CN107869653B - Pipeline flow sensitivity matrix leakage detection method - Google Patents
Pipeline flow sensitivity matrix leakage detection method Download PDFInfo
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Abstract
The invention discloses a method for detecting leakage of a pipeline flow sensitivity matrix, which comprises the following steps: acquiring pipe network information, wherein the pipe network information comprises pipe diameters, pipe lengths, pipe friction resistances and node water demands of all pipes; forming a hydraulic model of the pipe network under a normal operation state according to the pipe network information; obtaining a sensitivity matrix according to the hydraulic model, the node pressure and the pipeline flow; forming a gradient vector according to corresponding elements of the sensitivity matrix; acquiring the pressure variation and the flow variation of a pipe network monitoring point after leakage occurs; obtaining the residual error of each pipeline according to a least square method, the gradient vector, the pressure variation and the flow variation; and confirming the pipeline with the minimum residual error as a leakage pipeline. The leakage detection method provided by the invention reduces the investigation range of maintenance personnel and shortens the investigation time. Therefore, the technical scheme provided by the invention can quickly find the leakage point for maintenance, and finally reduces the leakage time and the economic loss.
Description
Technical Field
The invention relates to the technical field of pipeline detection, in particular to a pipeline flow sensitivity matrix leakage detection method.
Background
Urban pipe networks are one of important infrastructures of industrial society, and occupy an important position in economic development and normal life of people. In China, as the process of urbanization is accelerated continuously, in order to adapt to the requirement of urban development, an urban water supply network is also reconstructed and expanded rapidly, but most of the pipe networks are distributed according to experience, so that the reconstruction and the expansion of a pipe network system lack scientific basis, the water supply load is uneven, leakage easily occurs, and pipe explosion can occur in serious cases. The water supply pipe network in the old city area is aged day by day, and the corrosion appears, the intensity is reduced, and the leakage is easy to appear. According to the statistics in 2014, the total leakage loss of the whole country reaches 65 hundred million m3, and the leakage rate reaches 15%. These losses cause significant economic losses in the country. However, the existing method cannot position the leakage pipeline, only can position the node, and one node is connected with at least two pipelines, so that the investigation range is large, and a large amount of manpower and material resources are consumed.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for detecting leakage of a pipeline flow sensitivity matrix, which at least partially solves the above technical problems.
Therefore, the invention provides a method for detecting leakage of a pipeline flow sensitivity matrix, which comprises the following steps:
Acquiring pipe network information, wherein the pipe network information comprises pipe diameters, pipe lengths, pipe friction resistances and node water demands of all pipes;
Forming a hydraulic model of the pipe network under a normal operation state according to the pipe network information;
Obtaining a sensitivity matrix according to the hydraulic model, the node pressure and the pipeline flow;
Forming a gradient vector according to corresponding elements of the sensitivity matrix;
Acquiring the pressure variation and the flow variation of a pipe network monitoring point after leakage occurs;
Obtaining the residual error of each pipeline according to a least square method, the gradient vector, the pressure variation and the flow variation;
And confirming the pipeline with the minimum residual error as a leakage pipeline.
optionally, the sensitivity matrix is
wherein a and b are upstream and downstream nodes of the pipeline, and the sensitivity matrix of the pipeline flow is expressed as one half of the sum of the elements of the sensitivity matrix of the flow of the upstream and downstream nodes of the corresponding pipeline;
The node traffic sensitivity matrix is
Wherein B is a diagonal matrix
a is an n multiplied by m incidence matrix used for describing the topological relation of the pipe network, and n and m are the number of nodes and the number of pipelines respectively.
optionally, the step of forming a hydraulic model of the pipe network in the normal operation state according to the pipe network information includes:
the hydraulic model was developed using EPANET software.
Optionally, the step of obtaining a sensitivity matrix according to the hydraulic model, the node pressure, and the pipeline flow rate includes:
The sensitivity matrix is obtained analytically.
the invention has the following beneficial effects:
the invention provides a method for detecting leakage of a pipeline flow sensitivity matrix, which comprises the following steps: acquiring pipe network information, wherein the pipe network information comprises pipe diameters, pipe lengths, pipe friction resistances and node water demands of all pipes; forming a hydraulic model of the pipe network under a normal operation state according to the pipe network information; obtaining a sensitivity matrix according to the hydraulic model, the node pressure and the pipeline flow; forming a gradient vector according to corresponding elements of the sensitivity matrix; acquiring the pressure variation and the flow variation of a pipe network monitoring point after leakage occurs; obtaining the residual error of each pipeline according to a least square method, the gradient vector, the pressure variation and the flow variation; and confirming the pipeline with the minimum residual error as a leakage pipeline. The leakage detection method provided by the invention reduces the investigation range of maintenance personnel and shortens the investigation time. Therefore, the technical scheme provided by the invention can quickly find the leakage point for maintenance, and finally reduces the leakage time and the economic loss.
drawings
Fig. 1 is a flowchart of a method for detecting leakage based on a pipeline flow sensitivity matrix according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a hydraulic model according to an embodiment of the present invention;
Fig. 3 illustrates node variation after leakage occurs in different pipelines according to an embodiment of the present invention;
fig. 4 is a schematic diagram illustrating the result of leakage positioning after the pipeline 1 has a leakage according to an embodiment of the present invention;
fig. 5 is a schematic diagram illustrating statistics of results of 50 leakage localization experiments performed after the pipeline 1 provided by the first embodiment of the present invention has a leakage;
fig. 6 is a schematic diagram of a troubleshooting range for locating a leakage after a leakage occurs in the pipeline 1 according to an embodiment of the present invention;
Fig. 7 is a schematic view of another investigation range for locating a leakage after a leakage occurs in the pipeline 1 according to an embodiment of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the method for detecting leakage of a pipeline flow rate sensitivity matrix provided by the present invention is described in detail below with reference to the accompanying drawings.
example one
Pipe network leakage positioning can be roughly divided into two categories: 1) establishing a data model for leakage detection through the collected pipe network leakage monitoring data; 2) and constructing a hydraulic model for leakage detection, and fitting a leakage state through the hydraulic model to position the leakage. The first type is to establish a data model and detect the leakage by using the data model, and the common method is to train the neural network by using the collected leakage detection data through the neural network and use the trained model for the leakage detection. And judging whether the area has leakage or not by using data such as a support vector machine, flow, pressure and the like. However, the leakage detection using the data model requires a large amount of leakage detection data covering all the pipelines to achieve a good detection effect, and it is difficult to collect enough data in practice. And the second type is to establish a mechanism model and fit the leakage state of the pipe network by using a hydraulic model. This method enables leak detection without a large amount of monitoring data. However, the existing method cannot position the leakage pipeline, only can position the water supply node, and one node is connected with at least two pipelines, so that the investigation range is large, and a large amount of manpower and material resources are consumed.
According to the embodiment, information of pipe diameter, pipe length, pipe friction resistance, node water demand and the like of a pipe network is firstly obtained, an EPANET (electronic programming and engineering installation) is used for constructing a hydraulic model, the EPANET is open source software developed by the national environmental protection agency of the United states, and then a sensitivity matrix of node pressure and pipe flow to pipe flow is calculated by an analytical method. The present embodiment derives the sensitivity matrix described above from the continuity equation of the water supply network and the differential expression (1) of the energy equation.
wherein, Δ Q, and Δ h are respectively a pipeline flow change vector, a node flow change vector, and a pipeline leakage change vector, a is an n × m incidence matrix for describing the topological relation of the pipe network, and n and m are respectively the number of nodes and the number of pipelines. The elements of the A matrix are determined as follows:
then, this example obtains the partial differential of Haizhong-Williams equation (3) and carries it into equation (1)
Wherein k is a unit conversion coefficient, d, l, q and c are pipe diameter, pipe length, flow rate and Haizhen-Weilian coefficient of the pipeline, so that a sensitivity matrix (4) of node water pressure and pipeline flow rate to node flow rate can be obtained.
Wherein B is a diagonal matrix
In the embodiment, leakage is equivalent to two nodes, a sensitivity matrix of the pipeline flow is further deduced according to the two nodes, and the pipeline with the leakage is determined by least square fitting.
the objective function constructed in this embodiment is
The equivalent leakage amount of the node a and the node b connected with the leakage pipeline l is represented by wH and wq, which are weight coefficients of water pressure and flow, respectively, here, the inverse of the monitoring error variance is represented by Hi and qj, which represent the water pressure and flow monitoring values in the leakage state, and nH and mq represent the number of pressure detection points and the number of flow monitoring points, respectively. The meaning of the objective function provided by the present embodiment is: and adjusting the equivalent leakage of the nodes a and b connected with the pipeline l to ensure that the calculated value of the model is matched with the monitoring value under the leakage state as much as possible. The leakage detection method provided by the embodiment reduces the troubleshooting range of maintenance personnel and shortens the troubleshooting time. Therefore, the technical scheme provided by the embodiment can quickly find the leakage point for maintenance, and finally reduces the leakage time and the economic loss.
This embodiment performs a binary function first order Taylor expansion on equation (6), where equation (7) is
In the present embodiment, it is assumed that the leakage amount when leakage occurs is Δ Ql, the leakage amount is assumed that the water demand of the nodes at both ends of the pipeline increases, and the increase amounts are the same, that is, therefore, equation (7) can be expressed as
this embodiment may approximate the sensitivity matrix analytic expression of the pipe flow as:
where Δ H0 is H — H (Qa, Qb), and Δ q0 is q-qQaQb), and H and q are monitoring vectors of the water pressure and the flow rate in the leakage state, respectively. Therefore, formula (8) performs weighted least squares regression to obtain the leakage loss of the pipeline as:
the change values of the water pressure and the flow rate in the pipe network hydraulic model provided by the embodiment are as follows:
Substituting equation (10) into equation (11) yields:
The technical scheme that this embodiment provided can find the leakage point fast and maintain, has finally reduced leakage time and economic loss. In this embodiment, the residual error of the objective function is obtained by formula (13), where formula (13) is
In the embodiment, the pipeline with the minimum residual error is determined as the leakage pipeline, so that the investigation range of maintenance personnel is reduced, and the investigation time is shortened. Therefore, the technical scheme provided by the embodiment can quickly find the leakage point for maintenance, and finally reduces the leakage time and the economic loss.
the technical solution of the present embodiment is specifically described below by taking a complex analog pipe network as an example.
Fig. 1 is a flowchart of a method for detecting leakage based on a pipeline flow sensitivity matrix according to an embodiment of the present invention. As shown in fig. 1, in this embodiment, EPANET is used to construct a hydraulic model and a pipe network structure thereof, and two water pumps are arranged in the pipe network and a high-level water tank is arranged to supply water to the pipe network. The pipe network is provided with 14 pressure monitoring points and 2 flow monitoring points, and the positions are shown in figure 1. The embodiment utilizes EPANET to carry out leakage of different pipelines
And simulating the variable quantity of the pressure and the flow of the monitoring point after the leakage of the network management occurs. Fig. 2 is a schematic structural diagram of a hydraulic model according to a first embodiment of the present invention, and fig. 3 is a variation of a node after leakage occurs in different pipelines according to the first embodiment of the present invention. The pipe leakage amount simulated in the embodiment is 20L/S, the pressure change of part of the pressure measuring nodes is shown in FIG. 2, and the variation rule of the pressure measuring nodes are different for the leakage of different pipes, which is also the basis for the leakage positioning by the method. In order to evaluate the influence of uncertainty of the monitoring error on the leakage positioning result, so that the experiment provided by the embodiment better conforms to the working condition of an actual pipe network, the random error of the monitoring value is generated by adopting monte carlo simulation, and the variance σ H of the node water pressure monitoring error is 0.1 m. Since the uncertainty of the error leads to the uncertainty of the positioning, this example performed 50 missing positioning experiments.
After the pipeline 1 has a leakage, the present embodiment uses one of the positioning experiments to describe the leakage detection method.
the variation vector of the monitoring point in the experiment provided by this embodiment is
After the pipeline 1 is leaked, the least square method is used for fitting in the embodiment to obtain corresponding elements of node pressure and pipeline flow to the pipeline flow sensitivity matrix, so as to form a gradient vector, where the gradient vector is
the embodiment utilizes the weighted least square method to solve the leakage quantity of the pipeline as
The leakage detection method provided by the embodiment reduces the troubleshooting range of maintenance personnel and shortens the troubleshooting time. Therefore, the technical scheme provided by the embodiment can quickly find the leakage point for maintenance, and finally reduces the leakage time and the economic loss. When the leakage of the pipeline 1 is Δ Q1, the present embodiment calculates the variation value of the water pressure and the flow according to the hydraulic model of the pipe network as
Thus, the present embodiment obtains a residual error of
In this embodiment, the absolute values of the residuals are summed to obtain a total residual, and similarly, the residual of each pipeline is obtained by traversing each pipeline, and the final result is shown in fig. 4. Fig. 4 is a schematic diagram illustrating the result of performing leak location after a leak occurs in the pipeline 1 according to an embodiment of the present invention. The residual error of the pipe 1 is minimal and therefore the pipe 1 is a leaky pipe.
the leakage detection method provided by the embodiment reduces the troubleshooting range of maintenance personnel and shortens the troubleshooting time. Therefore, the technical scheme provided by the embodiment can quickly find the leakage point for maintenance, and finally reduces the leakage time and the economic loss.
Fig. 5 is a statistical diagram illustrating the results of 50 leakage localization experiments performed after the pipeline 1 provided by the embodiment of the present invention has a leakage. In the embodiment, 50 positioning experiments are performed, the leakage positioning condition is counted, and the ID of the pipeline positioned by the leakage and the positioning times are given. Of the 50 positions, 42 positions are to the pipe 1, 4 positions are to the pipe 7, and 2 positions are to the pipe 2 and the pipe 15. Therefore, the correct leakage pipeline can be positioned most of the time, and the average leakage quantity obtained by calculation in the embodiment is 20.059L/s, which is very close to the real leakage (20L/s).
Fig. 6 is a schematic view of a checking range of leakage location after a leakage occurs in the pipeline 1 according to an embodiment of the present invention. As shown in fig. 6, four pipes are positioned as circled in fig. 6, the leak is positioned in the range shown in fig. 6, and therefore, the pipes with inaccurate positioning are also very close to the real leak pipes. Therefore, the experiment provided by the embodiment sufficiently proves the feasibility and the correctness of the leakage detection method. The leakage detection method provided by the embodiment reduces the troubleshooting range of maintenance personnel and shortens the troubleshooting time. The leakage detection method provided by the embodiment reduces the troubleshooting range of maintenance personnel and shortens the troubleshooting time. Therefore, the technical scheme provided by the embodiment can quickly find the leakage point for maintenance, and finally reduces the leakage time and the economic loss.
The same method can be used for leakage simulation of different pipelines, and then leakage positioning can be carried out. Since too much data is involved, this embodiment does not fully demonstrate the positioning statistics after only some of the pipes have been lost as shown in table 1. Table 1 reflects similar properties, with most cases the correct leaking conduit being located and the inaccurately located conduit also being in the vicinity of the leaking conduit.
TABLE 1A positioning statistic data after leakage of part of pipelines
The leakage detection method provided by the present embodiment is compared with a positioning method based on a node traffic sensitivity matrix. This method allows locating the node where the leakage occurs. But one node connects at least two pipelines, and the checking range is large under the condition of correct positioning. In the case of inaccurate positioning, the pipelines connected by nodes near the positioning node are investigated, and then the investigation amount is exponentially increased. The leakage detection method provided by the embodiment reduces the troubleshooting range of maintenance personnel and shortens the troubleshooting time.
Fig. 7 is a schematic view of another investigation range for locating a leakage after a leakage occurs in the pipeline 1 according to an embodiment of the present invention. As shown in fig. 7, by using the same method, after the pipeline 1 is damaged, 50 times of leakage location experiments are performed, and fig. 7 shows the investigation range of leakage location, as can be seen from comparison with fig. 6, the leakage detection method provided by this embodiment obviously reduces the investigation range of leakage.
This embodiment carries out the leakage simulation to different pipelines, then carries out the leakage location, does the statistics to the leakage location condition. The partial positioning results are shown in table 2. As can be seen from table 2, the leakage localization situation shows similar properties, and this method can also roughly locate the range of the leakage node, but the leakage troubleshooting range is much larger than that of the present embodiment. Therefore, the advantages of the technical scheme provided by the embodiment can be illustrated, and the investigation range of leakage is greatly reduced.
TABLE 2 alternative positioning statistics after partial pipeline leakage
The method for detecting leakage of the pipeline flow sensitivity matrix provided by the embodiment comprises the following steps: acquiring pipe network information, wherein the pipe network information comprises pipe diameters, pipe lengths, pipe friction resistances and node water demands of all pipes; forming a hydraulic model of the pipe network under a normal operation state according to the pipe network information; obtaining a sensitivity matrix according to the hydraulic model, the node pressure and the pipeline flow; forming a gradient vector according to corresponding elements of the sensitivity matrix; acquiring the pressure variation and the flow variation of a pipe network monitoring point after leakage occurs; obtaining the residual error of each pipeline according to a least square method, the gradient vector, the pressure variation and the flow variation; and confirming the pipeline with the minimum residual error as a leakage pipeline. The leakage detection method provided by the embodiment reduces the troubleshooting range of maintenance personnel and shortens the troubleshooting time. Therefore, the technical scheme provided by the embodiment can quickly find the leakage point for maintenance, and finally reduces the leakage time and the economic loss.
it will be understood that the above embodiments are merely exemplary embodiments taken to illustrate the principles of the present invention, which is not limited thereto. It will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the spirit and substance of the invention, and these modifications and improvements are also considered to be within the scope of the invention.
Claims (4)
1. A method for detecting leakage of a pipeline flow sensitivity matrix is characterized by comprising the following steps:
Acquiring pipe network information, wherein the pipe network information comprises pipe diameters, pipe lengths, pipe friction resistances and node water demands of all pipes;
forming a hydraulic model of the pipe network under a normal operation state according to the pipe network information;
obtaining a sensitivity matrix according to the hydraulic model, the node pressure and the pipeline flow;
forming a gradient vector according to corresponding elements of the sensitivity matrix;
Acquiring the pressure variation and the flow variation of a pipe network monitoring point after leakage occurs;
obtaining the residual error of each pipeline according to a least square method, the gradient vector, the pressure variation and the flow variation;
And confirming the pipeline with the minimum residual error as a leakage pipeline.
2. The method for detecting the leakage of the pipeline flow sensitivity matrix according to claim 1, wherein the sensitivity matrix is:
H is a monitoring vector of water pressure under a leakage state, Q is a monitoring vector of flow under the leakage state, Q is a node flow vector, a and b are upstream and downstream nodes of the pipeline, and a sensitivity matrix of the pipeline flow is expressed as a half of the sum of elements of the sensitivity matrix of the flow of the upstream and downstream nodes of the corresponding pipeline;
the node traffic sensitivity matrix is:
Wherein B is a diagonal matrix:
a is an n multiplied by m incidence matrix used for describing the topological relation of the pipe network, and n and m are the number of nodes and the number of pipelines respectively.
3. The method of claim 1, wherein the step of forming a hydraulic model of the pipe network under normal operating conditions based on the pipe network information comprises: the hydraulic model was developed using EPANET software.
4. The method for detecting the leakage of the pipeline flow sensitivity matrix according to claim 1, wherein the step of obtaining the sensitivity matrix according to the hydraulic model, the node pressure and the pipeline flow comprises the following steps: the sensitivity matrix is obtained analytically.
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| CN112097125B (en) * | 2020-09-18 | 2021-07-20 | 同济大学 | Water supply pipe network pipe burst detection and positioning method based on self-adaptive checking |
| CN112460495B (en) * | 2020-11-14 | 2022-09-27 | 武汉众智鸿图科技有限公司 | Monitoring point layout method and system for leakage monitoring positioning |
| CN114542997A (en) * | 2022-03-04 | 2022-05-27 | 夏泽鑫 | Water supply pipe network abnormal leakage detection method based on digital twinning |
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