CN114971076A - Multi-objective optimal arrangement method for monitoring points of water supply network - Google Patents
Multi-objective optimal arrangement method for monitoring points of water supply network Download PDFInfo
- Publication number
- CN114971076A CN114971076A CN202210743102.7A CN202210743102A CN114971076A CN 114971076 A CN114971076 A CN 114971076A CN 202210743102 A CN202210743102 A CN 202210743102A CN 114971076 A CN114971076 A CN 114971076A
- Authority
- CN
- China
- Prior art keywords
- pipe
- monitoring points
- water supply
- bursting
- supply network
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000012544 monitoring process Methods 0.000 title claims abstract description 72
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 title claims abstract description 40
- 238000000034 method Methods 0.000 title claims abstract description 23
- 238000004880 explosion Methods 0.000 claims abstract description 31
- 230000009172 bursting Effects 0.000 claims abstract description 26
- 238000005457 optimization Methods 0.000 claims abstract description 20
- 239000011159 matrix material Substances 0.000 claims abstract description 18
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 15
- 238000001514 detection method Methods 0.000 claims abstract description 9
- 238000013178 mathematical model Methods 0.000 claims abstract description 9
- 238000004088 simulation Methods 0.000 claims abstract description 6
- 230000009977 dual effect Effects 0.000 claims 1
- 238000004364 calculation method Methods 0.000 abstract description 4
- 230000008901 benefit Effects 0.000 description 2
- LFQSCWFLJHTTHZ-UHFFFAOYSA-N Ethanol Chemical compound CCO LFQSCWFLJHTTHZ-UHFFFAOYSA-N 0.000 description 1
- 230000002159 abnormal effect Effects 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000002349 favourable effect Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
- 239000002699 waste material Substances 0.000 description 1
- 238000003911 water pollution Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
- G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
- G06Q50/06—Energy or water supply
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/14—Pipes
-
- 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
Landscapes
- Engineering & Computer Science (AREA)
- Business, Economics & Management (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Economics (AREA)
- Human Resources & Organizations (AREA)
- Strategic Management (AREA)
- Geometry (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Tourism & Hospitality (AREA)
- Marketing (AREA)
- General Business, Economics & Management (AREA)
- General Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Development Economics (AREA)
- Operations Research (AREA)
- Water Supply & Treatment (AREA)
- General Health & Medical Sciences (AREA)
- Primary Health Care (AREA)
- Game Theory and Decision Science (AREA)
- Entrepreneurship & Innovation (AREA)
- Public Health (AREA)
- Quality & Reliability (AREA)
- Computer Networks & Wireless Communication (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Examining Or Testing Airtightness (AREA)
- Pipeline Systems (AREA)
Abstract
The invention discloses a multi-objective optimization arrangement method for monitoring points of a water supply network, which comprises the steps of firstly, endowing pipe bursting flow to nodes added on each pipe section in a water supply network hydraulic model, sequentially carrying out pipe bursting simulation, and calculating and generating a pipe bursting event judgment matrix according to the relation between the pressure change value of each node and a background noise threshold value in a pipe bursting state; and then, constructing a mathematical model for optimal arrangement of the monitoring points by using an objective function of minimizing the number of the monitoring points and maximizing the leakage quantity of pipe explosion detection, and solving by adopting an NSGA-II algorithm, thereby obtaining optimal arrangement schemes under different numbers of the monitoring points. The method obtains the optimal arrangement scheme under different monitoring points through one-time optimization, and greatly improves the calculation efficiency.
Description
Technical Field
The invention belongs to the field of water supply network water pressure monitoring point optimal arrangement, and particularly relates to a water supply network monitoring point multi-target optimal arrangement method.
Background
The pipe explosion can cause serious waste of water resources and water pollution of a water supply system, and the normal operation of social life and production can be facilitated by timely discovering and repairing the pipe explosion. The real-time pressure of a water supply network can be known by arranging water pressure monitoring points in the water supply network, and pipe explosion is detected according to abnormal changes of pressure values. The monitoring points are limited in arrangement quantity under the influence of factors such as funds, and the purpose of improving the pipe explosion detection effect is one of the purposes of optimizing the arrangement of the monitoring points.
Currently, a single-target optimization algorithm is widely used for solving the problem of optimal arrangement of water pressure monitoring points of a water supply network. However, the single-target optimization algorithm can only obtain the optimal layout under a certain number of monitoring points through one-time optimization, so that the layouts of different monitoring points need to be optimized for multiple times, the problems of large workload and low calculation efficiency exist, and when the number of monitoring points is large, the global optimal solution is not easy to find. Therefore, the invention provides a multi-objective optimization arrangement method for monitoring points of a water supply network.
Disclosure of Invention
The invention aims to provide a multi-target optimal arrangement method for monitoring points of a water supply network, which solves the problems of large workload and low efficiency of a single-target optimization algorithm in the process of solving the optimal arrangement problem of the monitoring points.
The technical scheme adopted by the invention is as follows:
a multi-objective optimization arrangement method for monitoring points of a water supply network comprises the following steps:
(1) and constructing a water supply network hydraulic model.
(2) And the MATLAB calls the EPANET to acquire pipe network data information, and then the shortest path matrix between the nodes is calculated and generated through a Dijkstra shortest path algorithm.
(3) And (2) adding a virtual node to each pipe section on the water supply network hydraulic model constructed in the step (1), and sequentially giving a specific node flow Q.
(4) Calling EPANET through MATLAB to perform pipe bursting simulation on each pipe section in the water supply network hydraulic model constructed in the step (1), and calculating and generating a pipe bursting event judgment matrix according to the relation between the pressure drop of each node and a background noise threshold value in the pipe bursting state;
(5) and (4) establishing a mathematical model by taking the minimum number of monitoring points and the maximum leakage amount of pipe explosion detection as a double-objective function based on the shortest path matrix between the nodes obtained in the step (2) and the step (4) and a pipe explosion event judgment matrix.
(6) And solving by adopting an NSGA-II algorithm, and expressing the pipe explosion monitoring capability of the arrangement scheme by using a pipe explosion coverage rate.
The pipe bursting flow of different pipelines in the step (3) is as follows:
Q＝vd 2 π/4 (5)
in the formula: v is the increase of the flow rate of the pipeline; d is the diameter of the different pipe sections.
In the step (4), the pressure driving method (PDA) in the latest pipe network hydraulic simulation software EPANET2 is adopted to sequentially carry out pipe explosion simulation on each pipe, and the pressure drop of each node during pipe explosion is compared with the background noise threshold value, so that a 0-1 pipe explosion event judgment matrix [ B ] is generated] m×n 。
In the step (5), the optimized layout of the water pressure monitoring points aims to preferentially monitor the pipe explosion of the pipe section with the larger pipe diameter and the longer pipe section, and because the pipe explosion of the pipe sections can generate larger leakage loss and seriously affect the normal water supply of other nodes of the pipe network, a mathematical model is established by taking the minimization of the number of the monitoring points and the maximization of the leakage loss of pipe explosion detection as a double-objective function. Namely, it is
The constraints are as follows:
in the formula: n is the total number of monitoring points in a certain arrangement scheme; f is the fitness value corresponding to a certain arrangement scheme, X i Setting whether the node i is a pressure monitoring point or not; l is a radical of an alcohol j Is the length of segment j, m; q is the pipe bursting flow of the pipe section i, L/s; b i,j Matrix [ B ] is judged for cartridge rupture] m×n The corresponding elements in (1); b is j Whether the pipe section j can be detected for a certain arrangement scheme (the pipe section j is detected by two monitoring points at the same time and is considered to be effectively detected); length is the shortest path distance, m, between monitoring points in a certain arrangement scheme; d is the shortest path threshold between monitoring points, m.
In the step (6), the setting of the NSGA-ii algorithm parameters includes a crossover rate, a variation rate, and a maximum number of iterations, and in addition, an index of the pipe bursting capability detected by a certain arrangement scheme is represented by a pipe bursting coverage rate, that is:
in the formula: s is the tube bursting coverage rate, L, corresponding to a certain arrangement scheme i ，B i And n has the same meaning as the formula.
Compared with the prior art, the invention has the advantages that:
the monitoring point optimization arrangement model is constructed by a single objective function, and when a single objective optimization algorithm is adopted for solving, optimal layout under a certain monitoring point number can be obtained through one-time optimization, so that layout of different monitoring point numbers needs to be optimized for multiple times, and the problems of large workload and low calculation efficiency exist. The NSGA-II algorithm in the solving method adopts a 0-1 coding mode, and the solution space is not increased along with the increase of the number of the monitoring points, so that the method is favorable for finding a high-quality non-dominated solution when the number of the monitoring points is large; a plurality of non-dominated solutions under different monitoring points can be obtained only through one-time optimization, and the workload can be greatly reduced.
Drawings
FIG. 1 is a flow chart of a multi-objective optimization arrangement method for monitoring points of a water supply network;
FIG. 2 is a water supply network topology;
FIG. 3 is a relation between the number of monitoring points and the pipe burst coverage rate obtained by optimally arranging the monitoring points of the water supply network based on the NSGA-II algorithm;
the method comprises the following specific implementation steps:
the specific implementation steps of the present invention are described in detail with reference to fig. 1 and 2.
The first step is as follows: and (3) constructing a water supply pipe network model, wherein the length, the material, the roughness coefficient, the node flow and the pool elevation of the pipeline are required to be input when the pipe network model is constructed.
The second step is that: and the MATLAB calls the EPANET to obtain the basic information of the pipe network, and then the shortest path matrix between the nodes is calculated and generated through a Dijkstra shortest path algorithm.
The third step: and (3) performing hydraulic analysis on the constructed hydraulic model of the pipe network by adopting a pressure driving method (PDA) in EPANET2 to obtain the pressure of each node under the normal working condition.
The fourth step: sequentially giving pipe bursting flow Q (Q ═ vd) to nodes added in the middle of each pipe section 2 Pi/4) to carry out pipe explosion simulation, and obtain the pressure of each node. Constructing node pressure change matrix [ delta h ] according to node pressure drop during pipe explosion] m×n . Change the node pressure matrix [. DELTA.h [)] m×n Is compared with a background noise threshold value delta P if delta h i,j When not less than delta P, b i,j Setting to be 1, wherein a water pressure monitoring point of a node j can detect pipe explosion of a pipe section i; otherwise b i,j Is set to 0, thereby obtaining a 0-1 tube explosion event judgment matrix [ B] n×m As shown in table 1.
TABLE 1
Wherein: n is the total number of pipe sections of the pipe network; m is the total number of the nodes of the pipe network; i is the pipe section number, and j is the node number; 1,2, …, n; j is 1,2, …, m.
The fourth step: the purpose of optimizing layout of the water pressure monitoring points is to preferentially monitor the pipe burst of a pipe section with a large pipe diameter and a long pipe section, so that a mathematical model is established by taking the minimum number of the monitoring points and the maximum leakage loss of pipe burst detection as a double-objective function, namely:
the constraints are as follows:
Length(X j ，X j+1 …X m )≥D (12)
wherein: n is the total number of monitoring points in a certain arrangement scheme; f is the fitness value corresponding to a certain arrangement scheme, X i Whether the node i is set as a pressure monitoring point or not is judged; l is j Is the length of segment j, m; q is the pipe bursting flow of the pipe section i, L/s; b i,j Matrix [ B ] is judged for cartridge rupture] m×n The corresponding elements in (1); b is j Whether a pipe section j can be detected for a certain arrangement scheme; length is the shortest path distance, m, between monitoring points in a certain arrangement scheme; d is the shortest path threshold between monitoring points, m.
The fifth step: and solving the constructed mathematical model by using an NSGA-II algorithm so as to obtain a series of Pareto solution sets under the objective function. The pipe explosion coverage rate is used as the pipe explosion detection capability judgment index of the monitoring point arrangement scheme, namely:
in the formula: s is the tube bursting coverage rate, L, corresponding to a certain arrangement scheme i ，B i And n has the same meaning as the formula.
And (3) model verification:
the invention verifies the effectiveness of the multi-target optimization arrangement method for the monitoring points of the water supply network by taking a net3 pipe network in EPANET as a research case. The background noise threshold Δ P is specified herein to be 1.4m, the increase in duct flow velocity v is 0.8m/s, and the minimum distance threshold D between monitoring points is 1000 m. The relationship between the number of monitoring points and the pipe explosion coverage obtained by optimizing the constructed mathematical model once through the NSAG-II algorithm is shown in fig. 3, and it can be seen that the pipe explosion coverage rate is increased along with the increase of the number of the monitoring points, but it is worth noting that when the number of the monitoring points is more than 8, the increase amplitude of the pipe explosion coverage rate is smaller and smaller, so that the economic benefit is the best when the arrangement number of the monitoring points is 8. In conclusion, the multi-objective optimal arrangement method for the monitoring points of the water supply network, which is provided by the invention, can obtain a series of Pareto solution sets (optimal arrangement schemes under different numbers of monitoring points) through one-time optimization, and can greatly improve the calculation efficiency.
Claims (5)
1. A multi-objective optimization arrangement method for monitoring points of a water supply network is characterized by comprising the following steps:
(1) constructing a water supply network hydraulic model;
(2) MATLAB calls EPANET to obtain pipe network data information, and then a shortest path matrix between nodes is calculated and generated through a Dijkstra shortest path algorithm;
(3) adding a virtual node to each pipe section on the water supply network hydraulic model constructed in the step (1), and sequentially giving a specific node flow Q;
(4) calling EPANET through MATLAB to perform pipe bursting simulation on each pipe section in the water supply network hydraulic model constructed in the step (1), and calculating and generating a pipe bursting event judgment matrix according to the relation between the pressure drop of each node and the background noise threshold value in the pipe bursting state;
(5) establishing a mathematical model by taking the minimum number of monitoring points and the maximum leakage amount of pipe explosion detection as a double-objective function based on the shortest path matrix between the nodes obtained in the step (2) and the step (4) and a pipe explosion event judgment matrix;
(6) and solving by adopting an NSGA-II algorithm to obtain a series of Pareto solution sets under the objective function, and representing the tube explosion monitoring capability of the arrangement scheme under different monitoring point numbers by using the tube explosion coverage rate.
2. The multi-objective optimization arrangement method for the monitoring points of the water supply network according to claim 1, wherein the pipe bursting flow of different pipelines in the step (3) is defined as follows:
Q＝vd 2 π/4 (1)
in the formula: v is the increase of the flow rate of the pipeline; d is the diameter of the different pipe sections.
3. The method for multi-objective optimization arrangement of monitoring points of a water supply network according to claim 1, wherein in the step (4), pipe bursting simulation is performed on each pipe section in sequence by using a pressure driving method (PDA) in the latest pipe network hydraulic simulation software EPANET2, and the pressure drop of each node in the pipe bursting state is compared with a background noise threshold value, so that a pipe bursting event judgment matrix is generated.
4. The method for multi-objective optimization arrangement of monitoring points in a water supply pipe network as claimed in claim 1, wherein in step (5), the optimization arrangement of the water pressure monitoring points aims to monitor more pipe sections with larger pipe diameter and longer length, and because pipe explosion of the pipe sections can generate larger leakage loss amount, the normal water supply of other nodes of the pipe network is seriously affected, so that a mathematical model is established by taking minimization of the number of monitoring points and maximization of the leakage loss amount of pipe explosion detection as dual objective functions, namely, the mathematical model is established by taking minimization of the number of monitoring points and maximization of the leakage loss amount of pipe explosion detection as examples
The constraints are as follows:
in the formula: n is the total number of monitoring points in a certain arrangement scheme; f is a fitness value corresponding to a certain arrangement scheme, X i Is whether or not node i isSetting as a pressure monitoring point; l is j Is the length of segment j, m; q is the pipe bursting flow of the pipe section i, L/s; b i,j Matrix [ B ] is judged for cartridge rupture] m×n The corresponding elements in (1); b is j Whether the pipe section j can be detected for a certain arrangement scheme (the pipe section j is detected by two monitoring points at the same time and is considered to be effectively detected); length is the shortest path distance, m, between monitoring points in a certain arrangement scheme; d is the shortest path threshold between monitoring points, m.
5. The multi-objective optimal arrangement method for monitoring points of a water supply pipe network as claimed in claim 1, wherein in the step (6), the pipe bursting monitoring capability of a certain monitoring point arrangement scheme is expressed by pipe bursting coverage rate
In the formula: s is the tube bursting coverage rate, L, corresponding to a certain arrangement scheme i ，B i And n has the same meaning as the formula.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210743102.7A CN114971076A (en) | 2022-06-27 | 2022-06-27 | Multi-objective optimal arrangement method for monitoring points of water supply network |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210743102.7A CN114971076A (en) | 2022-06-27 | 2022-06-27 | Multi-objective optimal arrangement method for monitoring points of water supply network |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN114971076A true CN114971076A (en) | 2022-08-30 |
Family
ID=82964747
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210743102.7A Pending CN114971076A (en) | 2022-06-27 | 2022-06-27 | Multi-objective optimal arrangement method for monitoring points of water supply network |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114971076A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115758636A (en) * | 2022-11-03 | 2023-03-07 | 武汉正元环境科技股份有限公司 | Water supply pipe network water quality monitoring method and device based on Internet of things |
-
2022
- 2022-06-27 CN CN202210743102.7A patent/CN114971076A/en active Pending
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115758636A (en) * | 2022-11-03 | 2023-03-07 | 武汉正元环境科技股份有限公司 | Water supply pipe network water quality monitoring method and device based on Internet of things |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110108328B (en) | Method for acquiring water leakage amount of leakage area of water supply pipe network | |
| CN110939870B (en) | Water supply network pressure monitoring point arrangement method for pipe burst monitoring | |
| CN112989535A (en) | Water supply network pressure monitoring point optimal layout method based on pipe burst detection benefit | |
| WO2021174749A1 (en) | Running operation optimization method and system for steam power system | |
| CN114580786A (en) | Arrangement optimization method for monitoring points of urban water supply pipe network | |
| CN114971076A (en) | Multi-objective optimal arrangement method for monitoring points of water supply network | |
| CN110443407B (en) | Node flow optimal distribution method for improving transient hydraulic simulation precision of water supply series pipeline | |
| CN111859557B (en) | Liquid cooling plate structure size optimization method based on hyperstry and Fluent joint simulation | |
| CN103413023A (en) | Multi-state system dynamic reliability assessment method | |
| CN105302973A (en) | MOEA/D algorithm based aluminum electrolysis production optimization method | |
| CN104976517A (en) | Wharf water supply pipe network online supervision method | |
| CN110263960B (en) | Method for optimizing arrangement of pressure monitoring points of urban water supply network based on PDD | |
| CN105045091A (en) | Dredging process intelligent decision analysis method based on fuzzy neural control system | |
| CN108897936A (en) | A kind of sewage source heat pump unit method for diagnosing faults based on PSO-BP model | |
| CN114219334A (en) | Bayesian network natural gas pipeline leakage probability calculation method based on genetic algorithm | |
| CN105512383A (en) | Dredging process regulation and control parameter screening method based on BP neural network | |
| WO2024007840A1 (en) | Method and apparatus for predicting reaming torque in horizontal directional drilling, device and storage medium | |
| CN116862077A (en) | Electric heating operation cost prediction method and medium based on multi-mode combination model | |
| CN104675713A (en) | Centrifugal pump non-overload design method based on data sample | |
| CN110796295B (en) | Energy Internet air network transmission optimization method | |
| CN114818506A (en) | Comprehensive energy system heat supply network fault hazard assessment method, system and device | |
| CN105160062A (en) | Hydraulic check method for reverse return pipe network | |
| CN115017744B (en) | Modeling method and system of groundwater source water supply hydraulic calculation model | |
| CN104504289A (en) | Method for reducing calculating time of intelligent optimization algorithm | |
| CN114936522B (en) | Dynamic modeling method for natural gas system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |