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

Abstract

The invention discloses a method for monitoring node flow of a water supply network. The method includes the following steps that an original system equation set of the water supply network is established according to the loss relation between flow of the water supply network and a water head; a coefficient matrix of the original system equation set is decomposed so that a banded diagonal matrix and a residual matrix can be acquired, and then the banded diagonal matrix is divided into a plurality of small banded diagonal matrixes; the small banded diagonal matrixes are respectively combined with the residual matrix at the same time initial flow values of all nodes in the water supply network can be acquired; the initial flow values of all the nodes serve as initial input of a water supply system, and then final flow values of all the nodes are acquired after iteration. Superstrong parallel computing capacity of a computer CPU is fully utilized through matrix decomposition, the iteration convergence rate is increased when the node flow of the water supply network is computed, real-time data of the node flow are acquired, and the node flow is monitored.

Description

The method for supervising of node flow in a kind of water supply network

Technical field

The present invention relates to urban water supply and sewerage field, be specifically related to the method for supervising of node flow in a kind of water supply network.

Background technology

Water supply network in China city, the crude oil pipeline network of oil refining enterprise, farmland waterpower pipe network, steam supply pipe network, heating network etc. are very flourishing, and the scale of these pipe networks is all very large, node pressure, the fluid composition etc. of pipe network is the operational factor that must control in pipe network daily servicing.

Accurately these operational factors of analysis mode are that all pipe networks are safeguarded the common problem facing in real time, the key that solves this common problem is fluid pipe network mechanics and composition high-efficiency real-time dynamic emulation technology, and the application of these technology can provide in advance for the daily servicing of pipe network the functions such as planning, dynamic management in real time, emergent, security control afterwards, energy-saving and emission-reduction.

The at present management of fluid pipe network is mainly in the following ways:

The first kind is artificial designing and calculating, based on artificial sample and hand computation.This mode is comparatively backward, and efficiency is very low, and hand computation is loaded down with trivial details, and error rate is high, and can only calculate pipe network among a small circle, cannot carry out unified calculating to large-scale pipe network, conventionally can cause attending to one thing and lose sight of another, and is difficult to accomplish to make overall plans.

Equations of The Second Kind is the designing and calculating that appliance computer carries out pipe network, and this is also the mode being most widely used at present.But also there is a larger problem in this mode at present, be exactly in the time that pipe network is larger, travelling speed is not fully up to expectations, have a strong impact on the analysis speed of pipe network data, along with the expansion of pipe network scale, the real time dynamic simulation of pipe network mechanics, composition is possibility hardly, and the pipe network mechanical simulation of for example general 4000 nodes is calculated needs the internal memory of 12G and the iterative approach simulating actual conditions more exactly of about 30 minutes.

Cause the slow reason of travelling speed to mainly contain two, first is exactly most method in separating extensive system of equations, and iterations is too many, sometimes cannot restrain even at all; Second is exactly the travelling speed that is limited to current CPU, and computing velocity cannot be promoted again, therefore how to find the technical scheme that solves these two problems, and is applied in Practical Project, just becomes most important.

The software that has had at present a lot of waterpower water analyses, they have used technology above-mentioned mostly, and these softwares can solve the Hydraulic Calculation Problems of thousands of pipeline sections.By U.S. environment protection general administration country risk management review development in laboratory, be mainly used in and press the waterpower of pipe network system and the software of water analysis, there is the function of the aspects such as pipe network adjustment, operation simulation, information management, operational management.Its method based on separating modal equation, can process Direct Modeling without simplifying to pipe network, has reduced and has calculated needed time and storage unit, and the convenience based on its application and intuitive are applied to the compensating computation of pressing pipe network system more and more widely.

SynerGEE Gas can carry out simulation modeling and analysis to pipe network, pressure regulator, valve, compressor, gas storage field and gas collection well, SynerGEE Gas is as the universal pipe network emulation tool of one, be applicable to rock gas, propane, steam, oxygen, carbon dioxide, nitrogen, chlorine and air, and be not limited only to this.The function that SynerGEE Gas provides state-of-the-art commercialization pipe simulating device to have, and can in simple and easy and familiar windows operating system, move.

At present said system all exists speed too slow being applied to aspect the analog simulation of huge pipe network, the problem that efficiency is too low.The developing direction of following simulation software towards pipe network is: the speed and the efficiency that improve analog simulation by concurrent operation, strengthen software in the various mechanics of the huge pipe network of real Time Dynamic Simulation and the ability of composition, for the application such as planning in advance, early warning in advance, dynamic monitoring, safety is emergent provide in time efficient software support.

Summary of the invention

The invention provides the method for supervising of node flow in a kind of water supply network, utilize matrix decomposition to make full use of the superpower computation capability of computing machine GPU, iterative convergence speed when node flow calculates in quickening water supply network, obtain the real time data of node flow, realize the monitoring to node flow.

A method for supervising for node flow in water supply network, 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.

Build some preset time according to real data, the Flow continuity equation of the waterpower state of water supply network and loss of flood peak primal system system of equations, 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:

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

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.

Sgn (Q _ij) in, work as Q _ijwhen >0, sgn (Q _ij) value is 1, Q _ijfor water pump always for just.

(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.

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, the line number C=[m/h of each small band shape diagonal matrix Di], 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.

(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, concrete operations 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 (being also the vector matrix of the flow value composition of all nodes in water supply network) 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.

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.

(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, and step is as follows:

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.

In water supply network of the present invention, the method for supervising of node flow has built primal system system of equations according to the structured data of pipe network, and the matrix of coefficients of primal system system of equations is decomposed, and produces size roughly the same banded diagonal matrix and remaining matrix; Then the different threads that banded diagonal matrix is divided into some small band shape diagonal matrix and distributes to GPU calculates, take full advantage of the parallel data processing ability of GPU, greatly improve arithmetic speed, make the real time modelling of giant steel tube network data become possibility, and memory consumption is low, can expand to widely in application program.

The present invention is by decomposing the matrix of coefficients of primal system system of equations, the mini-system system of equations that each decomposition is obtained adopts the iterative operation of parallel processing, obtaining after the initial flow value of each node in water supply network, initial value (i.e. input) substitution primal system system of equations direct solution using the initial flow value of all nodes as primal system, in outside iterator, carry out a direct method and calculate complete solution, in the time of outside iteration convergence, complete and solve, can overcome the shortcoming of direct method and process of iteration

Scalable Performance than direct resolver is better, more healthy and stronger than traditional pretreatment iteration resolver.

Embodiment

Below the method for supervising of node flow in water supply network of the present invention is described in detail.

A method for supervising for node flow in water supply network, 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, construction method is referring to Mahmoud A.Elsheikh, Hazem I.Saleh, Ibrahim M.Rashwan.Hydraulic modelling of water supply distribution for improving itsquantity and quality.Sustain.Environ.Res., 23 (6), 403-411 (2013).

Having in the water supply network of N node and NF known water head node (being pond and reservoir), between node i and node j, the flowrate and delivery head of pipeline loss relation equation is as follows:

$h_{\mathrm{ij}}=H_i-H_j=r{Q}_{\mathrm{ij}}^n+m{Q}_{\mathrm{ij}}^2$

In formula: H _ifor the node head of node i; H _jfor the node head of node j; h _ijfor node i is to the loss of flood peak of node j; R is resistance coefficient (depending on the frictional head loss formula of use); Q _ijfor node i is to the flow of node j; N is the index of discharge; M is local loss coefficient.

Between node i and node j, the flowrate and delivery head of water pump loss (negative head) relation equation is as follows:

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

In formula: h ₀for the empty total (pumping) head of water pump; ω is the relative rotation speed of water pump; Q _ijfor node i is to the flow of node j; S and t represent the curve coefficients of water pump.

Build some preset time according to real data, Flow continuity equation and the loss of flood peak primal system system of equations of the waterpower state of water supply network are as follows:

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 Jacobi matrix is: A _ii=∑ _jp _ij;

The non-zero of 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 has comprised imbalance and the flux modification factor sum of net flow in node, and the 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.

∑ _fp _ifh _frepresent node i (node that node i is unknown head) to be connected to the pipeline section of the node f of known head.

(2) matrix of coefficients of primal system system of equations is decomposed, obtain a banded diagonal matrix and a remaining matrix, then banded diagonal matrix is divided into several small band shape diagonal matrix, concrete operations 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, banded diagonal matrix D approaches the coefficient matrices A of primal system equation as far as possible; 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, and banded diagonal matrix and remaining matrix meet A=D+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] (bracket represents downward rounding operation, for example c gets 10), 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.

The number of small band shape diagonal matrix depends on the check figure of GPU, and after small band shape diagonal matrix is divided, each small band shape diagonal matrix is distributed to respectively a thread of GPU, to carry out follow-up calculating.

(3) each small band shape diagonal matrix is combined with remaining matrix respectively simultaneously, obtains the initial flow value of all nodes in water supply network, concrete operations 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 expand to the matrix identical with coefficient matrices A size, as the approximate matrix of small band shape diagonal matrix to be similar to 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 the flow value composition of all nodes in water supply network;

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; (exist for the node that does not belong to non-zero node set in small band shape diagonal matrix Di in there is not the node of corresponding element), 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.

The thread of GPU is respectively to small band shape diagonal matrix D1, small band shape diagonal matrix D2, small band shape diagonal matrix D ₃small band shape diagonal matrix D _hcarry out the processing of step 3-2～step 3-5, obtain the initial flow value vector H of the node that each small band shape diagonal matrix is corresponding ₁, H ₂... H _h.

(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, and step is as follows:

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; For example, H ₁in the corresponding water supply network of certain element in i node (being node i), illustrate that this element is the initial flow value of i node in water supply network, the capable component of i using this element in vectorial H.

Due to initial flow value vector H ₁, H ₂..., H _hcombination covers all row in banded diagonal matrix D, therefore initial flow value vector H ₁, H ₂..., h _hcombination can obtain the initial flow value of all nodes.

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 (for example 0.001) 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.

The present invention utilizes existing fluid mechanics modeling technique, fluid pipe network composition modeling technique, computing machine parallel computing, for the feature of fluid mechanics and composition, improve the computation model that mechanics and composition calculate, accelerate the speed of convergence of equation, utilize matrix decomposition to make full use of the superpower parallel ability of computing machine GPU, solve the inefficiency problem of current large-scale fluid pipe network giving warning in advance, in energy-saving and emission-reduction, safety supply, planning and design real-time analysis, the speed that promotes emulation, meets real-time application demand.

The present invention is widely used in actual application, for example, in the time of known change of water level, utilize the inventive method can calculate soon to obtain the flow value of each node in water supply network quickly, particularly, in the time that the head of a certain reservoir changes, can calculate in time to obtain the flow of node corresponding to a certain region, check that whether this regional water supply is normal.

And for example, in the time that the flow of a certain node of needs reaches a certain numerical value, can continuously change the value of known head, until when a certain value, node can be calculated to obtain desired flow, known head is adjusted into after analog value, and node can access desired flow.

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.