied to construct pseudo labels; then, inputting the nodes with the pseudo labels into a two-layer graph convolution network for training, and then finishing the classification of the nodes in the network; finally, the most representative nodes are selected by applying the correlation among the nodes to arrange the sensors. The effectiveness and the superiority of the method are verified by two networks of Anytown and Net3, and in example 1, the method and the genetic algorithm provided by the invention are analyzed from three aspects of ACC, ATD and RMSE. The result shows that the method provided by the invention is superior to the genetic algorithm in all indexes. In example 2, the method of the present invention and two other semi-supervised strategies are analyzed from three aspects of ACC, ATD and RMSE, and the result shows that the method of the present invention is slightly better than the semi-JMI method subjected to FCM preprocessing, and is far better than the conventional semi-JMI method without FCM preprocessing.

While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable to various fields of endeavor for which the invention may be embodied with additional modifications as would be readily apparent to those skilled in the art, and the invention is therefore not limited to the details given herein and to the embodiments shown and described without departing from the generic concept as defined by the claims and their equivalents.

Claims

1. A water supply network leakage positioning sensor arrangement method based on a graph convolution network is characterized by comprising the following steps:

2. The method of water supply network leak location sensor placement based on graph convolution network of claim 1, wherein the three dimensional data includes:

3. The method for positioning water supply network leakage sensors based on the graph convolution network as recited in claim 2, wherein the step one further comprises sequentially performing noise processing and normalization processing on the data set, wherein the noise processing comprises:

4. The method of water supply network leak location sensor placement based on graph convolution network of claim 3, wherein the normalization process satisfies:

in the formula (I), the compound is shown in the specification,

5. The water supply pipe network leakage positioning sensor arrangement method based on the graph convolution network as claimed in claim 4, wherein the K-means clustering algorithm in the second step specifically includes the following steps:

wherein the cluster center satisfies:

Is the average of the i class centers;

step 4, stopping clustering when the square error reaches the minimum value;

wherein the square error is:

6. The water supply network leakage localization sensor arrangement method based on the graph convolution network as claimed in claim 5, wherein the graph convolution network satisfies:

is a matrix of the degrees, and the degree matrix,

is a self-circulating adjacency matrix;

wherein the degree matrix satisfies:

in the formula (I), the compound is shown in the specification,

a self-circulation matrix of the current node i;

the self-circulating adjacency matrix satisfies:

wherein A is an adjacent matrix, I_NIs an identity matrix.

7. The water supply network leakage localization sensor arrangement method based on the graph convolution network as claimed in claim 6, wherein the cross correlation function algorithm in the fourth step satisfies:

in the formula (I), the compound is shown in the specification,

8. The water supply network leak location sensor placement method based on graph convolution network of claim 7, further comprising:

the accuracy satisfies:

the average topological distance satisfies:

the root mean square error of the average topological distance satisfies:

where RMSE is the root mean square error of the mean topological distance.

9. The arrangement method of the water supply pipe network leakage positioning sensor based on the graph convolution network as claimed in claim 8, wherein the storage unit of the bidirectional long and short term memory network is composed of an input gate, a forgetting gate and an output gate, and the method specifically comprises the following processes:

f_t＝σ(W_f·(h_t-1,x_t)+b_f)；

i_t＝σ(W_i·(h_t-1,x_t)+b_i)；

is a temporary new state, W_cWeight matrix modified for cell state, b_cOffset value modified for cell state, C_tIs a current billA meta-state, tanh (·) represents the activation function by tanh;

the current output satisfies:

o_t＝σ(W_o·(h_t-1,x_t)+b_o)；

h_t＝tanh(C_t)×o_t；