A method for optimizing water distribution in single main canal of gravity irrigation area based on dynamic programming

Abstract

The present invention discloses a method for optimizing water distribution of a single main canal in a gravity irrigation area based on a dynamic programming method, comprising the following steps: (1) taking the minimum sum of squares of water shortages in the water receiving areas controlled by each branch canal under the jurisdiction of the single main canal during an irrigation period as the goal, establishing the following objective function; (2) setting constraints; (3) solving the model: (a) determining the position and number of the regulating gates at the head of the branch canal controlled by the single main canal, and determining the water demand of the crops in each water receiving area controlled by each branch canal during the irrigation period; (b) taking the position number of the regulating gates at the head of each branch canal as the stage, and taking the total amount of water distribution of the previous several regulating gates at the head of the branch canal as the state variable, constructing a state transfer equation, and determining the benefit-cost function of each stage; (c) adopting a sequential recursive method to obtain the optimal water distribution of each regulating gate at the head of each branch canal that satisfies the minimum sum of squares of water shortages in the area controlled by each branch canal. The present invention can obtain the method for optimizing water distribution of the regulating gates at the head of each branch canal, and obtain the optimal opening process of the regulating gates at the head of each branch canal.

Description

Technical Field

[0001] The invention relates to the technical field of channel optimized water distribution, and in particular to a method for optimizing water distribution of a single main channel in a gravity irrigation area based on a dynamic programming method. Background Art

[0002] The backbone water transfer channels in large and medium-sized irrigation areas are multi-level, long, and widely distributed with control buildings along the lines. Due to the control of water diversion rights and the uneven management, the efficiency of irrigation water utilization is often low, which affects agricultural production and farmers' income. How to optimize the scheduling of control gates along the backbone water transfer channels according to the agricultural planting structure of the irrigation area to maximize the comprehensive utilization of water resources in the irrigation area, improve the efficiency of irrigation water utilization, ensure food production in the irrigation area, and promote farmers' income. The traditional optimization canal water distribution model mainly optimizes the crop water demand based on the objective function, but the objective function parameters and constraints are relatively complex, making it difficult to achieve global optimization of water distribution. Summary of the invention

[0003] Purpose of the invention: In view of the above shortcomings, the present invention provides a method for optimizing water distribution of a single main canal in a gravity irrigation area based on a dynamic programming method. Taking a single main canal as the research object, it is possible to obtain a method for optimizing water distribution of branch canal head regulating gates with the goal of minimizing water shortage of crops in the receiving area, and obtain the optimal opening process of the regulating gates at the head of each branch canal along the single main canal.

[0004] Technical solution: To solve the above problems, the present invention provides a method for optimizing water distribution in a single main canal of a gravity irrigation area based on a dynamic programming method, comprising the following steps:

[0005] (1) Model establishment: Taking the minimum sum of squares of water shortage in the water receiving areas controlled by the branch canals under the jurisdiction of a single main canal during a flooding period as the goal, the following objective function is established;

[0006]

[0007] Where: F is the minimum sum of squares of water shortage in the water receiving area controlled by each branch canal under the jurisdiction of a single main canal during a flooding period; f is the sum of squares of water shortage in the water receiving area controlled by each branch canal under the jurisdiction of a single main canal; m is the number of branch canals controlled by the main canal; j is the branch canal number, j = 1, 2, ..., m; i is the number of irrigation time periods divided into a flooding period, i = 1, 2, ..., n, n is the total number of time periods; X j (K ji ) is the opening process K of the head control gate corresponding to the jth branch canal ji The water supply volume, in m 3 ;YS j is the crop water demand corresponding to the area controlled by the jth branch canal, in m 3 ;

[0008] (2) Setting constraints: According to the requirements of the total amount of water diverted from a single main canal, the duration of water injection, the flow rate of the main canal, the water level of the main canal, and the opening of the control gate at the head of the branch canal, set the constraints for solving the objective function;

[0009] (3) Model solution: The water distribution of each branch canal headwater regulating gate along the single main canal is taken as the decision variable, and the total water distribution of several branch canal headwater regulating gates is taken as the state variable. The one-dimensional dynamic programming method is used to solve the objective function in combination with the constraint conditions. The specific steps include:

[0010] (31) Determine the location and number of control gates at the head of the branch canal controlled by a single main canal, and determine the water demand of crops in each water receiving area controlled by each branch canal during the irrigation period;

[0011] (32) Taking the position number of each branch canal headwater control gate along the single main canal as the stage, and the total amount of water distribution of the previous branch canal headwater control gate as the state variable, the state transition equation is constructed to determine the benefit-cost function of each stage;

[0012] (33) The sequential recursive method is used to obtain the optimal water distribution of the regulating gates at the head of each branch canal to minimize the sum of the squares of the water shortages in the controlled areas of each branch canal.

[0013] Beneficial effect: Compared with the prior art, the significant advantages of the present invention are: based on the actual situation of main canal water distribution in large and medium-sized irrigation areas, constraints on the water diversion volume at the head of the main canal, the total time constraint on the main canal water distribution, the main canal flow constraint, the main canal water level constraint and the branch canal head gate opening constraint are set, which improves the practicability of the model solution results.

[0014] Furthermore, the present invention also comprises the steps of:

[0015] (4) A one-dimensional unsteady flow model is used to simulate the water level process above the regulating gates at the head of each branch canal; the water depth process above the regulating gates at the head of each branch canal is determined; and then the gate hole free outflow formula is used to determine the optimal gate opening process of the regulating gate at the head of each branch canal, which specifically includes the following steps:

[0016] (41) Determine the calculation parameters of a single main canal, including: the number of canal sections, the elevation of the bottom of each canal section, the width of the bottom of each canal section, the slope coefficient, and the roughness; determine the number of control gates at the head of each branch canal, the elevation of the bottom plate, the clear width of the gate hole, and the clear height of the gate hole;

[0017] (42) Based on the total amount of water diverted at one time and the total duration of water filling in a single main canal, the water diversion flow process at the head of the main canal is formulated; based on the optimal water distribution volume and total duration of water filling obtained for the control gates at the head of each branch canal, the water distribution flow process for the control gates at the head of each branch canal is determined;

[0018] (43) The obtained water distribution flow process of the regulating gates at the head of each branch canal is used as the flow boundary. On the basis of the known water diversion flow process at the head of the main canal, the initial water level of the main canal, the measured cross-sectional parameters of each section of the single main canal, and the parameters of the regulating gates at the head of each branch canal, a one-dimensional non-steady flow model is used to simulate and determine the water level process above the regulating gates at the head of each branch canal, and thereby determine the water depth process above the regulating gates at the head of each branch canal; then, the gate hole free outflow formula is used to calculate the optimal gate opening process of the regulating gates at the head of each branch canal.

[0019] Beneficial effect: Compared with the prior art, the significant advantage of the present invention is that the combination of dynamic programming method and one-dimensional non-steady flow numerical simulation can further obtain the optimal opening process of the gates of each branch canal head in each time period, improve the accuracy of model solution, and facilitate effective real-time scheduling of the gates of the branch canal head.

[0020] Furthermore, the constraints in step (2) include:

[0021] (21) Constraints on water diversion at the head of the main canal:

[0022]

[0023] (22) Constraints on total duration of main canal irrigation:

[0024] T s ≤T 0

[0025] (23) Main canal flow constraints:

[0026] Q min ≤Q≤Q max

[0027] (24) Main canal water level constraints:

[0028] Z min ≤Z≤Z max

[0029] (25) Branch canal head gate opening constraints:

[0030] 0≤K ji ≤H j

[0031] Where W 0 The total amount of water diverted from the main canal head at one time, in m 3 ; T s is the actual total irrigation time, in h; the total irrigation time T 0 , unit is h; Q is the main canal flow, unit is m 3 / s; maximum flow rate Q max , minimum flow Q min , unit is m 3 / s; Z is the water level of the main canal, in meters; the highest water level Z max , minimum water level Z min , unit is m; H j is the clear height of the j-th branch canal head gate, in meters.

[0032] Furthermore, step (32) specifically includes the following steps:

[0033] (321) Taking the branch canal head control gate number j as the stage variable and the total water distribution of the first j branch canal head control gates as the state variable λ, the following state transfer equation is constructed:

[0034] λ j =X j (K ji )+λ j-1

[0035] (322) According to the objective function and the state transition equation, the following benefit-cost function is determined:

[0036] g j (λ j )=min{[X j (K ji )-YS j ] 2 +g j-1 (λ j-1 )}

[0037] Furthermore, step (33) specifically includes the following steps:

[0038] (331) Stage j = 1:

[0039] g 1 (λ 1 )=min[X 1 (K 1i )-YS 1 ] 2

[0040] Ignore the control gate opening K 1i Influence, the state variable λ 1 Can be discretized in the corresponding feasible domain: 1 =0,W 1 ,W 2 ,…,W 0 ; For each discrete λ 1 , the decision variable X 1 Can be discretized in the corresponding feasible domain, and should satisfy: X 1 ≥λ 1 ; X that meets the requirements 1 Substitute into the above formula respectively, according to the known YS at this stage 1, and obtain each discrete λ 1 When the value is 1 * and its corresponding g 1 (λ 1 );

[0041] (332) Stage j = 2, 3, ..., m-1:

[0042] g j (λ j )=min{[X j (K ji )-YS j ] 2 +g j-1 (λ j-1 )}

[0043] The state variable λ at this stage j Also discretize: λ j =0,W 1 ,W 2 ,…,W 0 ; For each discrete λ j , the decision variable X j It can be discretized in the corresponding feasible domain and should satisfy: The state transfer equation is:

[0044] λ j =X j +λ j-1

[0045] Where: j = 2, 3, ..., m-1;

[0046] Each discrete X j Substitute the values ​​into [X j (K ji )-YS j ] 2 , according to the known YS at this stage j , according to the state transition equation, find the i-1 stage that satisfies Required j-1 (λ j-1 ) value, thereby obtaining the value that satisfies the λ j Optimal X required j * and its corresponding g j (λ j );

[0047] Using the state variables of each stage and the reverse optimization method, the total water distribution volume W of the single main canal is determined 0 Under the condition, the optimal water distribution of each branch canal head control gate is X j* , where j = 1, 2,…, m.

[0048] (333) Stage m:

[0049] g m (λ m )=min{[X m (K mi )-YS m ] 2 +g m-1 (λ m-1 )}

[0050] The state variable λ in this period m =W 0 ; Decision variable X m Similarly, in the corresponding feasible domain, the discretization should satisfy: m-1 =λ m -X m ; Using the method described in step (332), finally obtain the condition satisfying the λ m Requested X m * , and the corresponding minimum water shortage sum of squares F in the receiving area;

[0051] Furthermore, the one-dimensional unsteady flow model described in step (43) is as follows:

[0052]

[0053]

[0054] Where Z is the water level of the single main canal, in m; Q is the flow rate of the single main canal, in m 3 / s; B is the water surface width of the single main channel, in m; A is the cross-sectional area of ​​the single main channel, in m 2 ; R is the hydraulic radius of the single main canal; C is the single main canal coefficient; q is the lateral inflow per unit length of the single main canal, in m 3 / s; t and s are time and space coordinates respectively.

[0055] Furthermore, the water depth process above the regulating gates at the head of each branch channel described in step (43) is the water level process above the regulating gates at the head of each branch channel minus the elevation of the channel bottom of each section.

[0056] Furthermore, the main canal head water diversion flow process described in step (42) is the ratio of the total water diversion volume of a single main canal at one time to the total irrigation time.

[0057] Furthermore, the water distribution flow process of the regulating gates at the head of each branch canal described in step (42) is the ratio of the optimal water distribution volume of the regulating gates at the head of each branch canal to the total irrigation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The figure shows a schematic diagram of the structure of the single main canal optimized water distribution according to the present invention;

[0059] Figure 2 Shown is a flow chart of the single main canal optimized water distribution method of the present invention. DETAILED DESCRIPTION

[0060] The present invention is further described below in conjunction with the accompanying drawings.

[0061] like Figure 1 As shown, the single main canal in the gravity irrigation area based on the dynamic programming method of the present invention controls m branch canals, and the total amount of water diverted at the head of the canal is W 0 ; The crop water requirement corresponding to the area controlled by each branch canal is YS j , j is the branch channel number (j=1,2,…,m); the opening process of the control gate at the head of each branch channel K ji The water distribution is X j (K ji ), i is the number of the irrigation time period divided into one irrigation period (i = 1, 2, ..., n; where n is the total number of time periods).

[0062] like Figure 2 As shown, the method for optimizing water distribution of a single main canal in a gravity irrigation area based on a dynamic programming method according to the present invention comprises the following steps:

[0063] (1) Model establishment: Taking the minimum sum of squares of water shortage in the water receiving areas controlled by the branch canals under the jurisdiction of a single main canal during a flooding period as the goal, the following objective function is established;

[0064]

[0065] Where: F is the minimum sum of squares of water shortage in the water receiving area controlled by each branch canal under the jurisdiction of a single main canal during a flooding period; f is the sum of squares of water shortage in the water receiving area controlled by each branch canal under the jurisdiction of a single main canal; X j (K ji ) is the opening process K of the head control gate corresponding to the jth branch canal ji The water supply volume, in m 3 ;YS j is the crop water demand corresponding to the area controlled by the jth branch canal, in m 3 ;

[0066] (2) Set constraints: Based on the total amount of water W for a single main canal 0 (Unit: m 3 / s), total irrigation time T 0 (unit: h), main canal flow Q (unit: m 3 / s), main canal water level Z (in m), branch canal head gate opening K ji (unit is m), and the constraints for solving the objective function are set as follows:

[0067] (21) Constraints on water diversion at the head of the main canal:

[0068]

[0069] (22) Constraints on total duration of main canal irrigation:

[0070] T s ≤T 0 (3)

[0071] (23) Main canal flow constraints:

[0072] Q min ≤Q≤Q max (4)

[0073] (24) Main canal water level constraints:

[0074] Z min ≤Z≤Z max (5)

[0075] (25) Branch canal head gate opening constraints:

[0076] 0≤K ji ≤H j (6)

[0077] Where, T s is the total actual irrigation time, in h; the maximum flow rate Q max and minimum flow Q min , unit is m 3 / s; highest water level Z max and the lowest water level Z min , unit is m; H j is the clear height of the gate at the jth branch canal head, in meters;

[0078] (3) Model solution: The water distribution of each branch canal headwater regulating gate along the single main canal is taken as the decision variable, and the total water distribution of several branch canal headwater regulating gates is taken as the state variable. The one-dimensional dynamic programming method is used to solve the objective function in combination with the constraint conditions. The specific steps include:

[0079] (31) Determine the location and number of control gates at the head of the branch canal controlled by a single main canal, and determine the water demand of crops in each water receiving area controlled by each branch canal during the irrigation period;

[0080] (32) Taking the branch canal head control gate number j as the stage variable and the total water distribution of the first j branch canal head control gates as the state variable λ, the following state transfer equation is constructed:

[0081] λ j =X j (K ji )+λ j-1 (7)

[0082] According to the objective function and the state transfer equation, the following benefit-cost function is determined:

[0083] g j (λ j )=min{[X j (K ji )-YS j ] 2 +g j-1 (λ j-1 )} (8)

[0084] (33) The sequential recursive method is used to obtain the optimal water distribution of each branch canal head gate to minimize the sum of the squares of the water shortage in the controlled area of ​​each branch canal. The specific steps include:

[0085] (331) Stage j = 1:

[0086] g 1 (λ 1 )=min[X 1 (K 1i )-YS 1 ] 2 (9)

[0087] Ignore the control gate opening K 1i Influence, the state variable λ 1 Can be discretized in the corresponding feasible domain: 1 =0,W 1 ,W 2 ,…,W 0 ; For each discrete λ 1 , the decision variable X 1 Can be discretized in the corresponding feasible domain, such as 0m 3 、5m 3 、10m 3 、15m 3 ,…X 1,max Wait, X 1,max The maximum water supply of the first branch canal head should meet the following requirements: X 1 ≥λ 1 ,; X that meets the requirements 1 Substitute them into formula (9) respectively, according to the known YS 1 , and obtain each discrete λ 1 When the value is 1 * and its corresponding g 1 (λ1 );

[0088] (332) Stage j = 2, 3, ..., m-1:

[0089] g j (λ j )=min{[X j (K ji )-YS j ] 2 +g j-1 (λ j-1 )} (10)

[0090] The state variable λ at this stage j Also discretize: λ j =0,W 1 ,W 2 ,…,W 0 ; For each discrete λ j , the decision variable X j Can be discretized in the corresponding feasible domain, such as 0m 3 、5m 3 、10m 3 、15m 3 ,…X j,max Wait, X j,max is the maximum water supply of the jth branch canal head, which should satisfy: The state transfer equation is:

[0091] λ j =X j +λ j-1 (11)

[0092] Where: j = 2, 3, ..., m-1; each discrete X j Substitute the values ​​into [X j (K ji )-YS j ] 2 , according to the known YS at this stage j , according to the state transition equation (11), find the i-1 stage that satisfies Required j-1 (λ j-1 ) value, thereby obtaining the value that satisfies the λ j Optimal X required j * and its corresponding g j (λ j );

[0093] (333) Stage m:

[0094] g m (λm )=min{[X m (K mi )-YS m ] 2 +g m-1 (λ m-1 )} (12)

[0095] The state variable λ in this period m =W 0 ; Decision variable X m Similarly, in the corresponding feasible domain, the discretization should satisfy: m-1 =λ m -X m ; Using the method described in step (332), finally obtain the condition satisfying the λ m Requested X m * , and the corresponding minimum water shortage sum of squares F in the receiving area;

[0096] Using the state variables of each stage and the reverse optimization method, the total water distribution volume W of the single main canal is determined 0 Under the condition, the optimal water distribution of each branch canal head control gate is X j * , where j = 1, 2,…, m.

[0097] (4) One-dimensional unsteady flow numerical simulation is used to simulate the water level process on the regulating gates of each branch canal. ji , determine the water depth process H above the control gate of each branch canal ji ; Then use the gate hole free outflow formula to determine the optimal opening process K of each branch canal head control gate ji * ; Specifically include the following steps:

[0098] (41) Determine the calculation parameters of a single main canal, including: the number of canal sections, the elevation of the bottom of each canal section, the width of the bottom of each canal section, the slope coefficient, and the roughness; determine the number of control gates at the head of each branch canal, the elevation of the bottom plate, the clear width of the gate hole, and the clear height of the gate hole;

[0099] (42) Based on the total water diversion volume of a single main canal W 0 And the total irrigation time T 0 , using Q i =W 0 / T 0 , the proposed main canal headwater diversion flow process Q i (where i = 1, 2, ..., n, where n is the total number of time periods); according to the optimal water distribution of each branch canal X j * (K ji ) and the total irrigation time T 0 , using q ji =Xj * (K ji ) / T 0 , determine the water distribution flow process q of each branch canal head control gate ji (where j = 1, 2, ..., m; i = 1, 2, ..., n);

[0100] (43) The water distribution flow process of each branch canal head control gate is taken as the flow boundary q ji , simulate and determine the water level process on the control gate of each branch canal ji , obtain the optimal opening process K of each branch canal head control gate ji * ; Specifically include the following steps:

[0101] (431) The following one-dimensional unsteady flow model of a single main channel is constructed:

[0102]

[0103]

[0104] Where Z is the water level of the single main canal, in m; Q is the flow rate of the single main canal, in m 3 / s; B is the water surface width of the single main channel, in m; A is the cross-sectional area of ​​the single main channel, in m 2 ; R is the hydraulic radius of the single main canal; C is the single main canal coefficient; q is the lateral inflow per unit length of the single main canal, in m 3 / s; t and s are time and space coordinates respectively;

[0105] (432) The water distribution flow rate q obtained by the control gates at the head of each branch canal ji Set as the cross-section flow boundary and set the main canal head flow process boundary Q i Based on the measured channel section parameters of each section of the single main canal, the parameters of the regulating gates at the head of each branch canal and the initial water level, the Preissmann implicit format was used to establish the difference equation, and the pursuit method was used to solve the one-dimensional unsteady flow model to simulate and determine the water level process z above the regulating gates at the head of each branch canal. ji , using the water level process above the gate at the head of each section to control the gate ji Subtract the measured channel bottom elevation D of each section ji Obtain the water depth process H above the control gate of each branch canal ji ;

[0106] (433) According to the determined water depth process above the control gate of each section of the branch canal head, ji , using the gate free outflow formula Calculate and determine the water flow rate q required to meet the water distribution requirements of each branch canal head control gate jiThe optimal opening process K of the first control gate under the requirement ji * Among them, μ ji , b ji are the flow coefficient of the jth branch head section of a single main canal and the net width of the head regulating gate (m), j=1,2,…,m; i=1,2,…,n.

Claims

1. A method for optimizing water distribution in a single main canal in a gravity irrigation area based on dynamic programming. It is characterized in that The following steps are involved: (1) Model establishment: Taking the minimum sum of squares of water shortage in the water receiving areas controlled by the branch canals under the jurisdiction of a single main canal during a flooding period as the goal, the following objective function is established; Where: F is the minimum sum of squares of water shortage in the water receiving area controlled by each branch canal under the jurisdiction of a single main canal during a flooding period; f is the sum of squares of water shortage in the water receiving area controlled by each branch canal under the jurisdiction of a single main canal; m is the number of branch canals controlled by the main canal; j is the branch canal number, j = 1, 2, ..., m; i is the number of irrigation time periods divided into a flooding period, i = 1, 2, ..., n, n is the total number of time periods; X j (K ji ) is the opening process K of the head control gate corresponding to the jth branch canal ji The water supply volume, in m 3 ; YS j is the crop water demand corresponding to the area controlled by the jth branch canal, in m 3 ; (2) Setting constraints: According to the requirements of the total amount of water diverted from a single main canal, the duration of water injection, the flow rate of the main canal, the water level of the main canal, and the opening of the control gate at the head of the branch canal, set the constraints for solving the objective function; (3) Model solution: The water distribution of each branch canal headwater regulating gate along the single main canal is taken as the decision variable, and the total water distribution of several branch canal headwater regulating gates is taken as the state variable. The one-dimensional dynamic programming method is used to solve the objective function in combination with the constraint conditions. The specific steps include: (3.1) Determine the location and number of control gates at the head of the branch canal controlled by a single main canal, and determine the water demand of crops in each water receiving area controlled by each branch canal during the irrigation period; (3.2) Taking the position number of each branch canal headwater control gate along the single main canal as the stage, and the total amount of water distribution of the previous branch canal headwater control gate as the state variable, the state transfer equation is constructed to determine the benefit-cost function of each stage; (3.3) Using the sequential recursive method, the optimal water distribution of each branch canal head gate is obtained to minimize the sum of the squares of the water shortage in the controlled area of ​​each branch canal; (4) A one-dimensional unsteady flow model is used to simulate the water level process above the regulating gates at the head of each branch canal; the water depth process above the regulating gates at the head of each branch canal is determined; and then the gate hole free outflow formula is used to determine the optimal gate opening process of the regulating gate at the head of each branch canal, which specifically includes the following steps: (4.1) Determine the calculation parameters of a single main canal, including: the number of canal sections, the elevation of the bottom of each canal section, the width of the bottom of each canal section, the slope coefficient, and the roughness; determine the number of control gates at the head of each branch canal, the elevation of the bottom plate, the clear width of the gate hole, and the clear height of the gate hole; (4.2) Based on the total amount of water diverted at one time and the total duration of water filling in a single main canal, formulate the water diversion flow process at the head of the main canal; based on the optimal water distribution volume and total duration of water filling obtained by the regulating gates at the head of each branch canal, determine the water distribution flow process of the regulating gates at the head of each branch canal; (4.3) The obtained water distribution flow process of the regulating gates at the head of each branch canal is used as the flow boundary. Based on the known water diversion flow process at the head of the main canal, the initial water level of the main canal, the measured cross-sectional parameters of each section of the single main canal, and the parameters of the regulating gates at the head of each branch canal, a one-dimensional non-steady flow model is used to simulate and determine the water level process above the regulating gates at the head of each branch canal, and thereby determine the water depth process above the regulating gates at the head of each branch canal; then the gate hole free outflow formula is used to calculate the optimal gate opening process of the regulating gates at the head of each branch canal.

2. The method for optimizing water distribution in a single main canal of a gravity irrigation area according to claim 1, It is characterized in that The constraints in step (2) include: (2.1) Constraints on water diversion at the head of the main canal: (2.2) Constraints on total duration of main canal irrigation: T s ≤T 0 (2.3) Main canal flow constraints: Q min ≤Q≤Q max (2.4) Main canal water level constraints: WITH min ≤Z≤Z max (2.5) Branch channel head gate opening constraints: 0≤K ji ≤H j Where W 0 The total amount of water diverted from the main canal head at one time, in m 3 ; T s is the actual total irrigation time, in h; the total irrigation time T 0 , unit is h; Q is the flow rate of the main canal, unit is m 3 / s; maximum flow rate Q max , minimum flow Q min , unit is m 3 / s; Z is the water level of the main canal, in meters; the highest water level Z max , minimum water level Z min , unit is m; H j is the clear height of the j-th branch canal head gate, in meters.

3. The method for optimizing water distribution in a single main canal of a gravity irrigation area according to claim 1, It is characterized in that Step (3.2) specifically includes the following steps: (3.2.1) Taking the branch canal head control gate number j as the stage variable and the total water distribution of the first j branch canal head control gates as the state variable λ, the following state transfer equation is constructed: l j =X j (K ji )+λ j-1 (3.2.2) According to the objective function and the state transition equation, the following benefit-cost function is determined: g j (l j )=min{[X j (K ji )-YS j ] 2 +g j-1 (l j-1 )}。 4. The method for optimizing water distribution in a single main canal of a gravity irrigation area according to claim 1, It is characterized in that Step (3.3) specifically includes the following steps: (3.3.1) Stage j = 1: g 1 (l 1 )=min[X 1 (K 1i )-YS 1 ] 2 Ignore the control gate opening K 1i Influence, the state variable λ of this stage 1 Can be discretized in the corresponding feasible domain: 1 =0,W 1 ,W 2 ,…,W 0 ; For each discrete λ 1 , the decision variable X 1 Can be discretized in the corresponding feasible domain, and should satisfy: X 1 ≥λ 1 ; X that meets the requirements 1 Substitute into the above formula respectively, according to the known YS at this stage 1 , and obtain each discrete λ 1 When the value is 1 * and its corresponding g 1 (λ 1 ); (3.3.2) Stage j = 2, 3, ..., m-1: g j (l j )=min{[X j (K ji )-YS j ] 2 +g j-1 (l j-1 )} The state variable λ at this stage j Also discretize separately: j =0,W 1 ,W 2 ,…,W 0 ; For each discrete λ j , the decision variable X j It can be discretized in the corresponding feasible domain and should satisfy: The state transfer equation is: l j =X j +λ j-1 Where: j = 2, 3, ..., m-1; Each discrete X j Substitute the values ​​into [X j (K ji )-YS j ] 2 , according to the known YS at this stage j , according to the state transfer equation, find the i-1 stage that satisfies Required j-1 (λ j-1 ) value, thereby obtaining the value that satisfies the λ j Optimal X required j * and its corresponding g j (λ j ); (3.3.3) Phase m: g m (l m )=min{[X m (K mi )-YS m ] 2 +g m-1 (l m-1 )} The state variable λ at this stage m =W 0 ; Decision variable X m Also discretized in the corresponding feasible domain, satisfying: m-1 =λ m -X m ; Using the method described in step (3.3.2), we finally obtain m Requested X m * , and the corresponding minimum water shortage sum of squares F in the receiving area; Using the state variables of each stage and the reverse optimization method, the total water distribution volume W of the single main canal is determined 0 Under the condition, the optimal water distribution of each branch canal head control gate is X j * , where j = 1, 2,…, m.

5. The method for optimizing water distribution in a single main canal of a gravity irrigation area according to claim 1, It is characterized in that The one-dimensional unsteady flow model described in step (4.3) is as follows: Where Z is the water level of the single main canal, in m; Q is the flow rate of the single main canal, in m 3 / s; B is the water surface width of the single main channel, in m; A is the cross-sectional area of ​​the single main channel, in m 2 ; R is the hydraulic radius of the single main canal; C is the single main canal coefficient; q is the lateral inflow per unit length of the single main canal, in m 3 / s; t and s are time and space coordinates respectively.

6. The method for optimizing water distribution in a single main canal of a gravity irrigation area according to claim 1, It is characterized in that The water depth process above the regulating gates at the head of each branch channel described in step (4.3) is the water level process above the regulating gates at the head of each branch channel minus the elevation of the channel bottom of each section.

7. The method for optimizing water distribution in a single main canal of a gravity irrigation area according to claim 1, It is characterized in that The main canal headwater flow process described in step (4.2) is the ratio of the total water diversion volume of a single main canal to the total irrigation time.

8. The method for optimizing water distribution in a single main canal of a gravity irrigation area according to claim 1, It is characterized in that The water distribution flow process of the regulating gates at the head of each branch canal described in step (4.2) is the ratio of the optimal water distribution volume of each branch canal to the total irrigation time.

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