Real-time flood control multi-objective robust optimal regulation method for reservoirs against flood forecast error disturbances

Abstract

The present invention discloses a real-time flood control multi-objective robust optimization regulation method for reservoirs to resist flood forecast error disturbances, including collecting and sorting flood forecast error samples in the reservoir system database, and randomly simulating to generate a set of real-time flood control operation flood error scenarios; establishing a multi-objective robust optimization model for reservoir flood control operation: taking the conditional value-at-risk of the upstream and downstream flood control risk rates and the upstream and downstream flood control risk losses as the optimization objectives to generate a multi-objective robust optimization non-dominated solution set; multi-attribute risk decision-making under uncertainty: introducing different weight parameters according to different decision-making preferences, and using the TOPSIS method to obtain the optimal equilibrium solutions under different preferences. The present invention creates a set of decision support model sets for the whole process of "error scenario simulation - risk robust regulation - non-dominated solution set decision-making" in the field of reservoir flood control operation, which can improve the reliability and safety of reservoir flood control operation.

Description

Technical Field

[0001] The present invention relates to a reservoir operation method in the field of water conservancy projects, and particularly to a real-time flood control multi-objective robust optimization regulation method for a reservoir that resists the disturbance of flood forecast errors. Background Art

[0002] Reservoirs are important engineering measures to resist flood disasters and control the flood process. Scientific and reasonable use of reservoirs for flood control operation can significantly reduce the impact of flood disasters and effectively protect the lives and property safety of people in the upstream and downstream areas. With the continuous development of forecasting technology, traditional single-value flood forecasting no longer adapts to modern flood control operation, and probabilistic ensemble forecasting is adopted by more and more basin management agencies. Although probabilistic flood forecasting can greatly improve the forecasting accuracy and effectively cover the actual flood process during the forecasting process, the resulting forecasting uncertainty has correspondingly become the main risk source for reservoir flood control operation: the reservoir flood control operation under the disturbance of forecasting uncertainty needs to consider the risks that may cause the deviation and error of the reservoir and downstream operation safety indicators from the expected state due to the disturbance of the forecasting error source.

[0003] Stochastic programming methods are the main general methods for dealing with forecasting uncertainty and planning to reduce operation risks at present. However, the existing stochastic programming methods fail to simultaneously consider the control requirements of reservoir risk aversion and risk reduction, and lack comprehensiveness in dealing with risks: when dealing with uncertain forecasting scenarios, the goal is to reduce the occurrence probability of flood control risk events under different forecast inflow scenarios. Although it can effectively control the occurrence probability of risk events, it cannot effectively control the size of the losses caused by the occurrence of risk events. In the face of major flood events, its processing ability is insufficient, it is difficult to ensure the operation safety of super-standard major risk events, and it lacks robustness in the face of probabilistic flood forecasting. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to provide a real-time flood control multi-objective robust optimization regulation method for a reservoir that resists the disturbance of flood forecast errors, so as to achieve efficient control of the occurrence frequency and loss degree of risk events in the flood control system under the disturbance of forecast errors and improve the robust performance of the reservoir flood control system.

[0005] Technical Solution: A real-time flood control multi-objective robust optimization regulation method for a reservoir that resists the disturbance of flood forecast errors according to the present invention includes the following steps:

[0006] S1. Collect and sort out flood forecast error samples in the reservoir system database, and use the Monte Carlo method to randomly sample to generate a pre-real-time flood control flood forecast error scenario set; superimpose the generated forecast error scenarios on the forecast inflow mean process to obtain simulated forecast inflow scenarios, which are used as the input conditions for the real-time flood control multi-objective robust optimization model of the reservoir;

[0007] S2. Establish a multi-objective robust optimization model for reservoir flood control operation: Take the conditional value-at-risk of the upstream and downstream flood risk rates and the upstream and downstream flood risk loss indicators as the optimization objectives to generate a multi-objective robust optimization non-dominated solution set that can resist risks with different probabilities and degrees.

[0008] S3. Multi-attribute risk decision-making under uncertainty: For different decision-making preferences, introduce different weight parameters and use the TOPSIS method to obtain the optimal equilibrium solutions under different preferences.

[0009] Further, step S1 includes the following steps:

[0010] S11. Obtain several historical flood forecast samples and flood measured samples from the reservoir system database, and calculate the forecast errors for each lead time:

[0011]

[0012] Among them, ξ(τ) is the forecast error of the reservoir with a lead time of τ, IN(t) is the actual inflow value at time t, is the forecast inflow for time t at time t - τ, and the lead time is τ;

[0013] S12. Use the t-copula function to characterize the characteristics of flood forecast errors and simulate and generate a set of real-time flood forecast error scenarios, and superimpose them on the mean forecast process to obtain a set of real-time flood control inflow scenarios.

[0014] Even further, step S12 is specifically as follows:

[0015] S121. Establish the marginal distributions of the forecast errors for each lead time;

[0016] Based on the univariate hydrological frequency method, establish the marginal distributions of the forecast errors. Select the commonly used marginal distributions in the field of hydrological analysis as candidates, use the maximum likelihood estimation method to determine the parameters of each marginal distribution and evaluate the fitting status, and select the optimal marginal distribution as the actual distribution;

[0017] S122. Based on the t-copula function, establish the joint distributions of the forecast errors for different lead times;

[0018] The form of the joint distribution function of the forecast errors is as follows:

[0019]

[0020] Among them, Cor is the correlation coefficient matrix of variables u1…u n of, u is the variable matrix, v is the degree of freedom, n is the number of variables, Γ(·) is the Gamma function, u1 is the cumulative distribution function of the first random variable, un is the cumulative distribution function of the nth variable, and x is the integral vector of the formal parameter;

[0021] S123. Generation of the real-time flood control flood forecast inflow scenario set;

[0022] Based on the established joint distribution of forecast errors and the optimal marginal distribution as the actual distribution, the Monte Carlo method is used to randomly sample and generate the real-time flood control flood forecast error scenario set; the generated forecast error scenarios are superimposed on the forecast inflow mean process to obtain the simulated forecast inflow scenarios, as shown in Equation (3):

[0023]

[0024] where is the forecast inflow mean process at time t, ξs(τ) is the simulated forecast error scenario with a lead time of τ, and INs(t - τ, t) is the forecast inflow scenario with a lead time of τ at time t - τ; the forecast inflow process sets INs(t, t + 1), INs(t, t + 2), …, INs(t, t + T) with different lead times 1, 2, …, T generated from the same starting time t are abbreviated as INs(t + 1), INs(t + 2), …, INs(t + T); the real-time flood control flood forecast inflow scenario set has the same starting time and the same length of lead time.

[0025] Furthermore, step S2 includes the following steps:

[0026] S21. Introduce the robustness index of conditional value at risk to evaluate the possible risk losses of the reservoir in the face of adverse scenarios;

[0027] The flood control loss function is represented by L, and the conditional value at risk of the reservoir flood control risk loss is represented by Equations (4) and (5):

[0028]

[0029] VaR α (L) = min{cdf(L) ≥ α} (5);

[0030] where α is the confidence level, α ∈ [0, 1], and CVaR α (L) is the conditional value at risk of the reservoir risk loss at the confidence level α, and VaR α (L) is the minimum risk loss at the confidence level α, pdf(·) is the probability density function, and cdf(·) is the cumulative probability function;

[0031] S22. For the real-time flood control flood forecast inflow scenario set simulated in step S1, establish the optimization objective library of the multi-objective robust optimization model for reservoir flood control scheduling;

[0032] S23. For the real-time flood control flood forecast inflow scenario set simulated in step S1, in coordination with the optimization objective library of the model established in step S22, establish a constraint condition library for the multi-objective robust optimization model of reservoir flood control operation;

[0033] S24. Use the evolutionary multi-objective optimization algorithm NSGA-III based on the reference point non-dominated sorting method to solve the established multi-objective robust optimization model of reservoir flood control operation, and generate a non-dominated solution set that meets different risk flood control requirements.

[0034] Furthermore, in step S22, under the influence of real-time flood forecast error perturbation, the optimization objective library includes:

[0035] Objective 1: Minimize the maximum risk rate that the reservoir water level exceeds the water level safety threshold;

[0036] Facing the real-time flood control flood forecast inflow scenario set, minimize the maximum probability that the simulated reservoir water level exceeds the set threshold; this objective reflects the role of resisting the risk that the upstream of the reservoir exceeds the water level safety threshold caused by flood forecast errors; it is expressed by Equation (6):

[0037]

[0038] Among them, represents the maximum risk rate that the reservoir water level exceeds the water level safety threshold; is the reservoir water level at each moment under each inflow scenario simulated by this model for the real-time flood control flood forecast inflow scenario set, Z sa is the reservoir water level safety threshold, T is the duration of the scheduling plan period, and Prob(·) is the frequency statistical function;

[0039] Objective 2: Minimize the maximum risk rate that the reservoir discharge exceeds the downstream safety discharge;

[0040] Facing the real-time flood control flood forecast inflow scenario set, minimize the maximum probability that the simulated reservoir discharge exceeds the set threshold; this objective reflects the effect of resisting the risk that the downstream of the reservoir has a discharge exceeding the downstream safety control value caused by flood forecast errors; this objective is expressed by Equation (7):

[0041]

[0042] Among them, represents the maximum risk rate that the reservoir discharge exceeds the downstream safety discharge; is the reservoir discharge process under each inflow scenario simulated by this model facing the real-time flood control flood forecast inflow scenario set, Q sa is the downstream safety control flow threshold;

[0043] Objective 3: Minimize the conditional value-at-risk under the condition that the flood control storage capacity of the reservoir accounts for the largest proportion;

[0044] In this model, the proportion of the reservoir storage capacity process during flood control operation to the flood control storage capacity is selected as an approximation of the risk loss upstream of the reservoir. Equation (8) shows the calculation function of the flood control loss upstream of the reservoir.

[0045]

[0046] Among them, f z～v (·) is the reservoir water level - storage capacity curve, Z is the flood - limit water level, and V pro is the flood control storage capacity of the reservoir;

[0047] Based on the form of the upstream loss function, this objective is expressed by Equation (9):

[0048]

[0049] Among them, represents the conditional value - at - risk under the condition that the flood control storage capacity of the reservoir accounts for the largest proportion; is the conditional value - at - risk corresponding to the upstream flood control loss calculation function shown in Equation (4), and α is the confidence level. This objective reflects the effect of reducing the inundation loss upstream of the reservoir caused by flood forecasting errors;

[0050] Objective 4: Minimize the conditional value - at - risk of the maximum proportion of reservoir discharge;

[0051] In this model, the proportion of the reservoir discharge to the downstream safe discharge is selected as an approximation of the risk loss downstream of the reservoir. Equation (10) shows the flood control loss function downstream of the reservoir.

[0052]

[0053] Among them, Qs is the identification water level of the downstream flood control loss;

[0054] Based on the form of the downstream loss function, this objective is expressed by Equation (11):

[0055]

[0056] Among them, represents the conditional value - at - risk of the maximum proportion of reservoir discharge, is the conditional value - at - risk corresponding to the downstream flood control loss function shown in Equation (4). This objective reflects the effect of reducing the inundation loss downstream of the reservoir caused by flood forecasting errors;

[0057] The above 4 objectives constitute the optimization objective library of the multi - objective robust optimization model for reservoir flood control operation.

[0058] Further, the constraint library in step S23 includes:

[0059] Constraint 1: water balance constraint;

[0060] The water balance constraint controls the total water volume in the reservoir to remain consistent during iterative simulations in each time period, that is, the mass conservation constraint. The water balance constraint used in this model is expressed by Equation (12):

[0061]

[0062] where is the reservoir inflow forecast process set, is the reservoir storage at time t, and Δt is the calculation step size;

[0063] Constraint 2: storage limit constraint;

[0064] The storage limit constraint controls the reservoir storage during simulation operation not to exceed or be lower than the allowable upper and lower limits of storage. The storage limit constraint used in this model is expressed by Equation (13):

[0065]

[0066] where V and are the allowable lower and upper limits of storage during reservoir operation (m 3 );

[0067] Constraint 3: discharge limit constraint;

[0068] The discharge limit constraint controls the discharge during model operation not to exceed or be lower than the allowable upper and lower limits of discharge. This constraint can take into account the downstream ecological and domestic water demands and protect the safety of the downstream river channel to a certain extent. The storage limit constraint used in this model is expressed by Equation (14):

[0069]

[0070] where Q and are the allowable lower and upper limits of discharge of the reservoir respectively;

[0071] Constraint 4: discharge variation limit constraint;

[0072] The discharge variation limit constraint is to protect the safety of the downstream waterway and the slope stability. The discharge variation limit constraint used in this model is expressed by Equation (15):

[0073]

[0074] where ΔQ is the upper limit of the allowable discharge variation of the reservoir between each time period;

[0075] Constraint 5: Initial and boundary condition constraints;

[0076] The initial and boundary condition constraints used in this model are expressed by Equation (16):

[0077]

[0078] where Z ini is the initial water level, generally set as the flood limit water level, and V obj is the target storage volume at the end.

[0079] Furthermore, Step S3 includes the following steps:

[0080] S31. Establish a decision matrix, where each decision variable in the decision matrix is the optimized target value of each alternative solution, as shown in Equation (17):

[0081]

[0082] where x (i,j) is the jth decision variable in the ith evaluation solution, is the jth optimized target value of the ith evaluation solution, I is the total number of alternative solutions, and J is the number of optimization targets;

[0083] S32. Standardize the decision matrix, and the standardization method is as shown in Equation (18):

[0084]

[0085] where norx (i,j) is the standardized decision variable;

[0086] S33. Construct a weighted value decision matrix, and the weighting method is as shown in (19):

[0087] wx (i,j) = w j ·norx( i,j ) (19);

[0088] where wx (i,j) is the weighted attribute value, and w j is the weight of the jth index;

[0089] S34. Determine the positive and negative ideal solutions The calculation method is as shown in Equation (20):

[0090]

[0091] where, are the positive ideal solution and negative ideal solution of the jth index respectively;

[0092] S35. Calculate the Euclidean distances of each evaluation scheme from the positive and negative ideal solutions. The calculation method is shown in Equation (21):

[0093]

[0094] Among them, and are the Euclidean distances of the i-th evaluation scheme from the positive and negative ideal solutions respectively;

[0095] S36. Calculate the degree of fit of each evaluation scheme to the ideal scheme. The calculation method is shown in Equation (22):

[0096]

[0097] Among them, clo i is the degree of fit of the i-th scheme. Select the scheme with the highest degree of fit value among all schemes as the final equilibrium scheme of the TOPSIS method. Different equilibrium schemes are generated under different decision preference weights for the reservoir flood control decision-makers to choose.

[0098] Beneficial effects: Compared with the existing technology, a real-time flood control multi-objective robust optimization control method for reservoirs that resists flood forecast error disturbances proposed by the present invention introduces the concept of conditional value at risk on the basis of existing stochastic programming methods, and creates a control technology integrating "error scenario simulation - risk robust control - non-dominated solution set decision-making", providing a possible way to effectively describe flood losses. Compared with the existing technology, it has the following advantages: (1) Compared with the traditional planning method that combines single-value forecasting process with sensitivity analysis, the present invention directly conducts overall control on the entire flood scenario set under error disturbances, which can improve the stability of the system in dealing with flood control risks; (2) Compared with stochastic programming methods, the present invention not only considers the probability of occurrence of risk events, but also realizes the efficient control of the loss degree of risk events in the flood control system under forecast error disturbances, which can further improve the safety of the reservoir flood control scheduling system. Description of the Drawings

[0099] Figure 1 is the flow chart of the method of the present invention;

[0100] Figure 2 is the schematic diagram of the forecasting process set with error scenario simulation;

[0101] Figure 3 is the schematic diagram of the relationship between the loss function and the conditional value at risk;

[0102] Figure 4 is the non-dominated solution set generated by the scheduling model and the equilibrium solution preferably selected by TOPSIS under the equilibrium preference. Detailed Embodiment

[0103] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. However, it is obvious to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some well-known technical features in the art are not described. The order of the relevant steps in the present invention is not restrictive, that is, those skilled in the art can adjust it. The order in the present invention is a case-by-case writing method, rather than a restrictive description.

[0104] A real-time flood control multi-objective robust optimization control method for reservoirs that resists flood forecast error disturbances in the present invention introduces the concept of conditional value at risk on the basis of existing stochastic programming methods, and creates a control technology integrating "error scenario simulation - risk robust control - non-dominated solution set decision-making". From the description of the flood forecast error risk source to the flood forecast scenario simulation, from the establishment of a multi-objective robust optimization control model to the risk-based non-dominated decision-making, it provides a complete solution for reservoirs to resist flood forecast error disturbances, and can effectively improve the reliability and safety of reservoir flood control scheduling. This method provides a possible way to effectively characterize flood losses. On this basis, it realizes the efficient control of the occurrence frequency and loss degree of risk events in the flood control system under forecast error disturbances, and greatly improves the robust performance of the reservoir flood control system.

[0105] As Figure 1 shown, a real-time flood control multi-objective robust optimization control method for reservoirs that resists flood forecast error disturbances in the present invention includes the following steps:

[0106] S1. Collect and sort out the flood forecast error samples in the reservoir system database, and use the Monte Carlo method to randomly sample to generate a set of pre-real-time flood control flood forecast error scenarios; superimpose the generated forecast error scenarios on the forecast inflow mean process to obtain the simulated forecast inflow scenarios, which are used as the input conditions for the real-time flood control multi-objective robust optimization model of the reservoir;

[0107] At present, digital scheduling systems of a certain scale have been built in major river basins. Among them, the inflow runoff forecast is mostly stored in the form of a database. However, affected by the forecast method and the forecast time, the forecast time of such forecast products may not be consistent with the length of the forecast period. Therefore, this step mainly extracts the forecast products from the database, sorts them into the same form, standardizes the data format, and obtains the forecast error samples.

[0108] Specifically, it includes the following steps:

[0109] S11. Obtain several historical flood forecast samples and flood measurement samples from the reservoir system database, and calculate the forecast errors at each forecast period.

[0110]

[0111] Among them, ξ(τ) is the forecast error with a reservoir forecast period of τ, and IN(t) is the actual inflow value at time t. is the forecast inflow for time t at time t-τ (forecast period is τ);

[0112] S12. Characterizing and simulating the flood forecast error characteristics using the t-copula function mainly includes 3 steps: (1) Establishing the marginal distribution of the forecast error at each forecast period; (2) Establishing the joint distribution of the forecast errors at different forecast periods based on the t-copula function; (3) Randomly sampling according to the marginal distribution and the joint function of the forecast error to generate a set of forecast error scenarios, and superimposing them on the mean forecast process to obtain a set of real-time flood control flood inflow scenarios. Specifically:

[0113] S121. Establishing the marginal distribution of the forecast error at each forecast period: The present invention establishes the marginal distribution of the forecast error based on the univariate hydrological frequency method. Select the commonly used marginal distributions in the field of hydrological analysis (normal distribution, Weibull distribution, Gamma distribution, Gumbel distribution, P-III distribution, etc.) as candidates, apply the maximum likelihood estimation method to determine the parameters of each marginal distribution and evaluate the fitting status, and select the optimal marginal distribution as the actual distribution.

[0114] S122. Establishing the joint distribution of the forecast errors at different forecast periods based on the t-copula function: Taking the two-dimensional t-copula as an example, the form of the joint distribution function of the forecast error is as follows:

[0115]

[0116] Among them, Cor is the correlation coefficient matrix of variables u1…u n of, u is the variable matrix, v is the degree of freedom, n is the number of variables, Γ(·) is the Gamma function, u1 is the cumulative distribution function of the first random variable, u n is the cumulative distribution function of the nth variable, and x is the parametric integration vector.

[0117] S123. Generating a set of real-time flood control flood forecast inflow scenarios: According to the established joint distribution of the forecast error and the optimal marginal distribution as the actual distribution, use the Monte Carlo method to randomly sample to generate a set of pre-real-time flood control flood forecast error scenarios; superimpose the generated forecast error scenarios on the mean process of the forecast inflow to obtain the simulated forecast inflow scenarios, as shown in formula (3).

[0118]

[0119] Among them, is the expected forecast inflow process at time t, ξs(τ) is the simulated forecast error scenario with a lead time of τ, and INs(t-τ,t) is the forecast inflow scenario with a lead time of τ at time t-τ. The set of forecast inflow processes with different lead times 1, 2, …, T generated from the same starting forecast time t (also known as "inflow scenarios") INs(t,t+1), INs(t,t+2), …, INs(t,t+T) can be abbreviated as INs(t+1), INs(t+2), …, INs(t+T). This real-time flood control flood forecast inflow scenario set has the same starting forecast time and the same length of lead time, as Figure 2 shown.

[0120] S2. Establish a multi-objective robust optimization model for reservoir flood control operation: Using the conditional value-at-risk of the upstream and downstream flood control risk rates and the upstream and downstream flood control risk loss indicators as the optimization objectives, generate a set of non-dominated solutions of the multi-objective robust optimization that can resist risks of different probabilities and degrees.

[0121] Specifically, it includes the following steps:

[0122] S21. Introduce a robustness index of conditional value-at-risk to evaluate the possible risk losses of the reservoir in the face of adverse scenarios.

[0123] The flood control loss function is represented by L (excess loss: that is, flood control loss occurs when exceeding a certain set threshold). At this time, the conditional value-at-risk of the reservoir flood control risk loss can be represented by Equations (4) and (5).

[0124]

[0125] VaR α (L) = min{cdf(L) ≥ α} (5);

[0126] where α is the confidence level (α ∈ [0,1]) (dimensionless), CVaR α (L) is the conditional value-at-risk of the reservoir risk loss at the confidence level α (with the same dimension as the flood control loss L), VaR α (L) is the minimum risk loss at the confidence level α (with the same dimension as the flood control loss L), pdf(·) is the probability density function, and cdf(·) is the cumulative probability function.

[0127] Figure 3 shows the correspondence between the conditional value-at-risk index, value-at-risk, and risk loss function. The conditional value-at-risk is mainly used to describe the extreme expected loss in the tail of the risk loss function.

[0128] The embodiment of the present invention applies the conditional risk value index to optimize the maximum risk loss that may occur upstream and downstream of the reservoir in flood control scheduling, and cooperates with the risk rate index to meet the needs of ensuring the reliability and safety of flood control scheduling of a single reservoir.

[0129] S22. For the real-time flood forecast inflow scenario set simulated in step S1, establish an optimization target library for the reservoir flood control scheduling multi-objective robust optimization model. Flood control scheduling refers to fully utilizing the functions of flood control projects such as reservoirs to change flood characteristics, reduce flood peaks, store and retain flood water, extend flood propagation time, and minimize flood disasters. Under the influence of real-time flood forecast error disturbances, this model specifically includes the following four objectives:

[0130] Objective 1: The maximum risk rate of the reservoir water level exceeding the water level safety threshold is minimized (upstream flood control risk rate);

[0131] In the face of a set of real-time flood forecast inflow scenarios, the maximum probability of the simulated reservoir water level exceeding the set threshold is minimized. This goal reflects the role of resisting the risk of exceeding the water level safety threshold upstream of the reservoir caused by flood forecast errors.

[0132] It is expressed as formula (6).

[0133]

[0134] Among them, F1 is That is, the maximum risk rate of the reservoir water level exceeding the water level safety threshold, For real-time flood control and flood forecasting, the reservoir water level (m) at each moment under each inflow scenario simulated by this model is: sa is the reservoir water level safety threshold (m), T is the duration of the scheduling plan period (h), and Prob(·) is the frequency statistical function.

[0135] Objective 2: Minimize the maximum risk rate of reservoir discharge exceeding the downstream safe discharge volume (downstream flood control risk rate);

[0136] In the face of the real-time flood forecast inflow scenario set, the maximum probability of the simulated reservoir discharge exceeding the set threshold is minimized. This goal reflects the effect of resisting the risk of the reservoir discharge exceeding the downstream safety control value caused by flood forecast errors. This goal can be expressed by formula (7).

[0137]

[0138] Among them, F2 is That is, the maximum risk rate of reservoir discharge exceeding the downstream safe discharge, In order to face the real-time flood forecast inflow scenario set, the reservoir discharge process (m 3 / s), Qsa For the downstream safety control flow threshold (m 3 / s).

[0139] Objective 3: The conditional value at risk of the reservoir flood control storage ratio is minimized (upstream risk loss);

[0140] This model selects the ratio of the reservoir storage capacity process during flood control operation to the flood control storage capacity as an approximation of the upstream risk loss of the reservoir. Equation (8) shows the calculation function of the upstream flood control loss of the reservoir

[0141]

[0142] where f z～v (·) is the reservoir water level - storage capacity curve, Z is the flood - limit water level (m), and V pro is the flood - control storage capacity of the reservoir (m 3 ).

[0143] Based on the form of the upstream loss function, this objective can be expressed by Equation (9).

[0144]

[0145] where F3 is that is, the conditional value at risk of the maximum ratio of the reservoir flood - control storage capacity, is the conditional value at risk corresponding to the upstream flood - control loss calculation function shown in Equation (4), and α is the confidence level (dimensionless). This objective reflects the role of reducing the upstream inundation loss of the reservoir caused by flood - forecast errors.

[0146] Objective 4: The conditional value at risk of the maximum ratio of reservoir discharge is minimized (downstream risk loss);

[0147] This model selects the ratio of the reservoir discharge to the downstream safe discharge as an approximation of the downstream risk loss of the reservoir. Equation (10) shows the flood - control loss function of the reservoir downstream

[0148]

[0149] where Qs is the identification (warning) water level (m) of the downstream flood - control loss.

[0150] Based on the form of the downstream loss function, this objective can be expressed by Equation (11).

[0151]

[0152] where F4 is that is, the conditional value at risk of the maximum ratio of reservoir discharge, It is the conditional value at risk corresponding to the downstream flood control loss function shown in Equation (4). This objective reflects the role of reducing the inundation loss downstream of the reservoir caused by flood forecasting errors.

[0153] The above four objectives constitute the optimization objective library of the multi-objective robust optimization model for reservoir flood control operation. Based on this, the established flood control model can achieve dual effective control of the loss and occurrence probability of reservoir flood control risk under uncertain forecasts, thereby improving the robust performance of the reservoir flood control operation process against the impact of real-time forecast errors.

[0154] S23. For the set of real-time flood control flood forecast inflow scenarios simulated in step S1, in combination with the optimization objective library of the model established in step S22, establish the constraint condition library of the multi-objective robust optimization model for reservoir flood control operation.

[0155] Constraint 1: Water balance constraint;

[0156] The water balance constraint controls the total water volume of the reservoir to remain consistent during iterative simulations in each time period, that is, the mass conservation constraint. The water balance constraint used in this model is expressed by Equation (12).

[0157]

[0158] Among them, is the set of reservoir inflow forecast processes (m 3 / s), is the reservoir storage at time t (m 3 ), and △t is the calculation step size (h).

[0159] Constraint 2: Storage limit constraint;

[0160] The storage limit constraint controls the reservoir storage during simulation operation not to exceed or be lower than the allowable upper and lower limits of storage. The storage limit constraint used in this model is expressed by Equation (13).

[0161]

[0162] Among them, V and are respectively the lower and upper limits of the allowable storage during reservoir operation (m 3 ).

[0163] Constraint 3: Discharge limit constraint;

[0164] The discharge limit constraint controls the discharge of the reservoir during model operation not to exceed or be lower than the allowable upper and lower limits of discharge. This constraint can take into account the downstream ecological and domestic water demands and protect the safety of the downstream river channel to a certain extent. The storage limit constraint used in this model is expressed by Equation (14).

[0165]

[0166] Among them, and are respectively the lower and upper limits of the allowable discharge of the reservoir (m 3 / s).

[0167] Constraint 4: Discharge variation limit constraint;

[0168] The discharge variation limit constraint is to protect the safety of the downstream waterway and the slope stability. Because excessive discharge fluctuations during flood control scheduling may cause stranding of ships navigating in the downstream river or landslides, the discharge variation limit constraint used in this model is expressed by Equation (15).

[0169]

[0170] Among them, ΔQ is the upper limit of the allowable variation of the reservoir's discharge between periods (m 3 / s).

[0171] Constraint 5: Initial and boundary condition constraints

[0172] The initial and boundary condition constraints used in this model can be expressed by Equation (16).

[0173]

[0174] Among them, Z ini is the initial water level (m), generally set as the flood limit water level, V obj is the target storage volume at the end of the period (m 3 ), and this value can be flexibly changed in combination with the decision-maker's risk preference and the expected forecast inflow process and the post-flood operation benefit of the project.

[0175] S24. Solve the established multi-objective robust optimization model of reservoir flood control scheduling by using the evolutionary multi-objective optimization algorithm NSGA-III based on the reference point-based non-dominated sorting method to generate a set of non-inferior solutions that meet different risk flood control requirements.

[0176] S3. Multi-attribute risk decision-making under uncertainty: For different decision-making preferences, introduce different weight parameters and use the TOPSIS method to obtain the optimal equilibrium solutions under different preferences.

[0177] This model uses TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) for risk decision-making, and decision-makers can select a coordinated equilibrium solution according to their own knowledge and preferences. The TOPSIS method is a classic method in the field of decision-making, which can comprehensively consider multiple information such as decision-makers' weight preferences for different objective criteria and expected ideal solutions; it is a multi-criteria decision-making method based on the concepts of ideal point and anti-ideal point, where the equilibrium solution is considered to be the solution with the weighted distance closest to the ideal point and farthest from the anti-ideal point. The present invention selects the equilibrium solution under different scenarios based on the TOPSIS method, and simulates the preference solution of decision-makers in the actual decision-making process by setting different weight values.

[0178] Specifically, it includes the following steps:

[0179] S31. Establish a decision matrix, where each decision variable in the decision matrix is the optimized objective value of each alternative solution, as shown in Equation (17).

[0180]

[0181] Among them, x (i,j) is the jth decision variable (dimensionless) in the ith evaluation solution, is the jth optimized objective value (dimensionless) of the ith evaluation solution, I is the total number of alternative solutions (dimensionless), and J is the number of optimization objectives (dimensionless).

[0182] S32. Standardize the decision matrix, and the standardization method is as shown in Equation (18).

[0183]

[0184] Among them, norx (i,j) is the standardized decision variable (dimensionless).

[0185] S33. Construct a weighted value decision matrix, and the weighting method is as shown in (19).

[0186] wx (i,j) = w j ·norx (i,j) (19);

[0187] Among them, wx (i,j) is the weighted attribute value (dimensionless), and w j is the weight of the jth index (dimensionless).

[0188] S34. Determine the positive and negative ideal solutions The calculation method is as shown in Equation (20).

[0189]

[0190] Among them, are the positive ideal solution and the negative ideal solution of the j-th index, respectively.

[0191] S35. Calculate the Euclidean distances of each evaluation scheme from the positive and negative ideal solutions. The calculation method is shown in Equation (21).

[0192]

[0193] Among them, and are the Euclidean distances (dimensionless) of the i-th evaluation scheme from the positive and negative ideal solutions, respectively.

[0194] S36. Calculate the fitness degree of each evaluation scheme from the ideal scheme. The calculation method is shown in Equation (22).

[0195]

[0196] Among them, clo i is the fitness degree (dimensionless) of the i-th scheme. Select the scheme with the highest fitness degree among all schemes as the final equilibrium scheme of the TOPSIS method. Different equilibrium schemes can be generated under different decision preference weights for the reservoir flood control decision-makers to choose.

[0197] The decision-maker can select the equilibrium solution that meets the decision preference from the non-inferior solutions. Such equilibrium solutions can satisfy the dual control of the reservoir on flood control risk loss and occurrence probability (as Figure 4 shown).

Claims

1. A real-time flood control multi-objective robust optimization regulation method for reservoirs against flood forecast error disturbances, characterized in that It includes the following steps: S1. Collect and organize the flood forecast error samples in the reservoir system database, and use the Monte Carlo method to randomly sample to generate a set of pre-real-time flood control flood forecast error scenarios; superimpose the generated forecast error scenarios on the mean process of the forecast inflow to obtain the simulated forecast inflow scenarios, which are used as the input conditions for the reservoir real-time flood control multi-objective robust optimization model. S2. Establish a multi-objective robust optimization model for reservoir flood control operation: Use the conditional value-at-risk of the upstream and downstream flood control risk rates and the upstream and downstream flood control risk loss indicators as the optimization objectives to generate a set of non-dominated solutions of the multi-objective robust optimization that can resist different probabilities and degrees of risks, including the following steps: S21. Introduce a robustness index of conditional value-at-risk to evaluate the possible risk losses of the reservoir in the face of adverse scenarios. The flood control loss function is represented by L, and the conditional value-at-risk of the reservoir flood control risk loss is represented by Equations (1) and (2): VaR α (L) = min{cdf(L) ≥ α} (2); where α is the confidence level, α ∈ [0, 1], and CVaR α (L) is the conditional value at risk of the reservoir risk loss at the confidence level α, and VaR α (L) is the minimum risk loss at the confidence level α, pdf(·) is the probability density function, and cdf(·) is the cumulative probability function; S22. For the set of real-time flood control flood forecast inflow scenarios simulated in step S1, establish an optimization objective library for the reservoir flood control operation multi-objective robust optimization model. S23. For the set of real-time flood control flood forecast inflow scenarios simulated in step S1, and in conjunction with the optimization objective library of the model established in step S22, establish a constraint condition library for the reservoir flood control operation multi-objective robust optimization model. S24. Use the evolutionary multi-objective optimization algorithm NSGA-III based on the reference point non-dominated sorting method to solve the established reservoir flood control operation multi-objective robust optimization model, and generate a set of non-dominated solutions that meet different risk flood control requirements. S3. Multi-attribute risk decision-making under uncertainty: For different decision-making preferences, introduce different weight parameters, and use the TOPSIS method to obtain the optimal equilibrium solutions under different preferences.

2. The real-time flood control multi-objective robust optimization regulation method for reservoirs that resists the disturbance of flood forecast errors according to claim 1, characterized in that, Step S1 includes the following steps: S11. Obtain several historical flood forecast samples and flood measured samples from the reservoir system database, and calculate the forecast errors for each lead time: Among them, ξ(τ) is the forecast error of the reservoir's forecast period of τ, and IN(t) is the actual inflow value at time t. is the forecast inflow at time t - τ for time t, and the forecast period is τ. S12. Use the t-copula function to characterize the flood forecast error characteristics and simulate to generate a set of real-time flood forecast error scenarios, and superimpose them on the mean forecast process to obtain a set of real-time flood control flood inflow scenarios.

3. The real-time flood control multi-objective robust optimal regulation method for reservoirs that resists the disturbance of flood forecast errors according to claim 2, characterized in that, Specifically, step S12 is as follows: S121. Establish the marginal distributions of the forecast errors for each lead time. Based on the univariate hydrological frequency method, establish the marginal distributions of the forecast errors. Select the commonly used marginal distributions in the field of hydrological analysis as candidates, use the maximum likelihood estimation method to determine the parameters of each marginal distribution and evaluate the fitting status, and select the optimal marginal distribution as the actual distribution. S122. Based on the t-copula function, establish the joint distribution of the forecast errors for different lead times. The form of the joint distribution function of the forecast errors is as follows: Among them, Cor is the correlation coefficient matrix of variables u1…u n , u is the variable matrix, v is the degree of freedom, n is the number of variables, Γ(·) is the Gamma function, u1 is the cumulative distribution function of the first random variable, u n is the cumulative distribution function of the nth variable, and x is the parameter integration vector; S123. Generate a set of real-time flood control flood forecast inflow scenarios. According to the established joint distribution of the forecast errors and the optimal marginal distribution as the actual distribution, use the Monte Carlo method to randomly sample to generate a set of pre-real-time flood control flood forecast error scenarios; superimpose the generated forecast error scenarios on the mean process of the forecast inflow to obtain the simulated forecast inflow scenarios, as shown in Equation (5): Among them, is the mean process of the predicted inflow at time t, ξs(τ) is the simulated prediction error scenario with a lead time of τ, and INs(t-τ,t) is the predicted inflow scenario with a lead time of τ at time t-τ; the predicted inflow process sets INs(t,t+1), INs(t,t+2), …, INs(t,t+T) with different lead times 1, 2, …, T generated from the same initial forecasting time t are abbreviated as INs(t+1), INs(t+2), …, INs(t+T); the real-time flood forecasting inflow scenario set has the same initial forecasting time and the same lead time length.

4. The real-time flood control multi-objective robust optimal regulation method for reservoirs against flood forecast error disturbances according to claim 1, characterized in that In step S22, under the influence of the disturbance of real-time flood forecasting error, the optimization objective library includes: Objective 1: Minimize the maximum risk rate that the reservoir water level exceeds the water level safety threshold; Facing the real-time flood control flood forecasting inflow scenario set, minimize the maximum probability that the simulated reservoir water level exceeds the set threshold; this objective reflects the role of resisting the risk that the upstream of the reservoir exceeds the water level safety threshold caused by flood forecasting error; expressed by Equation (6): Among them, represents the maximum risk rate when the reservoir water level exceeds the water level safety threshold; is the reservoir water level at each moment under each inflow scenario simulated by this model for the real-time flood control flood forecast inflow scenario, Z sa is the reservoir water level safety threshold, T is the duration of the scheduling plan period, and Prob(·) is the frequency statistical function; Objective 2: Minimize the maximum risk rate that the reservoir discharge exceeds the downstream safety discharge; Facing the real-time flood control flood forecasting inflow scenario set, minimize the maximum probability that the simulated reservoir discharge exceeds the set threshold; this objective reflects the effect of resisting the risk that the downstream of the reservoir has a discharge exceeding the downstream safety control value caused by flood forecasting error; this objective is expressed by Equation (7): Among them, represents the maximum risk rate of the reservoir discharge exceeding the downstream safe discharge capacity; is the reservoir discharge process under each inflow scenario simulated by this model for the real-time flood control flood forecast inflow scenario set, Q sa is the downstream safety control flow threshold; Objective 3: Minimize the conditional value at risk of the maximum proportion of the reservoir flood control storage capacity; This model selects the proportion of the reservoir storage capacity process during flood control operation in the flood control storage capacity as an approximation of the risk loss upstream of the reservoir. Equation (8) shows the calculation function for the flood control loss upstream of the reservoir. Among them, f z～v (·) is the reservoir water level - storage capacity curve, Z is the flood - limit water level, V pro is the flood - control storage capacity of the reservoir; Based on the form of the upstream loss function, this objective is expressed by Equation (9): Among them, represents the conditional value at risk with the largest proportion of the flood control storage capacity of the reservoir; is the conditional value at risk corresponding to the upstream flood control loss calculation function shown in Equation (4), α is the confidence level, and this goal reflects the role of reducing the submerged loss upstream of the reservoir caused by flood forecast errors; Objective 4: Minimize the conditional value at risk of the maximum proportion of the reservoir discharge; This model selects the ratio of the reservoir discharge to the downstream safe discharge as an approximation of the risk loss downstream of the reservoir. Equation (10) shows the flood control loss function downstream of the reservoir. Among them, Qs is the recognition water level of downstream flood control losses; Based on the form of the downstream loss function, this objective is expressed by Equation (11): Among them, represents the maximum conditional value at risk of the reservoir discharge ratio, is the conditional value at risk corresponding to the downstream flood control loss function shown in Equation (4), and this objective reflects the role of reducing the inundation loss downstream of the reservoir caused by flood forecast errors; The above 4 objectives constitute the optimization objective library of the multi-objective robust optimization model for reservoir flood control operation.

5. The real-time flood control multi-objective robust optimization regulation method for reservoirs against flood forecast error disturbances according to claim 1, characterized in that In step S23, the constraint condition library includes: Constraint 1: Water balance constraint; The water balance constraint controls the total water volume of the reservoir to remain consistent during iterative simulation in each time period, that is, the mass conservation constraint. The water balance constraint used in this model is expressed by Equation (12): Among them, is the reservoir inflow forecast process set, is the reservoir storage at time t, and △t is the calculation step size; Constraint 2: Storage capacity limit constraint; The storage capacity limit constraint controls that the reservoir storage capacity does not exceed or is lower than the allowable upper and lower limits of the storage capacity during the simulation operation. The storage capacity limit constraint used in this model is expressed by Equation (13): wherein, V and are respectively the lower limit and the upper limit of the allowable storage volume during the operation of the reservoir; Constraint 3: Discharge limit constraint; The discharge limit constraint controls that the reservoir discharge does not exceed or is lower than the allowable upper and lower limits of the discharge during the model operation. This constraint can take into account the downstream ecological and domestic water demands and protect the safety of the downstream river channel to a certain extent. The storage capacity limit constraint used in this model is expressed by Equation (14): wherein, Q and are respectively the lower limit and the upper limit of the allowable discharge of the reservoir; Constraint 4: Discharge variation range limit constraint; The discharge variation range limit constraint is to protect the safety of the downstream waterway and slope stability. The discharge variation range limit constraint used in this model is expressed by Equation (15): where, ΔQ is the upper limit of the allowable discharge variation of the reservoir between each time period; Constraint 5: Initial and boundary condition constraints; The initial and boundary condition constraints used in this model are expressed by Equation (16): Among them, Z ini is the initial water level, and V obj is the target storage volume at the end.

6. The real-time flood control multi-objective robust optimal regulation method for a reservoir against flood forecast error disturbances according to claim 1, characterized in that Step S3 includes the following steps: S31. Establish a decision matrix, and each decision variable in the decision matrix is the optimization objective value of each alternative plan, as shown in Equation (17): where x (i,j) is the j-th decision variable in the i-th evaluation scheme, is the j-th optimization objective value of the i-th evaluation scheme, I is the total number of alternative schemes, and J is the number of optimization objectives; S32. Standardize the decision matrix, and the standardization method is as shown in Equation (18): Among them, norx (i,j) is the standardized decision variable; S33. Construct a weighted value decision matrix, and the weighting method is as shown in (19): wx (i,j) = w j ·norx (i,j) (19); Among them, wx (i,j) is the weighted attribute value, and w j is the weight of the j-th index; S34. Determine the positive and negative ideal solutions The calculation method is as shown in Equation (20): wherein, are respectively the positive ideal solution and the negative ideal solution of the j-th index; S35. Calculate the Euclidean distances of each evaluation plan from the positive and negative ideal solutions, and the calculation method is as shown in Equation (21): Among them, and are the Euclidean distances of the i-th evaluation scheme from the positive and negative ideal solutions, respectively. S36. Calculate the fitness of each evaluation plan from the ideal plan, and the calculation method is as shown in Equation (22): where, clo i is the fitting degree of the i-th scheme. The scheme with the highest fitting degree value among all schemes is selected as the final equilibrium scheme of the TOPSIS method. Different equilibrium schemes are generated under different decision preference weights for the reservoir flood control decision-makers to choose from.

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