CN116127671B - Water supply network parameter optimization method, system, equipment and storage medium - Google Patents
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Abstract
The invention discloses a method, a system, equipment and a storage medium for optimizing parameters of a water supply network, and belongs to the technical field of water power of the network. The optimization method of the invention comprises the following steps: acquiring pipe network GIS information through a pipe network GIS system, and acquiring a pipe network topological structure according to the pipe network GIS information; establishing a pipe network parameter optimization model based on the pipe network topological structure, wherein the pipe network parameter optimization model comprises an objective function and constraint conditions; converting the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem; and solving the unconstrained extremum problem by adopting a gradient flow method to obtain the optimal value of the pipe network parameter. According to the invention, the optimization problem of the pipe network parameter optimization model is converted into the unconstrained extremum problem, and the unconstrained extremum problem is solved iteratively by adopting a gradient flow method, so that the optimal value of the pipe network parameter can be obtained rapidly and accurately, and more reliable data support and technical support are provided for subsequent pipe network fault monitoring.
Description
Technical Field
The invention belongs to the technical field of pipe network waterpower, and particularly relates to a method, a system, equipment and a storage medium for optimizing parameters of a water supply pipe network.
Background
With the development of digital twinning, the traditional digital model can not meet the requirements of the pipe network industry scene. The digital model is used for not only describing the water supply network, but also training by depending on real-time data, so that the prediction of the water supply network is realized. Dynamic model checking is one of the important processes of optimization calculation, and the checked mathematical model can be abstracted into an optimization problem with constraint conditions.
The traditional thinking for solving the optimization problem is to find a local optimal point in European space, and the used methods comprise Newton's method, gradient descent method, ant colony algorithm or particle swarm algorithm and the like. The Newton method or gradient descent method relies on a Hessian matrix and an inverse matrix of the Hessian matrix for solving the problem, but when the obtained Hessian matrix is not positive, the value of an objective function on a newly found point is possibly larger than the original value, or the Hessian matrix is possibly singular, so that the inverse matrix does not exist, at the moment, the initial value or the step size is manually adjusted by manual intervention to achieve the purpose of final convergence, and the extremum can be obtained by solving for a plurality of times or only a suboptimal solution is output, so that the pipe network optimization efficiency is low or the pipe network optimization precision is not high.
The calculated amount of the ant colony algorithm is large, the convergence speed is low, and therefore the pipe network optimization efficiency is low; the particle swarm algorithm is easy to generate the problems of premature convergence and the like, so that the reliability of the pipe network optimization result is poor.
Disclosure of Invention
In order to solve the problems of poor reliability, low efficiency and the like in the conventional pipe network optimization technology, the invention provides a water supply pipe network parameter optimization method, a system, equipment and a storage medium. According to the invention, the pipe network hydraulic optimization solution based on the gradient flow method can be converged to the extremum faster, so that the optimization efficiency is improved; meanwhile, the physical parameters of each pipe network can be obtained rapidly and accurately, the prediction precision of the node water pressure and the pipe flow is improved, and technical support is provided for subsequent leakage detection and pipe explosion early warning.
The invention is realized by the following technical scheme:
a water supply network parameter optimization method, the method comprising:
acquiring pipe network GIS information through a pipe network GIS system, and acquiring a pipe network topological structure according to the pipe network GIS information;
establishing a pipe network parameter optimization model based on the pipe network topological structure, wherein the pipe network parameter optimization model comprises an objective function and constraint conditions;
converting the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem;
and solving the unconstrained extremum problem by adopting a gradient flow method to obtain the optimal value of the pipe network parameter.
According to the invention, the optimization problem of the pipe network parameter optimization model is converted into the unconstrained extremum problem, and the unconstrained extremum problem is solved iteratively by adopting a gradient flow method, so that the optimal value of the pipe network parameter can be obtained rapidly and accurately, and more reliable data support and technical support are provided for subsequent pipe network fault monitoring.
As a preferred embodiment, the pipe network GIS information of the present invention includes pipe network space data and pipe network attribute data;
obtaining a pipe network topological structure according to the pipe network GIS information, which specifically comprises the following steps:
and establishing pipelines, pipe points and equipment along the lines according to the pipe network space data and the pipe network attribute data to form a pipe network topological structure.
As a preferred embodiment, the objective function of the present invention is:
in the method, in the process of the invention,
and->
Is weight(s)>
And->
Respectively nodesiMeasured and predicted values of pressure, +.>
And (3) with
Respectively pipe sectionsjActual measurement value and prediction value of flow;
the constraints include continuity equations, pressure drop equations, virtual ring equations, and energy equations.
As a preferred embodiment, the method converts the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem, specifically expressed as follows:
wherein,,
for +.>
Dimension parameter->
Is a parameter space, ++>
Is the transformed equation, +.>
Is an objective function->
Is a pipe network parameter->
，/>
Is to->
Head loss function as parameter, +.>
For the actual measured value, +.>
Is a constraint condition (JavaScript)>
Is the lagrange multiplier.
As a preferred embodiment, the invention adopts a gradient flow method to solve the minimum value of the unconstrained problem in the parameter space, and the solving process specifically comprises the following steps:
initializing: setting an initial value and an initial time;
solving: solving a differential equation for the current point on the parameter curve;
updating: and determining an iteration step length, updating the current point, and returning to the solving step to continuously solve the differential equation until the iteration termination condition is met.
As a preferred embodiment, the iterative step of the present invention satisfies the following condition:
wherein,,
and->
Is weight(s)>
Is the parameter space->
Gradient operator on->
Is the parameter space->
A curve on ∈ ->
Is->
Derivative of>
Time of presentation->
For similarity, ->
，/>
And
。
As a preferred embodiment, the iteration termination conditions of the present invention include:
the iteration times are larger than a certain preset integer;
or the difference of the objective function before and after iteration is smaller than a difference preset value;
or, the updated time interval is greater than the time preset value.
In a second aspect, the present invention provides a water supply network parameter optimization system, which includes:
the data acquisition module acquires pipe network GIS information through a pipe network GIS system;
the topological structure construction module acquires a pipe network topological structure according to the pipe network GIS information;
the model construction module is used for constructing a pipe network parameter optimization model based on the pipe network topological structure, wherein the pipe network parameter optimization model comprises an objective function and constraint conditions;
the model conversion module is used for converting the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem;
and the solving module is used for solving the unconstrained extremum problem by adopting a gradient flow method to obtain the optimal value of the pipe network parameter.
In a third aspect, the present invention also proposes a computer device comprising a memory storing a computer program and a processor implementing the steps of the above-mentioned method of the present invention when said computer program is executed by said processor.
In a fourth aspect, the present invention also proposes a computer-readable storage medium, on which a computer program is stored, which computer program, when being executed by a processor, carries out the steps of the above-mentioned method of the invention.
The invention has the following advantages and beneficial effects:
compared with the prior art, the method adopts the gradient flow method to solve the pipe network hydraulic optimization model, can converge to the extremum faster, and improves the pipe network optimization efficiency; meanwhile, the invention can avoid the problem of poor reliability caused by non-convergence or early termination when the objective function Hessian matrix is not positive or singular in the solving process, can obtain the optimal parameters more quickly and reliably, and provides technical support for pipe network leakage detection, pipe explosion early warning and the like.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention. In the drawings:
FIG. 1 is a flow chart of a method according to an embodiment of the invention.
Fig. 2 is a schematic diagram of a model solving process according to an embodiment of the invention.
Fig. 3 is a system schematic block diagram of an embodiment of the present invention.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
Examples:
the traditional pipe network optimization technology generally adopts Newton method, gradient descent method, ant colony algorithm or particle swarm algorithm to solve the optimization problem; however, the Newton method or the gradient descent method requires that the Hessian matrix is positive and is a non-singular matrix, and if the Hessian matrix is non-positive or is a singular matrix, the optimization reliability of the pipe network is poor or the optimization efficiency is low; the ant colony algorithm has larger calculated amount and slower convergence speed, so that the pipe network optimization efficiency is lower; the particle swarm algorithm is easy to generate premature convergence, so that the reliability of pipe network optimization is poor, and the like. Based on this, the embodiment provides a water supply network optimization method.
As shown in fig. 1, the method provided in this embodiment includes the following steps:
step 1, acquiring pipe network GIS information and acquiring a pipe network topological structure according to the pipe network GIS information.
The embodiment obtains pipe network GIS information through a pipe network GIS system, wherein the pipe network GIS information comprises: pipe network space data and pipe network attribute data; the pipe network space data comprise information such as the geographical position of the pipe network, and the pipe network attribute data comprise pipe network material, valve, reducing, tee joint, four-way and other pipe network and equipment data.
In the embodiment, the spatial data and the attribute data of the pipe network are integrated, and the pipeline, the pipe point and the equipment along the line are established to form a topological structure diagram of the pipe network.
Step 2: and establishing a pipe network parameter optimization model based on the pipe network topological structure.
According to the pipe network topological structure obtained in the steps, constraint conditions such as a continuity equation, a pressure drop equation, a virtual ring equation and an energy equation are established. Wherein the continuity equation is
, />
Is the node number,/->
For the traffic of the node, +.>
Is +.>
Flow of connected pipe section,/">
Respectively inflow and outflow. The pressure drop equation is
Wherein->
For node->
Pressure of->
For slave node->
To node->
Head loss function of pipe section
，/>
For length of pipe section->
Is pipe diameter (I)>
For Hazen-Williams coefficients, or equivalently, let
, />
Is friction coefficient>
Is a pending parameter. The energy equation (including the virtual ring) is +.>
Wherein
Is a ring->
Is provided. We's handle->
?>
Value, friction coefficient->
And +.>
Etc. as parameters to be solved. The constraints define the variation of the required parametersThe range (boundary condition), i.e. each equation in the constraint, gives the feasible fields for these parameters.
According to pipe network optimization targets, for example, for each node pressure and pipe section flow, an optimization target function is established:
in the method, in the process of the invention,
and->
Is weight(s)>
And->
Respectively nodesiMeasured and predicted values of pressure, +.>
And (3) with
Respectively pipe sectionsjThe measured and predicted values of flow, the predicted values of node pressure and the predicted values of pipe section flow are functions of parameters, and by changing these parameters, such as friction coefficients used in pressure drop equations, virtual loop equations, and energy equation constraints, and the like, and the values of node flow used in continuity equations, and the like, the predicted values of node pressure and pipe section flow will be changed. For ease of description, these parameters may be collectively represented by a vector C.
Based on the above, the objective optimization function and the constraint condition together form a pipe network parameter optimization model.
Step 3: and converting the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem.
The model optimization problem can be converted into an unconstrained extremum problem by using, but not limited to, an outlier method:
wherein,,
for +.>
Dimension parameter->
Can be European space, or general Riemann manifold>
Is the converted equation.
Wherein,,
is an optimized objective function, in particular the mean square error between the measured value and the predicted value obtained from the head loss function, pipe network parameter ∈ ->
May be Hazen-Williams friction coefficient of pipe section, etc, +.>
Is a parameter requiring optimization, +.>
Is the actual measurement value, as in step 2 above +.>
And->
，/>
Is to->
The head loss function, etc. as parameters are vectors. />
Is a continuity equation which the hydraulic pipe network system must satisfy, and constraint equations such as a pressure drop equation, a virtual ring equation, an energy equation and the like, < >>
Is the lagrange multiplier.
And 4, solving an unconstrained extremum problem by adopting a gradient flow method, namely solving a minimum value of the unconstrained problem in a parameter space.
As shown in fig. 2, the solving process includes the following steps:
step 41, setting an initial value
Is +.>
。
Suppose that solution in parameter space is required
Objective function->
Is a minimum value of (2). The corresponding start position->
The gradient flow of (2) satisfies the following equation>
Parameter curves in space:
wherein,,
is the parameter space->
Gradient operator on, defined as +.>
，
,/>
Representing the inner product on the Riemann manifold, when the Riemann manifold is +.>
When (I)>
Which is the usual vector inner product.
Step 42, for the current point on the parameter curve, solve the differential equation:
wherein,,
is the parameter space->
A curve in>
Starting from, is an approximation of the gradient flow described above, i.e. +.>
，/>
Representation (Alexandrov) Hessian operator, < >>
Is a curve->
Is a derivative of (a). The approximation is adopted because only +_ at the current point can be obtained>
While the gradient of equation (1) is solved, it is not known in advance when +.>
Time gradient flow->
A gradient thereat.
Step 43, determining iteration step length and updating
And update->
Is->
。
Solving the equation (1) to obtain the following time
Is a gradient flow curve. And when the current position on a given curve +.>
At the next place +.>
Is important, firstly, to ensure that +.>
The value of the objective function is smaller than +.>
Where, let->
And->
As large as possible to ensure a fast convergence speed.
For this purpose, first consider vectors
And->
In a certain period of time->
Similarity of interior, i.e. define +.>
The following are provided:
wherein,,
,/>
representing the inner product on the Riemann manifold. If in time period->
Any time->
All have->
It is easy to know
From this, it can be seen that the objective function satisfies
I.e. guaranteed to be +.>
The value of the objective function is less than +.>
A value at.
To determine iteration steps, i.e.
Or equivalent, +.>
Is of such a size that
The value of (2) cannot be too small nor too large, and at the same time +.>
And->
The cosine similarity of (c) cannot be too small or too large. For this purpose, the parameter +.>
And +.>
So that
Obviously, when
When (I)>
. Thus->
When it is sufficiently small, the first formula in the formula (2) must be satisfied, but the second formula must not be satisfied. But is followed by->
Gradually satisfying both of the above equations. If there is more than one +.>
If the above conditions are satisfied, any +.>
. It can be demonstrated when->
I.e. +.>
When converging to the extremum of the objective function. />
The value of (2) is empirically set in the concrete implementation and can be obtained from a smaller valueABeginning and then followingnA，n=1,2, … to satisfy the formula (2).
Step 44, looping according to steps 42-43 until the iteration termination condition is met. The termination conditions include:
1) The iteration times are larger than a certain preset integer;
2) Or the difference of the objective functions before and after iteration is smaller than a certain preset small amount;
3) Or the updated time interval is greater than some preset value.
And 5, outputting an optimal result obtained by solving to realize pipe network parameter optimization.
According to the embodiment, through the optimization process, more accurate pipe network parameters, such as friction coefficient of each network segment and the like, can be obtained, on one hand, more accurate predicted values of the water pressure and the flow of the pipe network node can be obtained, and meanwhile, data support can be provided for pipe network leakage detection and pipe explosion early warning.
The embodiment also provides a water supply network optimization system, specifically as shown in fig. 3, the system includes:
the data acquisition module is used for acquiring the GIS information of the pipe network;
the topological structure construction module acquires a pipe network topological structure according to the GIS information of the pipe network;
the model construction module is used for constructing a pipe network parameter optimization model based on the pipe network topological structure, wherein the pipe network parameter optimization model comprises an objective function and corresponding constraint conditions;
the model conversion module is used for converting the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem;
the solving module adopts a gradient flow method to solve the unconstrained extremum problem, namely, the minimum value of the unconstrained problem on the manifold;
and the output module outputs an optimal result obtained by solving to realize the optimization of pipe network parameters.
The embodiment also provides a computer device for executing the method of the embodiment.
The computer device includes a processor, an internal memory, and a system bus; various device components, including internal memory and processors, are connected to the system bus. A processor is a piece of hardware used to execute computer program instructions by basic arithmetic and logical operations in a computer system. Internal memory is a physical device used to temporarily or permanently store computing programs or data (e.g., program state information). The system bus may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus. The processor and the internal memory may communicate data via a system bus. Where internal memory includes Read Only Memory (ROM) or flash memory, and Random Access Memory (RAM), which generally refers to the main memory loaded with an operating system and computer programs.
Computer devices typically include an external storage device. The external storage device may be selected from a variety of computer readable media, which refers to any available media that can be accessed by a computer device, including both removable and fixed media. For example, computer-readable media includes, but is not limited to, flash memory (micro-SD card), CD-ROM, digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by a computer device.
The computer device may be logically connected to one or more network terminals in a network environment. The network terminal may be a personal computer, server, router, smart phone, tablet computer, or other public network node. The computer device is connected to a network terminal through a network interface (local area network LAN interface). Local Area Networks (LANs) refer to computer networks of interconnected networks within a limited area, such as a home, school, computer laboratory, or office building using network media. WiFi and twisted pair wired ethernet are the two most common technologies used to construct local area networks.
It should be noted that other computer systems including more or fewer subsystems than computer devices may also be suitable for use with the invention.
As described in detail above, the computer device suitable for the present embodiment can perform the designated operation of the water supply network optimization method. The computer device performs these operations in the form of software instructions that are executed by a processor in a computer-readable medium. The software instructions may be read into memory from a storage device or from another device via a lan interface. The software instructions stored in the memory cause the processor to perform the method of processing group member information described above. Furthermore, the invention may be implemented by means of hardware circuitry or by means of combination of hardware circuitry and software instructions. Thus, implementation of the present embodiments is not limited to any specific combination of hardware circuitry and software.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (8)
1. The water supply network parameter optimization method is characterized by comprising the following steps:
acquiring pipe network GIS information through a pipe network GIS system, and acquiring a pipe network topological structure according to the pipe network GIS information;
establishing a pipe network parameter optimization model based on the pipe network topological structure, wherein the pipe network parameter optimization model comprises an objective function and constraint conditions; the objective function is:
wherein alpha is i And beta j As weight, mP i With PP i Respectively an actual measurement value and a predicted value of the pressure of the node i, and mQ j With PQ j Respectively an actual measurement value and a predicted value of the flow of the pipe section j;
the constraint conditions comprise a continuity equation, a pressure drop equation, a virtual ring equation and an energy equation;
converting the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem; converting the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem, which is specifically expressed as follows:
wherein,,
for the n+1-dimensional parameter to be solved, < ->
Is a parameter space, ++>
Is the equation after transformation, f is the objective function, C is the pipe network parameter, +.>
p (C) is a head loss function with C as a parameter, m is an actual measured value, g i Is a constraint, λ is the lagrange multiplier;
and solving the unconstrained extremum problem by adopting a gradient flow method to obtain the optimal value of the pipe network parameter.
2. The water supply network parameter optimization method according to claim 1, wherein the network GIS information comprises network space data and network attribute data;
obtaining a pipe network topological structure according to the pipe network GIS information, which specifically comprises the following steps:
and establishing pipelines, pipe points and equipment along the lines according to the pipe network space data and the pipe network attribute data to form a pipe network topological structure.
3. The water supply network parameter optimization method according to claim 1, wherein the minimum value of the unconstrained problem in the parameter space is solved by adopting a gradient flow method, and the solving process specifically comprises the following steps:
initializing: setting an initial value and an initial time;
solving: solving a differential equation for the current point on the parameter curve;
updating: and determining an iteration step length, updating the current point, and returning to the solving step to continuously solve the differential equation until the iteration termination condition is met.
4. A water supply network parameter optimization method according to claim 3, wherein the iterative step satisfies the following conditions:
wherein alpha is i And beta j As the weight of the material to be weighed,
is the parameter space->
Gradient operator on gamma i (t) is the parameter space->
A curve of gamma' i Is gamma i T represents time, S is similarity, 0 < alpha 1 ＜1，α 2 > 0 and 0 < beta 2 ＜β 1 ＜1。
5. A water supply network parameter optimization method as claimed in claim 3, wherein the iteration termination condition comprises:
the iteration times are larger than a certain preset integer;
or the difference of the objective function before and after iteration is smaller than a difference preset value;
or, the updated time interval is greater than the time preset value.
6. A water supply network parameter optimization system, the system comprising:
the data acquisition module acquires pipe network GIS information through a pipe network GIS system;
the topological structure construction module acquires a pipe network topological structure according to the pipe network GIS information;
the model construction module is used for constructing a pipe network parameter optimization model based on the pipe network topological structure, wherein the pipe network parameter optimization model comprises an objective function and constraint conditions; the objective function is:
wherein alpha is i And beta j As weight, mP i With PP i Respectively an actual measurement value and a predicted value of the pressure of the node i, and mQ j With PQ j Respectively an actual measurement value and a predicted value of the flow of the pipe section j;
the constraint conditions comprise a continuity equation, a pressure drop equation, a virtual ring equation and an energy equation;
the model conversion module is used for converting the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem; converting the optimization problem of the pipe network parameter optimization model into an unconstrained extremum problem, which is specifically expressed as follows:
wherein,,
for the n+1-dimensional parameter to be solved, < ->
Is a parameter space, ++>
Is the equation after transformation, f is the objective function, C is the pipe network parameter, +.>
p (C) is C as a referenceA head loss function of a number, m is an actual measured value, g i Is a constraint, λ is the lagrange multiplier;
and the solving module is used for solving the unconstrained extremum problem by adopting a gradient flow method to obtain the optimal value of the pipe network parameter.
7. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of any of claims 1-5 when the computer program is executed.
8. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method according to any of claims 1-5.
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| CN115495857A (en) * | 2022-08-22 | 2022-12-20 | 华能新华发电有限责任公司 | Heat supply pipe network planning method |
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| CN115062764B (en) * | 2022-06-17 | 2023-07-11 | 淮阴工学院 | Intelligent illuminance adjustment and environmental parameter Internet of things big data system |
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