CN116542001A - Water supply network independent metering partitioning method based on improved spectral clustering and genetic algorithm - Google Patents
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Abstract
An independent metering partition method of a water supply network based on improved spectral clustering and genetic algorithm belongs to the technical field of urban water supply network design, and solves the problem of optimizing DMA partitions of the water supply network by adopting the improved spectral clustering and genetic algorithm; the invention combines the topological structure information and the running condition information of the water supply network, improves the quality of the similarity graph, optimally divides the sample space with any shape by adopting improved spectral clustering, and obtains the partition layout with the least influence on the hydraulic performance; the genetic algorithm is adopted to solve the problem of arrangement of the flowmeter and the valve, and an arrangement scheme under the condition of optimal economy can be obtained by setting the minimum flowmeter number; through verification, the water supply network after DMA partitioning is greatly improved in indexes such as the quantity of boundary pipe sections, water demand uniformity and the like.
Description
Technical Field
The invention belongs to the technical field of urban water supply network design, and relates to an independent metering and partitioning method for a water supply network based on improved spectral clustering and genetic algorithm.
Background
Along with the rapid development of the urban process, the huge economic loss and negative social effect caused by the water supply network leakage problem are increased, the water supply network leakage problem is more and more valued by society, and meanwhile, the water supply network leakage problem is a great difficulty to be solved urgently. The practice of many years at home and abroad proves that the water supply network DMA (District Metering Area) technology has become one of the water supply network leakage control technologies according to the advanced management mode and the immediate leakage control performance. Because the topology of the water supply network is complex, the leakage points are not easy to be probed and repaired, the pressure optimization operation of the DMA partition is realized, and the establishment of the pressure optimization control system of the DMA partition is the best method for reducing the leakage quantity under the current water supply pipeline condition.
DMA partition development is divided into two major categories, namely an empirical partition method and an intelligent algorithm automatic partition according to the development process, and the specific description is as follows: the experience partitioning method is that a manager carries out manual partitioning based on familiarity of a water supply network, and the experience partitioning method can be divided into a direct partitioning method and an indirect partitioning method according to whether a hydraulic model is used or not; the object of the empirical partitioning method is mostly a simple small-sized water supply pipe network, and the subjective components of the partitioning result are more, but the empirical partitioning method cannot meet the requirement of large-sized water supply partitioning because the running condition of all pipe networks cannot be completely known by experience for large-sized annular pipe networks with complex structures. In recent years, researchers at home and abroad try to introduce an intelligent algorithm into DMA partition, and an intelligent algorithm automatic partition method enables a pipe network partition scheme to be scientific and dependent, and according to different methods and purposes, the algorithm can be automatically classified into the following categories: 1) A water supply dividing line method, namely, the water supply area of each water source can be regarded as a collection of all directional paths flowing out from the water source, so that the division of the water supply areas with multiple water sources is realized; 2) The community structure method is to equivalently convert a complex water supply network into a complex network based on a community structure to perform cluster analysis, and perform DMA cluster partition on local aggregation relations of the connection side relations in the network; 3) Single-objective or multi-objective optimization algorithm partitioning, namely an optimization partitioning method for single or multiple objectives such as water supply network hydraulic optimization and economic factors; 4) According to the graph theory-based method, an actual water supply network is equivalent to an undirected weighted topological graph, nodes of the undirected topological graph of the network are divided by adopting different methods to obtain DMA partitions, and a plurality of researchers study the method.
Disclosure of Invention
The method is used for solving the problem of optimizing the DMA partition of the water supply pipe network by adopting an improved spectral clustering and genetic algorithm.
The invention solves the technical problems through the following technical scheme:
as shown in fig. 1, the water supply network independent metering and partitioning method based on improved spectral clustering and genetic algorithm comprises the following steps:
1. establishing a water supply network micro hydraulic model in EPANET software, acquiring a water supply network topological structure, node water demand, elevation attribute and node coordinate position by calling an EPANET toolbox, and constructing an adjacency matrix capable of reflecting the water supply network topological structure
(1) Importing topological relation and pipe fitting operation parameters of a water supply network into EPANET software, and establishing a water supply network micro hydraulic model, wherein the water supply network node set is V= { V 1 ,v 2 ,v 3 ......v N Pipe segment set l= { L } 1 ,l 2 ,l 3 ,...,l M }。
(2) Calling an EPANET toolbox, and performing hydraulic analysis to obtain the coordinate position of the node of the water supply networkNode water demand q 1 ,q 2 ,...,q N ]Elevation attribute [ r ] 1 (3) ,r 2 (3) ,...,r N (3) ]Pressure attribute [ H ] 1 ,H 2 ,...,H N ]。
(3) Constructing an adjacency matrix capable of reflecting the topology structure of the water supply network according to the node v i and vj With or without directly connected pipesAnd (3) carrying out quantization into a natural neighbor relation of the nodes, wherein the formula is as follows:
and obtaining an adjacent matrix A of the equivalent undirected connection diagram of the water supply network by the natural adjacent relation among the nodes, wherein the adjacent matrix A is in the following form:
wherein ,Aij Representing node v i and vj Natural neighbor relation of s ij Representing the connection relationship of two nodes, if A ij 1, then represents node v i and vj Directly connected, namely, are natural adjacent nodes; if A ij 0, then represents node v i and vj Are not directly connected, i.e., are not natural neighbor relationships.
2. Constructing a node similarity matrix by utilizing the coordinate position and the elevation attribute of the nodes of the water supply network, and constructing a water demand similarity matrix by utilizing the adjacent matrix and the water demand of the nodes
2.1, the method for constructing the node similarity matrix by utilizing the coordinate positions and the elevation attributes of the nodes of the water supply network specifically comprises the following steps:
(1) And (2) positioning coordinates of nodes of the water supply network obtained in the step (1)Elevation attribute r 1 (3) ,r 2 (3) ,...,r N (3) ]Combining into node attribute feature matrix->
wherein ,hi An attribute feature vector formed by the ith node of the water supply network; r is (r) i (1) Is h i Column 1 of the table, represents the abscissa in the position coordinates of the ith node; r is (r) i (2) Is h i The 2 nd column value ofRepresenting the ordinate in the position coordinates of the ith node; r is (r) i (3) Is h i Column 3 of the table, represents the elevation of the ith node.
(2) The selected node attribute feature matrix H is standardized, the mean value of the processed data is 0, the standard deviation is 1, and the conversion formula is as follows:
wherein ,ri (t) For the ith row vector H in the node attribute matrix H i T-th value, mu t For the mean value, sigma, of all values in the t-th column of the node attribute matrix H t Standard deviation of all values of the t-th column in the node attribute matrix H;
the standardized node attribute matrix H' is:
wherein ,h'i For the ith row vector H in the node attribute matrix H i Normalized results.
(3) The ith row vector H 'in the normalized node attribute matrix H' i And the j-th row vector h' j The Euclidean distance calculating method is as follows:
wherein ,h'i ,h' j Respectively representing the ith row and the jth row vectors in the matrix H';
the Euclidean distance values among the row vectors in the matrix H' are calculated in sequence and form a vector D as follows:
wherein ,/>
(4) Establishing a node similarity matrix W based on a Gaussian kernel function by utilizing each element in the vector D 1 Gaussian kernel transformation formula and matrix W 1 The form is as follows:
wherein ,a ij for node similarity matrix W 1 The element value of the ith row and jth column of the vector D, std (D) is the standard deviation of all elements in the vector D, and the calculation formula of std (D) is as follows:
2.2, the method for constructing the water demand similarity matrix by utilizing the water demand of the adjacent matrix and the nodes is specifically as follows:
(1) Summing all columns of adjacent matrix A of water supply network micro hydraulic model to obtain degree z of each node ii ，z ii Can also be understood as the node v in the water supply network i The total number of directly connected pipe sections exists, and then the water supply network degree matrix degV is formed as follows:
wherein ,
(2) According to the water demand q of each node of the pipe network 1 ,q 2 ,...,q N ]And a water supply pipe network degree matrix degV, calculating adjacent nodes v of the water supply pipe network i and vj Similarity b of water distribution requirements between ij Thereby forming a water demand similarity matrix W 2 The following are provided:
wherein ,b ij for node similarity matrix W 2 Element values of the ith row and the jth column of the table; q i ,q j Respectively is a water supply network node v i and vj Water demand size.
3. Adding the node similarity matrix and the water demand similarity matrix to obtain an edge weight matrix, inputting the edge weight matrix into an improved weighted spectrum clustering algorithm to generate DMA configuration, and determining a DMA partition boundary pipe section set
As shown in fig. 2, the main steps of the clustering phase are as follows:
(1) In order to reflect the similarity of the nodes in the water supply network more truly, a node similarity matrix W 1 Similarity matrix with water demand W 2 Adding to obtain an edge weight matrix W, wherein the form of the edge weight matrix W is as follows:
wherein w is ij ＝a ij +b ij ，w ij The element value of the ith row and the jth column in the node similarity matrix W is obtained; a, a ij For node similarity matrix W 1 The element value of the ith row and jth column of (b) ij Is a water demand similarity matrix W 2 The element value of the ith row and jth column of the table.
(2) Defining the elements on the main diagonal of the diagonal matrix Y as the sum of the j-th columns of the edge weight matrix W, and the diagonal matrix Y is in the form as follows:
wherein ,
(3) Obtaining a standardized Laplace matrix L by using an edge weight matrix W and a diagonal matrix Y sym The following are provided:
due to the normalized Laplace matrix L sym Is a semi-positive definite matrix, when normalized to the Laplace matrix L sym When the eigenvalue decomposition is performed, the matrix can be obtained to have N non-negative real eigenvalues 0=λ 1 ≤λ 2 ≤…≤λ N 。
(4) Based on the N-cut graph cutting mode, accurate and stable clustering effect can be obtained by adopting multi-path division, and a standardized Laplace matrix L is calculated sym Corresponding first k minimum eigenvalues { lambda } 1 ,λ 2 ,…,λ k Corresponding feature vector u 1 ,u 2 ,...,u k And then forms a matrix U, the form is as follows:
wherein ,ux For standardizing Laplace matrix L sym The feature vector corresponding to the x-th value of the first k minimum feature values, i, j=1, 2,..n; x=1, 2,..k.
(5) The matrix U is normalized, and the normalized matrix U' is in the following form:
wherein ,u' ix representing the value U of the ith row and the xth column elements of the matrix U ix Normalized results.
(6) The matrix U' can be regarded as a set of N row vectors (o 1 ,o 2 ,o i ,...,o N ) T (i=1, 2,., N), each row vector o is calculated using the K-means algorithm i (i=1, 2,3,) N categorizes into k clusters (C 1 ,C 2 ,C f ..,C k ) In C f Representing a set of all row vectors belonging to class f.
(7) If set (o) 1 ,o 2 ,o i ,...,o N ) T (i=1, 2,.,. N.) the i-th row element is classified as the f-th cluster, then the pipe network node v corresponding to the original data i Also classified as the f-th region; outputting DMA configuration and determining boundary pipe segment set B= (G) composed of connected pipe segments among k independent areas 1 ,G 2 ,...G Nec ) Where Nec represents the total number of inter-DMA boundary pipe segments and G represents the boundary pipe segment index.
4. Optimizing flowmeter and valve arrangement in boundary pipe segment set through genetic algorithm to finally finish DMA partition of water supply pipe network
As shown in fig. 3, the main steps of the partitioning phase are as follows:
(1) In order to divide a complex water supply network into a plurality of independent areas to isolate the areas and measure the flow rate respectively, a set b= (G) of border tube segments is needed 1 ,G 2 ,...G Nec ) A valve or a flowmeter is arranged on the upper part; firstly, determining the length of codes according to the total number Nec of elements in the boundary pipe section set B, specifically to each pipe section, and if a flowmeter is arranged for a certain boundary pipe section, the codes corresponding to chromosomes are binary number 1; conversely, if a valve is placed in the border segment, the binary number corresponding to the chromosome code is 0, so a binary chromosome sequence I in the genetic algorithm is defined as follows:
I＝(g 1 ,g 2 ,...g Nec), wherein ,
meanwhile, in order to reduce the solution space of the genetic algorithm and minimize the DMA implementation budget, first, the total number of flowmeters Nfm =k inserted into the water supply network is defined, where k is the set number of DMA partitions, that is, only k 1 s exist in a set of binary chromosome sequences I of the genetic algorithm are limited here, and the rest positions are 0.
(2) The objective function is to maximize the power P dissipated by the water supply network node, so the fitness function F of the genetic algorithm is defined as the inverse of the objective function:
wherein gamma is the specific gravity of water, r i (3) ,H i ,q i Respectively representing the elevation, pressure and water demand data of the ith node after the valve and the flowmeter are arranged on the boundary pipe section set of the water supply network.
(3) Initializing population scale C and crossover probability P of genetic algorithm cro Probability of variation P het And sets an algorithm termination condition: maximum algebra J, convergence threshold T thr The method comprises the steps of carrying out a first treatment on the surface of the Meanwhile, the optimal solution output by the genetic algorithm also needs to meet the node pressure constraint conditions as follows:
H min ≤H i ≤H max
wherein ,Hmin Minimum service water pressure for node, H max For the highest allowable water pressure of the node, H i And (3) obtaining pressure data of each node for the hydraulic operation of the water supply network under the arrangement scheme of the valve and the flowmeter corresponding to the current solution.
(4) The flow meter and valve arrangement problem optimizing arrangement flow is as follows:
A. initializing a population, and randomly generating C binary chromosome sequences I, namely generating C individuals as an initial parent population;
B. calling an EPANET toolbox to generate a DMA partition result under a certain body code sequence corresponding arrangement scheme, and performing hydraulic analysis to obtain the elevation [ r ] of a node under the current DMA partition 1 (3) ,r 2 (3) ,...,r N (3) ]Water demand [ q ] 1 ,q 2 ,...,q N ]And pressure [ H ] 1 ,H 2 ,...,H N ]Data by fitness functionF, calculating to obtain the fitness value of the individual. Sequentially calculating the individual fitness value of the parent population C, and judging whether the algorithm termination condition (the maximum iteration number J is reached or the convergence threshold T is met thr ) If not, jumping to c; if yes, jumping to d;
C. selecting individuals to perform crossover and mutation operations according to the fitness function value of the individuals of the parent population C to generate offspring, and returning the generated offspring population as the parent population to b for next generation evolution;
D. if the current solution of the algorithm operation output does not meet the node pressure constraint condition, increasing the number of arranged flowmeters by one, namely Nfm = Nfm +1, returning to S2 after changing the chromosome coding form of the genetic algorithm, and recalculating the optimal solution under the newly increased number of flowmeters; and if the result obtained by the operation of the algorithm meets the node pressure constraint condition or reaches the maximum iteration frequency Nec-Nfm (namely, flowmeters are arranged on all boundary pipe sections), stopping calculating, outputting an optimal individual, obtaining an optimal arrangement mode of the flowmeters and valves in the corresponding boundary pipe section set, and finally finishing DMA planning.
The invention has the advantages that:
(1) According to the invention, a micro hydraulic model of the water supply network is built in the EPANET software, and the topology structure, the water demand of nodes, the elevation and the coordinate parameters of the water supply network are obtained by calling the EPANET toolbox; constructing coordinates and elevation parameters of pipe network nodes to form a node attribute feature matrix, standardizing, calculating Euclidean distance between the standardized node attribute feature matrix rows, and obtaining a node similarity matrix of the water supply pipe network through Gaussian kernel transformation; meanwhile, constructing a water demand similarity matrix of the water supply network by combining the network topology structure and the water demand parameters of the network nodes; adding the node similarity matrix and the water demand similarity matrix to obtain an edge weight matrix, inputting the matrix into an improved weighted spectrum clustering algorithm to generate DMA configuration, and determining a DMA partition boundary pipe section set; determining the optimal arrangement scheme of the water meter and the valve in the boundary pipe segment set by utilizing a genetic algorithm, and finally completing DMA partition; according to the invention, the quality of the similarity graph is improved by combining the topological structure information and the running condition information of the water supply network, and the improved spectral clustering is adopted to optimally divide the sample space with any shape, so that the partition layout with the least influence on the hydraulic performance is obtained; the genetic algorithm is adopted to solve the problem of arrangement of the flowmeter and the valve, and an arrangement scheme under the condition of optimal economy can be obtained by setting the minimum flowmeter number. Through verification, the water supply network after DMA partitioning is greatly improved in indexes such as the quantity of boundary pipe sections, water demand uniformity and the like.
(2) The literature (Liang Junqing, hole-driving, hydropower science, 2022,40 (1): 4.) discloses a water supply network DMA partitioning scheme based on a spectral clustering and evaluation mechanism, but the literature only utilizes node connection distances to form a similarity graph based on graph theory, and weights of connection edges of the similarity graph are used for constructing a similarity matrix through Gaussian kernel transformation, but the literature ignores the attributes such as elevation, water demand, coordinates and the like of nodes, and the similarity graph formed based on graph theory cannot completely describe the similarity relationship between the water supply network nodes due to the lack of the attributes. Therefore, the clustering result obtained by the weighted spectral clustering algorithm of the similarity matrix among nodes formed based on the lack of the similarity graph information has poor hydraulic performance (such as overhigh water demand uniformity) and high cost (such as a large number of boundary pipe sections). According to the invention, the water supply network is characterized by combining the physical properties and the hydraulic properties of the nodes, and the quality of the similarity graph is improved by mutually fusing the water demand, elevation, coordinate properties and nearest neighbor relations of the nodes of the water supply network, so that an accurate similarity matrix is constructed to balance the demand difference of the number of the nodes and the water supply quantity in the DMA partition. Secondly, the document does not consider the optimal arrangement scheme of valves and flow meters on the boundary pipe section, and the DMA implementation scheme needs to install flow meters on the DMA boundary pipe section of the water supply pipe network part to measure inflow and outflow, and install valves on the rest DMA boundary pipe section to isolate DMA, and related equipment is not installed, so that a complete DMA partition result cannot be formed. According to the invention, by arranging the valve and the flowmeter on the DMA boundary pipe section of the water supply network, the areas can be isolated from each other, the network can be protected from malicious pollution events, and the minimum night flow monitoring limit value of each DMA area of the water supply network can be determined by utilizing long-term continuous monitoring data so as to assist in judging newly increased leakage points.
(3) The Chinese patent application document with application publication number of 2021, 8-month and 17-day and application publication number of CN113312735A discloses a DMA partitioning method of an urban water supply network, but the patent document only utilizes the product of pipe diameter, flow and length attributes of the pipe section of the water supply network to define similarity, and related attributes of water supply network nodes are not considered, and the lack of the attributes can cause that a similarity graph based on graph theory cannot fully represent the similarity relationship between the water supply network nodes, so that the constructed similarity matrix cannot well reflect the similarity between clustering samples (water supply network nodes), and further influence the reliability of the subsequent spectral clustering algorithm result. According to the invention, the water supply network is characterized by combining the physical properties and the hydraulic properties of the nodes, and the quality of the similarity graph is improved by mutually fusing the water demand, elevation, coordinate properties and nearest neighbor relations of the nodes of the water supply network, so that an accurate similarity matrix is formed, the nodes are more close to the physical properties and the diversity of water demands of the nodes of the water supply network, and a foundation is laid for subsequent subareas. Second, the patent document optimizes the device placement scheme of the DMA boundary pipe segments using a multi-target particle swarm algorithm. The multi-objective particle swarm algorithm is good at handling continuously varying variables, but the optimization problem for discontinuous variables is poorly handled and is prone to falling into a locally optimal solution. The genetic algorithm not only can solve the problems of nonlinearity and discontinuity, but also has higher convergence rate, higher optimizing precision and stronger global optimizing capability. The problem of valve and flowmeter arrangement on the DMA boundary pipe section is the optimal solution searching problem of a group of discontinuous variables, so that the optimal arrangement scheme of the water meters and the valves in the boundary pipe section set is determined by utilizing a genetic algorithm, the algorithm running speed is high, and the optimal solution with high hydraulic performance can be searched.
(4) In addition, both documents use a k-means-based spectral clustering algorithm, which has the problem that clustering easily falls into a locally optimal solution. K-means is not sufficiently sensitive to outliers, which makes outlier data have a large impact on its algorithmic process. K-means is an optimization and improvement algorithm for K-means, the K-means algorithm selects actual data samples to replace the K-means algorithm to use sample mean values as clustering center points, and the rest data are divided into clusters nearest to the K-means according to Euclidean distance, so that influence of certain isolated data on a clustering process is reduced. According to the invention, the k-means-based spectral clustering algorithm is used for carrying out DMA preliminary partitioning, and from the DMA preliminary partitioning result, the k-means-based spectral clustering algorithm can balance the number of nodes in the DMA partition and obtain a clustering scheme with the minimum number of boundary pipe sections between the DMA, so that the optimal DMA preliminary partitioning result is obtained.
Drawings
FIG. 1 is a flow chart of the water supply network independent metering and partitioning method based on improved spectral clustering and genetic algorithm of the invention;
FIG. 2 is a flow chart of a clustering stage of the water supply network independent metering and partitioning method based on improved spectral clustering and genetic algorithm of the invention;
FIG. 3 is a flow chart of the partitioning phase of the independent metering partitioning method of the water supply network based on the improved spectral clustering and the genetic algorithm;
FIG. 4 is a pipe network model of an embodiment of a water supply network independent metering and partitioning method based on improved spectral clustering and genetic algorithm of the present invention;
FIG. 5 is a graph of a pipe network model subjected to spectral clustering according to an embodiment of the water supply network independent metering and partitioning method based on improved spectral clustering and genetic algorithm of the present invention;
FIG. 6 is a final DMA partitioning diagram of a pipe network model of an embodiment of a water supply network independent metering partitioning method based on improved spectral clustering and genetic algorithm of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The technical scheme of the invention is further described below with reference to the attached drawings and specific embodiments:
example 1
As shown in fig. 4, a water supply network of a certain city is selected as an experimental study object. The pipe network consists of 268 water-requiring nodes, 4 water-supplying reservoirs and 317 connecting pipe sections, wherein the total water-requiring amount is 406.94L/s, the minimum value of the elevation of the water-requiring nodes is 30.39m, the maximum value is 41.83m, and the minimum service water pressure of the pipe network is 14m. The water supply network has a complex network structure and can simulate an actual water supply network well. The partition number k of the water supply network is determined to be 4 according to comprehensive consideration of partition purposes, system scale, partition size, cost and the like.
The embodiment discloses an independent metering and partitioning method for a water supply network based on improved spectral clustering and genetic algorithm, which specifically comprises the following steps:
step 1, importing topological relation and pipe fitting operation parameters of an actual water supply network into EPANET software, and establishing a microscopic hydraulic model of the actual water supply network, wherein the number of water-requiring nodes of the water supply network is N=268, and the number of pipe sections is M=317; calling an EPANET toolbox, performing hydraulic analysis, and acquiring pipe network topological structure information and running condition information, wherein the pipe network topological structure information comprises an adjacent matrix of a water supply pipe network and position coordinates, elevation, water demand and pressure data of each node, and the hydraulic analysis method comprises the following specific steps:
the adjacent matrix form of the equivalent undirected connection diagram of the water supply network is as follows:
calling the EPANET toolbox to obtain position coordinates, elevation, water demand and pressure data of each node of the water supply network, wherein the data are displayed as follows in a table:
step 2, combining the water supply network topological structure and the network node parameter data to obtain a node similarity matrix and a water demand similarity matrix through calculation, wherein the specific steps are as follows:
2.1, combining the node position coordinates and the elevation data into a node attribute feature matrix H, wherein the matrix form is as follows:
the selected node attribute feature matrix H is standardized, and the obtained node attribute matrix H' is:
sequentially calculating an ith row vector H ' in the normalized node attribute matrix H ' ' i And the j-th row vector h' j The euclidean distance between them, the composition vector is as follows:
D＝[0.1645 0.5644 1.2443... 0.5848] 1×35778
the elements in the vector D are transformed by a Gaussian kernel to establish a node similarity matrix W 1 The matrix form is as follows:
2.2, calculating the degree d of each node according to the adjacency matrix A of the microscopic hydraulic model of the water supply network ii ，d ii It can also be understood that the total number of pipe sections directly connected with the node vi in the water supply network is calculated according to the water demand q of each node of the network i Degree d of each node of water supply network ii Calculating the node v of the water supply network i and vj Similarity b of water distribution requirements between ij Thereby forming a water demand similarity matrix W 2 The matrix form is as follows:
step 3 of the method, in which the step 3,matrix W of node similarity 1 Similarity to demand matrix W 2 Adding to obtain an edge weight matrix, inputting the matrix into an improved weighted spectral clustering algorithm to divide a water supply network into k clusters, dividing each node in a corresponding water supply network node set V into k areas, and obtaining each DMA boundary tube segment set B, wherein the method comprises the following steps of:
3.1, in order to reflect the similarity of the nodes in the water supply network more truly, adding the node similarity matrix and the water demand similarity matrix to be used as an edge weight matrix W, wherein the calculation formula is as follows:
3.2, defining a diagonal matrix D, wherein elements on main diagonal lines of the diagonal matrix D are the sum of all values of the ith column of the edge weight matrix W, and the formed diagonal matrix is as follows:
3.3, obtaining a standardized Laplace matrix by using the edge weight matrix W and the diagonal matrix D according to the following formula:
due to the normalized Laplace matrix L sym Is a semi-positive definite matrix, when normalized to the Laplace matrix L sym When the eigenvalue decomposition is carried out, N nonnegative real eigenvalues of the matrix can be obtained;
3.4, based on the N-cut graph cutting mode, adopting multi-path division to obtain accurate and stable clustering effect, and calculating a standardized Laplace matrix L sym The feature vectors corresponding to the first 4 minimum feature values {0,0.0039,0.0062,0.0089} further form a matrix u= (U) 1 ,u 2 ,u 3 ,u 4 )。
3.5, normalizing the matrix U to obtain a matrix U ', wherein the normalized matrix U' is as follows:
3.6, the matrix U' can be seen as a set of N row vectors (o 1 ,o 2 ,o i ,...,o N ) T (i=1, 2,., N), each row vector N is calculated using the K-means algorithm i (i=1, 2,3,) N groups into 4 clusters (C 1 ,C 2 ,C 3 ,C 4 ) In (a) and (b);
3.7 if set (o) 1 ,o 2 ,o i ,...,o N ) T I-th row in (i=1, 2,., N) is classified as f-th, then pipe network node v corresponding to the original data i Also classified as class f. The algorithm results output DMA configuration and determine the boundary pipe segment set in the partition as follows:
B＝(153,273,206,254,272,58,156,166,191,85,160,1,178,247,23,116,178,147) 1×17
wherein, each element in the set B is a boundary pipe section index, at this time, the total number of DMA time boundary pipe sections is 17, and the DMA configuration visualization result is shown in fig. 5.
And 4, coding boundary pipe sections of the water supply network in a binary coding mode to maximize power P dissipated by nodes of the water supply network as an objective function, searching an optimal arrangement scheme of valves and flow meters on a boundary pipe section set by using a genetic algorithm under the condition of meeting hydraulic constraint of the water supply network, and finally completing DMA partition planning, wherein the method comprises the following specific steps of:
4.1 in order to divide a complex water supply network into several independent areas to isolate the areas and measure the flow respectively, it is necessary to collect b= (153,273,..147) at the border tube segment 1×17 The valve and the flowmeter are arranged on the valve, the binary codes are respectively corresponding to 0 and 1, and the length of the code is 17 according to the quantity Nec=17 of the boundary pipe section set, so that a group of binary chromosome sequences is defined as I= (g) 1 ,g 2 ,...g 17 ) The number of flowmeters arranged in the set of boundary pipe segments is preset at the same time to be DMA number Nfm =4.
4.2, the objective function is to maximize the power Z dissipated by the water supply network node, so the fitness function of the genetic algorithm is defined as the inverse of the objective function:
wherein gamma is the specific gravity of water, r i (3) ,H i ,q i Respectively representing the elevation, the pressure and the water demand of the ith node after the valve and the flowmeter are arranged on the boundary pipe section set of the water supply network.
4.3, initializing population size of genetic algorithm C=50, crossover probability P cro =0.8, probability of variation P het =0.08, and sets an algorithm termination condition: maximum genetic algebra j=100, convergence threshold T thr ＝1×10 -6 . Meanwhile, the optimal solution output by the genetic algorithm also needs to meet the node pressure constraint condition H i ≥H min ＝14m：
4.4, the operation steps for solving the problems of flowmeter and valve arrangement based on a genetic algorithm are as follows:
a. initializing a population, and randomly generating a C=50 individual code sequence as an initial parent population;
b. calling an EPANET toolbox to generate a DMA partition result under a certain body code sequence corresponding arrangement scheme, and performing hydraulic analysis to obtain the elevation [ r ] of a node under the current DMA partition 1 (3) ,r 2 (3) ,...,r N (3) ]Water demand [ q ] 1 ,q 2 ,...,q N ]And pressure [ H ] 1 ,H 2 ,...,H N ]And calculating the data through a fitness function F to obtain the fitness value of the individual. Sequentially calculating fitness values of the parent population C=50 individuals, judging whether algorithm termination conditions are met, and if not, jumping to the step C; if yes, jumping to d;
c. selecting individuals to perform crossover and mutation operations to generate offspring according to the fitness function value of the parent population C=50 individuals, and returning the generated offspring population as the parent population to b for next generation evolution;
d. if the solution obtained by the operation of the algorithm does not meet the node pressure constraint condition, nfm = Nfm +1 is returned to S2, and the optimal solution under the current flowmeter number is recalculated; if the result obtained by the operation of the algorithm meets the constraint condition, stopping calculation, outputting an optimal individual, obtaining an optimal arrangement mode of the flowmeter and the valve in the corresponding boundary pipe section set, and finally finishing DMA planning.
As shown in fig. 6, after the first run is finished, the algorithm finds that the solution satisfying the current flow meter cannot be found, at this time, the number of flow meters is increased by 1, and the first iteration is started, namely, the individual chromosome codes in the initial parent population are defined as the combination of Nfm =5 flow meters and Nec-Nfm =12 valves, the genetic algorithm is restarted, and the optimal solution under the newly increased number of flow meters is searched; since the algorithm still does not meet the pressure constraint condition after the second operation is finished, the second iteration is started, finally, we find that when the number of flowmeters is set to be 6 in the chromosome coding of the genetic algorithm and the number of valves is 11, the hydraulic constraint condition is met, the corresponding optimal chromosome sequence is output, and finally, the DMA partition planning is completed. Fig. 6 shows the optimal DMA layout iteratively determined using genetic algorithms, while showing the placement of valves and flow meters in the set of border tube segments and the resulting topology changes of the water supply network are clearly visible in the figure.
Compared with the traditional clustering algorithm, the method has the advantage that the method can optimally divide the sample space with any shape. Because the graph is input into a spectral clustering algorithm, the quality of the graph has direct influence on a clustering result to a great extent, and how to construct a high-quality similarity graph is a key of whether the spectral clustering can obtain a good clustering result. The genetic algorithm is an adaptive artificial intelligence technology, is mainly optimized based on an objective function and calculation constraint, and is very suitable for discrete and nonlinear optimization problems. Since there are many possible water supply network DMA layout combinations for physically partitioning the water supply network by selecting a pipeline for inserting a flowmeter or a valve, it is computationally impossible to investigate all solution spaces, which is an NP-hard problem, and a heuristic algorithm is required to find an optimal solution, the present invention solves the problem of arranging the flowmeter and the valve by using a genetic algorithm, and can obtain an arrangement scheme under the optimal economical condition by setting the minimum number of flowmeters.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (7)
1. The independent metering and partitioning method for the water supply network based on the improved spectral clustering and the genetic algorithm is characterized by comprising the following steps of:
s1, establishing a water supply network micro hydraulic model in EPANET software, acquiring a water supply network topological structure, node water demand, elevation and coordinate parameters by calling an EPANET toolbox, and constructing an adjacent matrix capable of reflecting the water supply network topological structure;
s2, constructing a node similarity matrix by utilizing the coordinate positions and the elevation attributes of the nodes of the water supply network; meanwhile, constructing a water demand similarity matrix by utilizing the water demand of the adjacent matrix and the nodes;
s3, adding the node similarity matrix and the water demand similarity matrix to obtain an edge weight matrix, inputting the edge weight matrix into an improved weighted spectrum clustering algorithm to generate DMA configuration, and determining a DMA partition boundary pipe section set;
and S4, optimizing flowmeter and valve arrangement in the boundary pipe segment set through a genetic algorithm, and finally completing DMA partition of the water supply pipe network.
2. The method for independently metering and partitioning a water supply network based on improved spectral clustering and genetic algorithm according to claim 1, wherein the method for establishing a micro hydraulic model of the water supply network in the EPANET software in the step S1, and obtaining the topological structure, the node water demand, the elevation attribute and the node coordinate position of the water supply network by calling the EPANET toolbox is as follows:
(1) Importing topological relation and pipe fitting operation parameters of a water supply network into EPANET software, and establishing a water supply network micro hydraulic model, wherein the water supply network node set is V= { V 1 ,v 2 ,v 3 ......v N Pipe segment set l= { L } 1 ,l 2 ,l 3 ,...,l M }；
(2) Calling an EPANET toolbox, and performing hydraulic analysis to obtain the coordinate position of the node of the water supply networkNode water demand q 1 ,q 2 ,...,q N ]Elevation attribute [ r ] 1 (3) ,r 2 (3) ,...,r N (3) ]Pressure attribute [ H ] 1 ,H 2 ,...,H N ]。
3. The method for independently metering and partitioning a water supply network based on improved spectral clustering and genetic algorithm according to claim 2, wherein the method for constructing the adjacency matrix capable of reflecting the topology structure of the water supply network in the step S1 is as follows:
constructing an adjacency matrix capable of reflecting the topology structure of the water supply network according to the node v i and vj The pipeline directly connected with each other or not is quantized into a natural adjacent relation of nodes, and the formula is as follows:
and obtaining an adjacent matrix A of the equivalent undirected connection diagram of the water supply network by the natural adjacent relation among the nodes, wherein the adjacent matrix A is in the following form:
wherein ,Aij Representing node v i and vj Natural neighbor relation of s ij Representing the connection relationship of two nodes, if A ij 1, then represents node v i and vj Directly connected, namely, are natural adjacent nodes; if A ij 0, then represents node v i and vj Are not directly connected, i.e., are not natural neighbor relationships.
4. The method for independently measuring and partitioning a water supply network based on improved spectral clustering and genetic algorithm according to claim 3, wherein the method for constructing a node similarity matrix by using the coordinate positions and the elevation attributes of the nodes of the water supply network in the step S2 is as follows:
(1) And (2) positioning coordinates of nodes of the water supply network obtained in the step (1)Elevation attribute r 1 (3) ,r 2 (3) ,...,r N (3) ]Combining into node attribute feature matrix->
wherein ,hi An attribute feature vector formed by the ith node of the water supply network; r is (r) i (1) Is h i Column 1 of the table, represents the abscissa in the position coordinates of the ith node; r is (r) i (2) Is h i The 2 nd column value of the table represents the ordinate in the position coordinates of the ith node; r is (r) i (3) Is h i Column 3 of the node represents the elevation of the ith node;
(2) The selected node attribute feature matrix H is standardized, the mean value of the processed data is 0, the standard deviation is 1, and the conversion formula is as follows:
r i ' (t) ＝(r i (t) -μ t )/σ t (i＝1,2,3......N,t＝1,2,3)
wherein ,ri (t) For the ith row vector H in the node attribute matrix H i T-th value, mu t For the mean value, sigma, of all values in the t-th column of the node attribute matrix H t Standard deviation of all values of the t-th column in the node attribute matrix H;
the standardized node attribute matrix H' is:
wherein ,h'i For the ith row vector H in the node attribute matrix H i Standardized results;
(3) The ith row vector H 'in the normalized node attribute matrix H' i And the j-th row vector h' j The Euclidean distance calculating method is as follows:
wherein ,h'i ,h' j Respectively representing the ith row and the jth row vectors in the matrix H';
the Euclidean distance values among the row vectors in the matrix H' are calculated in sequence and form a vector D as follows:
wherein ,
(4) Establishing a Gaussian kernel function based on each element in the vector DNode similarity matrix W of (2) 1 Gaussian kernel transformation formula and matrix W 1 The form is as follows:
wherein ,a ij for node similarity matrix W 1 The element value of the ith row and jth column of the vector D, std (D) is the standard deviation of all elements in the vector D, and the calculation formula of std (D) is as follows:
5. the method for independently measuring and partitioning a water supply network based on improved spectral clustering and genetic algorithm as set forth in claim 4, wherein the method for constructing a water demand similarity matrix by using the adjacency matrix and the node water demand size in step S2 is as follows:
(1) Summing all columns of adjacent matrix A of water supply network micro hydraulic model to obtain degree z of each node ii ，z ii Can also be understood as the node v in the water supply network i The total number of directly connected pipe sections exists, and then the water supply network degree matrix degV is formed as follows:
wherein ,i,j＝1,2,...N；
(2) According to the water demand q of each node of the pipe network 1 ,q 2 ,...,q N ]And a water supply pipe network degree matrix degV, calculatingAdjacent node v of water supply network i and vj Similarity b of water distribution requirements between ij Thereby forming a water demand similarity matrix W 2 The following are provided:
wherein ,b ij for node similarity matrix W 2 Element values of the ith row and the jth column of the table; q i ,q j Respectively is a water supply network node v i and vj Water demand size.
6. The method for independently metering and partitioning a water supply network based on improved spectral clustering and genetic algorithm according to claim 5, wherein in the step S3, an edge weight matrix is obtained by adding a node similarity matrix and a water demand similarity matrix, the edge weight matrix is input into the improved weighted spectral clustering algorithm to generate a DMA configuration, and the method for determining a DMA partition boundary pipe section set is as follows:
(1) In order to reflect the similarity of the nodes in the water supply network more truly, a node similarity matrix W 1 Similarity matrix with water demand W 2 Adding to obtain an edge weight matrix W, wherein the form of the edge weight matrix W is as follows:
wherein w is ij ＝a ij +b ij ，w ij The element value of the ith row and the jth column in the node similarity matrix W is obtained; a, a ij For node similarity matrix W 1 The element value of the ith row and jth column of (b) ij Is a water demand similarity matrix W 2 Element values of the ith row and the jth column of the table;
(2) Defining the elements on the main diagonal of the diagonal matrix Y as the sum of the j-th columns of the edge weight matrix W, and the diagonal matrix Y is in the form as follows:
wherein ,
(3) Obtaining a standardized Laplace matrix L by using an edge weight matrix W and a diagonal matrix Y sym The following are provided:
due to the normalized Laplace matrix L sym Is a semi-positive definite matrix, when normalized to the Laplace matrix L sym When the eigenvalue decomposition is performed, the matrix can be obtained to have N non-negative real eigenvalues 0=λ 1 ≤λ 2 ≤…≤λ N ；
(4) Based on the N-cut graph cutting mode, accurate and stable clustering effect can be obtained by adopting multi-path division, and a standardized Laplace matrix L is calculated sym Corresponding first k minimum eigenvalues { lambda } 1 ,λ 2 ,…,λ k Corresponding feature vector u 1 ,u 2 ,...,u k And then forms a matrix U, the form is as follows:
wherein ,ux For standardizing Laplace matrix L sym The feature vector corresponding to the x-th value of the first k minimum feature values, i, j=1, 2,..n; x=1, 2,. -%, k;
(5) The matrix U is normalized, and the normalized matrix U' is in the following form:
wherein ,u' ix representing the value U of the ith row and the xth column elements of the matrix U ix Normalized results;
(6) The matrix U' can be regarded as a set of N row vectors (o 1 ,o 2 ,o i ,...,o N ) T (i=1, 2,., N), each row vector o is calculated using the K-means algorithm i (i=1, 2,3,) N categorizes into k clusters (C 1 ,C 2 ,C f ..,C k ) In C f Representing a set of all row vectors belonging to class f;
(7) If set (o) 1 ,o 2 ,o i ,...,o N ) T (i=1, 2,.,. N.) the i-th row element is classified as the f-th cluster, then the pipe network node v corresponding to the original data i Also classified as the f-th region; outputting DMA configuration and determining boundary pipe segment set B= (G) composed of connected pipe segments among k independent areas 1 ,G 2 ,...G Nec ) Where Nec represents the total number of inter-DMA boundary pipe segments and G represents the boundary pipe segment index.
7. The method for independently metering and partitioning a water supply network based on improved spectral clustering and genetic algorithm according to claim 6, wherein the method for optimizing the flowmeter and the valve arrangement in the boundary pipe segment set through the genetic algorithm in the step S4 finally completes DMA partitioning of the water supply network is as follows:
(1) In order to divide a complex water supply network into a plurality of independent areas to isolate the areas and measure the flow rate respectively, a set b= (G) of border tube segments is needed 1 ,G 2 ,...G Nec ) A valve or a flowmeter is arranged on the upper part; firstly, determining the length of the code according to the total number Nec of elements in the boundary pipe section set B, specifically to each pipe section, if a certain boundary pipe section is provided with a flowThe meter then corresponds to the chromosome code as a binary number 1; conversely, if a valve is placed in the border segment, the binary number corresponding to the chromosome code is 0, so a binary chromosome sequence I in the genetic algorithm is defined as follows:
I＝(g 1 ,g 2 ,...g Nec), wherein ,
meanwhile, in order to reduce the solution space of the genetic algorithm and minimize the DMA implementation budget, firstly, defining the total number Nfm =k of flow meters inserted into a water supply network, wherein k is the set DMA partition number, that is, only k 1 s exist in a group of binary chromosome sequences I of the genetic algorithm are limited, and the rest positions are 0;
(2) The objective function is to maximize the power P dissipated by the water supply network node, so the fitness function F of the genetic algorithm is defined as the inverse of the objective function:
wherein gamma is the specific gravity of water, r i (3) ,H i ,q i Respectively representing the elevation, pressure and water demand data of the ith node after the valve and the flowmeter are arranged on the boundary pipe section set of the water supply network;
(3) Initializing population scale C and crossover probability P of genetic algorithm cro Probability of variation P het And sets an algorithm termination condition: maximum algebra J, convergence threshold T thr The method comprises the steps of carrying out a first treatment on the surface of the Meanwhile, the optimal solution output by the genetic algorithm also needs to meet the node pressure constraint conditions as follows:
H min ≤H i ≤H max
wherein ,Hmin Minimum service water pressure for node, H max For the highest allowable water pressure of the node, H i The method comprises the steps that pressure data of all nodes obtained by hydraulic operation of a water supply network under a valve and flowmeter arrangement scheme corresponding to the current solution are obtained;
(4) The flow meter and valve arrangement problem optimizing arrangement flow is as follows:
A. initializing a population, and randomly generating C binary chromosome sequences I, namely generating C individuals as an initial parent population;
B. calling an EPANET toolbox to generate a DMA partition result under a certain body code sequence corresponding arrangement scheme, and performing hydraulic analysis to obtain the elevation [ r ] of a node under the current DMA partition 1 (3) ,r 2 (3) ,...,r N (3) ]Water demand [ q ] 1 ,q 2 ,...,q N ]And pressure [ H ] 1 ,H 2 ,...,H N ]Data, calculating to obtain the fitness value of the individual through a fitness function F; sequentially calculating individual fitness values of the parent population C, judging whether an algorithm termination condition is met, and if not, jumping to the step C; if yes, jumping to d;
C. selecting individuals to perform crossover and mutation operations according to the fitness function value of the individuals of the parent population C to generate offspring, and returning the generated offspring population as the parent population to b for next generation evolution;
D. if the current solution of the algorithm operation output does not meet the node pressure constraint condition, increasing the number of arranged flowmeters by one, namely Nfm = Nfm +1, returning to S2 after changing the chromosome coding form of the genetic algorithm, and recalculating the optimal solution under the newly increased number of flowmeters; and if the result obtained by the operation of the algorithm meets the node pressure constraint condition or reaches the maximum iteration frequency Nec-Nfm, stopping calculating, outputting an optimal individual, obtaining an optimal arrangement mode of the flowmeter and the valve in the corresponding boundary pipe section set, and finally finishing DMA planning.
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