Damming river fish migration habitat reconstruction method based on fuzzy interval planning

Abstract

The invention discloses a damming river fish migration habitat reconstruction method based on fuzzy interval planning. The method comprises the following steps: step 1, constructing a multi-target ecological scheduling model; the objective function of the multi-objective ecological scheduling model is to minimize the supersaturated TDG level and maximize the generating capacity; step 2, constructing constraint conditions of the target function; the constraint conditions comprise a water level balance constraint, an upstream and downstream water level constraint, a flow constraint, a power generation limitation, a supersaturated TDG horizontal constraint and a reservoir area flow velocity constraint; wherein the reservoir area flow velocity constraint is constrained by adopting a fuzzy membership function; and step 3, based on the constraint condition, solving the objective function, and according to the obtained solution, completing the reconstruction of the fish migration habitat of the damming river. According to the method, the cascade reservoir area flow velocity uncertainty multi-target ecological scheduling model considering fish migration safety is constructed, and the fish migration safety requirement and the power generation requirement can be considered.

Description

Technical Field

[0001] The present invention relates to the technical field of ecological protection, and in particular to a method for reconstructing fish migration habitats in dammed rivers based on fuzzy interval programming. Background Art

[0002] The construction of reservoirs and dams is a crucial means for humanity to transform nature. It is also essential for improving water resource utilization efficiency, developing new energy sources, and achieving ecological progress. While reservoir and dam construction has brought enormous social and economic benefits, it also has undeniably serious negative impacts on the ecological health of river basins. The most direct impact is the disruption of river connectivity, preventing fish from completing their normal migrations and severely impacting the habitats of migratory fish. Furthermore, flood discharge from high dams can lead to total dissolved gas (TDG) supersaturation, a significant contributor to gas bubble disease (GBD) and even mortality in fish downstream of the dams. This poses a significant risk to the safety of fish migration between cascade reservoirs.

[0003] The construction of reservoirs and dams disrupts river connectivity, altering natural flow conditions downstream, hindering fish migration, impacting spawning and survival, and reducing fish diversity. Furthermore, dam construction alters the hydrological conditions upstream of the dam. The dam's obstruction upstream slows flow rates, making these conditions unfavorable for fish migration. Migratory fish have a natural tendency to adjust their swimming direction according to current flow: swimming downstream or against the current when migrating upstream. This phenomenon is known as rheology. Numerous studies have shown that fish migration requires flow velocity to provide directional cues. However, existing reservoir management research primarily focuses on ensuring environmental flow velocities in downstream channels to ensure fish can migrate upstream to the reservoir. Limited research has examined whether fish can successfully navigate slow-flowing upstream reservoirs and continue their migration upstream. If the flow velocity within a reservoir's suitable temperature zone is insufficient to provide directional cues for migrating fish, they lose the ability to determine their migration direction, preventing them from crossing the reservoir and continuing upstream. Therefore, it is crucial to ensure that the minimum flow velocity within the reservoir triggers fish migration and provides them with a directional signal. Research has also found that different fish species have different optimal migration velocities, and that above a certain velocity, their migratory capacity actually decreases. Previous studies, based on China's national fishway design standards, have set a migratory velocity of greater than 0.2 m / s. This velocity is lower than the optimal velocity for fish migration, creating significant uncertainty regarding the ability of fish to successfully migrate within the reservoir. Few previous studies have considered this uncertainty. Therefore, this paper transforms this uncertainty into the uncertainty of the flow velocity constraints for fish migration.

[0004] Current models for solving uncertainty problems, such as fuzzy programming, interval parameter programming, and fuzzy feasibility-constrained programming, are difficult to accurately reflect the preferences of decision makers with different attitudes in the decision-making process in real water resources management problems. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the present invention provides a method for reconstructing fish migration habitats in dammed rivers based on fuzzy interval programming.

[0006] The technical solution adopted by the present invention is: a method for reconstructing fish migration habitats in dammed rivers based on fuzzy interval programming, comprising the following steps:

[0007] Step 1: Construct a multi-objective ecological scheduling model;

[0008] The objective function of the multi-objective ecological dispatch model is to minimize the level of oversaturated TDG and maximize the power generation;

[0009] Step 2: Construct the constraints of the objective function;

[0010] The constraints include water level balance constraints, upstream and downstream water level constraints, flow constraints, power generation restrictions, oversaturated TDG level constraints, and reservoir flow velocity constraints;

[0011] The flow rate constraint in the reservoir area is constrained by fuzzy membership function;

[0012] Step 3: Based on the constraints, solve the objective function and use the obtained solution to complete the reconstruction of the fish migration habitat in the dammed river.

[0013] Furthermore, the objective function in step 1 includes:

[0014]

[0015] Where: f1 ± is the minimum target supersaturated TDG level, For the maximum power generation target, C ± (t) is the supersaturated TDG level at time t, P ± (t) is the power generation at time t, and NT is the total time step.

[0016] Furthermore, the hierarchical analysis method is used to perform single-objective processing on the weight assignment of the objective function.

[0017] Furthermore, the objective function obtained after single-objective processing is:

[0018]

[0019] Where: α and β are target weight factors, P powerThe installed capacity of the hydropower station.

[0020] Furthermore, the water level balance constraint is as follows:

[0021] H1(t)=H1(t-1)-0.00007·(Q out -Q in )

[0022] H2(t)=0.0011·Q out +372.7

[0023] Q out =Q s +Q p

[0024] H3(t)=H3(t-1)-0.000011·(Q o -Q out )

[0025] Where: H1(t) is the water level in front of the first-stage reservoir dam at time t, H1(t-1) is the water level in front of the first-stage reservoir dam at time t-1, H2(t) is the water level downstream of the first-stage reservoir dam at time t, H3(t) is the water level in front of the second-stage reservoir dam at time t, H3(t-1) is the water level in front of the second-stage reservoir dam at time t-1, Q out is the outflow of the first-level reservoir, Q in is the inflow to the first-level reservoir, Q s is the discharge flow of the first-level reservoir, Q p is the power generation flow of the first-level reservoir, Q o It is the outflow of the second-level reservoir.

[0026] Furthermore, the upstream and downstream water level constraints are as follows:

[0027]

[0028] Where: is the minimum water level in front of the first-stage reservoir dam, is the maximum water level in front of the first-stage reservoir dam, is the minimum water level downstream of the first-stage reservoir dam, is the maximum water level downstream of the first-stage reservoir dam, is the minimum water level in front of the second-stage reservoir dam, is the maximum water level in front of the second-stage reservoir dam;

[0029] The flow constraints are:

[0030]

[0031] Where: and It is the minimum and maximum flood discharge of the upper reservoir; and It is the minimum and maximum flow rate of the upper reservoir used for power generation; and is the minimum and maximum flood discharge of the next level reservoir, Q o is the flood discharge of the next level reservoir;

[0032] The power generation constraint is:

[0033] P min ≤P≤P power

[0034] Where: P is the power generation after optimization, P min is the minimum power generation capacity of the hydropower station, P power Installed capacity for hydropower stations;

[0035] Supersaturated TDG level constraint:

[0036] C min ≤C≤C max

[0037] Where: C is the optimized supersaturated TDG level, C min is the minimum tolerance value of supersaturated TDG to fish, C max is the maximum tolerance value of supersaturated TDG to fish;

[0038] The flow rate constraint is:

[0039] V min ≤V≤V max

[0040] Where: V is the optimized flow rate, V min is the minimum flow velocity threshold for fish migration, V max is the maximum flow velocity threshold for fish migration.

[0041] Furthermore, the flow rate constraint in the reservoir area is constrained by a fuzzy membership function, and the process is as follows:

[0042] The constraints of the fuzzy interval set are subjected to credibility interception, and the nonlinear model is decomposed into upper limit sub-model and lower limit sub-model;

[0043] A fuzzy membership function based on credibility is constructed and substituted into the decision variables to obtain the flow velocity constraint in the reservoir area.

[0044] Furthermore, the flow rate constraints in the reservoir area are as follows:

[0045]

[0046] Where: Cr is the reliability measure, V± is the optimized value of flow rate (flow rate decision variable), is the minimum flow velocity interval of fish migration in the reservoir area, is the confidence level interval, is the lower limit of the minimum flow velocity of fish migration in the reservoir area, is the upper limit of the minimum flow velocity range of fish migration in the reservoir area, is the maximum flow velocity interval of fish migration in the reservoir area, is the lower limit of the maximum flow velocity of fish migration in the reservoir area, It is the upper limit of the maximum flow velocity range of fish migration in the reservoir area.

[0047] The beneficial effects of the present invention are:

[0048] This study constructs a multi-objective ecological scheduling model for cascade reservoirs, considering flow velocity uncertainty and fish migration safety. The model uses intermittent flood discharge to reduce the maximum retention time of supersaturated TDG in the reservoir, providing a safe habitat for migrating fish. Furthermore, the model solves fuzzy interval flow velocity constraints by combining multi-preference fuzzy interval credibility-constrained programming, reflecting the preferences of different decision makers regarding flow velocity requirements for fish migration. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of the process of the present invention.

[0050] Figure 2 is the membership function of the reservoir flow velocity constraint in the embodiment of the present invention.

[0051] Figure 3 is the average flow rate of decision makers with three attitudes at different α-cut levels in the embodiment of the present invention.

[0052] Figure 4 The figure shows the comparison between the actual power generation and the power generation obtained by the optimized operation in the embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0054] like Figure 1 As shown, a method for reconstructing fish migration habitats in dammed rivers based on fuzzy interval programming includes the following steps:

[0055] Step 1: Construct a multi-objective ecological scheduling model;

[0056] The water inflow to the lower reservoir of two adjacent reservoirs is primarily controlled by the outflow from the upper reservoir. Therefore, to ecologically regulate the river section between the two dams, the scheduling scheme of the upper dam must be changed. To mitigate the impact of oversaturated TDG on fish migration, ensure fish migration velocity, and improve power generation capacity, the model presented in this paper was constructed.

[0057] The objective function of the multi-objective ecological dispatch model is to minimize the level of oversaturated TDG and maximize the power generation;

[0058] The objective function includes:

[0059]

[0060] Where: f1 ± is the minimum target supersaturated TDG level, For the maximum power generation target, C ± (t) is the supersaturated TDG level at time t, P ± (t) is the power generation at time t, NT is the total time step; Q s is the flood discharge of the upper reservoir, P power is the installed capacity of the hydropower station, H1(t) is the water level in front of the first-stage reservoir dam, H2(t) is the water level downstream of the first-stage reservoir dam, Q p (t) is the flow rate of the upper reservoir used for power generation, and g and η are parameters.

[0061] The objective function weight assignment is processed into a single target using the analytic hierarchy process. The objective function obtained after the single target processing is:

[0062]

[0063] Step 2: Construct the constraints of the objective function;

[0064] The constraints include water level balance constraints, upstream and downstream water level constraints, flow constraints, power generation constraints, supersaturated TDG level constraints and reservoir flow velocity constraints;

[0065] The water level balance constraints are as follows:

[0066] H1(t)=H1(t-1)-0.00007·(Q out -Q in ) (6)

[0067] H2(t)=0.0011·Q out +372.7 (7)

[0068] Q out =Q s +Q p (8)

[0069] H3(t)=H3(t-1)-0.000011·(Q o -Q out ) (9)

[0070] Where: H1(t) is the water level in front of the first-stage reservoir dam at time t, H1(t-1) is the water level in front of the first-stage reservoir dam at time t-1, H2(t) is the water level downstream of the first-stage reservoir dam at time t, H3(t) is the water level in front of the second-stage reservoir dam at time t, H3(t-1) is the water level in front of the second-stage reservoir dam at time t-1, Q out is the outflow of the first-level reservoir, Q in is the inflow to the first-level reservoir, Q s is the discharge flow of the first-level reservoir, Q p is the power generation flow of the first-level reservoir, Q o It is the outflow of the second-level reservoir.

[0071] The upstream and downstream water level constraints are as follows:

[0072]

[0073] Where: is the minimum water level in front of the first-stage reservoir dam, is the maximum water level in front of the first-stage reservoir dam, is the minimum water level downstream of the first-stage reservoir dam, is the maximum water level downstream of the first-stage reservoir dam, is the minimum water level in front of the second-stage reservoir dam, It is the maximum water level in front of the second-stage reservoir dam.

[0074] The flow constraints are:

[0075]

[0076] Where: and It is the minimum and maximum flood discharge of the upper reservoir; and It is the minimum and maximum flow rate of the upper reservoir used for power generation; and is the minimum and maximum flood discharge of the next level reservoir, Q o It is the flood discharge of the next level reservoir.

[0077] The power generation constraint is:

[0078]

[0079] Where: P is the power generation after optimization, P min is the minimum power generation capacity of the hydropower station, Ppower Installed capacity for hydropower stations;

[0080] Supersaturated TDG level constraint:

[0081] C min ≤C≤C max (17)

[0082] Where: C is the optimized supersaturated TDG level, C min is the minimum tolerance value of supersaturated TDG to fish, C max is the maximum tolerance value of supersaturated TDG to fish;

[0083] The flow rate constraint is:

[0084] V min ≤V≤V max (18)

[0085] Where: V is the optimized flow rate, V min is the minimum flow velocity threshold for fish migration, V max is the maximum flow velocity threshold for fish migration.

[0086] The flow rate constraint in the reservoir area is constrained by the fuzzy membership function. The process is as follows:

[0087] The constraints of the fuzzy interval set are subjected to credibility interception, and the nonlinear model is decomposed into upper limit sub-model and lower limit sub-model;

[0088] When ± When ξ is a triangular fuzzy interval, ± =(a ± ,b ± ,c ± )={[a - ,a + ],[b - ,b + ],[c - ,c + ]}, its credibility function can be expressed as:

[0089]

[0090] Where: a ± 、b ± 、c ± are the minimum value interval, optimal value interval and maximum value interval of the interval respectively; r is the decision variable.

[0091] For credibility 0.5≤λ≤1:

[0092]

[0093] The upper limit submodel is obtained as:

[0094] r + ≤(2λ-1)a + +(2-2λ)b + (twenty three)

[0095] r + ≥(2-2λ)b + +(2λ-1)c + (twenty four)

[0096] The lower bound submodel is:

[0097] r - ≤(2λ-1)a - +(2-2λ)b - (25)

[0098] r - ≥(2-2λ)b - +(2λ-1)c - (26)

[0099] r - ≤r + (27)

[0100] The exact value of λ cannot well reflect the attitudes of different decision makers. When the attitudes of decision makers are fuzzy numbers, Based on the fuzzy set theory, the credibility level of the decision maker's attitude is expressed by fuzzy numbers, and the α-cut is defined as the fuzzy set The set of elements with a membership degree of at least α reflects the ambiguity of the decision maker's attitude, which can be expressed as:

[0101]

[0102] Where: is the fuzzy set of W, for The fuzzy membership function of the three attitudes is obtained as follows:

[0103]

[0104] Where: μ radical is the membership function of radical attitude, μ neutral is the membership function of neutral attitude, μ conservative is the membership function for the conservative attitude. Aggressive decision makers tend to provide the maximum flow velocity threshold that satisfies fish migration and assume the greatest safe migration risk. Conservative decision makers, on the other hand, tend to meet the fish migration velocity requirement while minimizing the safe migration risk. Neutral decision makers provide moderate fish migration velocity conditions and assume moderate safe migration risks.

[0105] Substitute the fuzzy membership function into the decision variable to obtain the flow velocity constraint of the reservoir area.

[0106] The flow velocity constraints in the reservoir area are as follows:

[0107]

[0108]

[0109] Where: Cr is the reliability measure, V ± is the optimized value of flow rate (flow rate decision variable), is the minimum flow velocity interval of fish migration in the reservoir area, is the credibility level interval, which is obtained by intercepting the membership function of the three attitudes by α-cut. is the lower limit of the minimum flow velocity of fish migration in the reservoir area, is the upper limit of the minimum flow velocity range of fish migration in the reservoir area, is the maximum flow velocity interval of fish migration in the reservoir area, is the lower limit of the maximum flow velocity of fish migration in the reservoir area, It is the upper limit of the maximum flow velocity range of fish migration in the reservoir area.

[0110] Fuzzy membership function is as follows Figure 2 shown.

[0111] Step 3: Based on the constraints, solve the objective function and use the obtained solution to complete the reconstruction of the fish migration habitat in the dammed river.

[0112] Example

[0113] In a cascade of reservoirs, supersaturated TDG water, generated by flood discharges from the upper reservoir, is transported through the river to the lower reservoir, causing fish in the lower reservoir to contract bubble disease and die. Furthermore, the slow flow rate in the lower reservoir, caused by dam construction, hinders fish migration to the upper reservoir. Therefore, to ensure that fish in the lower reservoir can successfully migrate to the upper reservoir, the two reservoirs must coordinate their operations to regulate flow rates and supersaturated TDG levels in the lower reservoir.

[0114] The model of the present invention is used to study the river section between two hydropower stations (XLD and XJB).

[0115] Although the model of the present invention predicts different supersaturated TDG levels at each moment under different α-cut values and decision-making attitudes, it does not exhibit a clear regularity in these changes. This is because the decision-maker's multi-preference decision fuzzy function constrains the flow rate constraint, so the α-cut value and decision-making attitude do not significantly restrict the supersaturated TDG level. However, changes in the α-cut value and decision-making attitude cause changes in the flow rate constraint, and consequently, the supersaturated TDG level in the downstream channel changes, an inevitable consequence of the influence of the model system.

[0116] Figure 3 The figure shows the average flow velocity for the three decision-makers at different α-cut levels. The figure shows the flow velocity distribution at 06:00, 12:00, 18:00, and 00:00 on July 10, 2010, under the neutral attitude (α = 0.6). It can be seen that at these four times, the flow velocity in the reservoir area can form a continuous flow velocity band of 0.3-0.4 m / s, and the flow velocity in most areas can form a flow velocity band of 0.6-0.7 m / s. This indicates that fish entering the XJB Reservoir area can continue to flow upstream smoothly. The flow velocity in the area downstream of the XLD Dam is greater than 1.2 m / s. This is because the XLD Dam's flood discharge has the greatest impact on the flow velocity in this area. To continue to flow upstream, migratory fish in this area need to use fish passages and other fish-passing facilities.

[0117] The power generation results are as follows Figure 4 As shown in the figure, the XLD dam can achieve full-load power generation under different α-cut values and decision-maker attitudes. The model constructed in this method also takes achieving maximum power generation of the reservoir as one of the model's operation objectives. Therefore, the model operation results show that our optimization method can achieve both the safety requirements of fish migration and the power generation needs.

[0118] From the perspective of the river section between the two dams in the embodiment, the constructed model can effectively reduce the supersaturated TDG level in the river channel downstream of the XLD Dam and increase the time for stopping flood discharge, which can provide recovery time for migratory fish exposed to the supersaturated TDG environment in the river channel; at the same time, the established model can effectively increase the water flow velocity in the river channel between the XLD Dam and the XJB Reservoir.

[0119] The present invention constructs a multi-objective ecological scheduling model of flow velocity uncertainty in cascade reservoirs considering the safety of fish migration. This model can minimize the maximum residence time of supersaturated TDG in the downstream river channel through the design of intermittent flood discharge, and uses a multi-preference fuzzy interval credibility constrained programming method to deal with the uncertainty problem of fish migration velocity. At the same time, it can reflect the attitude preferences of different decision makers towards the requirements of fish migration velocity.

Claims

1. A method for reconstructing fish migration habitat in dammed rivers based on fuzzy interval programming, characterized in that: The following steps are involved: Step 1: Construct a multi-objective ecological scheduling model; The objective function of the multi-objective ecological dispatch model is to minimize the level of oversaturated TDG and maximize the power generation; Step 2: Construct the constraints of the objective function; The constraints include water level balance constraints, upstream and downstream water level constraints, flow constraints, power generation restrictions, oversaturated TDG level constraints, and reservoir flow velocity constraints; The flow rate constraint in the reservoir area is constrained by fuzzy membership function; Step 3: Based on the constraints, solve the objective function and use the obtained solution to complete the reconstruction of the fish migration habitat in the dammed river.

2. The method for reconstructing fish migration habitat in dammed rivers based on fuzzy interval programming according to claim 1, characterized in that: The objective function in step 1 includes: Where: f1 ± is the minimum target supersaturated TDG level, For the maximum power generation target, C ± (t) is the supersaturated TDG level at time t, P ± (t) is the power generation at time t, and NT is the total time step.

3. The method for reconstructing fish migration habitat in dammed rivers based on fuzzy interval programming according to claim 2, characterized in that: The analytic hierarchy process is used to assign the weight of the objective function to a single objective.

4. The method for reconstructing fish migration habitat in dammed rivers based on fuzzy interval programming according to claim 3, characterized in that: The objective function obtained after single-objective processing is: Where: α and β are target weight factors, P power The installed capacity of the hydropower station.

5. The method for reconstructing fish migration habitat in dammed rivers based on fuzzy interval programming according to claim 1, characterized in that: The water level balance constraints are as follows: H1(t)=H1(t-1)-0.00007·(Q out -Q in ) H2(t)=0.0011@Q out +372.7 Q out =Q s +Q p H3(t)=H3(t-1)-0.000011·(Q o -Q out ) Where: H1(t) is the water level in front of the first-stage reservoir dam at time t, H1(t-1) is the water level in front of the first-stage reservoir dam at time t-1, H2(t) is the water level downstream of the first-stage reservoir dam at time t, H3(t) is the water level in front of the second-stage reservoir dam at time t, H3(t-1) is the water level in front of the second-stage reservoir dam at time t-1, Q out is the outflow of the first-level reservoir, Q in is the inflow to the first-level reservoir, Q s is the discharge of the first-level reservoir, Q p is the power generation flow of the first-level reservoir, Q o It is the outflow of the second-level reservoir.

6. The method for reconstructing fish migration habitat in dammed rivers based on fuzzy interval programming according to claim 5, characterized in that: The upstream and downstream water level constraints are as follows: Where: is the minimum water level in front of the first-stage reservoir dam, is the maximum water level in front of the first-stage reservoir dam, is the minimum water level downstream of the first-stage reservoir dam, is the maximum water level downstream of the first-stage reservoir dam, is the minimum water level in front of the second-stage reservoir dam, is the maximum water level in front of the second-stage reservoir dam; The flow constraints are: Where: and It is the minimum and maximum flood discharge of the upper reservoir; and It is the minimum and maximum flow rate of the upper reservoir used for power generation; and is the minimum and maximum flood discharge of the next level reservoir, Q o is the flood discharge of the next level reservoir; The power generation constraint is: P min ≤P≤P power Where: P is the power generation after optimization, P min is the minimum power generation capacity of the hydropower station, P power Installed capacity for hydropower stations; Supersaturated TDG level constraint: C min ≤C≤C max Where: C is the optimized supersaturated TDG level, C min is the minimum tolerance value of supersaturated TDG to fish, C max is the maximum tolerance value of supersaturated TDG to fish; The flow rate constraint is: In min ≤V≤V max Where: V is the optimized flow rate, V min is the minimum flow velocity threshold for fish migration, V max is the maximum flow velocity threshold for fish migration.

7. The method for reconstructing fish migration habitat in dammed rivers based on fuzzy interval programming according to claim 6, characterized in that: The flow rate constraint in the reservoir area is constrained by a fuzzy membership function, and the process is as follows: The constraints of the fuzzy interval set are subjected to credibility interception, and the nonlinear model is decomposed into upper limit sub-model and lower limit sub-model; A fuzzy membership function based on credibility is constructed and substituted into the decision variables to obtain the flow velocity constraint in the reservoir area.

8. The method for reconstructing fish migration habitat in dammed rivers based on fuzzy interval programming according to claim 7 is characterized in that: The flow rate constraints in the reservoir area are as follows: Where: Cr is the reliability measure, V ± is the optimized value of flow rate (flow rate decision variable), is the minimum flow velocity interval of fish migration in the reservoir area, is the confidence level interval, is the lower limit of the minimum flow velocity of fish migration in the reservoir area, is the upper limit of the minimum flow velocity range of fish migration in the reservoir area, is the maximum flow velocity interval of fish migration in the reservoir area, is the lower limit of the maximum flow velocity of fish migration in the reservoir area, It is the upper limit of the maximum flow velocity range of fish migration in the reservoir area.

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