CN103970610A - Method for monitoring node flow of water supply network - Google Patents

Abstract

The invention discloses a method for monitoring node flow in a water supply pipe network, comprising the following steps: constructing an original system equation group of the water supply pipe network according to the loss relationship between the flow rate of the water supply pipe network and the water head; and the coefficient matrix of the original system equation group Decompose to obtain a banded diagonal matrix and a residual matrix, then divide the banded diagonal matrix into several small banded diagonal matrices; each small banded diagonal matrix is respectively simultaneously with the described Combine the residual matrix to obtain the initial flow values of all nodes in the water supply network; take the initial flow values of all nodes as the initial input of the water supply system, and iterate until the final flow values of all nodes are obtained. The invention utilizes matrix decomposition to make full use of the super parallel computing capability of the computer GPU, accelerates the iterative convergence speed when calculating the node flow in the water supply pipe network, obtains real-time data of the node flow, and realizes the monitoring of the node flow.

Description

A method for monitoring node flow in a water supply network

technical field

The invention relates to the field of urban water supply and drainage, in particular to a method for monitoring node flow in a water supply pipe network.

Background technique

The water supply pipeline network in my country's cities, the crude oil pipeline network of petroleum refining and chemical enterprises, the farmland hydraulic pipeline network, the steam supply pipeline network, and the heat supply pipeline network are very developed, and the scale of these pipeline networks is very large, and the node pressure of the pipeline network , Fluid composition, etc. are the operating parameters that must be controlled in the daily maintenance of the pipeline network.

Accurate and real-time analysis and simulation of these operating parameters is a common problem faced by all pipeline network maintenance. The key to solving this common problem is the efficient real-time dynamic simulation technology of fluid pipeline network mechanics and components. The application of these technologies can provide advance Planning, real-time dynamic management, post-event emergency response, safety control, energy saving and emission reduction and other functions.

At present, the management of the fluid pipe network mainly adopts the following methods:

The first category is artificial design calculations, based on manual sampling and manual calculations. This method is relatively backward, the efficiency is very low, the manual calculation is cumbersome, the error rate is high, and it can only calculate a small-scale pipe network, and cannot perform a unified calculation for a large-scale pipe network. .

The second category is the application of computers to design and calculate pipe networks, which is currently the most widely used method. However, there is still a big problem with this method at present, that is, when the scale of the pipe network is large, the running speed is not satisfactory, which seriously affects the analysis speed of the pipe network data. With the expansion of the pipe network scale, the pipe network Real-time dynamic simulation of mechanics and components is almost impossible. For example, a general 4,000-node pipe network mechanics simulation calculation requires 12G of memory and about 30 minutes of iterative approximation to accurately simulate the actual situation.

There are two main reasons for the slow running speed. The first is that most current methods have too many iterations when solving large-scale equations, and sometimes they cannot converge at all; the second is that they are limited by the current running speed of the CPU. , so that the calculation speed can no longer be improved, so how to find a technical solution to these two problems and apply it to practical engineering becomes very important.

At present, there are many hydraulic and water quality analysis software, most of which use the technology mentioned above, and these software can solve the hydraulic calculation problems of thousands of pipe sections. Developed by the National Risk Management Research Laboratory of the United States Environmental Protection Agency, it is mainly used in the hydraulic and water quality analysis software of pressurized pipe network systems. It has the functions of pipe network adjustment, operation simulation, information management, and operation management. Based on the method of solving node equations, it can directly model the pipe network without simplification, reducing the time and storage units required for calculation. Based on its convenience and intuitiveness, it is more and more widely used in pressure Adjustment calculation for pipe network systems.

SynerGEE Gas can perform simulation modeling and analysis on pipeline networks, pressure regulators, valves, compressors, gas storage fields and gas gathering wells. As a general-purpose pipeline network simulation tool, SynerGEE Gas is suitable for natural gas, propane, steam, oxygen, Carbon dioxide, nitrogen, chlorine, and air, but not limited to. SynerGEE Gas provides the functionality of the most advanced commercial pipeline simulators and runs on the easy and familiar windows operating system.

At present, the above-mentioned systems are too slow and inefficient when applied to the simulation of giant pipe networks. The future development direction of simulation software for pipeline networks is to improve the speed and efficiency of simulation through parallel computing, and enhance the ability of the software to dynamically simulate various mechanics and components of giant pipeline networks in real time. Provide timely and efficient software support for monitoring, security emergency and other applications.

Contents of the invention

The invention provides a monitoring method for node flow in a water supply pipe network, which uses matrix decomposition to fully utilize the super parallel computing capability of a computer GPU, speeds up the iterative convergence speed when calculating node flow in a water supply pipe network, and obtains real-time information on node flow. data to monitor node traffic.

A method for monitoring node flow in a water supply network, comprising the following steps:

(1) According to the relationship between the flow rate and head loss of the water supply network, construct the original system equations of the water supply network.

Construct the flow continuity equation and head loss original system equations of the hydraulic state of the water supply pipe network at a given time point according to the actual data, and the original system equations are:

AH=F

In the formula: A is the Jacobian matrix of N×N; H is the vector matrix of unknown node water head in the N×1 water supply network; F is the vector matrix of N×1 constant items, and N is the total number of connected nodes;

The diagonal elements of the Jacobian matrix are: A _ii =∑ _j P _ij ;

The non-zero and off-diagonal elements of the Jacobian matrix are A _ij =-P _ij ;

In the formula: P _ij represents the reciprocal of the flow derivation of the head loss between node i and node j, for the pipeline between node i and node j:

In the formula: r is the resistance coefficient; Q _ij is the flow from node i to node j; n is the flow index; m is the local loss coefficient;

For a pump between node i and node j:

In the formula: ω is the relative speed of the water pump; Q _ij is the flow rate from node i to node j; s and t represent the curve coefficients of the water pump;

The elements in the constant item vector matrix F are:

F _ij ＝(∑ _j Q _ij -D _i )+∑ _j y _ij +∑ _f P _if H _f

In the formula: D _i represents the water demand of node i;

y _ij is the flow correction factor, for the pipeline between node i and node j:

y _ij ＝P _ij (r|Q _ij | ⁿ +m|Q _ij | ² )sgn(Q _ij )

For a pump between node i and node j:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>$

H _f is the known node water head of node f;

h ₀ is the virtual total lift of the pump;

P _if represents the inverse of the derivative of the head loss with respect to flow for the link linking node i to node f of known head.

In sgn(Q _ij ), when Q _ij >0, the value of sgn(Q _ij ) is 1, and Q _ij is always positive for the water pump.

(2) Decomposing the coefficient matrix of the original system of equations to obtain a banded diagonal matrix and a residual matrix, and then dividing the banded diagonal matrix into several small banded diagonal matrices.

The specific operation of decomposing the coefficient matrix A of the original system of equations AH=F is as follows:

Set the first and last non-zero elements of each row in the coefficient matrix A to zero to obtain a banded diagonal matrix D; retain the first and last non-zero elements of each row in the coefficient matrix A , the rest of the elements are set to zero, and the residual matrix R is obtained;

The banded diagonal matrix D is further divided into h small banded diagonal matrices D _i , as follows:

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\left(\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}\end{array}\right)$

If the number of rows of the striped diagonal matrix D is m, then the number of rows of each small striped diagonal matrix Di is C=[m/h], and the small striped diagonal matrix D _i of i<h is composed of striped pairs The (i-1)×C+1 to i×C rows in the corner matrix D are formed from the first non-zero element to the last non-zero element in each row; the small banded diagonal matrix D _h It is composed of the first non-zero element to the last non-zero element in each row of i×C+1 to m-th row in the banded diagonal matrix D.

(3) Combine each small banded diagonal matrix with the residual matrix at the same time to obtain the initial flow values of all nodes in the water supply network. The specific operations are as follows:

3-1. Let the odd-numbered row elements in the residual matrix R be zero, so that the residual matrix R is converted into an approximate residual matrix

3-2. Expand each small striped diagonal matrix to a matrix with the same size as the coefficient matrix A, as an approximate matrix of the small striped diagonal matrix

The approximate residual matrix and the approximation matrix of the small banded diagonal matrix Bringing it into the original system of equations AH=F, the approximate system equations are obtained as follows:

In the formula, is an approximate matrix of any small banded diagonal matrix;

is an approximate residual matrix,

H is the vector matrix of the unknown node water head in the N×1 water supply network (that is, the vector matrix composed of the flow values of all nodes in the water supply network);

F is the constant term vector matrix of the original system of equations;

3-3. Utilization The matrix G is calculated, and the nodes corresponding to all non-zero elements in the matrix G are regarded as a set of non-zero nodes. for the inverse matrix;

3-4. Use the obtained non-zero node set to construct a small system of equations:

In the formula:

I _Z is the identity matrix;

G _Z is a matrix formed by the flow values of all nodes in the non-zero node set corresponding to the nodes in the water supply network;

is a vector composed of node flow values corresponding to all nodes in the non-zero node set in the water supply network;

Among them, g ₁ , g ₂ ,…g _s are respectively The value of the 1st, 2nd, ... s components of , s is the number of nodes in the non-zero node set;

3-5. Use the preprocessing conjugate gradient iterative method to solve the small system equations, and obtain the initial flow values of all nodes in the non-zero node set; for the nodes in the small banded diagonal matrix D _i that do not belong to the non-zero node set, Take the initial flow value of the node with the smallest distance from the node in the non-zero node set as the initial flow value of the node, and obtain the initial flow value vectors H ₁ , H ₂ ,...H _h of the nodes corresponding to each small strip diagonal matrix .

Different threads of the GPU are used to calculate the combination of each small striped diagonal matrix and the residual matrix, and the number of cores of the GPU is equal to the number of small striped diagonal matrices.

(4) Take the initial flow values of all nodes as the initial input of the water supply system, iterate until the final flow values of all nodes are obtained, the steps are as follows:

4-1. The initial flow value of the node corresponding to each component of the initial flow value vector H ₁ , H ₂ , ... H _h is taken as the value of the component corresponding to the node in the vector H;

4-2. Solve the original system equations AH=F, after obtaining the new node water head, the new flow is:

Q _ij ＝Q _ij -(y _ij -P _ij (H _i -H _j ))

The new flow rate needs to satisfy the following flow continuity equation:

∑ _j Q _ij - D _i = 0; i = 1, ..., N;

In the formula: Q _ij is the flow from node i to node j; D _i is the water demand of node i; N is the total number of nodes;

4-3. If the sum of absolute flow changes is greater than the allowable value compared with the total flow of all pipe sections, use the new flow to re-solve the matrix equation AH=F to obtain a new flow;

4-4. Repeat step 4-3 until the sum of absolute flow changes is not greater than the allowable value compared with the total flow of all pipe sections, and the final flow value of all nodes is obtained.

The monitoring method of the node flow in the water supply pipe network of the present invention constructs the original system equation group according to the structural data of the pipe network, decomposes the coefficient matrix of the original system equation group, and produces a striped diagonal matrix and a residual matrix with approximately the same size; and then The banded diagonal matrix is divided into several small banded diagonal matrices and assigned to different threads of the GPU for calculation, making full use of the data parallel processing capability of the GPU, greatly improving the computing speed, and making the real-time simulation of giant pipe network data a possible, with low memory consumption, and scalable to a wide range of applications.

The present invention decomposes the coefficient matrix of the original system equation group, and adopts the iterative operation of parallel processing for each decomposed small system equation group. After obtaining the initial flow value of each node in the water supply network, the initial flow value of all nodes is The flow value is substituted into the original system equations as the initial value (i.e. input) of the original system to solve directly, and a direct method is executed in the external iterator to calculate the full solution. When the external iteration converges, the solution is completed, which can overcome the limitations of the direct method and the iterative method. shortcoming,

Better scalable performance than direct solvers and more robust than traditional preconditioned iterative solvers.

Detailed ways

The method for monitoring node flow in the water supply pipe network of the present invention will be described in detail below.

A method for monitoring node flow in a water supply network, comprising the following steps:

(1) According to the relationship between the flow rate and head loss of the water supply network, construct the original system equations of the water supply network. For the construction method, see Mahmoud A.Elsheikh, Hazem I.Saleh, Ibrahim M.Rashwan.Hydraulic modeling of water supply distribution for Improving its quantity and quality. Sustain. Environ. Res., 23(6), 403-411 (2013).

In a water supply network with N nodes and NF known head nodes (i.e., pools and reservoirs), the flow and head loss relationship equation of the pipeline between node i and node j is as follows:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; r</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

In the formula: H _i is the node head of node i; H _j is the node head of node j; h _ij is the head loss from node i to node j; r is the drag coefficient (depending on the formula of head loss along the way used); Q _ij is the flow from node i to node j; n is the flow index; m is the local loss coefficient.

The relationship equation between the pump flow and head loss (negative head) between node i and node j is as follows:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>$

In the formula: h ₀ is the virtual head of the pump; ω is the relative speed of the pump; Q _ij is the flow rate from node i to node j; s and t represent the curve coefficients of the pump.

Based on actual data, the flow continuity equation and head loss original system equations of the hydraulic state of the water supply network at a given time point are constructed as follows:

AH=F

In the formula: A is the Jacobian matrix of N×N; H is the vector matrix of unknown node water head in the N×1 water supply network; F is the vector matrix of N×1 constant items, and N is the total number of connected nodes;

The diagonal elements of the Jacobian matrix are: A _ii =∑ _j P _ij ;

The non-zero and off-diagonal elements of the Jacobian matrix are A _ij =-P _ij ;

In the formula: P _ij represents the reciprocal of the flow derivation of the head loss between node i and node j, for the pipeline between node i and node j:

In the formula: r is the resistance coefficient; Q _ij is the flow from node i to node j; n is the flow index; m is the local loss coefficient;

For a pump between node i and node j:

In the formula: ω is the relative speed of the water pump; Q _ij is the flow rate from node i to node j; s and t represent the curve coefficients of the water pump;

The elements in the vector matrix F of the constant items include the sum of the unbalance of the net flow in the node and the flow correction factor, and the elements in the vector matrix F of the constant items are:

F _ij ＝(∑ _j Q _ij -D _i )+∑ _j y _ij +∑ _f P _if H _f

In the formula: D _i represents the water demand of node i;

y _ij is the flow correction factor, for the pipeline between node i and node j:

y _ij ＝P _ij (r|Q _ij | ⁿ +m|Q _ij | ² )sgn(Q _ij )

For a pump between node i and node j:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>$

H _f is the known node water head of node f;

h ₀ is the virtual total lift of the pump;

P _if represents the inverse of the derivative of the head loss with respect to flow for the link linking node i to node f of known head.

∑ _f P _if H _f represents the pipe segment connecting node i (node i is a node with unknown water head) to node f with known water head.

(2) Decompose the coefficient matrix of the original system of equations to obtain a banded diagonal matrix and a residual matrix, and then divide the banded diagonal matrix into several small banded diagonal matrices. The specific operations are as follows:

Set the first and last non-zero elements of each row in the coefficient matrix A to zero to obtain a banded diagonal matrix D, which is as close as possible to the coefficient matrix A of the original system equation; keep the coefficient matrix The first and last elements of each row in A are not zero, and the remaining elements are set to zero to obtain the residual matrix R, that is, the banded diagonal matrix and the residual matrix satisfy A=D+R;

The banded diagonal matrix D is further divided into h small banded diagonal matrices D _i , as follows:

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\left(\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}\end{array}\right)$

If the number of rows of the banded diagonal matrix D is m, then the number of rows C=[m/h] of each small banded diagonal matrix D _i (the square brackets represent the rounding down operation, for example Then C takes 10), the small banded diagonal matrix D _i of i<h is formed from the (i-1)×C+1th to i×Cth rows in the banded diagonal matrix D. From the zero element to the last non-zero element; the small banded diagonal matrix D _h consists of the i×C+1th to the mth row in the banded diagonal matrix D, and the first one of each row is not zero elements to the last non-zero element.

The number of small striped diagonal matrices depends on the number of cores of the GPU. After the small striped diagonal matrices are divided, each small striped diagonal matrix is assigned to a thread of the GPU for subsequent calculations.

(3) Combine each small strip diagonal matrix with the residual matrix at the same time to obtain the initial flow values of all nodes in the water supply network. The specific operations are as follows:

3-1. Let the odd-numbered row elements in the residual matrix R be zero, so that the residual matrix R is converted into an approximate residual matrix

3-2. Each small striped diagonal matrix is expanded to a matrix with the same size as the coefficient matrix A, which is used as an approximate matrix of the small striped diagonal matrix will approximate the residual matrix and the approximation matrix of the small banded diagonal matrix Bringing it into the original system of equations AH=F, the approximate system equations are obtained as follows:

In the formula, is an approximate matrix of any small banded diagonal matrix;

is an approximate residual matrix,

H is a vector matrix composed of flow values of all nodes in the water supply network;

F is the constant term vector matrix of the original system of equations;

3-3. Utilization The matrix G is calculated, and the nodes corresponding to all non-zero elements in the matrix G are regarded as a set of non-zero nodes. for the inverse matrix;

3-4. Use the obtained non-zero node set to construct a small system of equations:

In the formula:

I _Z is the identity matrix;

G _Z is a matrix formed by the flow values of all nodes in the non-zero node set corresponding to the nodes in the water supply network;

is a vector composed of node flow values corresponding to all nodes in the non-zero node set in the water supply network;

Among them, g ₁ , g ₂ ,…g _s are respectively The value of the 1st, 2nd, ... s components of , s is the number of nodes in the non-zero node set;

3-5. Use the preprocessing conjugate gradient iterative method to solve the small system equations to obtain the initial flow values of all nodes in the non-zero node set; for the nodes in the small strip diagonal matrix Di that do not belong to the non-zero node set (ie exist There is no corresponding element in the node), and the initial flow value of the node with the smallest distance from the node in the non-zero node set is taken as the initial flow value of the node.

The threads of the GPU perform step 3-2 to step 3-5 on the small banded diagonal matrix D1, the small banded diagonal matrix D2, the small banded diagonal matrix D ₃ ... the small banded diagonal matrix D _h , to obtain the initial flow value vectors H ₁ , H ₂ , ... H _h of the nodes corresponding to each small strip diagonal matrix.

(4) Take the initial flow values of all nodes as the initial input of the water supply system, iterate until the final flow values of all nodes are obtained, the steps are as follows:

4-1. Take the initial flow value of the node corresponding to each component of the initial flow value vector H ₁ , H ₂ , ... H _h as the value of the component corresponding to the node in the vector H; for example, a certain value in H ₁ The element corresponds to the i-th node in the water supply network (namely, node i), which means that the element is the initial flow value of the i-th node in the water supply network, and this element is used as the component of the i-th row in the vector H.

Since the combination of initial flow value vectors H ₁ , H ₂ ,…,H _h covers all the rows in the banded diagonal matrix D, the combination of initial flow value vectors H ₁ , H ₂ ,…,h _h can get the initial flow of all nodes value.

4-2. Solve the original system equations AH=F, after obtaining the new node water head, the new flow is:

Q _ij ＝Q _ij -(y _ij -P _ij (H _i -H _j ))

The new flow rate needs to satisfy the following flow continuity equation:

∑ _j Q _ij - D _i = 0; i = 1, ..., N;

In the formula: Q _ij is the flow from node i to node j; D _i is the water demand of node i; N is the total number of nodes;

4-3. If the sum of absolute flow changes is greater than the allowable value (for example, 0.001) compared with the total flow of all pipe sections, then use the new flow to re-solve the matrix equation AH=F to obtain a new flow;

4-4. Repeat step 4-3 until the sum of absolute flow changes is not greater than the allowable value compared with the total flow of all pipe sections, and the final flow value of all nodes is obtained.

The present invention utilizes the existing fluid mechanics modeling technology, fluid pipe network composition modeling technology, and computer parallel computing technology, and aims at the characteristics of fluid mechanics and composition, improves the calculation model of mechanics and composition calculation, accelerates the convergence speed of the equation, and utilizes the matrix Decomposition to make full use of the super parallel capability of the computer GPU to solve the inefficiency of the current large-scale fluid pipeline network in early warning, energy saving and emission reduction, safe supply, planning and design real-time analysis, improve the speed of simulation, and meet real-time application requirements.

The present invention is widely used in practical applications. For example, when the water head changes, the method of the present invention can be used to quickly calculate the flow value of each node in the water supply pipe network. Specifically, when the water head of a certain reservoir changes, It can calculate the flow rate of the node corresponding to a certain area in time, that is, check whether the water supply in this area is normal.

For another example, when the flow of a certain node needs to reach a certain value, the value of the known water head can be continuously changed until it reaches a certain value, and the node can calculate the expected flow. After the known water head is adjusted to the corresponding value, the node can obtain expected traffic.

Claims (6)

1. a method for supervising for node flow in water supply network, is characterized in that, comprises the following steps:

(1), according to the loss relation of the flowrate and delivery head of water supply network, build the primal system system of equations of water supply network;

(2) matrix of coefficients of primal system system of equations is decomposed, obtain a banded diagonal matrix and a remaining matrix, then described banded diagonal matrix is divided into several small band shape diagonal matrix;

(3) each small band shape diagonal matrix is combined with described remaining matrix respectively simultaneously, obtains the initial flow value of all nodes in water supply network;

(4) initial input using the initial flow value of all nodes as water system, iteration is to the final flow rate value that obtains all nodes.

2. the method for supervising of node flow in water supply network as claimed in claim 1, is characterized in that, described primal system system of equations is:

AH＝F

In formula: the Jacobi matrix that A is N × N; H is the vector matrix of unknown node head in the water supply network of N × 1; F is the constant term vector matrix of N × 1, the sum that N is connected node;

The diagonal entry of described Jacobi matrix is: A _ii=∑ _jp _ij;

The non-zero of described Jacobi matrix and off diagonal element are A _ij=-P _ij;

In formula: P _ijrepresent between node i and node j that the pipeline section loss of flood peak is for the inverse of flow differentiate, the pipeline between node i and node j:

In formula: r is resistance coefficient; Q _ijfor node i is to the flow of node j; N is the index of discharge; M is local loss coefficient;

Water pump between node i and node j:

In formula: the relative rotation speed that ω is water pump; Q _ijfor node i is to the flow of node j; S and t represent the curve coefficients of water pump;

Every element in constant term vector matrix F is:

F _ij＝(∑ _jQ _ij-D _i)+∑ _jy _ij+∑ _fP _ifH _f

In formula: D _irepresent the water requirement of node i;

Y _ijfor the flux modification factor, the pipeline between node i and node j:

y _ij＝P _ij(r|Q _ij| ⁿ+m|Q _ij| ²)sgn(Q _ij)

Water pump between node i and node j:

$y_{\mathrm{ij}}=-P_{\mathrm{ij}}{\mathrm{\&omega;}}^2(h_0-s({\left(\frac{Q_{\mathrm{ij}}}{\mathrm{\&omega;}}\right)}^t)$

H _ffor the node head of known node f;

H ₀for the empty total (pumping) head of water pump;

P _ifrepresent that the pipeline section loss of flood peak of node f that node i is connected to known head is for the inverse of flow differentiate.

3. the method for supervising of node flow in water supply network as claimed in claim 2, is characterized in that, the concrete operations that the coefficient matrices A of primal system system of equations AH=F is decomposed are as follows:

First of every a line in coefficient matrices A is made as to zero with last non-vanishing element, obtains banded diagonal matrix D; First and last non-vanishing element of every a line in retention factor matrix A, all the other elements are made as zero, obtain remaining matrix R;

Be h small band shape diagonal matrix D by banded diagonal matrix D Further Division _i, as follows:

$D=\left(\begin{array}{cccc}{D}_1& 0& 0& 0\\ 0& D_2& 0& 0\\ 0& 0& ...& 0\\ 0& 0& 0& D_h\end{array}\right)$

If the line number of banded diagonal matrix D is m, each small band shape diagonal matrix D _iline number C=[m/h], the small band shape diagonal matrix D of i<h _iin capable to the i × C by (the i-1) × C+1 in banded diagonal matrix D, first non-vanishing element of every a line forms to last non-vanishing element; Small band shape diagonal matrix D _hin capable to m by the i × C+1 in banded diagonal matrix D, first non-vanishing element of every a line forms to last non-vanishing element.

4. the method for supervising of node flow in water supply network as claimed in claim 3, is characterized in that, each small band shape diagonal matrix is combined with described remaining matrix respectively simultaneously, and the concrete operations of initial flow value that obtain all nodes in water supply network are as follows:

3-1, to make the odd-numbered line element value in remaining matrix R be zero, makes remaining matrix R be converted into approximate remaining matrix

3-2, each small band shape diagonal matrix is expanded to the matrix identical with coefficient matrices A size, as the approximate matrix of small band shape diagonal matrix

By described approximate remaining matrix approximate matrix with small band shape diagonal matrix bring in primal system system of equations AH=F, obtain approximation system equation as follows:

In formula, for the approximate matrix of any one small band shape diagonal matrix;

for approximate remaining matrix,

H is the vector matrix of unknown node head in the water supply network of N × 1;

F is the constant term vector matrix of primal system system of equations;

3-3, utilize formula calculate matrix G, using the node that in matrix G, all nonzero elements are corresponding as non-zero node set, for inverse matrix;

The non-zero node set that 3-4, utilization obtain builds mini-system system of equations:

In formula:

I _zfor unit matrix;

G _zthe matrix forming for the flow value of the corresponding node in water supply network of all nodes in non-zero node set;

for the vector of node-flow value composition corresponding with all nodes in non-zero node set in water supply network;

wherein, g ₁, g ₂... g _sbe respectively the 1st, 2 ... the value of s component, s is the number of the node in non-zero node set;

3-5, use pre-service conjugate gradient alternative manner solve mini-system system of equations, obtain the initial flow value of all nodes in non-zero node set; For small band shape diagonal matrix D _iin do not belong to the node of non-zero node set, using in non-zero node set with the initial flow value of the node of this nodal distance minimum initial flow value as this node, obtain the initial flow value vector H of the node that each small band shape diagonal matrix is corresponding ₁, H ₂... H _h.

5. the method for supervising of node flow in water supply network as claimed in claim 4, is characterized in that, the initial input using the initial flow value of all nodes as water system, and iteration is as follows to the step of final flow rate value that obtains all nodes:

4-1, by initial flow value vector H ₁, H ₂... H _hthe initial flow value of node corresponding to each component as the value of the component that in vectorial H, this node is corresponding;

4-2, solve primal system system of equations AH=F, after obtaining new node head, new flow is:

Q _ij＝Q _ij-(y _ij-P _ij(H _i-H _j))

New flow need meet as down-off continuity equation:

∑ _jQ _ij-D _i＝0；i＝1，.......，N；

In formula: Q _ijfor node i is to the flow of node j; D _irepresent the water requirement of node i; N is total number of node;

If 4-3 absolute flow rate changes compared with the total flow of sum and all pipeline sections, be greater than the numerical value of permission, utilize new flow solution matrix equation AH=F again, obtain new flow;

4-4, repeating step 4-3, until absolute flow rate changes compared with the total flow of sum and all pipeline sections, are not more than the numerical value of permission, obtain the final flow rate value of all nodes.

6. the method for supervising of node flow in water supply network as claimed in claim 5, it is characterized in that, adopt the different threads of GPU respectively the combination of each small band shape diagonal matrix and remaining matrix to be calculated, the check figure of GPU equates with the number of small band shape diagonal matrix.