CN107657074A - A kind of Method of Stochastic for assessing public supply mains reliability - Google Patents
A kind of Method of Stochastic for assessing public supply mains reliability Download PDFInfo
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Abstract
The present invention relates to a kind of Method of Stochastic for assessing public supply mains reliability, belong to public supply mains quake-resistant safety technical field.The present invention includes step：Pipeline earthquake rate calculates；The damaged scene generation of water supply network based on Monte Carlo simulation；Low pressure water supply network hydraulic analysis based on " substep iteration " method；Aseismic reliability index calculates.The present invention, which need not change pipe network system file or write additional code, solves low-pressure pipe network waterpower equation, has the advantages of computational efficiency height and good stability.The present invention for earthquake when water supply network hydraulic analogy and reliability assessment provide new approaches, there is certain guidance meaning to the disaster relief, repair after earthquake.
Description
Technical Field
The invention relates to a random simulation method for evaluating reliability of an urban water supply pipe network, and belongs to the technical field of urban water supply pipe network anti-seismic safety.
Background
The city water supply system, the traffic system, the electric power system, the heat supply system and the communication system are the life lines of modern city operation and are called life line engineering systems of modern cities vividly. In recent years, as an infrastructure closely related to daily production and life of cities, city lifeline engineering systems have become increasingly dependent on such infrastructures, and their requirements have become more stringent. Unlike other common city infrastructures, the lifeline project has the characteristics of wide coverage area, close connection among systems, possibility of influencing system functions due to local damage and the like. Earthquake is one of natural disasters with large damage degree on the earth. Between two major seismic zones, namely the Eurasian seismic zone and the Pacific seismic zone, the China has many seismic frequency, large intensity and wide influence range, and is one of the countries which are seriously affected by the seismic in the world. Since the 20 th century, earthquakes frequently occur on the earth, statistics shows that new China is established for less than 70 years, 16 destructive earthquakes exceeding 7 levels occur in China, the number of population deaths caused by earthquakes in the world is up to 160 ten thousand, and the population of deaths caused by earthquakes in China exceeds 50 ten thousand.
According to the Chinese seismic oscillation parameter zoning map GB18306-2015, nearly 50% of China land and more than half of cities have defense intensity of VII or more. As an important component of a lifeline engineering system, once the urban water supply is subjected to a great earthquake action, the urban water supply can be damaged in different degrees, so that the loss of urban functions can be caused, and great adverse effects are brought to the city. A large amount of earthquake damage data show that the earthquake can cause the damage of different degrees of a water supply pipe network, so that the water supply capacity of the pipe network is reduced, the daily life and the production of people are influenced, the fire rescue capacity is weakened, and irreparable loss is brought to the national and people economic development and normal life due to secondary disasters such as fires after the earthquake.
With the continuous strengthening of urban infrastructure construction in China, the problems of more old cities, poor urban infrastructure and the like in the cities in China are improved to a certain extent, but most urban water supply networks in China have poor pipe anti-seismic performance, most water supply network systems are not subjected to the formal anti-seismic design, and the problems of insufficient seismic damage simulation of the water supply network systems and hydraulic analysis of damaged pipe networks after earthquake and the like are solved. In view of historical and actual national conditions, in the face of frequent earthquake disasters, it is necessary to develop a method for evaluating the earthquake resistance reliability of the urban water supply network, so that the method not only can ensure that the restoration and reconstruction work after earthquake is pertinent, but also is beneficial to optimizing the earthquake resistance design of the water supply network, and has important research significance and practical value for reducing personnel and property loss caused by the earthquake in the whole city.
Disclosure of Invention
The invention provides a random simulation method for evaluating the reliability of an urban water supply network, which is used for solving the technical problems of hydraulic simulation and reliability evaluation of the urban water supply network under the action of an earthquake.
The technical scheme of the invention for solving the technical problems is as follows: a random simulation method for evaluating reliability of an urban water supply pipe network comprises the following specific steps:
step1, calculating the earthquake damage rate of the pipeline;
collecting integrity attribute data of all elements of a water supply network, applying EPANET to construct a pipe network hydraulic model, determining earthquake and site condition parameters, and calculating the earthquake damage rate of a pipeline by using a formula (1):
R f ＝C g ×C p ×C d ×C y ×R (1)
wherein R is f Is the average earthquake damage rate (department/Km), C g 、C p 、C d 、C y Respectively correcting coefficients of topographic geology, pipes, pipe diameter and liquefaction influence; r is standard earthquake damage rate, the value of which is related to the vibration peak acceleration PGA, and the calculation is carried out by adopting the formula (2):
R＝2.88×10 -6 ×(PGA-100) 1.97 (2)
step2, generating a water supply pipe network seismic damage scene based on Monte Carlo simulation;
in Step2, the water supply pipe network seismic damage scene generation based on the Monte Carlo simulation comprises the following 3 steps:
step2.1, judging the working state of the pipeline;
after an earthquake, the pipeline has three working states of normal, leakage and pipe explosion; the invention adopts Poisson random number and uniform random number to judge the working state of the pipeline. Firstly, according to the calculated average earthquake damage rate R of the pipeline f Setting Poisson distribution expectation lambda = R f L, wherein L is a calculated pipeline length (Km), a poisson random number v is generated, if v =0, it indicates that there is no damage point on the pipeline, and the pipeline is determined to be normal; if v is&And gt, 0, indicating that a leakage or pipe explosion point exists on the pipeline. Then, N uniform random numbers w are generated 1 ,w 2 ...w N Examine it separatelyWhen all the random numbers do not fall into the pipe explosion interval, judging that the pipeline is in a leakage state; otherwise, judging that the pipeline is burst;
step2.2, pipeline leak simulation based on EPANET nozzle function;
nozzle flow calculation in EPANET is:
wherein Q is the nozzle discharge (L/s), C i Is the nozzle fluidic coefficient, H i Node i water pressure (m);
based on actual measurement data of the flow of the spray head in the automatic spraying system, the pipeline leakage is calculated by adopting the following formula:
wherein A is L Is the leakage area (mm) 2 )，Q L The leakage rate of the pipeline (L/s); h is a pressure head (m) at the leakage position;
simulating pipeline leakage by using EPANET self-contained nozzle function to enable H i ＝H，Q＝Q L According to the equations (3) and (4), the conversion formula of the leakage area and the jet coefficient is obtained as follows:
C i ＝4.43·A L ×10 -3 (5)
step2.3, tube explosion simulation based on the EPANET pipeline closing function;
when the pipe is burst, the pipe section of the pipe is broken, and two leakage points are newly added at the pipe burst position; based on EPANET, calling a built-in function to close the pipeline and adding corresponding jet flow coefficients at nodes at two ends for equivalent simulation, wherein the jet flow coefficients are determined according to 1 time of the sectional area of the pipeline, namely C i ＝4.43·A×10 -3 Wherein A is the cross-sectional area of the pipeline;
for a long-distance water pipeline, because the difference between the water pressure at the nodes at two ends and the water pressure at the pipe explosion position is large, the equivalent method can cause large simulation errors; likewise, pipeline segmentation is used to reduce simulation errors by adding virtual nodes.
Step3, hydraulic analysis of the low-pressure water supply pipe network based on a Step-by-Step iteration method: firstly, assuming that all water utilization nodes are in a low-pressure state, and performing outflow simulation by using the nozzle function of EPANET; then, correcting the node outflow type according to the calculated value of the node water pressure of the previous round until all the nodes meet the constraint of the formula (6);
in the formula, H i Is node i Water pressure (m), H des Minimum water pressure (m) required to ensure normal water supply to the water nodes; q i nor The water consumption (L/s) of the node i under the normal water supply pressure,
the specific steps of Step3 are as follows:
step3.1, assuming all water usage points are low pressure water usage points, replace them with nozzle outflow type and define the jet coefficient C i ＝S i ；
Step3.2, calling EPANET to solve a hydraulic equation of the pipe network;
step3.3, checking the water pressure of the node if H i ≥H i des Modifying the node into a normal outflow type; if H is i Setting the node flow and the leakage coefficient to be zero when the flow is less than or equal to 0;
and step3.4, calling the EPANET again to solve the hydraulic equation of the pipe network, finishing hydraulic calculation if the outflow states of all the nodes in the calculation result meet the constraint of the formula (6), and otherwise, turning to the step Step3.3.
Step4, calculating an anti-seismic reliability index:
taking the ratio of the statistical average value of the node flow under the random seismic damage scene to the normal node flow as a reliability index; the reliability calculation formula for a single node in the pipe network is as follows:
wherein (SI) i K is the reliability of the node i, k is the Monte Carlo simulation times,for the flow of the node i in the jth Monte Carlo simulation, the calculation formula of the integral anti-seismic reliability of the pipe network is as follows:
the beneficial effects of the invention are:
1. the working state of the pipeline is judged through the Poisson random number and the uniform random number, the leakage coefficient of the pipeline is determined through the normal random number, and enough random seismic damage scenes are generated;
2. the invention realizes equivalent simulation of pipeline leakage and pipe explosion by utilizing the closing function of the nozzle and the pipeline in the EPANET software, provides that a long pipeline is segmented and introduced into a step-by-step iteration method to solve a hydraulic equation of a low-pressure pipe network, and improves the hydraulic simulation precision of the seismic damage pipe network.
3. The method calls an EPANET programmer tool box program in MATLAB, takes the ratio of the statistical average value of the node flow under the random earthquake damage scene to the normal node flow as a reliability index, and the algorithms are all completed based on the built-in function of EPANET software without modifying pipe network system files or writing additional codes to solve a low-pressure pipe network hydraulic equation.
Drawings
FIG. 1 is a flow chart of a stochastic simulation method according to the present invention;
FIG. 2 is a plan view of a water supply piping network according to an embodiment;
FIG. 3 and FIG. 4 are reliability distribution diagrams of water supply pipe networks under seismic intensity of VIII and IX degrees.
Detailed Description
Example 1: as shown in FIGS. 1-4, a stochastic simulation method for evaluating the reliability of an urban water supply network comprises the steps of firstly, establishing a water supply network hydraulic model of the embodiment by using EPANET software, and calculating the earthquake damage rate of a pipeline; secondly, the Step1-4 in the method of the invention is utilized to call programming by taking MATLAB as a platform, and the functional reliability analysis of the water supply pipe network under VIII and IX degrees earthquake intensity is carried out. The method comprises the following specific steps:
(1) EPANET software is applied to establish a water supply network hydraulic model of the embodiment, and the earthquake damage rate of the pipeline is calculated.
EPANET is used for constructing a pipe network hydraulic model and exporting a pipe network system file, as shown in figure 2. The water supply network adopts a high-level water pool to supply water in a partitioned mode, the coverage area of the water supply network is 3.8 square kilometers, and the service population is about 2.5 ten thousand. The total length of the pipeline is about 58.6 kilometers, the pipeline comprises 612 water consumption nodes and 777 pipe sections, and the diameter of the pipeline is in the range of 150-400 mm. The water supply pipeline is made of nodular cast iron pipes, and the willingness factor of the sea cucumber is 130.
Step1, calculating the pipeline earthquake damage rate;
collecting integrity attribute data of all elements of a water supply network, applying EPANET to construct a pipe network hydraulic model, determining earthquake and site condition parameters, and calculating the earthquake damage rate of a pipeline by using a formula (1):
R f ＝C g ×C p ×C d ×C y ×R (1)
wherein R is f Is the average earthquake damage ratio (place/Km), C g 、C p 、C d 、C y Influence correction coefficients of terrain geology, pipes, pipe diameters and liquefaction are respectively set; r is standard earthquake damage rate, and the value of R is related to vibration peak acceleration (PGA)Calculating by adopting an equation (2):
R＝2.88×10 -6 ×(PGA-100) 1.97 (2)
the pipeline earthquake damage rate is calculated when the earthquake intensity is VIII and IX by utilizing Step1 in the method, and the peak acceleration of earthquake motion is 300cm/s respectively 2 And 700cm/s 2 The values of the correction coefficients are shown in table 1.
TABLE 1 correction coefficient Table
Step2, generating a water supply pipe network seismic damage scene based on Monte Carlo simulation:
the water supply network seismic damage scene generation based on Monte Carlo simulation comprises the following 3 steps:
step2.1, judging the working state of the pipeline;
after an earthquake, the pipeline has three working states of normal, leakage and pipe explosion; the invention adopts Poisson random number and uniform random number to judge the working state of the pipeline. Firstly, according to the calculated average earthquake damage rate R of the pipeline f Setting Poisson distribution expectation lambda = R f L, where L is the calculated pipeline length (Km), yielding a Poisson random number v. If v =0, indicating that no damage point exists on the pipeline, and judging that the pipeline is normal; if v is&And gt, 0, indicating that a leakage or pipe explosion point exists on the pipeline. Then, N uniform random numbers w are generated 1 ,w 2 ...w N Respectively inspecting the falling intervals, and judging that the pipeline is in a leakage state when all random numbers do not fall into the pipe explosion interval; otherwise, judging that the pipeline is exploded;
step2.2, pipeline leak simulation based on EPANET nozzle function;
nozzle flow calculation in EPANET is:
wherein Q is the nozzle outletFlow rate (L/s), C i Is the nozzle fluidic coefficient, H i Node i water pressure (m);
based on actual measurement data of the flow of the spray head in the automatic spraying system, the pipeline leakage is calculated by adopting the following formula:
wherein A is L Is the leakage area (mm) 2 )，Q L The leakage rate (L/s) of the pipeline; h is a pressure head (m) at the leakage position;
simulating pipeline leakage by using EPANET self-contained nozzle function to enable H i ＝H，Q＝Q L According to the equations (3) and (4), the conversion formula of the leakage area and the jet coefficient is obtained as follows:
C i ＝4.43·A L ×10 -3 (5)
step2.3, simulating tube explosion based on the EPANET pipeline closing function;
when the pipe is burst, the pipe section of the pipe burst is broken, and two leakage points are newly added at the pipe burst position; based on EPANET, calling a built-in function to close the pipeline and adding corresponding fluidic coefficients at nodes at two ends to perform equivalent simulation, wherein the fluidic coefficients are determined according to 1 time of the sectional area of the pipeline, namely C i ＝4.43·A×10 -3 Wherein A is the cross-sectional area of the pipeline;
for a long-distance water pipeline, because the difference between the water pressure at the nodes at two ends and the water pressure at the pipe explosion position is large, the equivalent method can cause large simulation errors; likewise, by adding virtual nodes, the pipeline is segmented to reduce simulation errors.
Step3, hydraulic analysis of the low-pressure water supply pipe network based on a Step iteration method: firstly, assuming that all water utilization nodes are in a low-pressure state, and performing outflow simulation by using the nozzle function of EPANET; then, correcting the node outflow type according to the calculated value of the node water pressure of the previous round until all nodes satisfy the constraint of the formula (6);
in the formula, H i Is node i Water pressure (m), H des Minimum water pressure (m), Q required to ensure normal water supply to the water nodes i nor The water consumption (L/s) of the node i under the normal water supply pressure,
the specific steps of Step3 are as follows:
step3.1, assuming all water usage points are low pressure water usage points, replace them with nozzle outflow type and define the jet coefficient C i ＝S i ；
Step3.2, calling EPANET to solve a hydraulic equation of the pipe network;
step3.3, checking the water pressure of the node if H i ≥H i des The node is modified into a normal outflow type; if H i Setting the node flow and the leakage coefficient to be zero when the flow is less than or equal to 0;
and step3.4, calling the EPANET again to solve the hydraulic equation of the pipe network, finishing hydraulic calculation if the outflow states of all the nodes in the calculation result meet the constraint of the formula (6), and otherwise, turning to the step Step3.3.
Step4, calculating an earthquake-resistant reliability index:
taking the ratio of the statistical average value of the node flow under the random seismic damage scene to the normal node flow as a reliability index; the reliability calculation formula for a single node in the pipe network is as follows:
wherein (SI) i K is the number of Monte Carlo simulations for the reliability of node i,for the flow of the node i in the jth Monte Carlo simulation, the calculation formula of the integral anti-seismic reliability of the pipe network is as follows:
and Step2, step3 and Step4 in the method are utilized to call programming by taking MATLAB as a platform, and functional reliability analysis under VIII and IX degrees of seismic intensity is carried out on the water supply pipe network.
As shown in fig. 2, the present invention writes a stochastic simulation method program for evaluating the reliability of a municipal water supply network in Matlab, and invokes a programming to perform monte carlo damage simulation on the water supply network using Matlab as a platform. The MATLAB is used as a platform to call and program to execute Monte Carlo simulation 10000 times, and the earthquake resistance reliability evaluation results of the water supply pipe network under the earthquake intensity of VIII and IX are shown in the figures 3 and 4, and the water supply reliability of key units is shown in the table 2.
TABLE 2 reliability of key unit water supply under VIII and IX seismic intensity
As can be seen from fig. 3 and 4, the greater the seismic intensity, the lower the reliability of the water supply in the pipe network. Besides earthquake intensity factors, the hydraulic conditions of the pipe network greatly affect the reliability of water supply during earthquake. Under the same seismic intensity, the farther the pipe network node is away from a water source or the greater the elevation of the terrain where the pipe network node is located, the lower the water supply reliability of the area is; furthermore, the reliability of the service area of the water main is much higher than that of the service area of the branch pipe. Specifically, when the earthquake intensity is VIII, the average water supply reliability of the service area is 0.79, the worst area is a water supply area of the Van building with high topography, and the water supply reliability is reduced to 0.32. When the earthquake intensity is IX, the reliability of the regional average water supply is reduced to 0.51, and the reliability of the water supply zone of the vancou building is 0.16.
Compared with the prior art, the method simplifies the leakage and pipe burst simulation of the pipe network by utilizing the hydraulic equivalent principle and combining the closing functions of the nozzles and the pipes in the EPANET software, avoids the modification of the topological structure of the pipes, reduces the program operation amount, and improves the program compatibility and the operation robustness; the low-pressure pipe network is solved by introducing a step-by-step iterative hydraulic calculation method, so that the unreasonable negative pressure condition is avoided, and the hydraulic simulation result precision is improved.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (3)
1. A random simulation method for evaluating the reliability of an urban water supply network is characterized by comprising the following steps: the method comprises the following specific steps:
step1, calculating the pipeline earthquake damage rate;
collecting integrity attribute data of all elements of a water supply network, applying EPANET to construct a pipe network hydraulic model, determining earthquake and site condition parameters, and calculating the earthquake damage rate of a pipeline by using a formula (1):
R f ＝C g ×C p ×C d ×C y ×R (1)
wherein R is f Is the average earthquake damage ratio (place/Km), C g 、C p 、C d 、C y Respectively correcting coefficients of topographic geology, pipes, pipe diameter and liquefaction influence; r is standard earthquake damage rate, the value of which is related to the vibration peak acceleration PGA, and the calculation is carried out by adopting the formula (2):
R＝2.88×10 -6 ×(PGA-100) 1.97 (2)
step2, generating a water supply pipe network seismic damage scene based on Monte Carlo simulation;
step3, hydraulic analysis of the low-pressure water supply pipe network based on a Step iteration method: firstly, assuming that all water utilization nodes are in a low-pressure state, and performing outflow simulation by using the nozzle function of EPANET; then, correcting the node outflow type according to the calculated value of the node water pressure of the previous round until all nodes satisfy the constraint of the formula (6);
in the formula, H i Is node i Water pressure (m), H des Minimum water pressure (m) required to ensure normal water supply to the water nodes; q i nor The water consumption (L/s) of the node i under the normal water supply pressure,
step4, calculating an earthquake-resistant reliability index:
taking the ratio of the statistical average of the node flow under the random seismic damage scene to the normal node flow as a reliability index; the reliability calculation formula for a single node in the pipe network is as follows:
wherein (SI) i K is the number of Monte Carlo simulations for the reliability of node i,for the flow of the node i in the jth Monte Carlo simulation, the calculation formula of the integral anti-seismic reliability of the pipe network is as follows:
2. the stochastic simulation method for assessing reliability of a municipal water supply network according to claim 1, wherein: in Step2, the water supply network seismic damage scene generation based on the Monte Carlo simulation comprises the following 3 steps:
step2.1, judging the working state of the pipeline;
after an earthquake, the pipeline has three working states of normal, leakage and pipe explosion; the invention adopts Poisson random number and uniform random number to judge the working state of the pipeline. Firstly, according to the calculated pipeline flatnessMean rate of earthquake damage R f Setting Poisson distribution expectation lambda = R f L, wherein L is a calculated pipeline length (Km), a poisson random number v is generated, if v =0, it indicates that there is no damage point on the pipeline, and the pipeline is determined to be normal; if v is&And gt, 0, the leakage or pipe explosion point exists on the pipeline. Then, N uniform random numbers w are generated 1 ,w 2 ...w N Respectively inspecting the falling intervals, and judging that the pipeline is in a leakage state when all random numbers do not fall into the pipe explosion interval; otherwise, judging that the pipeline is exploded;
step2.2, pipeline leak simulation based on EPANET nozzle function;
nozzle flow calculation in EPANET is:
wherein Q is the nozzle outflow (L/s), C i Is the nozzle fluidic coefficient, H i Node i water pressure (m);
based on actual measurement data of the flow of the spray head in the automatic spraying system, the pipeline leakage is calculated by adopting the following formula:
wherein A is L Is the leakage area (mm) 2 )，Q L The leakage rate (L/s) of the pipeline; h is a pressure head (m) at the leakage position;
simulating pipeline leakage by using EPANET self-contained nozzle function to enable H i ＝H，Q＝Q L According to the equations (3) and (4), the conversion formula of the leakage area and the jet coefficient is obtained as follows:
C i ＝4.43·A L ×10 -3 (5)
step2.3, simulating tube explosion based on the EPANET pipeline closing function;
when the pipe is burst, the pipe section of the pipe burst is broken, and two leakage points are newly added at the pipe burst position; based on EPANET, calling built-in function to close the pipeline and adding corresponding function at two end nodesEquivalent simulation of the jet coefficient, wherein the jet coefficient is determined by 1 time of the cross-sectional area of the pipe, i.e. C i ＝4.43·A×10 -3 Wherein A is the cross-sectional area of the pipeline;
for a long-distance water pipeline, because the difference between the nodes at two ends and the water pressure at the pipe explosion position is large, the equivalent method can cause large simulation errors; likewise, pipeline segmentation is used to reduce simulation errors by adding virtual nodes.
3. The stochastic simulation method for assessing reliability of a municipal water supply network according to claim 1, wherein: the specific steps of Step3 are as follows:
step3.1, assuming all water usage points are low pressure water usage points, replace them with nozzle outflow type and define the fluidic coefficient C i ＝S i ；
Step3.2, calling EPANET to solve a hydraulic equation of the pipe network;
step3.3, checking the water pressure of the node if H i ≥H i des Modifying the node into a normal outflow type; if H is i Setting the node flow and the leakage coefficient to be zero when the flow is less than or equal to 0;
and step3.4, calling the EPANET again to solve the hydraulic equation of the pipe network, finishing hydraulic calculation if the outflow states of all the nodes in the calculation result meet the constraint of the formula (6), and otherwise, turning to the step Step3.3.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108984873A (en) * | 2018-06-28 | 2018-12-11 | 武汉新烽光电股份有限公司 | The real-time soil's rigidity method of water supply network, equipment, system and storage medium |
| CN109948886A (en) * | 2019-01-22 | 2019-06-28 | 大连理工大学 | A kind of water supply network critical valves discrimination method |
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Cited By (11)
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| CN108984873A (en) * | 2018-06-28 | 2018-12-11 | 武汉新烽光电股份有限公司 | The real-time soil's rigidity method of water supply network, equipment, system and storage medium |
| CN108984873B (en) * | 2018-06-28 | 2023-10-24 | 武汉新烽光电股份有限公司 | Water supply network real-time leakage detection method, device, system and storage medium |
| CN109948886A (en) * | 2019-01-22 | 2019-06-28 | 大连理工大学 | A kind of water supply network critical valves discrimination method |
| CN109948886B (en) * | 2019-01-22 | 2022-09-06 | 大连理工大学 | Method for identifying key valve of water supply pipe network |
| CN111738531A (en) * | 2020-08-05 | 2020-10-02 | 韧科(浙江)数据技术有限公司 | Post-disaster function recovery analysis method for urban building community under situation earthquake |
| CN113418146A (en) * | 2021-08-03 | 2021-09-21 | 上海航天动力科技工程有限公司 | Leakage auxiliary positioning control method for water supply pipe network |
| CN113704999A (en) * | 2021-08-27 | 2021-11-26 | 河北工业大学 | Urban water supply pipe network post-earthquake analysis and optimization method based on time delay simulation |
| CN113704999B (en) * | 2021-08-27 | 2023-06-30 | 河北工业大学 | Urban water supply pipe network post-earthquake analysis and optimization method based on time delay simulation |
| CN114329974A (en) * | 2021-12-29 | 2022-04-12 | 武汉大学 | Monte Carlo simulation-based urban water supply pipe network earthquake damage assessment method |
| CN114329974B (en) * | 2021-12-29 | 2023-07-18 | 武汉大学 | Urban water supply network seismic damage assessment method based on Monte Carlo simulation |
| 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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