CN107869653A - A kind of pipeline flow sensitivity matrix soil's rigidity method - Google Patents
A kind of pipeline flow sensitivity matrix soil's rigidity method Download PDFInfo
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- CN107869653A CN107869653A CN201711341116.1A CN201711341116A CN107869653A CN 107869653 A CN107869653 A CN 107869653A CN 201711341116 A CN201711341116 A CN 201711341116A CN 107869653 A CN107869653 A CN 107869653A
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F17—STORING OR DISTRIBUTING GASES OR LIQUIDS
- F17D—PIPE-LINE SYSTEMS; PIPE-LINES
- F17D5/00—Protection or supervision of installations
- F17D5/02—Preventing, monitoring, or locating loss
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/15—Correlation function computation including computation of convolution operations
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
- Y02A20/00—Water conservation; Efficient water supply; Efficient water use
- Y02A20/152—Water filtration
Abstract
The invention discloses a kind of pipeline flow sensitivity matrix soil's rigidity method, including：Obtain pipe network information, caliber of the pipe network information including each pipeline, pipe range, pipe friction, node water requirement；The hydraulic model of pipe network under normal operating condition is formed according to the pipe network information；Sensitivity matrix is obtained according to the hydraulic model, node pressure, pipeline flow；Gradient vector is formed according to the corresponding element of the sensitivity matrix；The pressure variety and changes in flow rate amount of pipe network monitoring point after leakage loss occur for acquisition；The residual error of each pipeline is obtained according to least square method, the gradient vector, the pressure variety and the changes in flow rate amount；Confirm that the minimum pipeline of residual error is Leakage Pipes.Soil's rigidity method provided by the invention reduces the investigation scope of maintenance personal, shortens the investigation time.Therefore, technical scheme provided by the invention can be quickly found out leakage loss point and be repaired, and finally reduce leakage loss time and economic loss.
Description
Technical field
The present invention relates to pipeline inspection technology field, more particularly to a kind of pipeline flow sensitivity matrix soil's rigidity side
Method.
Background technology
Urban pipe network is one of important infrastructure of industrial society, is occupied in economic development and the normal life of people
Consequence.In China, because the process of urbanization is constantly accelerated, in order to adapt to the needs of urban development, urban water supply
Pipe network also extended therewith by quick transformation, but most of pipe network is laid out by rule of thumb so that pipe network system reorganization and expansion shortage section
Foundation is learned, causes water supply load uneven, leakage loss easily occurs, booster occurs when serious.The water supply network of old town
Increasingly aging, there is corrosion, intensity losses, leakage loss easily occur.Counted according to 2014, national leakage loss total amount reaches 65
Hundred million m3, leak rate reaches 15%.These leakage losses cause national heavy economic losses.However, existing method can not navigate to
Leakage Pipes, node can only be navigated to, at least two pipelines of connection, investigation scope are very big, it is necessary to expend substantial amounts of for a node
Manpower and materials.
The content of the invention
To solve the above problems, the present invention provides a kind of pipeline flow sensitivity matrix soil's rigidity method, at least partly
Solves above-mentioned technical problem.
Therefore, the present invention provides a kind of pipeline flow sensitivity matrix soil's rigidity method, including：
Obtain pipe network information, caliber of the pipe network information including each pipeline, pipe range, pipe friction, node water requirement；
The hydraulic model of pipe network under normal operating condition is formed according to the pipe network information；
Sensitivity matrix is obtained according to the hydraulic model, node pressure, pipeline flow；
Gradient vector is formed according to the corresponding element of the sensitivity matrix；
The pressure variety and changes in flow rate amount of pipe network monitoring point after leakage loss occur for acquisition；
Obtained according to least square method, the gradient vector, the pressure variety and the changes in flow rate amount each
The residual error of pipeline；
Confirm that the minimum pipeline of residual error is Leakage Pipes.
Optionally, the sensitivity matrix is
Wherein, a, b are pipeline upstream and downstream nodes, and the sensitivity matrix of pipeline flow is expressed as corresponding pipeline upstream and downstream node
The half of flow rate sensitive matrix element sum；
The node flow sensitivity matrix is
Wherein, B is diagonal matrix
A is n × m incidence matrix, and for describing the topological relation of pipe network, n and m is respectively nodes and pipe number.
Optionally, described the step of forming the hydraulic model of pipe network under normal operating condition according to the pipe network information, wraps
Include：
The hydraulic model is formed using EPANET softwares.
Optionally, described the step of obtaining sensitivity matrix according to the hydraulic model, node pressure, pipeline flow, wraps
Include：
The sensitivity matrix is obtained using analytic method.
The present invention has following beneficial effects：
Pipeline flow sensitivity matrix soil's rigidity method provided by the invention, including：Obtain pipe network information, the pipe network
Caliber of the information including each pipeline, pipe range, pipe friction, node water requirement；Normal operation is formed according to the pipe network information
The hydraulic model of pipe network under state；Sensitivity matrix is obtained according to the hydraulic model, node pressure, pipeline flow；According to
The corresponding element of the sensitivity matrix forms gradient vector；Obtain occur leakage loss after pipe network monitoring point pressure variety and
Changes in flow rate amount；Obtained according to least square method, the gradient vector, the pressure variety and the changes in flow rate amount each
The residual error of individual pipeline；Confirm that the minimum pipeline of residual error is Leakage Pipes.Soil's rigidity method provided by the invention reduces maintenance
The investigation scope of personnel, shorten the investigation time.Therefore, technical scheme provided by the invention can be quickly found out the progress of leakage loss point
Maintenance, finally reduces leakage loss time and economic loss.
Brief description of the drawings
Fig. 1 is the flow chart based on pipeline flow sensitivity matrix soil's rigidity method that the embodiment of the present invention one provides；
Fig. 2 is the structural representation for the hydraulic model that the embodiment of the present invention one provides；
Fig. 3 is the node variable quantity after the different pipelines generation leakage loss that the embodiment of the present invention one provides；
Fig. 4 is the result schematic diagram that progress leakage loss positioning after leakage loss occurs for the pipeline 1 that the embodiment of the present invention one provides；
Fig. 5 is the result that 50 leakage loss positioning experiments of progress after leakage loss occur for the pipeline 1 that the embodiment of the present invention one provides
Count schematic diagram；
Fig. 6 is a kind of investigation scope that progress leakage loss positioning after leakage loss occurs for the pipeline 1 that the embodiment of the present invention one provides
Schematic diagram；
Fig. 7 is another investigation model that progress leakage loss positioning after leakage loss occurs for the pipeline 1 that the embodiment of the present invention one provides
Enclose schematic diagram.
Embodiment
To make those skilled in the art more fully understand technical scheme, the present invention is carried below in conjunction with the accompanying drawings
The pipeline flow sensitivity matrix soil's rigidity method of confession is described in detail.
Embodiment one
Pipe network model positioning can be roughly divided into two classes：1) data model is established by the pipe network model Monitoring Data of collection
Carry out soil's rigidity；2) build hydraulic model and carry out soil's rigidity, being fitted leakage loss state by hydraulic model positions leakage loss.First
Class is to establish data model, and leakage loss is detected using data model, and conventional method will be collected into by neutral net
Soil's rigidity data neutral net is trained, the model trained is used for soil's rigidity.Can also utilize support to
The data such as amount machine, flow and pressure judge that the region whether there is leakage loss.However, carry out soil's rigidity needs using data model
The Detection results that the soil's rigidity data of whole pipelines can be only achieved largely are covered, in practice it is difficult to be collected into enough
Data.Second class is to establish mechanism model, and the leakage loss state of pipe network is fitted using hydraulic model.This method can be not a large amount of
Soil's rigidity is carried out in the case of Monitoring Data.However, existing method can not navigate to Leakage Pipes, water supply can only be navigated to
Node, at least two pipelines of connection, investigation scope are very big, it is necessary to expend substantial amounts of manpower and materials for a node.
The present embodiment obtains the information such as the caliber of pipe network, pipe range, pipe friction, node water requirement first, recycles
EPANET builds hydraulic model, and EPANET is the open source software of US Gov Env Protection Agency's exploitation, followed by analytic method meter
Operator node pressure, pipeline flow are to the sensitivity matrix of pipeline flow.The present embodiment according to the continuity equation of water supply network and
The differential expression (1) of energy equation derives above-mentioned sensitivity matrix.
Wherein, Δ q, Δ Q and Δ h are respectively pipeline flow change vector, node flow change vector and pipeline leakage
Change vector, A are n × m incidence matrix, and for describing the topological relation of pipe network, n and m is respectively nodes and pipe number.A squares
The determination method of the element of battle array is as follows：
Then, the present embodiment to sea once-William's equation (3) ask partial differential bring into formula (1) obtain
Wherein, k is unit conversion coefficient, d, l, q and c be pipeline caliber, pipe range, flow and sea once-William's coefficient,
So as to try to achieve node pressure, pipeline flow to the sensitivity matrix (4) of node flow.
Wherein, B is diagonal matrix
The present embodiment further derives the quick of pipeline flow on equivalent to two nodes of leakage loss according to the two nodes
Perceptual matrix, the pipeline occurred using least square fitting and determination leakage loss.
The present embodiment structure object function be
Wherein,For the equivalent ullage for a, b node being connected with Leakage Pipes l, wH, wqRespectively hydraulic pressure with
The weight coefficient of flow, herein the present embodiment for monitoring error variance inverse, HiWith qjHydraulic pressure under leakage loss state is represented respectively
With flow monitoring value, nH, mq represent pressure detecting point quantity and flow monitoring point quantity respectively.The target letter that the present embodiment provides
Several meanings are：Adjust node a, b of pipeline l connections equivalent ullage so that under the calculated value and leakage loss state of model
Monitor value as far as possible match.The soil's rigidity method that the present embodiment provides reduces the investigation scope of maintenance personal, the row of shortening
Look into the time.Therefore, the technical scheme that the present embodiment provides can be quickly found out leakage loss point and be repaired, when finally reducing leakage loss
Between and economic loss.
The present embodiment carries out binary function first order Taylor expansion to formula (6), and wherein formula (7) is
Present embodiment assumes that ullage when leakage loss occurs is Δ Ql, water is needed by what ullage was assumed to be pipe ends node
Amount increase, and incrementss are identical, i.e.,Therefore, formula (7) can be expressed as
The sensitivity matrix analytic expression of pipeline flow can be approximately by the present embodiment：
Wherein, Δ H0=H-H (Qa, Qb), Δ q0=q-qQaQb), H and q are respectively the hydraulic pressure and flow under leakage loss state
Monitoring vector.Therefore, formula (8) is weighted least square regression, and the ullage for solving pipeline is：
The changing value of hydraulic pressure and flow is among the hydraulic pipeline model that the present embodiment provides：
Formula (10) is substituted into formula (11) to obtain：
The technical scheme that the present embodiment provides can be quickly found out leakage loss point and be repaired, finally reduce the leakage loss time and
Economic loss.The present embodiment obtains the residual error of object function by formula (13), and formula (13) is
The minimum pipeline of residual error is confirmed as Leakage Pipes by the present embodiment, so as to reduce the investigation scope of maintenance personal,
Shorten the investigation time.Therefore, the technical scheme that the present embodiment provides can be quickly found out leakage loss point and be repaired, final to reduce
Leakage loss time and economic loss.
The technical scheme of the present embodiment is specifically described by taking a complicated simulation pipe network as an example below.
Fig. 1 is the flow chart based on pipeline flow sensitivity matrix soil's rigidity method that the embodiment of the present invention one provides.
As shown in figure 1, the present embodiment builds hydraulic model and its pipe network structure using EPANET, there are two water pumps, Er Qieyou in pipe network
One head-tank is pipe network water supply.14 pressure monitoring points and 2 flow monitoring points, position such as Fig. 1 institutes are provided with pipe network
Show.The present embodiment is carried out using EPANET to the leakage loss of different pipelines
Simulate, the pressure of monitoring point, the variable quantity of flow after simulation webmaster generation leakage loss.Fig. 2 is the embodiment of the present invention
The structural representation of one hydraulic model provided, Fig. 3 occur for the different pipelines that the embodiment of the present invention one provides after leakage loss
Node variable quantity.The pipeline leakage amount of the present embodiment simulation is 20L/S, and the pressure change of part pressure measurement node is as shown in Fig. 2 right
In the leakage loss of different pipelines, the variable quantity and changing rule of pressure measurement node are different, and this is also that this method carries out leakage loss positioning
Basis.In order to assess the uncertain influence to leakage loss positioning result of monitoring error so that the experiment that the present embodiment provides
The working condition of actual pipe network is more conformed to, the present embodiment is produced in the random error of monitor value using Monte Carlo simulation, section
The variances sigma of point water pressure monitoring errorH=0.1m.Because the uncertainty of error causes the uncertainty of positioning, the present embodiment enters
50 leakage loss positioning experiments of row.
After leakage loss occurs for pipeline 1, the present embodiment is tested with wherein one-time positioning to illustrate soil's rigidity method.
The change vector of monitoring point is among this experiment that the present embodiment provides
After leakage loss occurs for pipeline 1, the present embodiment is fitted using least square method, obtains node pressure, pipeline stream
The corresponding element to pipeline flow sensitivity matrix is measured, so as to form gradient vector, the gradient vector is
The present embodiment utilizes weighted least-squares method to solve the ullage of pipeline
The soil's rigidity method that the present embodiment provides reduces the investigation scope of maintenance personal, shortens the investigation time.Cause
This, the technical scheme that the present embodiment provides can be quickly found out leakage loss point and be repaired, and finally reduce leakage loss time and economy
Loss.When the ullage of pipeline 1 is Δ Q1When, the changing value that the present embodiment calculates hydraulic pressure and flow according to hydraulic pipeline model is
Therefore, the present embodiment acquisition residual error is
The present embodiment is summed to residual absolute value, obtains total residual error, similarly travels through each pipeline, tries to achieve each pipe
The residual error in road, final result are as shown in Figure 4.Fig. 4 is that the pipeline 1 that the embodiment of the present invention one provides occurs to carry out leakage loss after leakage loss
The result schematic diagram of positioning.The residual error of pipeline 1 is minimum, therefore pipeline 1 is Leakage Pipes.
The soil's rigidity method that the present embodiment provides reduces the investigation scope of maintenance personal, shortens the investigation time.Cause
This, the technical scheme that the present embodiment provides can be quickly found out leakage loss point and be repaired, and finally reduce leakage loss time and economy
Loss.
Fig. 5 is the result that 50 leakage loss positioning experiments of progress after leakage loss occur for the pipeline 1 that the embodiment of the present invention one provides
Count schematic diagram.The present embodiment carries out 50 positioning experiments, and leakage loss positioning scenarios are counted, give what leakage loss navigated to
Pipeline ID and the number navigated to.Among 50 positioning, have and navigate to pipeline Isosorbide-5-Nitrae for 42 times to navigate to pipeline 7,2 times fixed
Pipeline 2 and pipeline 15 are arrived in position.As can be seen here, correct Leakage Pipes can be navigated to when most, the present embodiment, which calculates, to be obtained
Average ullage be 20.059L/s, be sufficiently close to true leakage loss (20L/s).
Fig. 6 is a kind of investigation scope that progress leakage loss positioning after leakage loss occurs for the pipeline 1 that the embodiment of the present invention one provides
Schematic diagram.As shown in fig. 6, four pipelines being positioned are circled among Fig. 6, leakage loss is positioned among the scope shown in Fig. 6,
Therefore, the pipeline of position inaccurate is also very close real Leakage Pipes.Therefore, the experiment that the present embodiment provides fully is demonstrate,proved
Understand the feasibility and correctness of soil's rigidity method.The soil's rigidity method that the present embodiment provides reduces the row of maintenance personal
Scope is looked into, shortens the investigation time.The soil's rigidity method that the present embodiment provides reduces the investigation scope of maintenance personal, shortens
Investigation time.Therefore, the technical scheme that the present embodiment provides can be quickly found out leakage loss point and be repaired, and finally reduce leakage
Damage time and economic loss.
The present embodiment can also carry out leakage loss simulation using same method to different pipelines, then carry out leakage loss positioning.
Too many due to being related to data, the present embodiment is not shown all, and the positioning statistical conditions after leakage loss occur for an exposition pipeline
As shown in table 1.1 table reflects similar property, and most cases navigate to correct Leakage Pipes, the pipeline of position inaccurate
Near Leakage Pipes.
A kind of positioning statistics after leakage loss occurs for the section of tubing of table 1
The soil's rigidity method that the present embodiment is provided below is with utilizing the positioning side based on node flow sensitivity matrix
Method is contrasted.This method can navigate to node, and leakage loss occurs near nodal.But a node is at least connected with two pipes
Road, it is very big that scope is investigated in the case of positioning correctly.In the case of position inaccurate, investigate near positioning node
Node connection pipeline, then investigation amount can exponentially increase.The soil's rigidity method that the present embodiment provides reduces maintenance
The investigation scope of personnel, shorten the investigation time.
Fig. 7 is another investigation model that progress leakage loss positioning after leakage loss occurs for the pipeline 1 that the embodiment of the present invention one provides
Enclose schematic diagram.As shown in fig. 7, using same method, after leakage loss occurs for pipeline 1,50 leakage loss positioning experiments, figure are carried out
7 show the investigation scope of leakage loss positioning, with Fig. 6 contrasts as can be seen that the soil's rigidity method that the present embodiment provides substantially contracts
Small leakage loss investigation scope.
The present embodiment carries out leakage loss simulation to different pipelines, then carries out leakage loss positioning, leakage loss positioning scenarios are counted.
Part positioning result displaying is as shown in table 2.From table 2 it can be seen that leakage loss positioning scenarios show similar property, this method
The scope of leakage loss node can also be substantially oriented, but leakage loss investigation scope is more much bigger than the investigation scope of the present embodiment.
It is possible thereby to illustrate the superiority for the technical scheme that the present embodiment provides, the investigation scope of leakage loss is greatly reduced.
Another positioning statistics after leakage loss occurs for the section of tubing of table 2
The pipeline flow sensitivity matrix soil's rigidity method that the present embodiment provides, including：Obtain pipe network information, the pipe
Caliber of the net information including each pipeline, pipe range, pipe friction, node water requirement；Normal fortune is formed according to the pipe network information
The hydraulic model of pipe network under row state；Sensitivity matrix is obtained according to the hydraulic model, node pressure, pipeline flow；Root
Gradient vector is formed according to the corresponding element of the sensitivity matrix；The pressure variety of pipe network monitoring point after leakage loss occurs for acquisition
With changes in flow rate amount；Obtained according to least square method, the gradient vector, the pressure variety and the changes in flow rate amount
The residual error of each pipeline；Confirm that the minimum pipeline of residual error is Leakage Pipes.The soil's rigidity method that the present embodiment provides reduces
The investigation scope of maintenance personal, shorten the investigation time.Therefore, the technical scheme that the present embodiment provides can be quickly found out leakage loss
Point is repaired, and finally reduces leakage loss time and economic loss.
It is understood that the principle that embodiment of above is intended to be merely illustrative of the present and the exemplary implementation that uses
Mode, but the invention is not limited in this.For those skilled in the art, the essence of the present invention is not being departed from
In the case of refreshing and essence, various changes and modifications can be made therein, and these variations and modifications are also considered as protection scope of the present invention.
Claims (4)
- A kind of 1. pipeline flow sensitivity matrix soil's rigidity method, it is characterised in that including：Obtain pipe network information, caliber of the pipe network information including each pipeline, pipe range, pipe friction, node water requirement；The hydraulic model of pipe network under normal operating condition is formed according to the pipe network information；Sensitivity matrix is obtained according to the hydraulic model, node pressure, pipeline flow；Gradient vector is formed according to the corresponding element of the sensitivity matrix；The pressure variety and changes in flow rate amount of pipe network monitoring point after leakage loss occur for acquisition；Each pipeline is obtained according to least square method, the gradient vector, the pressure variety and the changes in flow rate amount Residual error；Confirm that the minimum pipeline of residual error is Leakage Pipes.
- 2. pipeline flow sensitivity matrix soil's rigidity method according to claim 1, it is characterised in that the sensitiveness Matrix is<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>J</mi> <mi>H</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>Q</mi> <mi>l</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>J</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>Q</mi> <mi>l</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0.5</mn> <mo>(</mo> <msub> <mi>J</mi> <mi>H</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>l</mi> <mi>a</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>J</mi> <mi>H</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>l</mi> <mi>b</mi> </msubsup> <mo>)</mo> </mrow> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mn>0.5</mn> <mo>(</mo> <msub> <mi>J</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>l</mi> <mi>a</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>J</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>l</mi> <mi>b</mi> </msubsup> <mo>)</mo> </mrow> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> </mrow>Wherein, a, b are pipeline upstream and downstream nodes, and the sensitivity matrix of pipeline flow is expressed as corresponding pipeline upstream and downstream node flow The half of sensitivity matrix element sum；The node flow sensitivity matrix is<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&part;</mo> <mi>H</mi> </mrow> <mrow> <mo>&part;</mo> <mi>Q</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>ABA</mi> <mi>T</mi> </msup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&part;</mo> <mi>q</mi> </mrow> <mrow> <mo>&part;</mo> <mi>Q</mi> </mrow> </mfrac> <mo>=</mo> <msup> <mi>BA</mi> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <msup> <mi>ABA</mi> <mi>T</mi> </msup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>Wherein, B is diagonal matrixA is n × m incidence matrix, and for describing the topological relation of pipe network, n and m is respectively nodes and pipe number.
- 3. pipeline flow sensitivity matrix soil's rigidity method according to claim 1, it is characterised in that described according to institute Stating the step of pipe network information forms the hydraulic model of pipe network under normal operating condition includes：The hydraulic model is formed using EPANET softwares.
- 4. pipeline flow sensitivity matrix soil's rigidity method according to claim 1, it is characterised in that described according to institute Stating the step of hydraulic model, node pressure, pipeline flow obtain sensitivity matrix includes：The sensitivity matrix is obtained using analytic method.
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| CN108647470A (en) * | 2018-05-29 | 2018-10-12 | 杭州电子科技大学 | A kind of localization method at the beginning of based on the leakage loss with depth belief network is clustered |
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| CN110043808A (en) * | 2019-05-29 | 2019-07-23 | 浙江大学 | Water supply network leakage monitoring method for early warning based on time series analysis |
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