CN103617563B - A kind of water supply network theoretical based on geo-statistic spatial analysis is without monitoring node pressure determination statement - Google Patents
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Abstract
The invention discloses a kind of water supply network theoretical based on geo-statistic spatial analysis without monitoring node pressure determination statement, choose water supply network Water Source Pumping Station node and other with the pressure of the node of pressure monitoring devices as known pressure, being then based on known node pressure uses general kriging analysis method to carry out interpolation calculation to without monitoring node pressure, thus obtains the water supply network node pressure without monitoring point；During interpolation calculation, by the Euclidean distance during change substitutes general kriging analysis method relatively of pressure between node.The present invention uses general kriging analysis method, in conjunction with system-head curve, Euclidean distance is substituted with relative pressure change, use the relative change of the calculation of design parameters pressure of water supply network, choose the variation function model being suitable for grid hydraulic characteristic(s), water supply network is calculated without the node pressure of monitoring point and predicted, computational accuracy is high, and feasibility is strong.
Description
Technical Field
The invention relates to a method for determining the pressure of a non-monitoring node of a water supply network, which is beneficial to data expansion under the condition of insufficient water monitoring data of the pipe network, can provide technical support for optimized dispatching and leakage detection of the pipe network, and belongs to the field of hydraulic analysis, pipe network dispatching and leakage detection of urban water supply networks.
Background
The safe and stable operation of the water supply network is related to the normal life of urban residents, the normal production of urban enterprises, the safe operation of public facilities, the urban fire protection safety and the like. In recent years, with the rapid development of computer technology, an automatic water pressure or flow detection system, i.e., scada (supervisory Control And data acquisition) system, of a water supply network is gradually established, And the system automatically monitors the water pressure And flow of some important nodes of the water supply network in real time by using sensors And periodically transmits water pressure And flow signals back to a Control center in a wireless or wired transmission manner to analyze the hydraulic state of the pipe network. However, for reasons of economy, maintenance and the like, the number of the distributed pressure monitoring points is usually much less than that of nodes of the pipe network, so that the accurate grasping and simulation of the hydraulic state of the pipe network is not only dependent on the limited water pressure or flow monitoring points in the pipe network, but also is particularly important for expanding the obtained data by adopting an effective hydraulic state analysis method.
The analysis method of the hydraulic state of the pipe network can be divided into a microscopic method and a macroscopic method. The method is characterized in that a macroscopic method based on a black box theory is a main method for analyzing the hydraulic state of a pipe network because the macroscopic method is simple and feasible, the complexity of a water distribution system structure is not considered, only a plurality of main input and output variables in the system, such as the water supply amount of a pump station, the water supply pressure, the pressure of a pressure measuring point and the like, are considered, and on the basis of the data, a statistical modeling method is adopted to carry out macroscopic simulation on the operation state of the water supply pipe network. The current macroscopic model mainly comprises: the system comprises a proportional time-interval pipe network model, a time-interval proportional water supply pipe network macroscopic model, a water distribution pipe network equivalent network model, a pipe network macroscopic model established based on a neural network method and the like.
The proportion time period pipe network model assumes that the proportion of the water supply quantity of the water supply pipe network in each time period in the water supply period to the total water quantity of the pipe network is unchanged, and the water outlet pressure of any water plant in the pipe network is related to the total water quantity of all nodes of the pipe network and other water plants. Because most urban industrial water supply and resident water supply are supplied in a mixed mode in China, the proportional relation between the node water consumption and the total water consumption is uncertain, and a proportional time period pipe network model is not suitable for urban water supply networks in China.
The macroscopic model of the time-interval proportional water supply network is an improvement of a time-interval proportional pipe network model, one day of the model is used as a water supply period, one water supply period is divided into a plurality of time intervals, and the node flow proportion in each time interval is assumed to be constant. The problem that the water consumption of nodes accounts for the total is solved by a time-interval proportion pipe network macroscopic model
The proportion problem of water consumption, but establish the model of different periods, increaseed the complexity of work load and model to neglected the change in season and the influence that the festival and holiday produced the fluctuation of water consumption proportion, the proportion macroscopic pipe network model of dividing the period needs constantly to check and revise, and the model is comparatively loaded down with trivial details.
The equivalent network model of the water distribution network not only considers the water supply pressure and water supply quantity of each water plant of the pipe network, but also considers the pressure distribution of each node of the pipe network and the mutual influence and internal relation of the pressure distribution, and a simplified equivalent network is constructed by using limited monitoring points and pump station nodes which reflect the distribution condition of the pipe network. The model introduces real-time information of monitoring points in the water supply network, can reflect and predict the actual running state of the pipe network, and improves the accuracy of the model.
The neural network model is a mathematical model for simulating animal neural network behavior characteristics and performing distributed parallel information processing. The pipe network macroscopic model established based on the neural network method is characterized in that the water supply pressure of a water supply pump station in a water supply pipe network, the water supply quantity of the pipe network, the pressure of a pressure monitoring point in the pipe network and other obtainable pipe network attribute variables are used as input and output of the pipe network macroscopic model, a hidden network is trained through a large amount of acquired input and output data, the hidden network can numerically simulate to obtain unknown variables from known variables, namely after the water supply quantity and other known variables are input, the monitoring point pressure corresponding to the unknown variables can be output. The neural network model has the advantages that the nonlinear mapping simulation capability is high, but when macroscopic working condition simulation is carried out on the water supply network, the water supply network structure is completely avoided, and the simulation precision is not high.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for determining the pressure of the non-monitoring node of the water supply network based on the geostatistical spatial analysis theory, which has high calculation precision and strong feasibility.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for determining pressure of a water supply network non-monitoring node based on a geostatistical spatial analysis theory is characterized by selecting pressure of a water supply network water source pump station node and other nodes with pressure monitoring equipment as known pressure, and then performing interpolation calculation on the pressure of the non-monitoring node by adopting a pan-kriging interpolation method based on the known node pressure so as to obtain the node pressure of the water supply network non-monitoring point; during interpolation calculation, relative change of pressure between nodes is used for replacing Euclidean distance in the method of pan-Kriging interpolation.
The method comprises the following specific steps:
1) characterization of the magnitude of the relationship between the nodes:
calculating the relative change of the pressure between all nodes by using the design parameters of the water supply network, and representing the relation between the two node spaces by using the relative change magnitude of the design pressure;
2) obtaining a variation function of the generic kriging interpolation method:
taking a water source pump station monitoring node as a starting point, sequencing the relative pressure variation quantity between other monitoring nodes and the water source pump station monitoring node from small to large according to the step 1), and obtaining a variation function value according to the definition of the variation function; drawing a relation curve between the relative distance and the function value in a rectangular coordinate system by taking the relative distance as an abscissa and the function value as an ordinate; comparing the graph with a variation function theoretical model graph, selecting a similar theoretical model and fitting by a least square method so as to determine a variation function;
3) substituting the relative pressure change obtained in the step 1) into the variation function obtained in the step 2) to obtain variation function values among all nodes;
4) in the process of the Pankrige interpolation, the pressure of each node is related to the relative pressure change between the node and the node of the water source pumping station, and the pressure function of the node is h (x) α0+α1x；
Wherein x is the relative pressure change between the required node and the water source pump station node α0And a1Is a coefficient of a function, wherein Is the weight coefficient; k is the number of known monitoring nodes;
5) determining the pan-kriging interpolation equation Λ Xt＝Bt’The variogram matrix Λ and the variogram vector B in (t 0,1)tWherein the variation function value among each node in the variation function matrix Λ can be obtained from step 3);
6) calculating matrix equation, and calculating inverse matrix Λ of variogram matrix Λ-1Taking t as 0 and 1 to respectively perform matrix calculation Xt＝Λ-1BtAnd (t 0,1) yields a coefficient α0And α1Vector of weight coefficients
7) Vector of weight coefficientsSubstitution intoDetermining α nodal pressure function coefficient0And α1The node pressure function is determined;
8) the relative pressure change x of each non-monitoring node and each water source pump station node in the water supply network can be obtained in the step 1), and the x is substituted into a node pressure functionAnd (5) calculating the pressure value of each non-monitoring node.
Wherein the relative change of the pressure between the nodes in the step 1) is obtained by the following method: assuming the total water consumption of the pipe network at the T moment, carrying out flow distribution according to an area ratio flow method to obtain the simulated water consumption of each node in the pipe network at the T moment; the matrix Q is obtained by using each node in the water supply network to simulate water consumption, design pipe length, pipe diameter and pipe friction coefficient as known conditions and adopting a finite difference method
Wherein,the influence of the change of the flow of the nodes of the pipe network on the pressure of all the nodes is avoided;
dividing each column in the matrix Q by its corresponding diagonal element can be converted into the relative pressure variation matrix V,
the ith row and jth column elements of the matrix V represent the relative pressure changes between node i and node j;
according to the comparison between the drawn relation curve and the graph of the theoretical model of the variation function and the hydraulic characteristics of the water supply network, the actually selected theoretical model of the variation function is a spherical model, and the covariance variation function is
Wherein: h is the relative pressure change between known pressure nodes in the water supply network;
c0the value of the gold of the nesting structure model;
a is the variation range of the nesting structure model;
c is a base deviation value of the nesting structure model;
c0+ c is the base value of the registration structure model.
And obtaining coefficients in the function by adopting a least square method according to the pressure of the known monitoring node.
Compared with the prior art, the invention has the following beneficial effects:
the method adopts a pan-kriging interpolation method, combines the characteristics of the pipe network, replaces Euclidean distance with relative pressure change, adopts design parameters of the water supply pipe network to calculate the relative change of the pressure, selects a variation function model suitable for the hydraulic characteristics of the water supply pipe network, calculates and predicts the node pressure without monitoring points of the water supply pipe network, and has high calculation precision and strong feasibility.
Drawings
FIG. 1-a schematic view of a water supply network to which embodiments of the present invention are directed.
FIG. 2 is a schematic diagram showing comparison between the interpolation result of the Pankriging and the simulation result of the pipe network.
Detailed Description
The invention introduces a geostatistical spatial analysis theory into the analysis and calculation of the pressure of the nodes of the water supply network which meet the randomness and the structuredness, selects the pressure of the nodes of the water supply network water source pump station and other nodes with pressure monitoring equipment as the known pressure, and then interpolates the pressure of the nodes without monitoring by adopting a Universal Kriging interpolation method based on the known node pressure, thereby obtaining the pressure of the nodes without monitoring points of the water supply network. During interpolation calculation, relative change of pressure between nodes is used for replacing Euclidean distance in a pan-Kriging interpolation method; and simultaneously selecting a variation function model suitable for the hydraulic characteristics of the water supply network.
The method comprises the following specific steps:
1) characterization of the magnitude of the relationship between the nodes:
calculating the relative change of the pressure between all the nodes by using the design parameters of the water supply network, and representing the spatial relationship between the two nodes by using the relative change magnitude of the design pressure;
the topological structure, nodes, the pipe section numbers, the pipe diameters of all the pipe sections, the pipe lengths and hydraulic parameters of a certain city pipe network are known. Assuming the total water consumption of the pipe network at the time T, obtaining the pressure of each node of the pipe network by adopting a pipe network state estimation method, and numbering the pressure (because the flow and the pressure of each node can not be actually measured in the running process of the urban water supply network, usually, obtaining the simulated pressure of the pipe network by adopting the pipe network state estimation method as reference pressure, the concrete method is that the accurate water consumption of all nodes of the pipe network at a certain time is assumed and is different from the designed water consumption, the hydraulic simulation is carried out by taking the accurate water consumption as a known condition, and the relatively accurate pressure condition of each node at the time is obtained by calculation).
The relative change of the pressure between the nodes is obtained as follows: assuming the total water consumption of the pipe network at the T moment, carrying out flow distribution according to an area ratio flow method to obtain the simulated water consumption of each node in the pipe network at the T moment; the matrix Q is obtained by using each node in the water supply network to simulate the water consumption, design the length of the pipe, the diameter of the pipe and the friction coefficient of the pipeline as known conditions and adopting a finite difference method,
wherein,the influence of the change of the flow of the nodes of the pipe network on the pressure of all the nodes is avoided;
each column in the matrix Q is divided by its corresponding diagonal element, respectively, to convert into a relative pressure change matrix V,
the ith row and jth column elements of the matrix V represent the relative pressure changes between node i and node j;
2) obtaining a variation function of the generic kriging interpolation method:
taking a water source pump station monitoring node as a starting point, sequencing the relative pressure variation quantity between other monitoring nodes and the water source pump station monitoring node from small to large according to the step 1), and obtaining a variation function value according to the definition of the variation function; drawing a relation curve between the relative distance and the function value in a rectangular coordinate system by taking the relative distance as an abscissa and the function value as an ordinate; comparing the graph with a variation function theoretical model graph, selecting a similar theoretical model and fitting by a least square method so as to determine a variation function;
in a water supply network, the random variable representing the pressure at a node is denoted as h (x), and the mathematical definition of the variogram γ(s) ═ Var [ h (x) -h (x + s) ]]/2＝E[h(x)-h(x+s)]2/2-{E[h(x)]-E[h(x+s)]}2/2. When performing the bikuke interpolation (Kriging), the preconditions exist: the regionalized variable (i.e., the random variable h (x) representing the node pressure) satisfies the second order stationary assumption. Then, for any distance s, there is E [ h (x)]＝E[h(x+s)]. The variation function γ(s) ═ E [ h (x) -h (x + s)]2When there is only one measured value of the node pressure, the measured value may be directly substituted into γ(s) ═ h (x) -h (x + s)]2/2。
According to the comparison between the drawn relation curve and the graph of the theoretical model of the variation function and the hydraulic characteristics of the water supply network, the theoretical model of the variation function selects a spherical model, and the covariance variation function of the spherical model is
Wherein:
h is the relative pressure change between known pressure nodes in the water supply network;
c0the value of the gold of the nesting structure model;
a is the variation range of the nesting structure model;
c is a base deviation value of the nesting structure model;
c0+ c is the base value of the registration structure model.
According to the pressure of the known monitoring node (obtaining the relative change of the pressure), the coefficient (c) in the function can be obtained by adopting a least square method0A, c). The specific process of performing least square fitting on the test sample comprises the following steps:
in the formula, h is the relative pressure change between known pressure nodes in the water supply network and is an independent variable. When the relative distance is more than 0 and less than or equal to h and less than or equal to a, the following steps are carried out:
the least square fitting is adopted for the method, and the following can be recorded: y ═ y(s), b0＝c0，b1＝3c/2a，b2＝-c/2a3，x1＝h，x2＝h3The above formula may be changed as:
y＝b0+b1x1+b2x2(2)
when the kriging interpolation estimation is carried out on the pressure of the nodes of the water supply pipe network, the relative distance between target nodes in the pipe network and the pressure of the target nodes are known, and the pressure is calculated according to x1＝h，x2＝h3Independent variable x of the above formula1、x2The dependent variable y is γ(s) and is defined mathematically by the variation function γ(s):
therefore, after all the measured node pressure data are screened, the covariance is solved by adopting the formula, and the calculation result gamma(s) is the value of y.
At this time, the known conditions are several sets of variables x1、x2Y, the coefficients of formula (2) can be obtained by fitting using the least squares method: b0、b1、b2. Solving the following equation system to obtain the block value c of the variation function0A variation a and a bias base value c.
And substituting the result to obtain a fitted variation function formula.
3) The method for solving the covariance matrix (solving the covariance through the variation function) in the pan-kriging interpolation method comprises the following steps:
substituting the relative pressure change obtained in the step 1) into the variation function obtained in the step 2) to obtain variation function values among all nodes;
4) in the process of the Pankrige interpolation, the pressure of each node is related to the relative pressure change between the node and the node of the water source pumping station, and the pressure function of the node is h (x) α0+α1x；
Wherein x is the relative pressure change between the required node and the water source pump station node α0And α1Is a coefficient of a function, wherein Is the weight coefficient; k is the number of known nodes (monitoring points);
5) determining the pan-kriging interpolation equation Λ Xt＝BtA variogram matrix Λ and a variogram vector B in (t ═ 0, 1.. times.p)tWherein:
in order to be a vector of weight coefficients,
the necessary conditions that the estimation of the pressure function coefficients should satisfy unbiasedness are:
wherein:
in which P is a different term of a polynomial of the pressure functionAmount, in this method P ═ 1; gamma (x)i-xii) Is node xiAnd node xiiThe function value of variation between the two groups can be obtained in the step 3);the Lagrange multiplier represents that the object to be solved is the coefficient of the tth term of the pressure function; h isl(xi) Variable x of i node being the polynomial l term of pressure functioniThe meaning of the rest mathematical symbols can refer to the basic method of Pankriging;
6) calculating matrix equation, and calculating inverse matrix Λ of variogram matrix Λ-1Taking t as 0 and 1 to respectively perform matrix calculation Xt＝Λ-1BtAnd (t 0,1) yields a coefficient α0And α1Vector of weight coefficients
7) Vector of weight coefficientsSubstitution intoDetermining α nodal pressure function coefficient0And α1The node pressure function is determined;
8) obtaining the relative pressure change x of each non-monitoring node and a water source pump station node in the water supply network in the step 1), and substituting x into a node pressure function h (x) α0+α1And x, calculating the pressure value of each non-monitoring node.
The invention provides a new research direction in the field of water supply network macroscopic analysis, introduces the geostatistical spatial analysis principle into the pipe network state calculation, and fully considers the pipe network structure characteristics and the hydraulic parameter randomness to form a new pipe network state macroscopic analysis method. Meanwhile, aiming at the correlation degree of the structural characteristics of the pipe network and the properties of the pipe sections between nodes (pipe diameter, pipe length, pipe section resistance coefficient and the like), the Euclidean distance is replaced by the relative distance suitable for pipe network state analysis, the principle of a ground statistical method is organically combined with the characteristics of the pipe network, and the method has reference and guiding significance for the research and development of the pipe network state analysis method.
The method is described in detail below with reference to a specific example.
FIG. 1 is a schematic view of a water supply network. The topological structure, the nodes, the pipe section numbers, the pipe diameters of all the pipe sections, the pipe lengths and the hydraulic parameters of the pipe network are known.
Except for the water source pump station node 1, 4 nodes of the pipe network [6, 9, 14 and 20] are respectively provided with a pressure monitoring device, so that the total water heads of 5 nodes including the water source pump station node at the time T can be measured as [82.15, 67.17, 35.78, 31.22 and 21.28], and the unit is 10 kPa.
And interpolating the pressure of other nodes of the water supply network by using a pan-kriging interpolation method. The method comprises the following steps:
1) and assuming that the total water consumption of the pipe network at the T moment is 338L/s, carrying out flow distribution according to an area ratio flow method to obtain the simulated water consumption of each node in the pipe network at the T moment. The method comprises the steps of taking the simulated water consumption of each node of a water supply network, the design of pipe length, pipe diameter and pipe friction coefficient as known conditions, obtaining a matrix Q by adopting a finite difference method, converting the matrix Q into a relative pressure change matrix V, and representing the relative pressure change between a node i and a node j by the ith row element and the jth column element of the matrix V (table 1).
TABLE 1 relative pressure changes at each node
Continuation table
2) And (4) with the water source pumping station node 1 as a starting point, searching relative pressure change with other known monitoring points in the relative pressure change matrix V. The relative pressure changes are sorted from small to large, and the variation function values of the two corresponding nodes are respectively solved according to the variation function definitions (table 2).
TABLE 2 ranking by relative pressure change and the value of the corresponding variation function
3) And (5) solving a variation function. And selecting a proper theoretical model through comparison of the fitting curve and the model, and determining the coefficient of the variation function by adopting a least square method. In this example, a fitting structure based on a spherical model is selected, and the fitting result is:
4) in the process of the pan-kriging interpolation, the pressure of the node is related to the relative pressure change between the node and the node of the water source pumping station, and the pressure function form of the node is h (x) α0+α1x。
Wherein: x is the relative pressure change from the node to the pump station; the weight coefficient is obtained;
5) calculate the pan-kriging interpolation equation Λ Xt＝Bt’(t 0,1) variogram matrix Λ and variogram vector Bt(ii) a The relative pressure change between each node is found in a relative pressure change matrix V and substituted into a variation function for calculation;
6) calculating matrix equation solving inverse matrix Λ of variogram matrix Λ-1Taking t as 0 and 1, respectively, and performing matrix calculation Xt＝Λ-1BtAnd (t 0,1) yields a coefficient α0And α1Vector of weight coefficientsThe calculation results are as follows:
TABLE 3 weight coefficient calculation results
7) Vector of weight coefficientsSubstitution intoCalculated node pressure function coefficient α0And α1The values of (a) are 78.26 and-31.69, respectively. The estimated nodal pressure function is then: h (x) 78.26-31.69 x;
8) and obtaining the relative pressure change of each node in the water supply network and the node of the water source pump station from the relative pressure change matrix V difference, and substituting the relative pressure change into the formula to calculate the pressure value of each node.
The calculation results of the pan-kriging interpolation method are listed in fig. 2 for comparative analysis, and it can be seen in the figure that the simulation results are satisfactory, the simulation accuracy is high, and the maximum relative error is less than 2%.
The above examples of the present invention are merely illustrative of the present invention and are not intended to limit the embodiments of the present invention. Variations and modifications in other variations will occur to those skilled in the art upon reading the foregoing description. Not all embodiments are exhaustive. All obvious changes and modifications of the present invention are within the scope of the present invention.
Claims (2)
1. A method for determining pressure of a water supply network non-monitoring node based on geostatistical spatial analysis theory is characterized by comprising the following steps: selecting the pressure of a water supply network water source pump station node and other nodes with pressure monitoring equipment as known pressure, and then carrying out interpolation calculation on the pressure of the non-monitoring nodes by adopting a pan-kriging interpolation method based on the known node pressure so as to obtain the node pressure of the non-monitoring points of the water supply network; during interpolation calculation, relative change of pressure between nodes is used for replacing Euclidean distance in a pan-Kriging interpolation method;
the specific steps for determining the pressure of the non-monitoring node of the water supply network are as follows:
1) characterization of the magnitude of the relationship between the nodes:
calculating the relative change of the pressure between all nodes by using the design parameters of the water supply network, and representing the relation between the two node spaces by using the relative change magnitude of the design pressure;
2) obtaining a variation function of the generic kriging interpolation method:
taking a water source pump station monitoring node as a starting point, sequencing the relative pressure variation quantity between other monitoring nodes and the water source pump station monitoring node from small to large according to the step 1), and obtaining a variation function value according to the definition of the variation function; drawing a relation curve between the relative distance and the function value in a rectangular coordinate system by taking the relative distance as an abscissa and the function value as an ordinate; comparing the graph with a variation function theoretical model graph, selecting a similar theoretical model and fitting by a least square method so as to determine a variation function;
3) substituting the relative pressure change obtained in the step 1) into the variation function obtained in the step 2) to obtain variation function values among all nodes;
4) in the process of the Pankrige interpolation, the pressure of each node is related to the relative pressure change between the node and the node of the water source pumping station, and the pressure function of the node is h (x) α0+α1x；
Wherein x is the relative pressure change between the required node and the water source pump station node α0And α1Is a coefficient of a function, wherein Is the weight coefficient; k is the number of known monitoring nodes;
5) determining the pan-kriging interpolation equation Λ Xt＝BtThe variance function matrix Λ and the variance function vector B in (t ═ 0,1)tWherein the variation function value among each node in the variation function matrix Λ can be obtained from step 3);
6) calculating a matrix equation; calculating the function of variationInverse matrix Λ of number matrix Λ-1Taking t as 0 and 1 to respectively perform matrix calculation Xt＝Λ-1BtAnd (t 0,1) yields a coefficient α0And α1Vector of weight coefficients
7) Vector of weight coefficientsSubstitution intoDetermining α nodal pressure function coefficient0And α1The node pressure function is determined;
8) obtaining the relative pressure change x of each non-monitoring node and a water source pump station node in the water supply network in the step 1), and substituting x into a node pressure function h (x) α0+α1In x, calculating the pressure value of each non-monitoring node;
the relative change of the pressure between the nodes in the step 1) is obtained by the following method: assuming the total water consumption of the pipe network at the T moment, carrying out flow distribution according to an area ratio flow method to obtain the simulated water consumption of each node in the pipe network at the T moment; the matrix Q is obtained by using each node in the water supply network to simulate the water consumption, design the length of the pipe, the diameter of the pipe and the friction coefficient of the pipeline as known conditions and adopting a finite difference method,
wherein,the influence of the change of the flow of the nodes of the pipe network on the pressure of all the nodes is avoided;
dividing each column in the matrix Q by its corresponding diagonal element can be converted into the relative pressure variation matrix V,
the ith row and jth column elements of matrix V represent the relative pressure changes between node i and node j.
2. The method for determining pressure of a non-monitored node of a water supply network of claim 1, wherein: according to the comparison between the drawn relation curve and the graph of the theoretical model of the variation function and the hydraulic characteristics of the water supply network, the theoretical model of the variation function selects a spherical model, and the covariance variation function of the spherical model is
Wherein: h is the relative pressure change between known pressure nodes in the water supply network;
c0the value of the gold of the nesting structure model;
a is the variation range of the nesting structure model;
c is a base deviation value of the nesting structure model;
c0+ c is the base value of the nesting structure model;
according to the pressure of the known monitoring node, a least square method is adopted to obtain a coefficient c in the covariance variation function0A and c.
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| CN104111731B (en) * | 2014-07-14 | 2017-06-13 | 上海交通大学 | The discrimination method of water cycle factors relation between a kind of water supply network node |
| CN108009562B (en) * | 2017-10-25 | 2021-07-13 | 中山大学 | Method for identifying characteristic spatial variability of hydrology and water resource |
| CN111080064A (en) * | 2019-11-18 | 2020-04-28 | 上海城投水务(集团)有限公司供水分公司 | Method and system for generating water supply network pressure-stabilizing water supply scheme |
| CN113704942B (en) * | 2021-09-03 | 2024-04-09 | 清华大学 | Method, device and computer system for estimating pressure of unknown node of water supply pipe network |
| CN116090605A (en) * | 2022-12-07 | 2023-05-09 | 南栖仙策(南京)科技有限公司 | Pipe network early warning method and device, electronic equipment and storage medium |
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