Method for optimizing distribution of water in a network based on complex supply and demand relationships

Abstract

The application is based on a complex supply-demand relationship canal system optimal water distribution method, the canal system includes a primary channel and multiple secondary channels, and is specifically implemented according to the following steps: collecting canal system water distribution data; establishing a canal system optimal water distribution model according to the canal system water distribution data; using a geatpy toolbox to realize a genetic algorithm to solve the canal system optimal water distribution model to obtain optimal water distribution time; and summarizing the data in the above steps to obtain a water distribution scheme. An irrigation mode of 'group rotation irrigation and group continuous irrigation' is adopted, a complex supply-demand relationship canal system optimal water distribution model is established, the travel time of water in the canal is added to the model, and finally the model is solved by using a genetic algorithm, so that the water distribution time meeting the complex supply-demand relationship is obtained.

Description

Technical Field

[0001] This invention belongs to the field of canal system water allocation and scheduling technology, specifically involving a canal system optimized water allocation method based on complex supply and demand relationships. Background Technology

[0002] Optimized irrigation canal systems aim to meet crop irrigation requirements by employing specific methods and technologies to rationally allocate water flow and timing within the canals, distributing water to the fields. Due to the limited flow capacity of irrigation canals, rotational irrigation groups are often necessary. The supply and demand relationships within the irrigation canal system are complex; a single canal may supply water to multiple fields, and a single field may receive water from multiple canals—a scenario not considered in existing irrigation models. Furthermore, neglecting to account for water travel time within the canals during distribution can lead to inaccurate water allocation timing. Summary of the Invention

[0003] The purpose of this invention is to provide a canal system optimization water distribution method based on complex supply and demand relationships, which solves the problem of water distribution in canal systems with complex supply and demand relationships that cannot be solved by existing water distribution methods.

[0004] The technical solution adopted in this invention is a water distribution optimization method for a canal system based on complex supply and demand relationships. This canal system includes one primary canal and multiple secondary canals, and is implemented according to the following steps:

[0005] Step 1: Collect water distribution data for the canal system;

[0006] Step 2: Establish an optimized water distribution model for the canal system based on the canal system water distribution data;

[0007] Step 3: Use the geatpy toolbox to implement the genetic algorithm to solve the canal system water distribution optimization model and obtain the optimal water distribution time;

[0008] Step 4: Summarize the data from steps 1-3 above to obtain the water distribution plan.

[0009] The invention is further characterized by:

[0010] The water distribution data for the canal system in step 1 includes:

[0011] (1) Design traffic Q for primary channels d m 3 / s;

[0012] (2) Design flow rate q for N secondary channels id m 3 / s, where 1≤i≤N, and N is the number of secondary channels;

[0013] (3) The length l of N secondary channels i , km;

[0014] (4) The number and name of the fields supplied by each canal;

[0015] (5) The number and names of water supply channels for each field;

[0016] (6) Water requirement W for each field j m 3 ;

[0017] (7) Minimum water distribution from channel i to field j (minW) i j m 3 ;

[0018] (8) Water distribution cycle T, d.

[0019] Step 2 is as follows:

[0020] (1) Adopting an irrigation method of "inter-group rotation irrigation and intra-group continuous irrigation", the secondary channels are first divided into different irrigation groups; the number of irrigation groups is:

[0021]

[0022] In the formula, M is the number of irrigation groups, and Q is... d Traffic designed for higher-level channels, q id Design traffic for the lower-level channel i, where i is the total number of lower-level channels, and ceil is rounded up;

[0023] (2) Decision variables: ① Rotation irrigation group situation, decision variable X mi ={0,1} represents the on / off state of the i-th outlet of the m-th irrigation group, X mi =0 indicates the outlet is closed, X mi =1 indicates that the outlet is open, ② the water distribution flow from channel i to field j The amount of water distributed from channel i to field j, W i j ;

[0024] (3) Objective function:

[0025] Objective Function 1: To facilitate administrator operations, the difference in water distribution completion time among channels within the same group should be minimized. The objective function is established as follows:

[0026] ΔT1=min|et a -et b | (2)

[0027]

[0028]

[0029]

[0030]

[0031] In the formula, ΔT1 represents the absolute value of the difference in water distribution completion time between different channels within the same group, a and b represent the water distribution completion times between any two channels within the same group, and et a et b These represent the water distribution completion times of channels a and b, respectively, and x…j represent the fields supplied by channel a. This indicates the end time of water supply from channel a to fields x…j. The duration of water supply from channel a to field j is represented by the formula shown in Formula 5. This indicates the start time of water supply from channel a to field j. The calculation formula and same, Let i be the travel time of water flowing to channel i, if i = 1. Let h, ..., k represent the travel time of water from the inlet of the upper channel to channel i, where h, ..., k are channels within the (m-1)th group, r represents the downstream channel from group 1 to group (m-1), and et... b The calculation method and et a same;

[0032] Objective function 2:

[0033] The objective function is to make the water supply termination times of different channels supplying the same field as similar as possible.

[0034]

[0035] In the formula, ΔT2 represents the difference in water supply end time between different channels supplying water to the same field. These represent the water supply termination times from channels c and d to field j, respectively.

[0036] Objective function 3:

[0037] The goal of a short water distribution cycle is expressed as:

[0038]

[0039] In the formula, T represents the water distribution cycle of the entire canal system. Indicates the end time of water supply from channel i to field j;

[0040] (4) The constraints include:

[0041] 1) Overcurrent capacity constraints:

[0042] The sum of the water flow rates within each group should not exceed the design flow rate of the upstream channel. Therefore:

[0043]

[0044] Among them, I m q represents the total number of channels in the m-th group. id Q represents the design traffic for channel i. d This indicates the design traffic for the superior channel;

[0045] 2) Flow constraint: The sum of the water supply flow from a certain channel to different fields should equal the design flow of the channel. Therefore:

[0046]

[0047] 3) Supply and demand balance constraint: The sum of the water supply from different channels to a certain field should equal the water demand of that field. Therefore:

[0048]

[0049] Among them, W j Water requirement for field j; W i j This represents the amount of water supplied from channel i to field j.

[0050] 4) Water supply start time constraint: The water supply start time from the same canal to different fields should be the same, therefore:

[0051]

[0052] Where x and y represent any two fields supplied by channel i. This indicates the start time of water supply from channel i to fields x and y.

[0053] Rotation period constraint: The start and end times of water distribution for each lower-level channel should fall within the rotation period T.

[0054]

[0055] Minimum water supply constraint: The water supply from a certain canal to a certain field should not be less than the minimum water supply requirement.

[0056] W i j ≥minW i j (14)

[0057] In the formula W i j This represents the minimum water distribution from channel i to field j.

[0058] Step 3 is as follows:

[0059] Step 3.1 Initialization: Set the evolutionary generation counter t=0, set the maximum evolutionary generation T, and generate a population chromosome matrix P(0) by using the crtpc ​​function in combination with the constraints and decision variables in the canal system optimization water distribution model;

[0060] Step 3.2, Individual Evaluation: Using the ranking function and the objective function in the canal system optimization water distribution model, calculate the fitness of each individual in the population P(t);

[0061] Step 3.3, Selection Operation: Apply the selection operator to the population using the tour function, i.e., the tournament selection operator;

[0062] Step 3.4, Crossover Operation: Apply the crossover operator to the population P(t) using the xovdp function;

[0063] Step 3.5, Mutation Operation: The mutation operator is applied to the population using the mutuni function. After selection, crossover, and mutation operations, the population P(t) is used to obtain the next generation population P(t+1).

[0064] Step 3.6 Termination condition judgment: If t = T, then the individual with the highest fitness obtained in the evolution process is output as the optimal solution and the calculation is terminated; otherwise, return to step 3.2, and the water allocation time corresponding to the optimal solution is the optimal water allocation time.

[0065] Step 4 includes the data from steps 1-3, such as the amount of water supplied from the canal to the field, the water distribution flow rate, the optimal water distribution time, and the grouping situation.

[0066] The beneficial effects of this invention are:

[0067] This invention is based on a canal system optimization water allocation method for complex supply and demand relationships. It adopts an irrigation method of "inter-group rotation irrigation and intra-group continuous irrigation", establishes a canal system optimization water allocation model for complex supply and demand relationships, and incorporates the travel time of water in the canal into the model. Finally, a genetic algorithm is used to solve the model, thereby obtaining the water allocation time that satisfies the complex supply and demand relationship. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the canal system distribution in an embodiment of the present invention;

[0069] Figure 2 This is a schematic diagram of the channel grouping and water distribution time in an embodiment of the present invention;

[0070] Figure 3 This is a schematic diagram of the water distribution time for the field in an embodiment of the present invention. Detailed Implementation

[0071] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0072] This invention relates to a canal system optimization water distribution method based on complex supply and demand relationships. The canal system includes a primary canal and multiple secondary canals, and is implemented according to the following steps:

[0073] Step 1: Collect water distribution data for the canal system; the water distribution data for the canal system includes:

[0074] (3) Traffic Q for primary channels d m 3 / s;

[0075] (4) Design flow rate q for N secondary channels id m 3 / s, where 1≤i≤N, and N is the number of secondary channels;

[0076] (3) The length l of N secondary channels i , km;

[0077] (4) The number and name of the fields supplied by each canal;

[0078] (5) The number and names of water supply channels for each field;

[0079] (6) Water requirement W for each field j m 3 ;

[0080] (7) Minimum water distribution from channel i to field j (minW) i j m 3 ;

[0081] (8) Water distribution cycle T, d.

[0082] Step 2: Establish an optimized water distribution model for the canal system based on the canal system water distribution data; the specific process is as follows:

[0083] (1) Adopting an irrigation method of "inter-group rotation irrigation and intra-group continuous irrigation", the secondary channels are first divided into different irrigation groups; the number of irrigation groups is:

[0084]

[0085] In the formula, M is the number of irrigation groups, and Q is... d Traffic designed for higher-level channels, q id Design traffic for the lower-level channel i, where i is the total number of lower-level channels, and ceil is rounded up;

[0086] (2) Decision variables: ① Rotation irrigation group situation, decision variable X mi={0,,1} represents the on / off state of the i-th outlet of the m-th irrigation group, X mi =0 indicates the outlet is closed, X mi =1 indicates that the outlet is open, ② the water distribution flow from channel i to field j The amount of water distributed from channel i to field j, W i j ;

[0087] (3) Objective function:

[0088] Objective Function 1: To facilitate administrator operations, the difference in water distribution completion time among channels within the same group should be minimized. The objective function is established as follows:

[0089] ΔT1=min|et a -et b | (2)

[0090]

[0091]

[0092]

[0093]

[0094] In the formula, ΔT1 represents the absolute value of the difference in water distribution completion time between different channels within the same group, a and b represent the water distribution completion times between any two channels within the same group, and et a et b These represent the water distribution completion times of channels a and b, respectively, and x…j represent the fields supplied by channel a. This indicates the end time of water supply from channel a to fields x…j. The duration of water supply from channel a to field j is represented by the formula shown in Formula 5. This indicates the start time of water supply from channel a to field j. The calculation formula and same, Let i be the travel time of water flowing to channel i, if i = 1. Let h, ..., k represent the travel time of water from the inlet of the upper channel to channel i, where h, ..., k are channels within the (m-1)th group, r represents the downstream channel from group 1 to group (m-1), and et... b The calculation method and et a same;

[0095] Objective function 2:

[0096] The objective function is to make the water supply termination times of different channels supplying the same field as similar as possible.

[0097]

[0098] In the formula, ΔT2 represents the difference in water supply end time between different channels supplying water to the same field. These represent the water supply termination times from channels c and d to field j, respectively.

[0099] Objective function 3:

[0100] The goal of a short water distribution cycle is expressed as:

[0101]

[0102] In the formula, T represents the water distribution cycle of the entire canal system. Indicates the end time of water supply from channel i to field j;

[0103] (4) The constraints include:

[0104] 1) Flow capacity constraint: The sum of the channel water distribution flow rates within each group should not exceed the design flow rate of the upstream channel, therefore:

[0105]

[0106] Among them, I m q represents the total number of channels in the m-th group. id Q represents the design traffic for channel i. d This indicates the design traffic for the superior channel;

[0107] 2) Flow constraint: The sum of the water supply flow from a certain channel to different fields should equal the design flow of the channel. Therefore:

[0108]

[0109] 3) Supply and demand balance constraint: The sum of the water supply from different channels to a certain field should equal the water demand of that field. Therefore:

[0110]

[0111] Among them, W j Water requirement for field j; W i j This represents the amount of water supplied from channel i to field j.

[0112] 4) Water supply start time constraint: The water supply start time from the same canal to different fields should be the same, therefore:

[0113]

[0114] Where x and y represent any two fields supplied by channel i. This indicates the start time of water supply from channel i to fields x and y.

[0115] Rotation period constraint: The start and end times of water distribution for each lower-level channel should fall within the rotation period T.

[0116]

[0117] Minimum water supply constraint: The water supply from a certain canal to a certain field should not be less than the minimum water supply requirement.

[0118] W i j ≥minW i j (14)

[0119] In the formula W i j This represents the minimum water distribution from channel i to field j.

[0120] Step 3: Use the `geatpy` toolbox to implement a genetic algorithm to solve the canal system water allocation optimization model and obtain the optimal water allocation time; the specific process is as follows:

[0121] Step 3.1 Initialization: Set the evolutionary generation counter t=0, set the maximum evolutionary generation T, and generate a population chromosome matrix P(0) by using the crtpc ​​function in combination with the constraints and decision variables in the canal system optimization water distribution model;

[0122] Step 3.2, Individual Evaluation: Using the ranking function and the objective function in the canal system optimization water distribution model, calculate the fitness of each individual in the population P(t);

[0123] Step 3.3, Selection Operation: Apply the selection operator to the population using the tour function, i.e., the tournament selection operator;

[0124] Step 3.4, Crossover Operation: Apply the crossover operator to the population P(t) using the xovdp function;

[0125] Step 3.5, Mutation Operation: The mutation operator is applied to the population using the mutuni function. After selection, crossover, and mutation operations, the population P(t) is used to obtain the next generation population P(t+1).

[0126] Step 3.6 Termination condition judgment: If t = T, then the individual with the highest fitness obtained in the evolution process is output as the optimal solution and the calculation is terminated; otherwise, return to step 3.2, and the water allocation time corresponding to the optimal solution is the optimal water allocation time.

[0127] Step 4: Summarize the water supply from the canal to the field, the water distribution flow rate, the optimal water distribution time, and the grouping situation from the above steps to obtain the water distribution plan.

[0128] Example

[0129] This study focuses on the fourth branch canal and its distribution canals within the Bojili Irrigation District. Located in the north-central part of Shandong Province, with geographical coordinates of 117°14′37″-117°58′44″ E and 37°07′41″-38°14′57″ N, the Bojili Irrigation District controls an area of ​​3.365 million mu (approximately 228,667 hectares) and has a designed irrigation area of ​​900,000 mu (approximately 66,667 hectares). It is one of China's 434 large-scale irrigation districts. A map showing the canal system distribution is available below. Figure 1 The selected area contains 9 irrigation canals and 12 fields.

[0130] Step 1: Data collection and channel design traffic (m) 3 The travel time (in seconds) and travel time (in minutes) are shown in Table 3.

[0131] Table 3

[0132]

[0133]

[0134] The water requirements of the fields are shown in Table 4, where the water requirement is per unit (10). 3 m 3 ):

[0135] Table 4

[0136]

[0137] Minimum water supply requirements from canals to fields (unit: 10) 3 m 3 As shown in Table 5:

[0138] Table 5

[0139]

[0140] *A number of 0 in the table indicates that the canal does not supply water to the field. A number greater than 0 indicates that the canal supplies water to the field, and the value represents the minimum water supply requirement. The bolded number indicates that the field has only one canal supplying water, and the value represents the water demand of the field.

[0141] Step 2: Apply the canal system optimization water distribution model;

[0142] Step 3: Solve using a genetic algorithm;

[0143] Step 4: The water distribution plan is as follows:

[0144] Water supply from irrigation canals to fields (unit: 10) 3 m 3 As shown in Table 6:

[0145] Table 6

[0146]

[0147] Water flow rate distributed from the canal to different fields (unit: m) 3 / s), as shown in Table 7:

[0148] Table 7

[0149]

[0150]

[0151] Table 6 shows the water allocation to different fields through each channel. The allocated water volumes all meet the requirements of supply and demand balance and minimum water supply constraints. The table shows that fields 1, 7, 9, and 12 are supplied by only one channel, while other fields are supplied by two channels. Channels 4 and 6 supply water to three fields, and other channels supply water to two fields.

[0152] Table 7 shows the water distribution flow from each canal to different fields. The sum of the water distribution flow from each canal to different fields is equal to the design flow of that canal, thus satisfying the flow constraint.

[0153] Figure 2 The irrigation grouping of the reaction channel, the start and end times of water distribution. Figure 2 As can be seen, the model divides the nine canals into two groups. Canals 1, 4, 5, and 7 form the first group, while canals 2, 3, 6, 8, and 9 form the second group. The irrigation method adopts "inter-group rotation irrigation, intra-group continuous irrigation." At the start of irrigation, the four canals in the first group are irrigated simultaneously. After all the canals in the first group have been irrigated, the canals in the second group begin irrigation.

[0154] This invention considers the travel time of water in the channels. The start time of water distribution in the first group of channels is the time it takes for water to travel from the inlet of the branch canal to the inlet of the branch canal. The start time of water distribution in branch canal 1 is 60 minutes. The start times of water distribution in branch canals 4, 5, and 7 are the sum of the travel times of the previous 4, 5, and 7, respectively, which are 260 minutes, 340 minutes, and 400 minutes. The end time of water distribution in the channels is the sum of the start time and the duration of water distribution. The end time of water distribution in the first group is the maximum value of the end times of water distribution in all branch canals, which is 2098 minutes.

[0155] The start time of water distribution in the second group of channels depends on the channel's location. The downstream channel in the first group is branch canal 7. If a channel in the second group is upstream of branch canal 7, its water distribution start time is the end time of the first group's distribution (because the water has already reached the branch canal's inlet). Therefore, the water distribution start time for branch canals 2, 3, and 6 is 2098 minutes. If a channel in the second group is downstream of branch canal 7, its water distribution start time is the sum of the end time of the first group's distribution and the travel time from branch canal 7 to the channel (the water only flows to branch canal 7). Therefore, the water distribution start times for branch canals 8 and 9 are 2218 minutes (the sum of 2098 and 120) and 2278 minutes (the sum of 2218 and 60), respectively. The water distribution end time for the second group is 2367 minutes, which is also the total irrigation duration of the entire channel.

[0156] Figure 3 This reflects the water distribution time for each field. Fields 1, 7, 9, and 12 are supplied with water from only one channel. Fields 2, 5, 6, 8, and 10 have water channels in the same group, and their water distribution end times are relatively close. Fields 3, 4, and 11 have water channels in different groups, and their water distribution end times vary considerably.

[0157] Through the above methods, this invention establishes a canal system optimization water allocation method based on complex supply and demand relationships. It adopts an irrigation method of "inter-group rotation irrigation and intra-group continuous irrigation" to establish a canal system optimization water allocation model with complex supply and demand relationships. The travel time of water in the canal is added to the model. Finally, a genetic algorithm is used to solve the model to obtain the water allocation time that satisfies the complex supply and demand relationship.

Claims

1. A method for optimizing water distribution in a canal system based on complex supply and demand relationships, wherein the canal system comprises a primary canal and multiple secondary canals, characterized in that... The specific steps are as follows: Step 1: Collect water distribution data for the canal system; The water distribution data of the canal system includes: (1) Traffic design for primary channels m 3 / s; (2) Design flow of N secondary channels m 3 / s, where N represents the number of secondary channels; (3) The length of N secondary channels , km; (4) The number and name of the fields supplied by each canal; (5) The number and names of the water supply channels for each field; (6) Water requirements for each plot m 3 ; (7) Minimum water distribution from channel i to field j m 3 ; (8) Water distribution cycle T, d; Step 2: Establish an optimized water distribution model for the canal system based on the canal system water distribution data; Step 3: Use the geatpy toolbox to implement the genetic algorithm to solve the canal system water distribution optimization model and obtain the optimal water distribution time; Step 3.1 Initialization: Set the evolutionary generation counter t=0, set the maximum evolutionary generation T, and generate a population chromosome matrix P(0) by using the crtpc ​​function in combination with the constraints and decision variables in the canal system optimization water distribution model; Step 3.2, Individual Evaluation: Using the ranking function and the objective function in the canal system optimization water distribution model, calculate the fitness of each individual in the population P(t); Step 3.3, Selection Operation: Apply the selection operator to the population using the tour function, i.e., the tournament selection operator; Step 3.4, Crossover Operation: Apply the crossover operator to the population P(t) using the xovdp function; Step 3.5, Mutation Operation: The mutation operator is applied to the population using the mutuni function. After selection, crossover, and mutation operations, the population P(t) is used to obtain the next generation population P(t+1). Step 3.6 Termination condition judgment: If t=T, then the individual with the highest fitness obtained in the evolution process is output as the optimal solution and the calculation is terminated; otherwise, return to step 3.2 and the water allocation time corresponding to the optimal solution is the optimal water allocation time. Step 4: Summarize the data from steps 1-3 above to obtain the water distribution plan.

2. The canal system optimization water allocation method based on complex supply and demand relationships according to claim 1, characterized in that, Step 2 is as follows: (1) Adopting the irrigation method of "inter-group rotation irrigation and intra-group continuous irrigation", the secondary channels are first divided into different irrigation groups; the number of irrigation groups is: (1) In the formula, For the number of irrigation groups, Traffic is designed for higher-level channels. Design traffic for the lower-level channel i, where i is the total number of lower-level channels. To round up; (2) Decision variables: ① Rotation irrigation group situation, decision variables This indicates the on / off state of the i-th outlet in the m-th irrigation group. This indicates that the water outlet is closed. This indicates that the outlet is open, and ② the water distribution flow from channel i to field j. The amount of water allocated from channel i to field j ; (3) Objective function: Objective Function 1: To facilitate administrator operations, the difference in water distribution completion time among channels within the same group should be minimized. The objective function is established as follows: (2) (3) (4) (5) (6) In the formula This represents the absolute value of the difference in water distribution completion time between different channels within the same group, where a and b represent the water distribution completion times between any two channels within the same group. These represent the water distribution completion times of channels a and b, respectively, and x…j represent the fields supplied by channel a. This indicates the end time of water supply from channel a to fields x…j. The duration of water supply from channel a to field j is represented by the formula shown in Formula 5. This indicates the start time of water supply from channel a to field j. The calculation formula and same, Let i be the travel time of water flowing to channel i, if i=1. Let represent the travel time of water from the inlet of the upper channel to channel i, h…k represent the channels within the (m-1)th group, and r represent the downstream channel within the first group to the (m-1)th group. The calculation method and same; Objective function 2: The objective function is to make the water supply termination times of different channels supplying the same field as similar as possible. (7) In the formula This indicates the difference in the end time of water supply from different channels to the same field. These represent the water supply termination times from channels c and d to field j, respectively. Objective function 3: The goal of a short water distribution cycle is expressed as: (8) In the formula This indicates the water distribution cycle of the entire canal system. Indicates the end time of water supply from channel i to field j; (4) The constraints include: 1) Overcurrent capacity constraint: The sum of the water flow rates within each group should not exceed the design flow rate of the upstream channel. Therefore: (9) in, This represents the total number of channels in the m-th group. This represents the design traffic for channel i. This indicates the design traffic for the superior channel; 2) Flow constraint: The sum of the water supply flow from a certain channel to different fields should equal the design flow of the channel. Therefore: (10) 3) Supply and demand balance constraint: The sum of the water supply from different channels to a certain field should equal the water demand of that field. Therefore: (11) in, The required water volume for field j; This represents the amount of water supplied from channel i to field j. 4) Water supply start time constraint: The water supply start time from the same canal to different fields should be the same, therefore: (12) Where x and y represent any two fields supplied by channel i. This indicates the start time of water supply from channel i to fields x and y. Rotation period constraint: The start and end times of water distribution for each lower-level channel should fall within the rotation period T. (13) Minimum water supply constraint: The water supply from a certain canal to a certain field should not be less than the minimum water supply requirement. (14) In the formula This represents the minimum water distribution from channel i to field j.

3. The canal system optimization water allocation method based on complex supply and demand relationships according to claim 1, characterized in that, The data in steps 1-3 mentioned in step 4 include the amount of water supplied from the canal to the field, the water distribution flow rate, the optimal water distribution time, and the grouping situation.

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