CN114580786A - Arrangement optimization method for monitoring points of urban water supply pipe network - Google Patents

Arrangement optimization method for monitoring points of urban water supply pipe network Download PDF

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CN114580786A
CN114580786A CN202210332084.3A CN202210332084A CN114580786A CN 114580786 A CN114580786 A CN 114580786A CN 202210332084 A CN202210332084 A CN 202210332084A CN 114580786 A CN114580786 A CN 114580786A
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龙志宏
蔡艳伟
俞亭超
邵煜
郑飞飞
楚士鹏
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Guangzhou Water Supply Co ltd
Zhejiang University ZJU
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Abstract

The invention discloses an arrangement optimization method for monitoring points of an urban water supply network, which comprises the steps of constructing a minimum response flow meter for retrieving and acquiring the minimum monitoring flow of all pipe sections in an arrangement scheme of any monitoring point in an area to be optimized, setting efficiency evaluation functions of three pipe network monitoring networks as optimization targets according to pipe section monitoring coverage, pipe section space partition nonuniformity and pipe section average similarity, carrying out iterative calculation and multi-objective optimization on the arrangement scheme of the monitoring points, and acquiring a Pareto optimal solution set for determining the number and the arrangement positions of the optimized monitoring points. According to the method, the minimum response flow meter is searched to replace the traditional hydraulic model calculation to obtain the minimum monitoring flow of all the pipe sections, so that the problem that the simulation calculation amount is too large in the pipe section space partition optimization process is solved, and the feedback speed and accuracy of pipe burst positioning work of the final arrangement scheme are improved.

Description

Arrangement optimization method for monitoring points of urban water supply pipe network
Technical Field
The invention relates to the technical field of urban water supply network monitoring points, in particular to a step optimization method for the urban water supply network monitoring points.
Background
The water supply network is one of the most important public infrastructures in cities, the reliable operation of the water supply network is related to the safety of drinking water for residents and the normal operation of industrial production, however, pipe section connecting structures of the water supply network system are complex, corrosion, uneven ground drop, pipe explosion such as construction operation and the like sometimes occur, meanwhile, a large number of water-requiring nodes exist in the water supply network, the installation of monitoring points on each node is not economical, and on the other hand, data has a large amount of redundant information and needs more equipment to store, calculate equipment to store and process corresponding data. Therefore, part of the nodes are reasonably selected to arrange the monitoring points so as to achieve better monitoring and positioning effects, namely the problem of optimal arrangement of the pressure monitoring points of the water supply network.
The optimal arrangement of the pressure monitoring points of the water supply network is mainly divided into an empirical method and a theoretical method. Monitoring point arrangement is generally arranged at nodes such as the most unfavorable points and important users by using an empirical method, but the development requirements of water business enterprises are difficult, and the monitoring point arrangement is generally only used as an auxiliary method. The theoretical rule is that mathematical knowledge is used, and monitoring point installation nodes are determined through calculation and analysis, and the method is divided into a clustering method, a sensitivity matrix analysis method, a multi-objective optimization method and the like. The clustering method has the problem that nodes cannot form communication after clustering, and is mainly used as an auxiliary step of a monitoring point at present so as to improve the efficiency or reduce the information redundancy of a sensor; in the sensitivity matrix analysis, the phenomenon that monitoring points are gathered due to the fact that the sensitivity of nodes near the nodes with high sensitivity is relatively high possibly exists; multiple targets can be considered simultaneously by multi-target optimization, the method is used in various fields, is suitable for solving the problem of optimal arrangement of monitoring points, and can meet the requirements of modern water supply enterprises on monitoring and positioning water supply network events.
When the problem of pipe section pipe burst positioning is researched, the nonuniformity of pipe section space partitions can affect the work efficiency of searching pipe sections when pipe burst occurs, if the nonuniformity of the pipe section space partitions is not considered when monitoring points are arranged, the workload of subsequent pipe burst positioning can be increased, and therefore the objective function can be considered when the monitoring points are arranged, and the workload of the subsequent pipe burst positioning is reduced. However, in the conventional multi-objective function optimization, because the number of nodes for which monitoring points can be selected and arranged in a water supply network in a certain area is large, potential arrangement schemes can reach tens of millions, and each arrangement scheme needs to be evaluated by performing hydraulic simulation on each pipe section of the water supply network from 0 to the maximum pipe bursting flow, the difficulty in optimizing the spatial partition of the pipe sections can be greatly increased.
Patent document CN112989535A discloses a water supply network pressure monitoring point optimal arrangement method based on pipe burst detection benefits, which includes calculating pressure drops under pipe bursts of different levels of each pipeline in EPANET by using a pipe network hydraulic model, and constructing a pipe burst event coverage matrix according to the calculated pressure drop result; and then, for a given number of water pressure monitoring points, constructing an optimized water pressure monitoring point layout by taking the maximum pipe explosion event coverage rate as an objective function, and solving by adopting a distribution estimation algorithm, thereby determining the optimal layout of the monitoring belt points under the given number. The method is based on the pipe bursting event coverage rate and the minimum detectable flow rate of pipe bursting as indexes, and solves the problems of how many water pressure monitoring points are required to be arranged and where the water pressure monitoring points are arranged in engineering practice, but the arrangement mode only considers the economy of the arrangement, but does not consider the problem of subsequent pipe bursting positioning.
Patent document CN112503400A discloses a multi-objective optimization arrangement method for pressure measurement points of a water supply network, which includes (1) obtaining basic water pressures of each point under normal working conditions through basic pipe network model hydraulic calculation; (2) establishing a pressure driving model, setting a minimum service water head, a minimum water outlet water head and an ejector index, and performing pipe bursting simulation on all pipe sections to obtain the water pressure of each node and the flow of the corresponding pipe bursting events under different pipe bursting events; (3) setting three effective energy evaluation functions of the monitoring network from the covering surface, the sensitivity and the positioning precision of the monitoring network respectively, and calculating to obtain three evaluation function values according to the calculation result for a given monitoring point arrangement scheme; (4) and setting the number of newly added monitoring points, performing multi-objective optimization on the arrangement scheme by using a BORG algorithm for multiple iterations, and obtaining a Pareto optimal solution set. The method can provide data support for subsequent pipe explosion positioning, but has higher requirement on computing capacity and can not finish positioning quickly.
Disclosure of Invention
In order to solve the problems, the invention provides an arrangement optimization method for monitoring points of a municipal water supply network, which obtains the minimum monitoring flow of all pipe sections by retrieving a minimum response flow meter to replace the traditional hydraulic model calculation, thereby solving the problem of excessively large simulation calculation amount in the pipe section space partition optimization process and improving the feedback speed and accuracy of pipe burst positioning work of the final arrangement scheme.
A method for optimizing the arrangement of monitoring points of a municipal water supply network comprises the following steps:
step 1, acquiring pipe network data in an optimized area to be arranged, wherein the pipe network data comprises pipe section data and node numbers of monitoring points which can be arranged;
step 2, constructing a minimum response flow meter according to a monitoring point collection with pressure smaller than threshold pressure in a simulated pipe bursting test, corresponding node numbers and pipe section data, wherein the minimum response flow meter is used for retrieving and acquiring minimum monitoring flow of all pipe sections in any monitoring point arrangement scheme in an area to be optimized;
step 3, respectively setting efficiency evaluation functions of three pipe network monitoring networks from the pipe segment monitoring coverage rate, the pipe segment spatial partition nonuniformity and the pipe segment average similarity, and calculating and obtaining corresponding three efficiency evaluation function values according to the pipe network data obtained in the step 1 and the minimum response flow table constructed in the step 2 for the monitoring point arrangement scheme of the given pipe network;
and 4, setting the number range of the newly added monitoring points, performing iterative computation on the arrangement scheme of the monitoring points, and performing multi-target optimization on the iterative computation result according to the three energy efficiency evaluation functions in the step 3 to obtain a Pareto optimal solution set for determining the number and the arrangement positions of the optimized monitoring points.
Preferably, the threshold pressure in step 2 is set after statistical analysis of historical monitoring data, the threshold pressure is a difference between a pressure value at a normal flow rate of the pipe section and a standard deviation of 2 times of the monitoring data in any time period, and the alarm threshold is selected to conform to normal distribution, so that a final pipe burst positioning result is more accurate.
Specifically, the construction of the minimum response flow table in the step 2 includes the following steps:
step 2.1, performing a pipe explosion simulation test on the pipe section to obtain a monitoring point collection for sending an alarm in an area where the pipe section is located;
step 2.2, according to the monitoring point collection obtained in the step 2.1, selecting all monitoring points with pressure less than threshold pressure, and calculating to obtain a minimum monitoring flow collection corresponding to all the monitoring points;
step 2.3, uniformly setting a non-alarm flow value for all monitoring points which do not send out an alarm in a pipe burst simulation test, wherein the non-alarm flow value is the sum of the maximum pipe burst flow value of the pipe section and a constant;
step 2.4, according to the node numbers corresponding to all the monitoring points, filling the minimum flow value or the non-alarm flow value corresponding to each monitoring point into a form in sequence to obtain a minimum response flow sequence of the pipe section;
and 2.5, repeating the steps 2.1-2.4, obtaining the minimum response flow sequences of all the pipe sections, and sequencing the minimum response flow sequences of all the pipe sections according to the pipe section index numbers to obtain a minimum response flow table, wherein row and column titles of the minimum response flow table are respectively a node number and a pipe section index number.
Specifically, the mathematical expressions of step 2.2 and step 2.3 are as follows:
when i ∈ Salarm_sensor(j,t)：
Figure BDA0003573461820000051
When in use
Figure BDA0003573461820000052
Figure BDA0003573461820000053
Wherein S isalarm_sensor(j,t)＝{i:I[pi(t,j),pa(t,i)]1} denotes the response sensor sequence, pa(t, i) represents the threshold pressure of node i at time t, pi(t, j) represents the water pressure at node i of segment j at time t, qjIndicating the minimum burst flow, Q, of pipe section jjmaxRepresents the maximum burst flow of the pipe section j, C represents a constant, C>0；
Preferably, the specific expression of the performance evaluation function in step 3 is as follows:
the method comprises the following steps of solving a monitoring point arrangement scheme X by taking the maximization of the monitoring coverage rate of a pipe section as an objective function, wherein the arrangement scheme is provided with K sensors in total, and the expression of the objective function is as follows:
Figure BDA0003573461820000061
Figure BDA0003573461820000062
Figure BDA0003573461820000063
wherein, F1XIndicating the monitoring coverage of the pipe network, j indicatesNumber of pipe sections for bursting, L representing total number of pipe sections, QjIndicates the pipe section flow,/jIndicating the length of the pipe section, Sj(t, X) represents a function whether the pipe section j at the time of t can be monitored by any monitoring point K in K monitoring points in X arrangement of given monitoring points, when the monitored value is 1, otherwise, the monitored value is 0, pj(t, k) represents the water pressure at the monitoring point k when the pipe section j has the maximum flow rate and pipe explosion at the time t, pa(t, k) threshold pressure set for sensor k, when pj(t,k)<pa(t, k), alarming at the monitoring point, otherwise not alarming, wherein alpha and beta are weight coefficients;
minimizing the nonuniformity of the pipe section space partition into an objective function, wherein the expression of the objective function is as follows:
Figure BDA0003573461820000064
Figure BDA0003573461820000065
wherein, F2XRepresenting the spatial zonal non-uniformity of the pipe section,
Figure BDA0003573461820000066
representing the total length of the pipe divided into the spatial partition in which the monitoring point k is located,
Figure BDA0003573461820000067
represents the average tube length of the spatial partition in which the K monitoring points are positioned, Spipe(t, k) represents a tube space partition;
minimizing the average similarity between the pipe sections to be an objective function, wherein the expression of the objective function is as follows:
Figure BDA0003573461820000071
wherein, F3XDenotes the average degree of similarity, gamma, between the tube sectionsj,j′Denotes the phase between the tube sections j and jSimilarity.
Specifically, the expression of the spatial partition of the pipeline is as follows:
Spipe(t,k)＝{j:fsensor(j,t)＝k,j∈{1,…,L.}}
Figure BDA0003573461820000072
wherein q isjAnd for the simulated minimum pipe burst flow of the pipe section j, retrieving the minimum response flow table according to the index number of the pipe section j to obtain the minimum monitoring flow corresponding to the simulated minimum pipe burst flow.
Specifically, the similarity between the pipe segment j and the pipe segment j' is obtained as follows:
step 3.1, L pipe sections are arranged in the pipe network, N is the total number of nodes, and the pressure value P of the node i under the normal working conditioniPressure value P corresponding to the occurrence of pipe explosion eventi' difference of riThe residual error r at each node can be obtained:
r＝(r1,r2,…,ri,…,rN)，i＝1,2,…,N
step 3.2, obtaining a sensitivity matrix S' according to the residual error r and the pipe bursting flow calculation of the pipe section j:
Figure BDA0003573461820000073
wherein the content of the first and second substances,
Figure BDA0003573461820000074
qjsearching a minimum response flow meter according to the index number of the pipe section j to obtain the minimum monitoring flow corresponding to the simulated minimum pipe burst flow for the simulated minimum pipe burst flow of the pipe section j;
step 3.3, normalization processing is carried out on the sensitivity matrix S':
Figure BDA0003573461820000081
wherein the content of the first and second substances,
Figure BDA0003573461820000082
represents the maximum value of the j row in the S matrix, S'jminRepresents the minimum value of the jth row in the S matrix;
and 3.4, calculating the similarity between the pipe section j and the pipe section j':
Figure BDA0003573461820000083
wherein s isjThe influence of pipe section j explosion on the water pressure change of each monitoring point is shown, and the influence is formed by each row vector of the normalized sensitivity matrix S', namely Sj＝(sj1,sj2,…,sjN)。
Preferably, the step 4 adopts a multi-objective optimization algorithm Borg MOEA to perform optimization calculation, the iteration times are set between 5000-15000, and an epsilon-box domination file is set, so that the search diversity is ensured, and the local optimization is favorably avoided; meanwhile, an epsilon-progress mechanism is introduced into the algorithm, so that the algorithm has a search stagnation restarting function; the method has various recombination operation operators, can establish a feedback mechanism according to the proportion of offspring generated by different operators, and can adjust the application proportion of different operators on line according to specific problems so as to adapt to the solution of problems in different fields.
Preferably, the Pareto optimal solution set in step 4 generates a corresponding monitoring point arrangement scheme set based on the number of monitoring points that are continuously increased, performs multi-objective optimization on each scheme in the monitoring point arrangement scheme set to obtain a corresponding Pareto value, stops increasing the number of monitoring points when the Pareto value is not increased any more, and outputs the monitoring point arrangement scheme corresponding to the highest Pareto value as a final optimized arrangement scheme.
Compared with the prior art, the invention has the beneficial effects that:
(1) three optimization targets, namely pipe section monitoring coverage rate, pipe section spatial partition nonuniformity and pipe section average similarity, are provided, and the monitoring point arrangement scheme in the area is optimized, so that the pipe burst positioning work feedback speed of the final arrangement optimization scheme is higher and more accurate.
(2) Based on the optimization target of the spatial zoning heterogeneity of the pipe sections, the minimum monitoring flow of all the pipe sections is obtained by constructing a minimum response flow meter to replace the traditional hydraulic model calculation, so that the problem of overlarge simulation calculation amount in the pipe section spatial zoning optimization process is solved.
Drawings
Fig. 1 is a pipe network topology diagram of an area to be optimally arranged in this embodiment;
FIG. 2 is a schematic flow chart of a method for optimizing the arrangement of monitoring points of a municipal water supply network according to the present invention;
FIG. 3 is a distribution diagram of the multi-objective optimization pareto solution set in the embodiment;
fig. 4 is a schematic view of the arrangement of monitoring points optimized by the method provided by the invention.
Detailed Description
As shown in fig. 1, a pipe network topological graph of an area to be optimally arranged is provided in this embodiment, and basic data of the pipe network: the node 550 that impounds, pipeline section 735 root, current 7 pressure monitoring points, node index (number) are: 436. 2303, 1394, 6383, 87, 6370, and 1026.
As shown in FIG. 2, the method for optimizing the arrangement of monitoring points in the urban water supply network optimizes the arrangement of the monitoring points in the area, and comprises the following steps:
step 1, acquiring pipe network data in an optimized area to be arranged, wherein the pipe network data comprises pipe section data and node numbers of monitoring points which can be arranged.
Pipe explosion simulation is carried out to obtain the maximum pipe explosion flow Q of each pipe sectionjmax: sequentially enabling each pipe section to carry out pipe bursting simulation under the condition of complete fracture, setting a sufficiently large initial water demand value before simulation, setting the actual water demand after iteration of hydraulic simulation software as the maximum pipe bursting flow of the pipe section, wherein the maximum pipe bursting flow of each pipe section is shown in table 1 (735 rows in total, and the part is intercepted):
TABLE 1 maximum burst flow for each section
Figure BDA0003573461820000101
The normal state node heads are shown in table 2 (550 columns, truncated part in total):
TABLE 2 Water head of each node in normal state
Figure BDA0003573461820000102
Each pipe section is subjected to pipe bursting simulation sequentially at the maximum pipe bursting flow, and the pressure of each node is obtained as shown in table 3 (table size is 735 rows and 550 columns, and the part is intercepted):
TABLE 3 pressure of each node after each pipe section is at the maximum pipe burst flow
Figure BDA0003573461820000111
The case is 1m3Step-length increasing pipe explosion flow of/h, and simulating 0-QjmaxA pipe bursting event; 735 the total number of pipe bursting events simulated for a total of 9,712,750 pipe burst events; taking pipe segment 1 as an example, as shown in table 4 (total 86846 rows, cut out):
TABLE 4 pipe sections correspond to 0-QjmaxPressure at each node of a pipe burst event
Figure BDA0003573461820000112
Step 2, constructing a minimum response flow meter according to a monitoring point collection with pressure smaller than threshold pressure in a simulated pipe bursting test, corresponding node numbers and pipe section data, wherein the minimum response flow meter is used for retrieving and acquiring the minimum monitoring flow of all pipe sections in any monitoring point arrangement scheme in an area to be optimized;
the arrangement scheme of the monitoring points can be formed by any node combination, so that the number of the arrangement schemes is
Figure BDA0003573461820000121
N is the total number of nodes, L is the number of pipe sections, and K is the number of sensors to be arranged, when a water supply network is large, the potential arrangement schemes can reach tens of millions, and therefore optimization work in a large area is very difficult.
The invention provides a minimum response flow meter which records the corresponding pipe section pipe bursting flow when a pipe section j pipe bursting node i is lower than a set threshold pressure
Figure BDA0003573461820000122
With Tabmin_alarmIs represented as follows:
Figure BDA0003573461820000123
in order to determine the just-breaking threshold pi(t,qj)>pa(t, i)) burst flow rate of pipe segment j
Figure BDA0003573461820000124
An enumeration method needs to be applied, and the specific process is as follows: pipe bursting flow q of pipe section jjAt a certain step size Δ qjUp to qjIs equal to Qjmax。
When p isi(t,qj) Below alarm pressure pa(t, i), shot flow
Figure BDA0003573461820000125
The node which is not always alarmed records a value (Q) which is larger than the maximum pipe burst flow of the pipe section at the corresponding positionjmax+ C), C is a constant, indicating that the pipe section will not cause the node to alarm no matter how large a pipe burst event occurs.
The mathematical expression of the above is:
when i ∈ Salarm_sensor(j,t)：
Figure BDA0003573461820000126
When in use
Figure BDA0003573461820000131
Figure BDA0003573461820000132
Wherein S isalarm_sensor(j,t)＝{i:I[pi(t,j),pa(t,i)]1} denotes the response sensor sequence, pa(t, i) represents the threshold pressure of node i at time t, pi(t, j) represents the water pressure at node i of segment j at time t, qjIndicating the minimum burst flow, Q, of pipe section jjmaxRepresents the maximum burst flow of the pipe section j, C represents a constant, C>0；
The construction method of the minimum response flow meter comprises the following specific steps:
step 2.1, performing pipe explosion simulation test on the pipe section to obtain a monitoring point collection which sends an alarm in an area where the pipe section is located;
step 2.2, according to the monitoring point collection obtained in the step 2.1, selecting all monitoring points with pressure less than threshold pressure, and calculating to obtain a minimum monitoring flow collection corresponding to all the monitoring points;
step 2.3, uniformly setting a non-alarm flow value for all monitoring points which do not send out an alarm in a pipe burst simulation test, wherein the non-alarm flow value is the sum of the maximum pipe burst flow value of the pipe section and a constant;
step 2.4, according to the node numbers corresponding to all the monitoring points, filling the minimum flow value or the non-alarm flow value corresponding to each monitoring point into a form in sequence to obtain a minimum response flow sequence of the pipe section;
and 2.5, repeating the steps 2.1-2.4, obtaining the minimum response flow sequences of all the pipe sections, and sequencing the minimum response flow sequences of all the pipe sections according to the pipe section index numbers to obtain a minimum response flow table, wherein row and column titles of the minimum response flow table are respectively a node number and a pipe section index number.
After the minimum response flow meter is established, hydraulic simulation is not needed to be carried out on different monitoring point arrangement schemesCalculating, but directly selecting Tabmin_alarmAnd (4) calculating the target function value of the spatial partition nonuniformity of the pipe section by corresponding rows and columns so as to realize the optimization target.
The minimum response flow table is shown in table 5 (table size 735 row 550 column, truncated):
TABLE 5 minimum response flow meter
Figure BDA0003573461820000141
Step 3, respectively setting efficiency evaluation functions of three pipe network monitoring networks from the pipe segment monitoring coverage rate, the pipe segment spatial partition nonuniformity and the pipe segment average similarity, and calculating and obtaining corresponding three efficiency evaluation function values according to the pipe network data obtained in the step 1 and the minimum response flow table constructed in the step 2 for the monitoring point arrangement scheme of the given pipe network;
in a pipe network with K sensors, at the time of t, when a pipe section j is gradually increased from a small flow, pressure drops at different sensor positions are different due to pipe explosion of the pipe section j at a specific flow, the sensor which gives an alarm firstly is most sensitive to the pipe explosion of the pipe section, and if the sensor K gives an alarm firstly, the pipe section j is divided into areas where the sensors K are located. By calling f for L root canals in sequencesensorAnd (j, t) simulating pipe explosion of each pipe section, dividing the pipe sections into K areas one by one, and realizing the spatial division of the pipe sections, wherein the mathematical expression is as follows:
Spipe(t,k)＝{j:fsensor(j,t)＝k,j∈{1,…,L.}}
Figure BDA0003573461820000151
wherein q isjAnd for the simulated minimum pipe burst flow of the pipe section j, retrieving the minimum response flow table according to the index number of the pipe section j to obtain the minimum monitoring flow corresponding to the simulated minimum pipe burst flow.
The specific expressions of the three efficacy evaluation functions are:
the method comprises the following steps of solving a monitoring point arrangement scheme X by taking the maximization of the monitoring coverage rate of a pipe section as an objective function, wherein the arrangement scheme is provided with K sensors in total, and the expression of the objective function is as follows:
Figure BDA0003573461820000152
Figure BDA0003573461820000153
Figure BDA0003573461820000154
wherein, F1XThe monitoring coverage rate of the pipe network is shown, j represents the number of pipe sections of the pipe burst, L represents the total number of the pipe sections, and QjIndicates the pipe section flow,/jIndicating the length of the pipe section, Sj(t, X) represents a function whether the pipe section j at the time of t can be monitored by any monitoring point K in K monitoring points in X arrangement of given monitoring points, when the monitored value is 1, otherwise, the monitored value is 0, pj(t, k) represents the water pressure at the monitoring point k when the pipe section j has the maximum flow rate and pipe explosion at the time t, pa(t, k) threshold pressure set for sensor k, when pj(t,k)<pa(t, k), alarming at the monitoring point, otherwise not alarming, wherein alpha and beta are weight coefficients;
minimizing the nonuniformity of the pipe section space partition into an objective function, wherein the expression of the objective function is as follows:
Figure BDA0003573461820000161
Figure BDA0003573461820000162
wherein, F2XRepresenting the spatial zonal non-uniformity of the pipe section,
Figure BDA0003573461820000163
representing the total length of the pipe divided into the spatial partition in which the monitoring point k is located,
Figure BDA0003573461820000164
represents the average tube length of the spatial partition in which the K monitoring points are positioned, Spipe(t, k) represents a pipe spatial partition;
minimizing the average similarity between the pipe sections to be an objective function, wherein the expression of the objective function is as follows:
Figure BDA0003573461820000165
wherein, F3XDenotes the average degree of similarity, gamma, between the tube sectionsj,j′Representing the similarity between segments j and j'.
The method comprises the following steps of:
l pipe sections are arranged in the pipe network, N is the total number of nodes, and the pressure value P of the node i under the normal working conditioniPressure value P corresponding to the occurrence of pipe explosion eventi' difference of riThe residual error r at each node can be obtained:
r＝(r1,r2,…,ri,…,rN)，i＝1,2,…,N.
defining a sensitivity matrix S':
Figure BDA0003573461820000171
wherein
Figure BDA0003573461820000172
Normalization of the sensitivity matrix:
Figure BDA0003573461820000173
wherein the content of the first and second substances,
Figure BDA0003573461820000174
s′jmaxrepresents the maximum value of the jth row, S 'in the S matrix'jminRepresenting the minimum value of the jth row in the S matrix.
Wherein i represents the node serial number of the pressure measuring point, j represents the pipe section serial number of the pipe explosion, and qjFor the occurring pipe burst flow, each row constitutes a sensitivity vector sj＝(sj1,sj2,…,sjN) And represents the influence on the water pressure change of each monitoring point when pipe section j explodes. Different pipe sections passing through gammaj,j′And measuring the similarity, wherein the expression is as follows:
Figure BDA0003573461820000175
γj,j′the larger the value of (a) is, the more similar the pressure changes caused by the pipe sections j and j 'at the respective pressure measuring points are, and the more difficult the distinction between the pipe sections j and j' is made.
The difference between the water head of each node in a normal state and the pressure of each node after each pipe section is subjected to pipe bursting at the maximum pipe bursting flow is calculated, and the residual matrix is shown in table 6 (the matrix size is 735 rows and 550 columns, and the truncated part):
TABLE 6 residual matrix
Figure BDA0003573461820000181
The pressure sensitive matrix is shown in the following table (matrix size 735 rows and 550 columns, truncated):
TABLE 7 pressure sensitivity matrix
Figure BDA0003573461820000182
Step 4, setting the number range of the newly added monitoring points, performing iterative computation on the arrangement scheme of the monitoring points, performing multi-objective optimization on the iterative computation result according to the three energy efficiency evaluation functions in the step 3, and obtaining a Pareto optimal solution set for determining the number and the arrangement positions of the optimized monitoring points:
optimizing and calculating by using a multi-objective optimization algorithm Borg MOEA, increasing the number n of monitoring points to increase progressively, and obtaining a solution set after each optimization, wherein the multi-objective optimization pareto front solution set is shown in a table 8 (88 solutions in total, and a part is intercepted):
TABLE 8 Multi-objective optimization Pareto frontier solution set
Figure BDA0003573461820000191
And drawing a corresponding solution set graph according to the Pareto leading edge solution set, as shown in FIG. 3.
When the number n of monitoring points is increased to be between 1 and 29, the optimization amplitude is improved fastest. The optimization amplification is gradually reduced along with the increase of the number of the monitoring points, and when the monitoring point n is equal to 41, the optimization amplification is already small, so that a good optimization effect can be considered to be achieved.
From the trend of the whole Pareto solution set, when n is 41, the difference of the function values of the solutions on different targets is not large, each solution can obtain a better optimization result on each target dimension, and has better convergence, and a monitoring point arrangement diagram (the solution set serial number in table 8 is 83) with n being 41 is drawn, as shown in fig. 4, where a black point is a monitoring point.
By the optimized monitoring point arrangement scheme, quick pipe burst positioning can be carried out by utilizing pipe section space subareas, the uniformity of the pipe section space subareas can influence the pipe section searching range during pipe burst positioning, and if 24 pipe sections in one area are respectively divided into 3 subareas, the probability of pipe burst of each pipe section is set to be equal, and if three monitoring points are arranged, the expected expressions of the number of the searched pipe sections are as follows:
Figure BDA0003573461820000201
the upper typeThe middle K is the number of the pipe section space partitions, namely the number of the sensors; a is the number of alarm sensors;
Figure BDA0003573461820000202
representing the number of times each pipe segment space partition is selected into the partition combination; m is the total number of alarm partition combination modes; n is a radical ofmThe total number of the pipe sections in the mth partition combination;
Figure BDA0003573461820000203
the combined tube bursting probability of the mth zone.
Assuming that the number of the partition pipe sections of the first arrangement scheme is 2,7 and 15 (the pipe sections are spatially partitioned unevenly), and the number of the partition pipe sections of the second arrangement scheme is 8, 8 and 8 (the pipe sections are spatially partitioned evenly):
1. when only one monitoring point gives an alarm, the number of the search pipe sections of the first arrangement scheme is 11.58, and the number of the search pipe sections of the second arrangement scheme is 8.
2. When two monitoring points alarm, the number of the search pipe sections of the first arrangement scheme is 17.79, and the number of the search pipe sections of the second arrangement scheme is 16.
3. When the three monitoring points give full alarms, the number of the search pipe sections of the first arrangement scheme is 24, and the number of the search pipe sections of the second arrangement scheme is 24.
According to the difference of the number of the search pipe sections, the more uniform the spatial partition of the pipe sections in the area is, the corresponding reduction of the number of the pipe sections to be searched when pipe explosion occurs, so that the quick feedback of pipe explosion positioning is realized.

Claims (8)

1. A method for optimizing the arrangement of monitoring points of a urban water supply network is characterized by comprising the following steps:
step 1, acquiring pipe network data in an optimized area to be arranged, wherein the pipe network data comprises pipe section data and node numbers of monitoring points which can be arranged;
step 2, constructing a minimum response flow meter according to a monitoring point collection with pressure smaller than threshold pressure in a simulated pipe bursting test, corresponding node numbers and pipe section data, wherein the minimum response flow meter is used for retrieving and acquiring minimum monitoring flow of all pipe sections in any monitoring point arrangement scheme in an area to be optimized;
step 3, respectively setting efficiency evaluation functions of three pipe network monitoring networks from the pipe segment monitoring coverage rate, the pipe segment spatial partition nonuniformity and the pipe segment average similarity, and calculating and obtaining corresponding three efficiency evaluation function values according to the pipe network data obtained in the step 1 and the minimum response flow table constructed in the step 2 for the monitoring point arrangement scheme of the given pipe network;
and 4, setting the number range of the newly added monitoring points, performing iterative computation on the arrangement scheme of the monitoring points, and performing multi-target optimization on the iterative computation result according to the three energy efficiency evaluation functions in the step 3 to obtain a Pareto optimal solution set for determining the number and the arrangement positions of the optimized monitoring points.
2. The method for optimizing the arrangement of the monitoring points of the urban water supply network according to claim 1, wherein the threshold pressure in the step 2 is set after statistical analysis of historical monitoring data, and the threshold pressure is the difference between a pressure value at a normal flow rate of a pipe section and 2 times of standard deviation of the monitoring data in any time period.
3. The method for optimizing the arrangement of the monitoring points of the urban water supply network according to claim 1, wherein the step 2 of constructing the minimum response flow meter comprises the following specific steps:
step 2.1, performing a pipe explosion simulation test on the pipe section to obtain a monitoring point collection for sending an alarm in an area where the pipe section is located;
step 2.2, according to the monitoring point collection obtained in the step 2.1, selecting all monitoring points with pressure less than threshold pressure, and calculating to obtain a minimum monitoring flow collection corresponding to all the monitoring points;
step 2.3, uniformly setting a non-alarm flow value for all monitoring points which do not send out an alarm in a pipe burst simulation test, wherein the non-alarm flow value is the sum of the maximum pipe burst flow value of the pipe section and a constant;
step 2.4, according to the node numbers corresponding to all the monitoring points, filling the minimum flow value or the non-alarm flow value corresponding to each monitoring point into a form in sequence to obtain a minimum response flow sequence of the pipe section;
and 2.5, repeating the steps 2.1-2.4, obtaining the minimum response flow sequences of all the pipe sections, and sequencing the minimum response flow sequences of all the pipe sections according to the pipe section index numbers to obtain a minimum response flow table, wherein row and column titles of the minimum response flow table are respectively a node number and a pipe section index number.
4. The method for optimizing the arrangement of monitoring points of the urban water supply network according to claim 1, wherein the specific expression of the performance evaluation function in the step 3 is as follows:
the method comprises the following steps of solving a monitoring point arrangement scheme X by taking the maximization of the monitoring coverage rate of a pipe section as an objective function, wherein the arrangement scheme is provided with K sensors in total, and the expression of the objective function is as follows:
Figure FDA0003573461810000031
Figure FDA0003573461810000032
Figure FDA0003573461810000033
wherein, F1XThe monitoring coverage rate of the pipe network is shown, j represents the number of pipe sections of the pipe burst, L represents the total number of the pipe sections, and QjIndicating the flow of the pipe section, /)jIndicating the length of the pipe section, Sj(t, X) represents a function whether the pipe section j at the time of t can be monitored by any monitoring point K in K monitoring points in X arrangement of given monitoring points, when the monitored value is 1, otherwise, the monitored value is 0, pj(t, k) represents the water pressure at the monitoring point k when the pipe section j has the maximum flow rate and pipe explosion at the time t, pa(t, k) threshold pressure set for sensor kForce when pj(t,k)<pa(t, k), alarming at the monitoring point, otherwise not alarming, wherein alpha and beta are weight coefficients;
minimizing the nonuniformity of the pipe section space partition into an objective function, wherein the expression of the objective function is as follows:
Figure FDA0003573461810000034
Figure FDA0003573461810000035
wherein, F2XRepresenting the spatial zonal non-uniformity of the pipe section,
Figure FDA0003573461810000036
representing the total length of the pipe divided into the spatial partition in which the monitoring point k is located,
Figure FDA0003573461810000037
represents the average tube length of the spatial partition in which the K monitoring points are positioned, Spipe(t, k) represents a pipe spatial partition;
minimizing the average similarity between the pipe sections to be an objective function, wherein the expression of the objective function is as follows:
Figure FDA0003573461810000041
wherein, F3XDenotes the average degree of similarity, gamma, between the tube sectionsj,j′Representing the similarity between segments j and j'.
5. The method for optimizing the arrangement of monitoring points of a municipal water supply network according to claim 4, wherein the spatial division of the pipes is expressed by:
Spipe(t,k)＝{j:fsensor(j,t)＝k,j∈{1,…,L.}}
Figure FDA0003573461810000042
wherein q isjAnd for the simulated minimum pipe burst flow of the pipe section j, searching the minimum response flow meter according to the index number of the pipe section j to obtain the minimum monitoring flow corresponding to the simulated minimum pipe burst flow.
6. The method for optimizing the arrangement of monitoring points of the urban water supply network according to claim 4, wherein the similarity between the pipe sections j and j' is obtained by the following steps:
step 3.1, L pipe sections are arranged in the pipe network, N is the total number of nodes, and the pressure value P of the node i under the normal working conditioniPressure value P corresponding to the occurrence of pipe explosion eventi' difference of riThe residual error r at each node can be obtained:
r＝(r1,r2,…,ri,…,rN)，i＝1,2,…,N
step 3.2, obtaining a sensitivity matrix S' according to the residual error r and the pipe bursting flow calculation of the pipe section j:
Figure FDA0003573461810000043
wherein the content of the first and second substances,
Figure FDA0003573461810000044
wherein q isjSearching a minimum response flow meter according to the index number of the pipe section j to obtain the minimum monitoring flow corresponding to the simulated minimum pipe burst flow for the simulated minimum pipe burst flow of the pipe section j;
step 3.3, normalization processing is carried out on the sensitivity matrix S':
Figure FDA0003573461810000051
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003573461810000052
s′jmaxrepresents the maximum value of the j row in the S matrix, S'jminRepresents the minimum value of the jth row in the S matrix;
step 3.4, calculating the similarity between the pipe section j and the pipe section j':
Figure FDA0003573461810000053
wherein s isjThe influence of pipe section j explosion on the water pressure change of each monitoring point is shown, and the influence is formed by each row vector of the normalized sensitivity matrix S', namely Sj＝(sj1,sj2,…,sjN)。
7. The method for optimizing the arrangement of the monitoring points of the urban water supply network as claimed in claim 1, wherein the step 4 adopts a multi-objective optimization algorithm Borg MOEA to perform optimization calculation, and the iteration number is set between 5000-15000.
8. The arrangement optimization method for monitoring points of the urban water supply network according to claim 1, wherein the Pareto optimal solution set of step 4 generates a corresponding monitoring point arrangement scheme set based on the number of monitoring points which are continuously increased, performs multi-objective optimization on each scheme in the monitoring point arrangement scheme set to obtain a corresponding Pareto value, stops the increase of the number of monitoring points when the Pareto value is not increased any more, and outputs the monitoring point arrangement scheme corresponding to the highest Pareto value as a final optimization arrangement scheme.
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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
CN115859068A (en) * 2023-03-03 2023-03-28 四川三思德科技有限公司 Environmental information sensing method and system for intelligent water conservancy architecture
CN115859068B (en) * 2023-03-03 2023-05-16 四川三思德科技有限公司 Environment information sensing method and system for intelligent water conservancy architecture
CN116701970A (en) * 2023-06-12 2023-09-05 宁波大学 Drainage pipe network monitoring point optimal arrangement method based on double-layer similarity clustering
CN116701970B (en) * 2023-06-12 2024-06-04 宁波大学 Drainage pipe network monitoring point optimal arrangement method based on double-layer similarity clustering
CN117216949A (en) * 2023-08-21 2023-12-12 长江生态环保集团有限公司 Sensor-crossing tube explosion positioning domain self-adaption method based on deep learning
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