Water diversion project annual scheduling plan generation multi-agent evolutionary game method and system

Abstract

The application discloses a kind of water diversion engineering annual scheduling plan generation multi-agent evolutionary game method and system, collect research area data, research area is divided into water source area and water receiving area, and the water use plan strategy set of water receiving area is formulated;Three-dimensional joint distribution function of the current time water diversion quantity of water source area, the current time water inflow of water receiving area and the water inflow of water receiving area last time is constructed, and the random sample of the water diversion quantity and the water inflow process of water receiving area is generated;Water quantity scheduling model of water diversion engineering annual is constructed, and the water supply of each water receiving area is calculated;The expected income value of water receiving area is calculated;Water use plan strategy adjustment is carried out to water receiving area and iteration, until the probability of water receiving area selecting specific water use plan strategy approaches to 1, and the stable decision combination of the annual water use plan of water receiving area corresponding to random sample is obtained.The application obtains the stable strategy of annual water use plan of water receiving area under different water inflow conditions and uncertainty risk.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of water resources regulation, and relates to the generation decision of the annual regulation plan of water transfer projects, in particular to a multi-agent evolutionary game method and system for generating the annual regulation plan of water transfer projects. BACKGROUND

[0002] The annual water quantity regulation plan is a prerequisite for the operation of cross-regional and cross-basin water transfer projects. The goal of preparing the annual water quantity regulation plan is to develop a time-by-time water storage and supply plan based on the predicted inflow in the water source area and the water receiving area, the annual water use plan proposed by each water receiving area, and the regulation and storage function of the reservoirs along the project, so as to achieve timely and appropriate water allocation, reasonable allocation of water quantity between different regions and industries under different inflow conditions, and ultimately improve the water allocation efficiency and achieve the design water supply target of the water transfer project.

[0003] On the one hand, water transfer projects involve a wide range of regions, and the inflow in the water source area and the water receiving area is unevenly distributed, showing superimposed uncertainty, which brings the risk of deviation from the water supply plan target to the strict implementation of the annual water quantity regulation of the project. A reasonable regulation plan of the water transfer project should be developed under the premise of considering the double uncertainty of inflow to enhance the adaptability of the regulation operation to the risk and improve the water supply guarantee degree. On the other hand, the determination of the time-by-time water supply plan of the water transfer project is the result of the comprehensive balance of the water use demand of each water receiving area according to the annual water use plan proposal. Therefore, the water supply benefit obtained by the water receiving area and the water use cost borne by it are affected by the water use plan proposal of the water receiving area itself, and also related to the water use plan proposal of other water receiving areas. If the water receiving area is regarded as a decision-making agent representing the interests of different regions, the process of proposing the water use plan proposal by each water receiving area has a competitive game relationship, and the strategy for developing the annual water use plan of the water receiving area will be adjusted by referring to the actual water supply effect of the previous year, so it is an evolutionary game process.

[0004] In summary, modeling and analyzing the evolutionary game process of the annual water quantity regulation plan generation of the water transfer project under uncertainty conditions is helpful to optimize the determination of the stable strategy of the water use plan of the water receiving area which is adaptive to the uncertainty risk. The existing methods involve the analysis of the precipitation wet and dry encounters in the water source area and the water receiving area, the modeling of the joint water supply regulation under uncertainty conditions, the cooperative game of water resources allocation, etc., but there is still a lack of evolutionary game decision-making method and system for the water use plan proposal of the water receiving area under uncertainty conditions.

[0005] The present application proposes a multi-agent evolutionary game method and system for generating the annual regulation plan of water transfer projects, which solves the above-mentioned problems existing at present, and provides technical support for further research on water supply and demand balance, water price determination, market-oriented allocation of water rights, etc. in water network projects. SUMMARY

[0006] The application aims to provide a multi-agent evolutionary game method for generating an annual operation plan of a water diversion project to solve the above problems in the prior art. In another aspect, a multi-agent evolutionary game system for generating an annual operation plan of a water diversion project is provided.

[0007] Technical solution: The multi-agent evolutionary game method for generating an annual operation plan of a water diversion project comprises the following steps:

[0008] Collect data of a study area, divide the study area into a water source area and a water receiving area, and develop a set of water use planning strategies for the water receiving area;

[0009] Construct a three-dimensional joint distribution function of the current water diversion amount of the water source area, the current water inflow amount of the water receiving area, and the water inflow amount of the water receiving area at the previous time, generate random samples of the water diversion amount and the water inflow process of the water receiving area;

[0010] Extract the random samples and combine them with the water use planning strategies (selected from the set of water use planning strategies) of the water receiving area, input an annual water quantity operation plan compilation model of the water diversion project, and obtain the water supply amount of each water receiving area at each time period under the combination of the water use planning strategies;

[0011] Based on the water supply amount, generate a multi-objective benefit vector of the water receiving area under the combination of the water use planning strategies, calculate the comprehensive benefit value of the water receiving area, and calculate the expected benefit value of the water receiving area after traversing the combination of the water use planning strategies;

[0012] Adjust and iterate the water use planning strategies of the water receiving area until the probability of the water receiving area selecting a specific water use planning strategy approaches 1, and obtain the stable decision combination of the annual water use plan of the water receiving area corresponding to the random samples.

[0013] According to one aspect of the application, the adjustment and iteration of the water use planning strategies of the water receiving area comprises:

[0014] A dynamic equation containing a learning ability coefficient and a risk preference coefficient is used to calculate a risk-adjusted utility based on the expected benefit value of the water receiving area;

[0015] According to the difference between the risk-adjusted utility and the average expected benefit, the probability of the water receiving area selecting each water use planning strategy is updated in combination with the learning ability coefficient;

[0016] The strategy selection probability is iteratively updated until the probability of the water receiving area selecting a specific water use planning strategy approaches 1 and the probability of selecting other strategies approaches 0, and a stable decision combination is obtained.

[0017] According to one aspect of the application, the calculation of the risk-adjusted utility comprises:

[0018] The benefit variance of the water user area selection water plan strategy is calculated, the benefit variance is multiplied by a risk preference coefficient to obtain a risk adjustment term;

[0019] The expected benefit value is subtracted by the risk adjustment term to obtain a risk adjustment utility;

[0020] The probability of updating the water user area selection of each water plan strategy includes:

[0021] The difference between the risk adjustment utility and the average expected benefit of the water user area is calculated, the difference is multiplied by a learning ability coefficient and a current strategy selection probability to obtain a probability update amount, and the strategy selection probability is adjusted according to the probability update amount.

[0022] According to an aspect of the present application, the stable decision combination includes:

[0023] A convergence threshold of the strategy selection probability is set, when the probability of the water user area selecting a certain water plan strategy exceeds the convergence threshold, the strategy is determined as the stable strategy of the water user area;

[0024] After all the water user areas determine the stable strategy, a stable decision combination corresponding to the random sample is formed;

[0025] According to the annual water inflow level of the water user area of the random sample, the stable decision combination is classified into annual water plan strategies corresponding to wet years, normal years and dry years.

[0026] According to an aspect of the present application, the three-dimensional joint distribution function of the water source area current time water diversion amount, the water user area current time water inflow amount and the water user area last time water inflow amount includes:

[0027] The historical water diversion data of the water source area and the historical water inflow data of the water user area are extracted from the research area data, and the water source area water diversion amount edge distribution, the water user area current time water inflow amount edge distribution and the water user area last time water inflow amount edge distribution are fitted respectively;

[0028] A two-dimensional Copula function is used to construct the joint distribution of the water source area water diversion amount and the water user area current time water inflow amount, and the conditional distribution of the water user area current time water inflow amount under the given water source area water diversion amount is obtained;

[0029] Based on the conditional distribution, a conditional Copula function is used to connect the water user area last time water inflow amount, and a three-dimensional joint distribution function is constructed.

[0030] According to an aspect of the present application, the conditional Copula function connecting the water user area last time water inflow amount includes:

[0031] The edge distribution of water diversion amount of the water source area and the edge distribution of current time water inflow of the water receiving area are converted into uniform distribution, the Kendall rank correlation coefficient is calculated, and the parameters of the two-dimensional Copula function are determined;

[0032] The partial derivative of the two-dimensional Copula function is obtained, and the conditional distribution function of the current time water inflow of the water receiving area under the condition of the given water diversion amount of the water source area is obtained.

[0033] Based on the conditional distribution function and the edge distribution of the water inflow of the water receiving area at the previous time, the conditional Kendall rank correlation coefficient is calculated, the conditional Copula function parameters are determined, and the complete three-dimensional joint distribution is constructed.

[0034] According to one aspect of the present application, the generation of the random sample of the water inflow process of the water receiving area includes:

[0035] Based on the three-dimensional joint distribution function, an initial random number matrix is generated, and the rows represent time periods and the columns represent the water source area and the water receiving area.

[0036] The time series correlation matrix between adjacent months in the historical data is calculated, and the type association matrix between different water receiving areas is constructed.

[0037] The initial random number matrix is reordered according to the time series correlation matrix and the type association matrix by using the improved Latin hypercube sampling method, and a random sample that maintains the spatio-temporal correlation is generated.

[0038] According to one aspect of the present application, the calculation of the time series correlation matrix and the construction of the type association matrix include:

[0039] The water inflow sequence of each month in the historical data is extracted, the Pearson correlation coefficient between adjacent months is calculated, and a 12x12 time series correlation matrix is formed.

[0040] The spatial distance weight is calculated according to the geographical location of the water receiving area, and the type association matrix between the water receiving areas is constructed by combining the water supply feature similarity of the water receiving areas.

[0041] The time series correlation matrix and the type association matrix are respectively subjected to Cholesky decomposition to obtain lower triangular matrices, and the initial random number matrix is multiplied by the lower triangular matrices to realize the generation of random samples under the correlation constraint.

[0042] According to one aspect of the present application, the calculation of the comprehensive benefit value of the water receiving area includes:

[0043] Based on the water supply amount, the water supply guarantee target, the water use benefit target, the water transfer cost target and the fairness target of the water receiving area are calculated, a four-dimensional benefit vector is formed and normalized.

[0044] The water supply guarantee target is measured by a water supply guarantee rate, which is calculated as a ratio of a number of time periods satisfying water demand to a total number of time periods;

[0045] The water use benefit target is calculated by a weighted sum of benefits such as power generation and water supply;

[0046] The water transfer cost target is calculated by a product of an actual water supply amount and a water transfer cost coefficient;

[0047] The fairness target is measured by a difference between a water supply guarantee degree of the water receiving area and water supply guarantee degrees of other areas;

[0048] The multi-objective benefit vector set is Pareto non-dominantly sorted to determine non-dominant levels of each strategy combination, and a crowding distance is calculated in the same non-dominant level;

[0049] A strategy dispersion degree of the water use plan strategy combination is calculated, and a comprehensive benefit value is obtained by weighted combination of the non-dominant level, the crowding distance and the strategy dispersion degree.

[0050] According to an aspect of the present application, the calculation of the strategy dispersion degree comprises:

[0051] A frequency of occurrence of each strategy in the water use plan strategy combination is counted, a strategy distribution entropy is calculated, and a normalized strategy dispersion degree is obtained by dividing the strategy distribution entropy by a maximum possible entropy value;

[0052] A calculation formula of the comprehensive benefit value is that a reciprocal of the non-dominant level is taken as a level score, a normalized crowding distance is taken as a distance score, and the level score, the distance score and the strategy dispersion degree are respectively given weight coefficients a, b and c, and a weighted sum is taken to obtain the comprehensive benefit value.

[0053] According to an aspect of the present application, the generation of the random sample of the water receiving process of the water receiving area adopts a master-slave calculation method comprising:

[0054] From the three-dimensional joint distribution function, first, a uniform distribution random number of water transfer amount of the water source area is generated by inverse transformation sampling;

[0055] Based on the generated water transfer amount of the water source area, a current time water inflow amount of the water receiving area is generated by a conditional distribution function;

[0056] According to the water transfer amount of the water source area and the current time water inflow amount of the water receiving area, a last time water inflow amount of the water receiving area is generated by a conditional Copula function, and the uniform distribution random number is inversely transformed to the original variable space to form a random sample maintaining spatio-temporal correlation.

[0057] According to an aspect of the present application, further comprising classification processing of stable decision combinations:

[0058] According to the annual total amount of water in the water receiving area in the random sample, the stable decision combination is divided into three categories: wet year, normal year and dry year;

[0059] The frequency distribution of the water receiving area selecting each water plan strategy under each type of water condition is counted, and the strategy difference degree between different water conditions is calculated;

[0060] When the strategy difference degree exceeds the set threshold, the stable decision combination under different water conditions is stored as a classified scheduling plan respectively; otherwise, a unified stable decision combination is used as an annual scheduling plan.

[0061] According to an aspect of the present application, the improved Latin hypercube sampling method comprises:

[0062] The local weighted regression method is used to perform seasonal-trend decomposition on the historical water consumption sequence, to extract the trend item, the seasonal item and the residual item, and to determine the water consumption benchmark range of different months;

[0063] The ARIMA model is used to fit the time sequence relationship between the monthly water consumption, and a 12x12 time sequence correlation matrix is constructed;

[0064] The Pearson correlation coefficient of the same period and different types of water consumption is calculated, the Archimedean Copula function is used to fit the joint distribution for the weak linear correlation, and the inter-type association matrix is obtained;

[0065] The marginal distribution of each month-water type dimension is divided into N equal probability intervals, and N is the sampling sample size of the random strategy and N≥50;

[0066] The first month is taken as the benchmark to randomly sample from N layers, and the sampling layer of the subsequent months is constrained according to the time sequence correlation matrix, to ensure the dependence of the sample of each month on the previous months;

[0067] The current association matrix of the sample of different types of water in each month is calculated, and when the association deviation from the inter-type association matrix is greater than 5%, the Cholesky decomposition is used to embed the target association matrix into the sample for correction.

[0068] According to another aspect of the present application, a water diversion project annual scheduling plan generation multi-agent evolutionary game system is provided, comprising:

[0069] At least one processor; and

[0070] The memory is in communication connection with the at least one processor; wherein,

[0071] The memory stores instructions executable by the processor, and the instructions are executed by the processor to implement the water diversion project annual scheduling plan generation multi-agent evolutionary game method of any one of the above technical solutions.

[0072] Beneficial effects: the water diversion project annual scheduling plan generation multi-agent evolutionary game method can reflect the dynamic game relationship of different water receiving areas in the process of proposing annual water plan suggestions, and conforms to the actual situation of multi-stakeholder participation in decision-making of cross-regional and cross-basin water diversion management; the water diversion evolutionary game decision model is solved by optimizing on the basis of random samples of water diversion in the water source area and incoming water in the water receiving area, which is helpful to obtain the stable strategy of the water receiving area in formulating annual water plan under different incoming water conditions and uncertainty risks, achieve the comprehensive balance between water supply benefit and water cost of the water receiving area, and more effectively guarantee the realization of water supply benefit of the water diversion project. BRIEF DESCRIPTION OF DRAWINGS

[0073] Figure 1 is a flowchart of the present application.

[0074] Figure 2 is a flowchart of the present application provided for adjusting and iterating the water plan strategy of the water receiving area.

[0075] Figure 3 is a flowchart of the present application provided for constructing a three-dimensional joint distribution function of the current time water diversion amount of the water source area, the current time incoming water amount of the water receiving area and the last time incoming water amount of the water receiving area.

[0076] Figure 4 is a flowchart of the present application provided for generating random samples of the water diversion amount and the water receiving area incoming water process.

[0077] Figure 5 is a flowchart of the present application provided for calculating the comprehensive benefit value of the water receiving area.

[0078] Figure 6 is a flowchart of the present application provided for classification processing of stable decision combination. DETAILED DESCRIPTION

[0079] As shown in Figure 1 , the following technical solutions are proposed. According to one aspect of the present application, a water diversion project annual scheduling plan generation multi-agent evolutionary game method is provided, characterized in that it comprises the following steps:

[0080] Collecting research area data, dividing the research area into a water source area and a water receiving area, and formulating a water plan strategy set of the water receiving area;

[0081] Constructing a three-dimensional joint distribution function of the current time water diversion amount of the water source area, the current time incoming water amount of the water receiving area and the last time incoming water amount of the water receiving area, and generating random samples of the water diversion amount and the water receiving area incoming water process;

[0082] The random sample is extracted and combined with the water use plan strategy of the water receiving area, input into the water transfer project annual water quantity scheduling plan compilation model, and the water supply quantity of each time period and each water receiving area under the combination of the water use plan strategy is obtained;

[0083] Based on the water supply quantity, a multi-objective income vector of the water receiving area under the combination of the water use plan strategy is generated, the comprehensive income value of the water receiving area is calculated, and the expected income value of the water receiving area after traversing the combination of the water use plan strategy is calculated;

[0084] The water use plan strategy of the water receiving area is adjusted and iterated until the probability of the water receiving area selecting a specific water use plan strategy tends to 1, and the stable decision combination of the annual water use plan of the water receiving area corresponding to the random sample is obtained.

[0085] The embodiment provides a water transfer project annual scheduling plan generation multi-agent evolutionary game method, which is used for solving the annual water use plan decision problem of the water transfer project under uncertainty.

[0086] Data of a research area is collected, the research area is divided into a water source area and a water receiving area, and a water use plan strategy set of the water receiving area is formulated; a three-dimensional joint distribution function of current time water diversion quantity of the water source area, current time water inflow quantity of the water receiving area and last time water inflow quantity of the water receiving area is constructed, and random samples of the water diversion quantity and the water inflow process of the water receiving area are generated.

[0087] In the embodiment, the research area refers to the entire water supply area covered by the water transfer project, including a water source area for water diversion and a water receiving area for receiving water diversion. The water source area is usually a river, lake or reservoir with relatively abundant water resources, and the water receiving area is a water shortage area, which can be divided into an upper reservoir water receiving area, a reservoir direct supply area and a lower reservoir water receiving area according to geographical location and water supply characteristics. The water use plan strategy set refers to a set of annual water use schemes that can be selected by each water receiving area, each strategy including monthly water use quantity of 12 months, covering four types of water use, i.e. life, industry, agriculture and ecology. The three-dimensional joint distribution function is used to describe the correlation of water diversion quantity of the water source area and water inflow quantity of the water receiving area in time and space. The random samples generated through the distribution function can reflect the uncertainty characteristics of water inflow.

[0088] The water use plan of the water receiving area is formulated based on water use quantity historical records, and the monthly plan water use quantity has time sequence correlation. In view of the above characteristics, the present application proposes an improved Latin hypercube sampling method driven by big data and coupled with time sequence to generate the water use plan strategy set of the water receiving area. Compared with the conventional Latin hypercube sampling method, the method can highlight the advantages of high sampling efficiency and good coverage of high-dimensional variables, and can generate a monthly water use plan strategy set that is closer to the actual situation and meets the time sequence correlation through the anchoring embedding of historical data, thereby providing high-quality input samples for evolutionary game decision.

[0089] In a certain embodiment, specifically:

[0090] Based on the actual demand of the water diversion project in the receiving area, 10 years of monthly scale historical data of domestic, industrial, agricultural irrigation and ecological water, as well as hydro-meteorological, local water resources availability, related engineering, population economic and social data are collected, the missing values are completed by time series interpolation method, and a three-dimensional database is established according to the receiving area-month-water type;

[0091] For a single water type, the seasonal-trend decomposition of locally weighted regression (STL) is used to decompose the water sequence, extract the trend item, seasonal item and residual item, and determine the water benchmark range in different months. The ARIMA model is used to fit the time series relationship between monthly water consumption, and the time series correlation matrix of 12 months is obtained. For different water types of life, industry, agriculture and ecology, the Pearson correlation coefficient of water consumption of different types in the same period is calculated, and the Archimedean Copula function is used to fit the joint distribution of linear correlation, and the correlation matrix between types is obtained. Kernel density estimation (KDE) or parameter distribution fitting is used to fit the marginal distribution of 48-dimensional month-water type combination, and KS test (p>0.05) is used;

[0092] Determine the sample size N of the random strategy (N is greater than 50), and divide the marginal distribution of each month-water type dimension into N equal probability intervals; Take January as the benchmark, randomly sample from N stratification, and sample the next month according to the time series correlation matrix constraint to ensure the dependence of each month's sample on the previous month, and obtain the initial sampling matrix of 12 months x 4 types of water; For different types of water samples in each month, calculate their current correlation matrix and compare it with the inter-type correlation matrix. If the correlation deviation is >5%, use Cholesky decomposition to embed the target correlation matrix into the sample for correction;

[0093] According to the annual total water consumption control index constraint, water balance constraint, engineering water supply capacity constraint, ecological discharge constraint, water supply priority constraint, engineering operation stability constraint and other constraint conditions required by the operation of the water diversion project, the generated strategy is verified one by one, and the invalid strategy is removed, and the sampling is supplemented until the number of feasible strategies reaches N, forming a candidate strategy set;

[0094] The candidate strategy set is verified in three aspects of distribution consistency (KS test), time series rationality (comparison of candidate set and historical data ACF error ≤10%), and scenario diversity (the minimum Euclidean distance between samples is not less than the set threshold). If the distribution consistency and time series rationality verification do not pass, return to adjust the fitting of the time series correlation matrix and the inter-type correlation matrix, and if the diversity is insufficient, increase the sampling size or adjust the stratification interval, and regenerate the strategy set.

[0095] The random sample is extracted and combined with the water use plan strategy of the water receiving area, input into the water transfer project annual water quantity scheduling plan compilation model, to obtain the water supply quantity of each time period and each water receiving area under the water use plan strategy combination.

[0096] Specifically, each water receiving area independently selects a water use plan strategy from its strategy set to form a strategy combination. The water transfer project annual water quantity scheduling plan compilation model determines the actual water supply quantity of each time period to each water receiving area according to the water source area water diversion capacity, water receiving area inflow quantity, water use plan demand and engineering constraint conditions. The model considers multiple constraint conditions such as water balance constraint, engineering water supply capacity constraint, ecological discharge constraint and water supply priority constraint.

[0097] The decision variables include: W _supply (i, t, k) represents the water supply quantity of the t time period to the i th water receiving area k type water use; S _res (j, t) represents the storage quantity of the j th reservoir at the end of the t time period; Q channel (l, t) represents the water conveyance flow of the l th water conveyance channel at the t time period; W _spill (j, t) represents the abandoned water quantity of the j th reservoir at the t time period;

[0098] The main objective function is to minimize the total water shortage: minF1=Σ t Σ i Σ k [D(i, t, k)-W _supply (i, t, k)], wherein D(i, t, k) is the water use demand;

[0099] The secondary objectives include: minimizing the water supply imbalance degree F2=Σ t Σ i [(W _supply (i, t) / D(i, t)-W avg / D avg ) 2 ]; wherein W _supply (i, t) is the water supply quantity of the t time period to the i th water receiving area; D(i, t) is the water use demand of the i th water receiving area at the t time period; Q channel (l, t) represents the water conveyance flow of the l th water conveyance channel at the t time period; W avg / D avg is the ratio of the total water supply quantity of all water receiving areas to the total water use demand; minimizing the water transfer cost F3=Σ t Σ _l C unit (l)×Q channel (l, t)×Δt, wherein C unit (l) is the unit water transfer cost; maximizing the reservoir storage quantity at the end of the year F_4=Σ j S_res (j, t) end );

[0100] The multi-objective is handled by hierarchical sequence method, and the optimization is carried out according to the priority: firstly, the basic water supply demand is ensured, then the fairness is considered, and finally the economy is optimized.

[0101] Water balance constraint: for reservoir j, S _res (j, t) = S _res (j, t-1) + I natural (j, t) + I transfer (j, t) - O _supply (j, t) - O ecology (j, t) - E(j, t) - W _spill (j, t), where I natural is natural inflow, I transfer is the amount of water transferred in, O _supply is the amount of water supplied, O ecology is the amount of ecological discharge, and E is evaporation loss;

[0102] Reservoir storage capacity constraint: S dead (j) ≤ S_res(j, t) ≤ S normal (j), where S dead is dead storage, and S normal is the storage capacity corresponding to the normal water level. During special periods, it can be temporarily over-stored to S _flood , which is the storage capacity corresponding to the flood control water level;

[0103] Channel water delivery capacity constraint: 0 ≤ Q channel (l, t) ≤ Q max (l) × η(l, t), where Q max (l) is the designed water delivery capacity, and η(l, t) is the time-varying water delivery efficiency coefficient, considering factors such as channel maintenance and ice period, generally taking 0.85-0.95;

[0104] Ecological flow constraint: Q ecology (j, t) ≥ max(Q eco-min (j), β × Q natural (j, t)), where Q eco-min is the minimum ecological flow, and β is the ecological flow proportionality coefficient, usually taking 0.1-0.2;

[0105] Water supply priority constraint: when the water quantity is insufficient, water is supplied according to the priority order, and the priority coefficient ω(k) is defined: domestic water ω(1) = 1.0, industrial water ω(2) = 0.9, ecological water ω(3) = 0.7, and agricultural water ω(4) = 0.5. The actual water supply rate satisfies: W _supply (i, t, k) / D(i, t, k) ≥ ω(k) × W_supply (i, t, k') / D(i, t, k'), when ω(k) > ω(k').

[0106] Linearize the nonlinear constraints, for evaporation loss E(j, t) = e _rate (t) x A(S _res (j, t)), where A is the water surface area of the reservoir; adopt piecewise linearization: divide the storage interval [S min , S max ] into K segments, and approximate the water surface area-storage relationship with a linear function in each segment, and introduce 0-1 variable δ(j, t, k) to represent that the storage falls in the kth segment, satisfying Σ k δ(j, t, k) = 1.

[0107] Solve using the branch and bound algorithm, set the solution precision ε = 0.01, the maximum number of iterations N max = 10000, and the initial solution is obtained using the greedy algorithm: sort according to priority and economy, and sequentially satisfy each demand until the water is exhausted;

[0108] In some optional embodiments, the dynamic programming method can be used to solve the problem, which divides the problem into T stages, the state variable is the storage of each reservoir, the decision variable is the water supply and water transfer, and the state transition equation is: V t (S t ) = min{C t (S t , U t ) + V t+1 (S t+1 )}, where V t is the optimal value function at t period, C t is the current cost, and U t is the decision variable set;

[0109] Further, the stochastic optimization can be introduced to deal with uncertainty, the future water quantity is regarded as a random variable, the scene tree method is used to describe the uncertainty evolution, and the objective function is modified to the expected value form: min E[F(x, ξ)], where ξ is a random variable, and the L-shaped algorithm or the progressive hedging algorithm is used to solve the two-stage stochastic programming problem.

[0110] Test whether all constraint conditions are strictly satisfied, and the allowable error range is 0.1%, for the solution that violates the constraints, correct it by local adjustment: preferentially adjust the water abandonment and non-critical water supply, and keep the critical water unchanged;

[0111] Calculate the water supply guarantee rate index: P _guarantee (i, k) = Σ t I(W _supply(i, t, k) ≥ a x (D(i, t, k)) / T, wherein I(·) is an indicator function, a is a rate threshold, generally 0.9-0.95, the life and industrial water guarantee rate should be not less than 95%, and the agricultural water guarantee rate should be not less than 75%;

[0112] Output the complete scheduling scheme, including: the storage and release process of each reservoir in each period; the water delivery process of each channel; the water supply process of each water receiving area; and key index summary (total water supply, water shortage, guarantee rate, etc.), which is the optimal scheduling result under the given strategy combination, and provides basic data for subsequent benefit calculation.

[0113] Based on the water supply, a multi-objective benefit vector of the water receiving area under the water use plan strategy combination is generated, the comprehensive benefit value of the water receiving area is calculated, and the expected benefit value of the water receiving area is calculated after traversing the water use plan strategy combination.

[0114] The multi-objective benefit vector includes four dimensions: the water supply guarantee target reflects the water supply reliability, and is measured by the water supply guarantee rate; the water use benefit target reflects the economic benefit, and is calculated by the weighted sum of power generation, water supply and other beneficial effects; the water transfer cost target reflects the economic cost, and is calculated by the product of the actual water supply and the water transfer cost coefficient; and the fairness target reflects the regional balance, and is measured by the difference between the water supply guarantee degree of the water receiving area and other areas. The comprehensive benefit value is calculated by using the Pareto non-dominated sorting method, which avoids the influence of subjective weight setting, and the expected benefit value is the average benefit obtained by the water receiving area under all possible strategy combinations.

[0115] The water use plan strategy of the water receiving area is adjusted and iterated until the probability of the water receiving area selecting a specific water use plan strategy approaches 1, and the stable decision combination of the annual water use plan of the water receiving area corresponding to the random sample is obtained.

[0116] In the embodiment, the strategy adjustment is realized by copying the dynamic equation, simulating the evolution process of the strategy selection probability of the water receiving area according to the historical benefit, and increasing the probability of selecting the strategy when the benefit of the strategy is higher than the average expected benefit, and vice versa. Through multiple iterations, each water receiving area will converge to a stable strategy, forming a stable decision combination in the Nash equilibrium state, which represents the equilibrium state reached by each water receiving area after mutual game under the given water inflow condition.

[0117] Through the above steps, the evolutionary game decision of the annual water use plan of the water transfer project under the uncertainty condition is realized, the stable decision combination obtained considers the uncertainty of water inflow and reflects the interest game relationship between different water receiving areas, and a scientific basis is provided for the actual operation and management of the water transfer project.

[0118] For example, Figure 2As shown, according to one aspect of the present application, the water-receiving area water plan strategy adjustment and iteration includes:

[0119] A replication dynamic equation containing a learning ability coefficient and a risk preference coefficient is adopted to calculate a risk-adjusted utility based on the expected income value of the water-receiving area;

[0120] According to the difference between the risk-adjusted utility and the average expected income, the learning ability coefficient is combined to update the probability of the water-receiving area selecting each water plan strategy;

[0121] The strategy selection probability is iteratively updated until the probability of the water-receiving area selecting a specific water plan strategy approaches 1 and the probability of other strategies approaches 0, and a stable decision combination is obtained.

[0122] In some embodiments, specifically:

[0123] The strategy probability distribution of each water-receiving area is initialized, assuming that area i has n i selectable strategies, the initial probability vector p i (0) = [p i，1 (0), p i，2 (0),..., p i，ni (0)] is adopted, and a uniform distribution p i，j (0) = 1 / n i is used to represent that the probability of each strategy being selected at the initial stage is equal. A small perturbation ε j ~ N(0, σε2) is introduced, where σε= 0.01, so that the initial probability is p i，j (0) = (1 + ε j ) / n i , and normalization is performed to ensure that Σ j p i，j = 1.

[0124] The expected income of area i selecting strategy j is: π i，j (t) = Σ_{k≠i}Σ_{s k}p k ,s k (t) × V i (j, s_ -i ), where p k , s k (t) is the probability of area k selecting strategy s k at time t, and V i (j, s_ -i ) is the income when area i selects strategy j and other areas select strategy combination s_ -i .

[0125] The average expected income of area i is: π i (t) = Σ_ jp i，j (t)×π i，j (t);

[0126] The replication dynamic equation is: dp i，j / dt=p i，j (t)×[π i，j (t)-π¯ i (t)], which shows that when the return of strategy j is higher than the average return, the probability of its selection increases; otherwise, it decreases. The discrete form is: p i，j (t+1)=p i，j (t)+δ×p i，j (t)×[π i，j (t)-π¯ i (t)], where δ is the learning rate, taking values 0.01-0.1.

[0127] Introducing a noise term to simulate the uncertainty of decision-making: p i，j (t+1)=p i，j (t)+δ×p i，j (t)×[π i，j (t)-π¯ i (t)]+η i，j (t), where η i，j (t)~N(0,σ η 2 ), σ η =0.001, the noise intensity decays with the number of iterations: σ η (t)=σ η (0)×exp(-t / τ decay ), τ decay =100 is the decay time constant.

[0128] Different water-receiving areas have different risk preferences, and the risk-adjusted utility function is defined as: U i (π)=π^(1-r i ) / (1-r i ), where r i is the relative risk aversion coefficient of area i, the water-receiving area above the reservoir depends on water diversion, and the risk aversion degree is high, r1=0.8; the water-supplying area has storage capacity, and is risk-neutral, r2=0.5; the water-receiving area below the reservoir has diversified water sources and is risk-seeking, r3=0.2.

[0129] The modified replication dynamic equation is: dp i，j / dt=p i，j (t)×[U i (π i，j (t))-U¯ i (t)], where U¯ i (t)=Σjpi，j (t) x U i (t) i，j (t) is the risk-adjusted average utility;

[0130] Further, the bounded rationality assumption is introduced, and the Logit response dynamics is adopted: p i，j (t+1) = exp(β i x π i，j (t)) / ∑ k exp(β i x π i , k(t)), where β i is the rationality degree parameter, β i →∞ represents complete rationality, which immediately selects the optimal strategy; β i →0 represents random selection, and β i = β0x (1 + t / T max ) is set to gradually improve the rationality degree with the learning process, β0= 1, and T max = 500.

[0131] The convergence condition is defined: when the selection probability of a certain strategy for all regions exceeds the threshold θ conv , it is considered to reach convergence, which is formally expressed as: for any i, there exists j: p i，j (t) ≥ θ conv , where θ conv = 0.95.

[0132] The auxiliary convergence criterion includes: the probability change rate criterion: max i，j |p i，j (t) - p i，j (t-1)| < ε_p, where ε_p = 0.001; max i，j represents the maximum probability change amplitude corresponding to all regions and all strategies; p i，j (t) is the probability of the i-th region selecting the j-th strategy at time t; p i，j (t-1) is the probability of the i-th region selecting the j-th strategy at time t-1; the moving average criterion: |P i，j (t) - P i，j (t-τ)| < ε avg , where P i，j (t) = (1 / τ)∑_k=0^τ-1 p i，j (t-k) is a τ-period moving average, τ = 20; the entropy criterion: H i (t) = -∑_jp i，j (t) x log(p i，j (t)) < H threshold , where H threshold= 0.1, indicating that the uncertainty of the strategy distribution is small enough.

[0133] Set the maximum number of iterations T max = 1000, if it still does not converge after the maximum number of iterations, select the strategy with the maximum probability as the result, and mark it as a weakly convergent state.

[0134] Adopt adaptive learning rate: δ(t) = δ0 / (1 + α_δ×t), where δ0=0.1 is the initial learning rate, and α_δ=0.01 is the decay coefficient. When oscillation is detected (the strategy probability repeatedly changes in the last 5 iterations), the learning rate is halved.

[0135] Implement momentum method to accelerate convergence: p i，j (t+1) = p i，j (t) + δ × [p i，j (t) × (π i，j (t) - π i ) + γ m ×Δp i，j (t-1)], where γ m = 0.9 is the momentum coefficient, and Δp i，j (t-1) = p i，j (t) - p i，j (t-1) is the change of the last step.

[0136] In some optional embodiments, a parallel evolutionary strategy is adopted, and the water area is grouped, and the group is updated synchronously, and the groups are updated asynchronously. Specifically, I pieces of area are divided into G groups, each group contains I / G pieces of area, and the gth group is updated at time t_g = t0+g×Δt group , where Δt group is the group update interval. This method can reduce the computational complexity from O(I 2 ×n 2 ) to O((I / G) 2 ×n 2 ).

[0137] Optionally, a reinforcement learning method is used instead of copying dynamics, and the strategy selection is modeled as a multi-agent reinforcement learning problem, where each piece of area is an agent, the state space S i contains historical water supply, current inventory, season, etc. Information; action space A i is the strategy set; reward function R i = V i , and independent Q-learning or Actor-Critic algorithm is used to learn the optimal strategy by interacting with the environment.

[0138] Record the converged strategy combination S* = {s1*, s2*,..., s iwhere s i is the stable strategy of region i, calculate the Nash equilibrium property of this combination: verify that for any i, for any s i ' i (s i , s i - i ) ≥ V i (s i ', s i - i ), that is, unilateral deviation cannot obtain higher income.

[0139] Sensitivity analysis is carried out, and the key parameters (learning rate δ, risk coefficient r i , rationality parameter β reliability ) are disturbed by ±20%, the evolutionary process is re-run, and the change of stable strategy is counted. If more than 90% of the parameter combinations converge to the same strategy, it is considered that the result has good robustness.

[0140] According to an aspect of the application, the calculation of the risk-adjusted utility includes:

[0141] The income variance of the water consumption plan strategy selected by the water receiving region is calculated, the income variance is multiplied by the risk preference coefficient to obtain a risk adjustment term;

[0142] The expected income value is reduced by the risk adjustment term to obtain the risk-adjusted utility;

[0143] The probability of updating the water consumption plan strategy selected by the water receiving region includes:

[0144] The difference between the risk-adjusted utility and the average expected income of the water receiving region is calculated, the difference is multiplied by the learning ability coefficient and the current strategy selection probability to obtain a probability update amount, and the strategy selection probability is adjusted according to the probability update amount.

[0145] In an embodiment, specifically:

[0146] A four-dimensional income vector R i =[R reliability (i), R _benefit (i), R cost (i), R equity (i)] is constructed, corresponding to the four targets of water supply security, water use benefit, water transfer cost and fairness respectively.

[0147] The calculation of the water supply security target R _reliability (i): R _reliability (i)=Σ k w k ×P k (i), where P k (i)=Σ tmin (W _supply(i, t, k) / D(i, t, k), 1) / T is the water supply satisfaction rate of the kth type of water, w k is a weight coefficient, and w life = 0.4, w industry = 0.3, w ecology = 0.2, w agriculture = 0.1, considering the importance difference of time periods, a time period weight P k (i) = Σ t γ t × min(W _supply (i, t, k) / D(i, t, k), 1) / Σ t γ t , where γ t is the importance coefficient of the time period t, and is 1.2 in the dry season and 0.8 in the wet season.

[0148] Calculation of the water use benefit target R _benefit (i): R _benefit (i) = Σ k Σ t B -unit (i, k) × W _supply (i, t, k) × (1-L rate (i, k, t)), where B -unit (i, k) is the benefit generated by unit water, 50 yuan / m 3 for domestic water, 120 yuan / m 3 for industrial water, 3 yuan / m 3 for agricultural water, and 15 yuan / m 3 for ecological water according to its environmental value; L rate (i, k, t) is a loss rate, reflecting the benefit loss caused by insufficient water supply, and the calculation formula is L rate (i, k, t) = a k × [1-W _supply (i, t, k) / D(i, t, k)]^b k , where a k and b k are empirical parameters, and a = 0.8 and b = 2 for industrial water, and a = 0.6 and b = 1.5 for agricultural water.

[0149] Calculation of the water transfer cost target R cost (i): R cost (i) = -[C water (i) + C energy (i) + C maintain (i)], where C water (i) = Σ t c_ w × Wtransfer (i, t) is water resource fee, c w Take 0.5-2 yuan / m 3 ; C energy (i) =∑ t c e ×H(i, t) ×W transfer (i, t) ×g / (η pump ×3600) is the cost of water pumping energy consumption, H(i, t) is the lift, g = 9.8 m / s 2 , η pump is the efficiency of the pump station; C maintain (i) = c m ×L(i) ×T is the channel maintenance cost, c m is the unit length maintenance fee, L(i) is the channel length.

[0150] Fairness target R equity (i) is calculated: R equity (i) = -σ _supply (i) / μ _supply , where σ _supply (i) = sqrt(∑_j≠i[P _guarantee (i) - P _guarantee (j)] 2 / (N-1)) is the standard deviation of the water supply guarantee rate of the area and other areas, μ _supply =∑_jP _guarantee (j) / N is the average water supply guarantee rate, the smaller the index indicates the more fair the water supply.

[0151] Define the dominance relationship: strategy A dominates strategy B if and only if A is not worse than B on all targets, and at least one target is strictly better than B, formally represented as: A > B is (any one m: R m (A) ≥ R m (B)) ∧ (there is m: R m (A) > R m (B)).

[0152] Perform fast non-dominated sorting algorithm: initialize the dominated number n_ p =0 and the dominated set S_ p is not 0 for each strategy p; for any two strategies p and q, if p dominates q, then S_ p =S_ p ∪{q}, n_ q =n_ q +1; if n_ p =0, then p belongs to the first non-dominated layer F1; for each strategy p in F1, traverse the strategies q in its dominated set S_ p , let n_q =n_ q -1, if n_ q If q = 0, then q is added to F2; repeat this process until all strategies are layered.

[0153] Calculate the crowding distance: For policies within the same undominated layer, calculate their crowding level in the target space. For the k-th target, sort the policies according to the target value. The crowding distance contribution of policy i is: d k (i)=[R k (i+1)-R k (i-1)] / [R k max -R k min ], where R k max and R k min For the maximum and minimum values ​​of this objective, the total congestion distance D(i) = Σ k d k (i).

[0154] The overall return value is calculated as follows: V(i) = α / rank(i) + β × D(i), where rank(i) is the non-dominated level of the strategy, α = 0.7 is the level weight, and β = 0.3 is the diversity weight. This formula ensures that the frontier solution obtains a high return value, while rewarding sparsely distributed solutions in the target space.

[0155] Iterate through all possible strategy combinations, and let the size of the strategy set for each water-receiving area be n1, n2, ..., n i The total number of combinations is N total =∏ i n i For region i, the number of strategy combinations for other regions is N_ -i =N total / n i .

[0156] Calculate the conditional expected return when choosing strategy s for region i: E[V i |s i =s]=(1 / N_ -i )×Σ_{s_ -i}V i (s,s_ -i ), where s_ -i V represents the strategy combination for other regions. i (s,s_ -i ) represents region i in the complete strategy combination (s, s_ -i The overall return value under )

[0157] Optionally, the Monte Carlo method is used to approximate the expected value. When the number of combinations is too large, M = 10,000 strategy combinations are randomly sampled, and the expected return is approximately: E[V i |s i =s]≈(1 / M)×Σ_{m=1}^MV i (s,s_ -i ^(m)). Importance sampling is used to improve efficiency, and the sampling probability distribution is set based on historical experience or prior knowledge.

[0158] Furthermore, risk adjustment is introduced to calculate the variance of returns, Var[V]. i |s i =s] and CVaR (Conditional Value at Risk): CVaR _α (V i )=E[V i |V i ≤VaR _α ], where VaR _α Given the α quantile, the risk-adjusted expected return is: E[V] i ]-λ _risk ×sqrt(Var[V i ]), where λ _risk The risk aversion coefficient is set at 0.5-1.0 for conservative decisions and 0-0.3 for aggressive decisions.

[0159] According to one aspect of this application, obtaining a stable decision combination includes:

[0160] Set a convergence threshold for the probability of strategy selection. When the probability of a water-receiving area selecting a certain water use plan strategy exceeds the convergence threshold, the strategy is determined as the stable strategy for that water-receiving area.

[0161] Once a stable strategy has been determined for all water-receiving areas, a stable decision combination corresponding to the random sample is formed.

[0162] Based on the annual water inflow levels of the water-receiving areas in the random sample, the stable decision combination is classified into annual water use planning strategies corresponding to wet years, normal years, and dry years.

[0163] like Figure 3 As shown, according to one aspect of this application, the three-dimensional joint distribution function of the current water diversion volume of the water source area, the current water inflow volume of the water receiving area, and the previous water inflow volume of the water receiving area includes:

[0164] Historical water diversion data of the water source area and historical water inflow data of the water receiving area were extracted from the data of the study area. Marginal distributions of water diversion volume in the water source area, current water inflow volume in the water receiving area, and previous water inflow volume in the water receiving area were fitted respectively.

[0165] A two-dimensional Copula function is used to construct the joint distribution of water diversion from the water source area and the current water inflow from the water receiving area, so as to obtain the conditional distribution of the current water inflow from the water receiving area under the given water diversion from the water source area.

[0166] In one embodiment, specifically:

[0167] Collect monthly historical hydrological data for no less than 30 years from the water source area and each water-receiving area, and set X as... t Y represents the amount of water available for diversion in the water source area at time t. i,t Y represents the inflow volume of the i-th water-receiving area at time t. i，t-1 This represents the water inflow to the area at time t-1. For each water-receiving area i, a three-dimensional random vector Z is constructed. i =(X t Y i ,t,Y i , t-1);

[0168] For the water diversion capacity X t Density estimation is performed using the Gaussian kernel function with adaptive bandwidth: f x (x)=(1 / (n×h x ))×Σ_ j K((x-x_ j ) / h x ), where n is the number of samples, h x Let K(·) be the bandwidth parameter, K(·) be the standard normal kernel function, and h be the bandwidth. x The Silverman rule is used to determine: h x =1.06×σ x ×n^(-1 / 5), where σ x The standard deviation is the sample standard deviation.

[0169] For the water inflow Y of the water-receiving area i，t Considering its seasonality, kernel density estimation is performed monthly. Historical data are grouped by month, and the inflow sequence Y for each month m is calculated. i m={y i，m，1 y i，m，2 , ..., y i，m，k Fit the marginal distributions F respectively Y，i，m (y), during the fitting process, for months with zero or extreme values, a mixed distribution model is used: F Y，i，m (y)=p0×I(y=0)+(1-p0)×F continuous (y|y>0), where p0 is the zero probability, I(·) is the indicator function, and F continuous The distribution function for the continuous portion;

[0170] Kendall rank correlation coefficient τ and tail correlation coefficient λ between three variables are calculated, and a Copula function family is selected according to the correlation characteristics: when τ xY > 0.5 and there is an upper tail correlation, Gumbel Copula is selected; when τ xY > 0.5 and there is a lower tail correlation, Clayton Copula is selected; when there is no obvious tail correlation, Frank Copula is selected; when the correlation is weak (|τ| < 0.3), an independent Copula can be considered;

[0171] Specifically, a three-dimensional Archimedean Copula function C(u1, u2, u3; θ) = φ^(-1)(φ(u1) + φ(u2) + φ(u3)) is used, where φ is a generator function and θ is a dependence parameter. For Frank Copula, the generator function φ(t) = -ln((exp(-θt)-1) / (exp(-θ)-1)); the parameter θ is estimated by maximum likelihood method: θ mLE = argmax_θΣ k lnc(F X (x k ), F Y，i，t (y i，t，k ), F Y，i，t-1 (y i，t-1，k ) ; θ), where c(·) is a Copula density function;

[0172] In some optional embodiments, a more complex dependence relationship can be captured by using a Vine Copula structure, and a C-vine structure is constructed: the first layer constructs a two-dimensional Copula C t of X i，t and Y 12 , and a two-dimensional Copula C t of X i，t-1 and Y 13 ; the second layer constructs a conditional Copula C 23|1 , which describes the dependence relationship between Y t and Y i，t given X i，t-1 , and this method can flexibly select different Copula function types for different variable pairs;

[0173] The conditional sampling method is used to generate relevant random samples. First, a uniform random number u1 on [0, 1] is generated; then u2 is generated according to the conditional distribution C2|1(u2|u1)=ΞC12(u1, u2) / Ξu1; and finally u3 is generated according to C3|12(u3|u1, u2)=Ξ²C123(u1, u2, u3) / (Ξu1Ξu2), where Ξ is the partial derivative, and the sample in the original space is obtained through inverse transformation: x=F x (-1)(u1), y i，t =F Y，i，t^(-1)(u2) , y i，t-1 =F Y，I，t-1^(-1)(u3) ;

[0174] To improve sampling efficiency, the quasi-Monte Carlo method is used to replace the traditional Monte Carlo method, and Sobol sequence or Halton sequence is used to generate a low-bias point set, which is uniformly distributed in [0, 1] 3 space. M=1000 groups of random samples {(x m , y i , t m , y i，t-1 m )} are generated, m=1, 2,..., M, forming a set of incoming water scenarios;

[0175] The statistical characteristics of the sample are tested to be consistent with the historical data, including: mean test |μ _sample -μ _history | / μ _history <0.05; standard deviation test |σ _sample -σ _history | / σ _history <0.1; correlation coefficient test |ρ _sample -ρ _history |<0.1; and extreme value test to ensure that the maximum value of the sample is not more than 1.2 times the maximum value of the historical data;

[0176] For samples that do not meet the test conditions, the acceptance-rejection method is used to regenerate, and the acceptance probability p_ accept =exp(-d² / 2σ d ²), where d is the distance measure between the sample and the target distribution, and σ d is the tolerance parameter. Through multiple iterations, it is ensured that the generated sample set not only maintains the dependent structure between variables, but also meets the physical law of hydrological sequence;

[0177] Further, climate change scenarios can be introduced, and the edge distribution can be adjusted according to the climate change prediction published by IPCC: F _future (x)=F _history (x / α), where F_ history (·) is the cumulative distribution function of historical incoming water; F_future (·) represents the cumulative distribution function of future water inflow; x represents the random variable of future water inflow; α represents the coefficient of variation, reflecting the trend of future water inflow. The random samples generated by this method can reflect the potential impact of climate change on water resources.

[0178] Based on conditional distribution, a three-dimensional joint distribution function is constructed by connecting the water inflow volume of the water receiving area at the previous moment using a conditional Copula function.

[0179] According to one aspect of this application, the use of a conditional Copula function to connect the water inflow volume of the receiving area at the previous moment includes:

[0180] The marginal distribution of water diversion volume in the water source area and the marginal distribution of water inflow in the water receiving area at the current moment are transformed into a uniform distribution. The Kendall rank correlation coefficient is calculated and the parameters of the two-dimensional Copula function are determined.

[0181] By taking the partial derivative of the two-dimensional Copula function, we can obtain the conditional distribution function of the water inflow to the water-receiving area at the current moment under the given water diversion volume from the water source area.

[0182] Based on the conditional distribution function and the marginal distribution of water inflow in the water-receiving area at the previous moment, the conditional Kendall rank correlation coefficient is calculated, the parameters of the conditional Copula function are determined, and a complete three-dimensional joint distribution is constructed.

[0183] like Figure 4 As shown, according to one aspect of this application, the generation of random samples of the water drawable volume and the water inflow process in the receiving area includes:

[0184] An initial random number matrix is ​​generated based on a three-dimensional joint distribution function, where rows represent time periods and columns represent water source areas and water receiving areas.

[0185] Calculate the temporal correlation matrix between adjacent months in historical data, and construct the type correlation matrix for different water-receiving areas;

[0186] According to one aspect of this application, the calculation of the time-series correlation matrix and the construction of the typological correlation matrix include:

[0187] Extract the water volume series for each month from the historical data, calculate the Pearson correlation coefficient between adjacent months, and form a 12×12 time series correlation matrix;

[0188] Spatial distance weights are calculated based on the geographical location of the water-receiving areas, and a type association matrix between the water-receiving areas is constructed by combining the similarity of water supply characteristics of the water-receiving areas.

[0189] The time series correlation matrix and the type correlation matrix are respectively subjected to Cholesky decomposition to obtain lower triangular matrices, and the initial random number matrix is multiplied by the lower triangular matrices to realize random sample generation under the correlation constraint.

[0190] As shown in Figure 5 According to one aspect of the present application, the calculation of the comprehensive benefit value of the water-receiving area includes:

[0191] Based on the water supply amount, the water supply guarantee target, the water use benefit target, the water transfer cost target and the fairness target of the water-receiving area are calculated to form a four-dimensional benefit vector and perform normalization processing;

[0192] The water supply guarantee target is measured by the water supply guarantee rate and is calculated as the ratio of the number of time periods satisfying the water demand to the total number of time periods;

[0193] The water use benefit target is calculated by weighted summation of power generation, water supply and other beneficial effects;

[0194] The water transfer cost target is calculated by the product of the actual water supply amount and the water transfer cost coefficient;

[0195] The fairness target is measured by the difference in water supply guarantee degree between the water-receiving area and other areas;

[0196] The multi-objective benefit vector set is subjected to Pareto non-dominated sorting to determine the non-dominated level of each strategy combination, and the crowding distance is calculated within the same non-dominated level;

[0197] The strategy dispersion degree of the water use plan strategy combination is calculated, and the non-dominated level, the crowding distance and the strategy dispersion degree are weighted combined to obtain the comprehensive benefit value.

[0198] According to one aspect of the present application, the calculation of the strategy dispersion degree includes:

[0199] The frequency of occurrence of each strategy in the water use plan strategy combination is counted, the strategy distribution entropy is calculated, and the normalized strategy dispersion degree is obtained by dividing the strategy distribution entropy by the maximum possible entropy value;

[0200] The calculation formula of the comprehensive benefit value is: the reciprocal of the non-dominated level is taken as the level score, the crowding distance is normalized as the distance score, the level score, the distance score and the strategy dispersion degree are respectively given the weight coefficients a, b and c, and the weighted summation is taken to obtain the comprehensive benefit value.

[0201] According to one aspect of the present application, the generation of the random sample of the water-receiving area water inflow process adopts a master-slave calculation method including:

[0202] From the three-dimensional joint distribution function, first, uniform distribution random numbers of water source area water inflow are generated by inverse transformation sampling;

[0203] Based on the generated water source area water diversion amount, the current time water inflow of the water receiving area is generated through a conditional distribution function;

[0204] According to the water source area water diversion amount and the current time water inflow of the water receiving area, the last time water inflow of the water receiving area is generated through a conditional Copula function, and uniform distribution random numbers are inversely transformed into original variable space to form random samples that maintain spatial and temporal correlation.

[0205] As shown in Figure 6 According to one aspect of the present application, it also includes a classification process for stable decision combination:

[0206] According to the annual water inflow of the water receiving area in the random sample, the stable decision combination is divided into three categories: wet year, normal year and dry year;

[0207] The frequency distribution of the water receiving area selecting each water plan strategy under each type of water inflow condition is counted, and the strategy difference degree between different water inflow conditions is calculated;

[0208] When the strategy difference degree exceeds the set threshold, the stable decision combination under different water inflow conditions is stored respectively as a classified scheduling plan; otherwise, a unified stable decision combination is used as an annual scheduling plan.

[0209] According to one aspect of the present application, the improved Latin hypercube sampling method comprises:

[0210] The local weighted regression method is used to perform seasonal-trend decomposition on the historical water consumption sequence, to extract the trend item, seasonal item and residual item, and to clearly define the water consumption benchmark range of different months;

[0211] The ARIMA model is used to fit the time series relationship between monthly water consumption, and a 12x12 time series correlation matrix is constructed;

[0212] The Pearson correlation coefficient of the same period water consumption of different types is calculated, the Archimedean Copula function is used to fit the joint distribution for weak linear correlation, and the inter-type correlation matrix is obtained;

[0213] The marginal distribution of each month-water type dimension is divided into N equal probability intervals, and N is the sampling sample size of the random strategy and N≥50;

[0214] The first month is taken as the benchmark to randomly sample from N layers, and the sampling layer of the subsequent months is constrained according to the time series correlation matrix, to ensure the dependence of the sample of each month on the previous months;

[0215] The current correlation matrix of different type water samples of each month is calculated, and when the correlation deviation from the inter-type correlation matrix is greater than 5%, the Cholesky decomposition is used to embed the target correlation matrix into the sample for correction.

[0216] The improved Latin hypercube sampling method is used to reorder the initial random number matrix according to the time series correlation matrix and the type correlation matrix, so as to generate random samples that maintain the spatiotemporal correlation.

[0217] Firstly, the 10-year or more monthly historical data of domestic, industrial, agricultural irrigation and ecological water use in the study area are collected, including: monthly domestic water consumption sequence W life (i, t), wherein i represents the water receiving area number, and t represents the time month; monthly industrial water consumption sequence W industry (i, t); monthly agricultural irrigation water consumption sequence W agriculture (i, t); monthly ecological water consumption sequence W ecology (i, t), and hydro-meteorological data including monthly precipitation P(i, t) and monthly average temperature T(i, t) are collected; local water resource availability data including surface water resources SW(i, t) and groundwater resources GW(i, t); relevant engineering data including reservoir storage S(i, t) and channel water conveyance capacity C(i); population, economic and social data including population Pop(i, t), GDP value G(i, t) and irrigation area A(i, t).

[0218] Each type of water consumption sequence W(i, t) is decomposed by STL: W(i, t) = T(i, t) + S(i, t) + R(i, t), wherein T(i, t) is a trend item reflecting the long-term change trend of water consumption; S(i, t) is a seasonal item reflecting the periodic change rule within a year; R(i, t) is a residual item reflecting random fluctuations; the trend item is fitted by local weighted regression, and the window width is set to 13 months; the seasonal item is extracted by moving average method, and the period is set to 12 months; the residual item is the remaining part after the original sequence is subtracted by the trend item and the seasonal item.

[0219] The time series correlation matrix M temporal is a 12x12 matrix, and the element M temporal (m, n) represents the correlation coefficient of the water consumption in the mth month and the nth month, and the calculation formula is: M temporal (m, n) = Cov(W m , W n ) / (σ m x σ n ), wherein Cov represents covariance, σ represents standard deviation, W m represents the water consumption sequence in the mth month of all years.

[0220] The type correlation matrix M type is a 4x4 matrix, and the element M type(p, q) represents the correlation coefficient of the pth type of water and the qth type of water, for the linear correlation strong type pair of water (the correlation coefficient is greater than 0.7), the Pearson correlation coefficient is directly used; for the type pair of non-linear correlation, the Frank Copula function is used to fit its joint distribution, and the correlation strength is calculated by the Kendall rank correlation coefficient τ: τ = 4∫∫C(u, v)dC(u, v)-1, wherein C(u, v) is a Copula function.

[0221] The sampling sample size N = 100 is set, and the strategy set has sufficient diversity. For each dimension of 48 dimensions (12 months x 4 types of water), first, the marginal distribution F d (x) is fitted, wherein d ∈ {1, 2,..., 48}. The value range [0, 1] of the cumulative distribution function is divided into N intervals: [0, 1 / N], [1 / N, 2 / N],..., [(N-1) / N, 1]. A uniformly distributed random number u d , k is randomly extracted in each interval, wherein k ∈ {1, 2,..., N} represents the kth sample. The sample value in the original space is obtained by inverse transformation x d , k = F d ^(-1)(u d , k).

[0222] The initial sampling matrix X init is an N x 48 matrix, each row represents a candidate strategy, and each column represents a month-water type combination. In order to maintain the time correlation, the sampling layer is randomly selected from the N layers after the 1st month is taken as the benchmark. The sampling layer selection of the subsequent months is constrained according to the time correlation matrix M temporal . Specifically, if the water quantity of a type in January is located in the kth layer, the sampling layer k' of the water quantity of the type in February is determined by the conditional probability P(k'|k) = exp(-|k'-k| / λ) / Σexp(-|j-k| / λ), wherein λ is a correlation strength parameter, and the value of the corresponding element in M temporal is used to determine.

[0223] The annual total water quantity control constraint: Σ t Σ type W(t, type) ≤ W total , wherein W total is an annual total water quantity control index; the water quantity balance constraint: for any time period t, the water supply quantity does not exceed the available water quantity; the engineering water supply capacity constraint: the water supply quantity of each time period does not exceed the channel water conveyance capacity C max ; the ecological discharge constraint: the river ecological base flow Q eco is ensured to be satisfied; the water supply priority constraint: domestic water > industrial water > ecological water > agricultural water; the engineering operation stability constraint: the change of water supply quantity of adjacent time periods does not exceed the threshold ΔWmax .

[0224] Constraint checking is performed on each candidate strategy of the initial sampling matrix X init , and strategies that do not meet the constraints are eliminated. If the number of feasible strategies is less than N, supplementary sampling is performed until N feasible strategies are obtained, and a final strategy set S i ={P i 1 , P i 2 ,..., P i N} is formed, where P i j represents the jth water use planning strategy of the ith water receiving area.

[0225] Through the improved Latin hypercube sampling method described above, the strategy set generated not only maintains the time sequence correlation and type association of historical water use, but also ensures the diversity and representativeness of the strategies through hierarchical sampling, providing high-quality input for subsequent evolutionary game analysis.

[0226] In another embodiment, the uncertainties of inflow, demand and model parameters are comprehensively considered to build a more perfect decision-making framework, which is as follows:

[0227] The uncertainty of inflow is processed by the method of embodiment three, and the demand uncertainty is modeled as: D actual (i, t, k) = D plan (i, t, k) x (1 + ξ demand ), where ξ demand ~N(0, σ d 2 ), σ d is determined according to the historical demand prediction error, σ d = 0.05 for domestic water, σ d = 0.10 for industrial water, and σ d = 0.20 for agricultural water.

[0228] The uncertainty of model parameters is processed by the Bayesian method. For the benefit coefficient B unit (i, k), the prior distribution B unit ~Gamma(α _B , β _B ) is set, where the shape parameter α _B and the scale parameter β _B are estimated according to historical data. The posterior samples {B unit m} of the parameters are generated by the MCMC method, m = 1,..., M _param .

[0229] First stage (beginning of the year): each water-receiving area determines the annual water plan based on historical information and prediction through evolutionary game; second stage (during the year): adaptive adjustment is performed according to actual inflow and demand.

[0230] Definition of information set I t ={X τ , Y τ , D τ : τ≤t} represents all historical information available at time t, the strategy mapping σ i :I t →A i (t), where A i (t) is the set of available actions at time t, and the information value analysis VOI is introduced: VOI = E[V|perfect info ]-E[V|current info ], which quantifies the value of perfect information.

[0231] Divide the annual planning period T into K decision stages, each stage containing T / K time periods, and update the strategy of the subsequent stage based on the latest information I k at the beginning of the kth stage.

[0232] Prediction-correction mechanism: the prediction step uses the historical model to generate future scenarios; the correction step updates the model parameters according to actual observations, and uses Kalman filtering for state estimation: x k |k=x k |k-1+K k ×(z k -H×x k |k-1), where x is the system state, z is the observation value, and K k is the Kalman gain.

[0233] Adaptive strategy adjustment: Δs i , k = f_ adjust (e k , σ e , k), where e k = actual k - forecast k is the prediction error, σ e , k is the error standard deviation, and the adjustment function f_ adjust uses a piecewise linear form: when |e k | < σ e , k, Δs = 0; when σ e , k ≤ |e k | < 2σ e , k, Δs = sign(e k ) × λ1 × |e k ||;when |e k |≥2σ e , k, trigger emergency response mechanism.

[0234] Generate N scenario = 500 future scenarios, covering different hydrological years (wet, normal, dry and their combinations), demand growth patterns (high, medium, low) and climate change impacts (RCP2.6, RCP4.5, RCP8.5).

[0235] For each scenario s, run the full evolutionary game process to get the stable strategy S_s*, construct the scenario-strategy matrix M scenario , element M ij represents the performance of strategy i in scenario j.

[0236] Select the final strategy using robust optimization: min_smax_scenarioRegret(s, scenario), where Regret(s, scenario)=V best (scenario)-V(s, scenario) is the regret value, optionally, use CVaR criterion: min_sCVaR_α(Loss(s)), focus on tail risk.

[0237] Establish a trigger-response mechanism, define the trigger index set T indicator ={inventory level, inflow deviation, demand deviation, water supply guarantee rate}, when the index exceeds the threshold, trigger the corresponding management response: first-level response (yellow warning): strengthen monitoring, increase prediction frequency; second-level response (orange warning): start standby water source, implement restrictive water supply; third-level response (red warning): start emergency plan, re-play strategy game.

[0238] Learning and updating mechanism: establish case library to store historical decisions and their effects; use case-based reasoning (CBR) method to find similar historical cases for new situations; generate initial strategy suggestions based on similarity weighted average; continuously improve decision rules through incremental learning.

[0239] In some optional implementations, introduce distribution robust optimization, without assuming precise probability distribution, but considering the uncertainty set P of distribution: min_ssup_P∈PE_P[Loss(s, ξ)], the uncertainty set uses L matrix constraint or Wasserstein ball.

[0240] Further, deep reinforcement learning can be used to handle high-dimensional state space, using deep Q network (DQN) or proximal policy optimization (PPO) algorithm to learn the strategy directly from the raw data. The network input includes historical hydrological data, current inventory, seasonal information, etc. The output is the Q value or selection probability of each strategy, and the learning stability is improved through experience replay and target network.

[0241] In the random sample generation process, the embodiment can maintain the spatio-temporal correlation of the hydrological sequence, ensure that the generated random field scene can reflect uncertainty and maintain the inherent regularity of the hydrological process, specifically:

[0242] First, analyze the spatio-temporal correlation characteristics of historical hydrological data. For the inflow sequence of M water source areas and N time periods, a complete correlation matrix R is constructed, with a dimension of (M×N)×(M×N).

[0243] The time correlation analysis uses autocorrelation function (ACF) and partial autocorrelation function (PACF). For the inflow sequence Q m (t) of water source area m, the autocorrelation coefficient ρ m (k) of lag k period is calculated: ρ m (k)=Cov[Q m (t),Q m (t-k)] / Var[Q ij (t)], it is found in practice that the monthly runoff sequence usually shows significant annual periodicity, ρ(12)≈0.6-0.8; the lag 1 correlation coefficient of seasonal runoff ρ(1)≈0.3-0.5.

[0244] The spatial correlation is described by the cross-correlation function (CCF). For water source areas i and j, the spatial correlation coefficient ρ i =Cov[Q j (t),Q i (t)] / (σ j ×σ 11 ), the correlation coefficient of upstream and downstream water source areas is usually between 0.7-0.9, while the correlation coefficient of adjacent basins is about 0.4-0.6, and the correlation of basins with long geographical distance is reduced to below 0.2.

[0245] The block correlation matrix is constructed as follows:

[0246] R=[R 11 R 12 ...R 1N ];

[0247] [R 21 R 22 ...R 2N ]; [............];

[0249] [R n1 R n2 ...R nN ];

[0250] Where the submatrix R ij This represents the cross-correlation matrix of all water source areas between time periods i and j, with dimensions M×M. The diagonal block R... ii Reflecting spatial correlation within the same time period, off-diagonal block R ij (i≠j) reflects the spatiotemporal cross-correlation between different time periods.

[0251] To ensure numerical stability, the original correlation matrix is ​​corrected for positive definiteness using eigenvalue decomposition R = QΛQ. T Set the negative eigenvalues ​​to zero or to a small positive number ε = 10^-6, and reconstruct the matrix R' = QΛ'Q. T Another approach is to add a regularization term: R_ reg =(1-α)R+αI, where α=0.01 is the regularization parameter.

[0252] The corrected correlation matrix R' is decomposed using Cholesky: R' = LL^T, where L is a lower triangular matrix. Since the matrix dimension is large (typically 60×60 to 120×120), a block-based Cholesky algorithm is used to improve computational efficiency.

[0253] Block-based recursive algorithm implementation:

[0254] Divide R' into blocks: R'=[AB] T ]; [BC];

[0255] Where A is a k×k principal submatrix.

[0256] Recursive calculation:

[0257] L_A=chol(A), performing Cholesky decomposition on A;

[0258] L_B=B×(L A T ) -1 Solve by forward substitution;

[0259] L c =chol(CL B ×L B T ), decompose Schur complement;

[0260] Assembly: L=[L A0 ];[L B L c ].

[0261] For sparsity optimization, when |ρ ij | < threshold (such as 0.05), the correlation coefficient is set to zero, the sparse matrix is stored in the compressed column storage (CSC) format, and the sparse Cholesky decomposition is performed using the CHOLMOD or SuiteSparse library. The computational complexity is reduced from O(n 3 ) to O(n 1.5 ).

[0262] Numerical precision control: Calculations are performed using double-precision floating-point numbers (float64); after each column vector calculation, numerical stability is checked: ||LL T - R'||_F / ||R'||_F < 10^-10; if numerical instability occurs, modified Cholesky decomposition or LDL T decomposition is used.

[0263] Standardized random number generation: Generate independent and identically distributed standard normal random vectors Z ~ N(0, I), with dimensions M × N. The Mersenne Twister algorithm (MT19937) is used as the random number generator, with a period of up to 2^19937 - 1. To ensure reproducibility, the random seed is set as seed = hash(scenario i d + timestamp).

[0264] Correlated random vector generation: Y = LZ + μ, where μ is the mean vector. Y preserves the correlation structure of the original data: E[Y] = μ, Cov[Y] = LL T = R'.

[0265] Inverse standardization transformation: Convert the standard normal distributed Y back to the original distribution. For the incoming water volume, the log-normal distribution is usually used: Q = exp(σY + μ_log), where μ_log and σ are determined based on the logarithmic mean and standard deviation of historical data. For the precipitation, the Gamma distribution is used, implemented through quantile mapping: P = F_ gamma ^(-1)[Φ(Y)], where Φ is the standard normal CDF, and F gamma -1 is the inverse CDF of the Gamma distribution.

[0266] Partition the random vector X into the known part X o (observed) and the unknown part X u (unobserved):

[0267] X = [X o ], μ = [μ o ], Σ = [Σ oo Σou ];

[0268] [X u ][μ u ][Σ uo Σ uu ];

[0269] Conditional distribution is: X u |X o ~N(μ u |o, Σ u |o), where:

[0270] Conditional mean: μ u |o=μ u +Σ uo ×Σ oo -1 ×(X o -μ o );

[0271] Conditional covariance: Σ u |o=Σ uu -Σ uo ×Σ oo -1 ×Σ ou ;

[0272] Implementation steps:

[0273] Cholesky decomposition of conditional covariance matrix: Σ u |o=L c ×L c T ;

[0274] Generate independent standard normal random vector: Z c ~N(0, I);

[0275] Calculate conditional random sample: X u =μ u |o+L c ×Z c ;

[0276] Example of application scenario: Given the measured inflow of the upstream reservoir, the random flow of each section downstream needs to be generated; Given the current month's precipitation, the possible scenarios of the next few months are predicted.

[0277] After generating the sample, it needs to be verified whether the spatiotemporal correlation is maintained.

[0278] Correlation test: Calculate the empirical correlation matrix R emp =(1 / N _sample )×Σ(X i -μ)(Xi -μ) T ; compare theoretical correlation matrix and empirical correlation matrix: ||R emp -R target ||_F / ||R target ||_F<tolerance (e.g. 5%); use Kolmogorov-Smirnov test to check consistency of marginal distribution.

[0279] Correlation adjustment: if correlation deviation is large, use iterative adjustment algorithm, define objective function: f(θ)=||R emp (θ)-R target || F 2 ; use quasi-Newton method (L-BFGS) to optimize adjustment parameter θ; adjustment methods include: fine-tuning elements of L matrix, or post-processing transformation on generated samples.

[0280] Multi-scale correlation preservation: annual scale: preserve annual runoff total correlation; seasonal scale: preserve correlation structure of flood season and non-flood season; monthly scale: preserve monthly process correlation; extreme value correlation: preserve spatial synchronization of flood peaks and dry periods.

[0281] In some optional embodiments, Copula function method can be used, suitable Copula function (such as Gaussian Copula, t-Copula, Archimedean Copula) is selected to describe the dependence structure between variables; separate marginal distribution and dependence structure modeling; generate uniform distribution random numbers that preserve dependence through Copula function; then get the final sample through the inverse transformation of the marginal distribution.

[0282] Further, for non-stationary time series, first perform detrending and deperiodization processing: separate trend term T(t), periodic term S(t) and random term R(t); apply correlation preservation sampling method to random term; superimpose generated random term and deterministic component to restore complete sequence.

[0283] To realize fine scheduling management of reservoir group, the embodiment constructs reservoir scheduling rules based on a reservoir scheduling rule system of six limit water supply lines and one limit water diversion line, specifically:

[0284] A scheduling diagram composed of six limit water supply lines and one limit water diversion line is established, the six limit water supply lines are in turn from top to bottom:

[0285] The first limit water supply line (normal water supply line) Z1(t): when the reservoir water level is higher than this line, each water user is supplied with 100% of the planned water supply, the setting principle of this line is: Z1(t)=Z_ flood (t)-ΔH_safety where Z flood (t) is the flood control water level, ΔH safety is the safety freeboard, 2-3 m in flood season and 1-2 m in non-flood season, and the annual variation is considered: gradually reduced before the flood season (March-May) to reserve flood control capacity; maintained at a lower level during the flood season (June-September); rapidly increased after the flood season (October); and maintained at a high level during the dry season (November-February of the next year);

[0286] The second water supply restriction line (light restriction line) Z2(t): when the water level drops to this line, agricultural water is reduced by 10%, and other water is normal, which is set 3-5 m below the normal water supply line to ensure a certain buffer space, and the calculation formula is: Z2(t)=Z1(t)-V buffer1 / A(Z), where V buffer1 is the first-stage buffer capacity, usually 0.5-1 month of normal water supply, and A(Z) is the water level-area relationship;

[0287] The third water supply restriction line (moderate restriction line) Z3(t): triggers the second-stage water restriction measures, agricultural water is reduced by 25%, industrial water is reduced by 5%, and domestic water is normal, and the position is determined as: Z3(t)=Z dead +0.7×(Z1(t)-Z dead ), to ensure that the remaining capacity can support 2-3 months of basic water use;

[0288] The fourth water supply restriction line (severe restriction line) Z4(t): implements the third-stage water restriction, agricultural water is reduced by 40%, industrial water is reduced by 15%, and domestic water is reduced by 5%, and is set based on probability analysis: P(Z

[0289] The fifth water supply restriction line (special restriction line) Z5(t): enters the emergency state, agricultural water is reduced by 60%, industrial water is reduced by 30%, and domestic water is reduced by 10%, and the setting principle is to ensure basic domestic water use during the critical period (such as 3 consecutive dry months), and the calculation is: Z5(t)=Z dead +V emergency / A(Z), V emergency =3×W lifemin ;

[0290] The sixth water supply restriction line (extreme water supply line) Z6(t): only guarantees the most basic domestic water and ecological base flow, and all other water is stopped, which is usually set 5-10 m above the dead water level, Z6(t)=Z dead +ΔH extreme , to ensure that the water pump can still take water normally;

[0291] The water supply restriction line Z transfer(t): control the start time of inter-basin water transfer, set between the second and third water supply lines: Z transfer (t) = Z2(t) - a x (Z2(t) - Z3(t)), where a = 0.3-0.5, when the water level is below this line, start emergency water transfer; water transfer amount Q transfer = β x (Z transfer - Z_actual) x A(Z) / Δt, where β is the adjustment coefficient.

[0292] According to the interval where the current reservoir water level Z(t) is located, determine the water supply and water transfer strategy.

[0293] Decision logic implementation:

[0294] if Z(t) ≥ Z1(t):

[0295] Normal water supply area;

[0296] W _supply = W plan x 1.0;

[0297] Q transfer = 0;

[0298] elif Z2(t) ≤ Z(t) < Z1(t):

[0299] First-level water supply area:

[0300] W _agriculture = W _agr_plan x 0.9;

[0301] W industry = W ind_plan x 1.0;

[0302] W _life = W _life_plan x 1.0;

[0303] Q transfer = 0;

[0304] elif Z3(t) ≤ Z(t) < Z2(t):

[0305] Second-level water supply area:

[0306] W _agriculture = W _agr_plan x 0.75;

[0307] W industry = W ind_plan x 0.95;

[0308] W _life = W _life_plan x 1.0;

[0309] if Z(t) < Z transfer (t) :

[0310] Q transfer = min(Q transfer-capacity , Q transfer-needed ) ;

[0311] and so on.

[0312] Water supply priority dynamic adjustment: basic priority is: life > ecology > industry > agriculture; special period adjustment, such as spring irrigation period to increase the priority of agricultural; consider economic benefits, high single water efficiency of users priority; establish emergency water supply plan to ensure key user water supply.

[0313] Multi-reservoir joint regulation rule: compensation regulation principle, more water supply when the water level of upstream reservoir is high, to reduce the pressure of downstream; balanced drawdown principle, each reservoir is synchronized drawdown according to the proportion: (Z i -Z idead ) / (Z inormal- Z idead )≈constant; peak regulation principle, different reservoirs staggered water supply peak period.

[0314] Based on historical operation data and simulation results, the regulation rule line is optimized.

[0315] Parameter optimization model:

[0316] min F =∑ t ∑ i [α_ shortage ×D_ shortage (i, t) + α_ spill ×W_ spill (i, t)] ;

[0317] s.t. water balance constraints;

[0318] water level constraints;

[0319] water supply capacity constraints;

[0320] Decision variables: control point coordinates of each limited water supply line {Z k (t, j)} ;

[0321] Genetic algorithm optimization: chromosome coding is the key point coordinates of each rule line; fitness function includes water loss, water loss and operation cost; crossover operation uses simulated binary crossover (SBX); mutation operation uses polynomial mutation; population size 100, evolution algebra 500.

[0322] Sensitivity analysis: analyze the impact of ±1m variation of each rule line on system performance; identify critical scheduling periods and critical control points; results show that the third and fourth limiting water supply lines have the greatest impact on water supply guarantee rate.

[0323] Dynamic adjustment of scheduling rules according to real-time information to improve adaptability.

[0324] Forecast-based proactive adjustment: obtain water inflow forecasts for the next 15-30 days; if the forecast shows a large amount of water inflow, the restrictions can be appropriately relaxed; if the forecast shows a persistent drought, the water supply can be tightened in advance; correction amount: ΔZ k (t)=f(Q _forecast , P confidence ), where P confidence is the forecast confidence.

[0325] State-based feedback adjustment: define system state indicators S=(S_ water , S demand , S ecology ); adjust the rule line when S deviates from the normal range; the adjustment magnitude is proportional to the deviation: ΔZ=K_p×(S target -S_ actual ); set upper and lower limits to prevent excessive adjustment.

[0326] Seasonal correction coefficient: spring (March-May): k_ spring =1.1, appropriately increase water supply standards to support spring plowing; summer (June-August): k_ summer =0.9, reserve flood control storage capacity; autumn (September-November): k_ autumn =1.0, normal operation; winter (December-February): k_ winter =0.95, considering the impact of ice period.

[0327] Coordinate scheduling rules with other objectives to form a comprehensive scheduling scheme.

[0328] Flood control and water supply coordination: dynamically control the flood control water level during the flood season to increase storage under the premise of ensuring flood control safety; use forecast-based scheduling to pre-discharge or store water based on rainfall forecasts; set graded flood control limit water levels for different levels of flood.

[0329] Water supply and power generation coordination: optimize power generation scheduling under the premise of meeting water supply; use time-of-use electricity prices to increase power generation during high electricity price periods; set a minimum discharge flow to ensure downstream cascade power station operation.

[0330] Ecology and economy coordination: ensure ecological base flow: Q ecology ≥max(0.1×Q_ annualmean , Q minimum_history) ; pulse water release during key ecological periods (fish spawning season) ; establish an ecological compensation mechanism to balance the economic losses of ecological water use.

[0331] Emergency handling rules: all rules are temporarily invalid during extreme floods, and flood control plans are operated; during extreme droughts, emergency water supply plans are started, and quantitative water supply is implemented; during engineering failures, standby water intakes or emergency water diversion channels are started.

[0332] In some optional embodiments, machine learning optimization rules can be introduced, and LSTM network is used to learn historical scheduling decision patterns; the input is the current state (water level, inflow, water demand), and the output is the recommended water supply ratio; the neural network output is used as a correction reference for rule scheduling.

[0333] Further, adaptive scheduling rules can be implemented, and the performance index PI = w1 x water supply guarantee rate + w2 x reservoir fullness rate - w3 x water shortage loss is defined; PI is evaluated after each scheduling period; reinforcement learning algorithm (such as Q-learning) is used to update rule parameters; the learning rate α = 0.01 is set to ensure gradual optimization of the rules.

[0334] Visualization of scheduling rules: develop an interactive scheduling chart system to display water levels and various limit lines in real time; color code different water supply states (green for normal, yellow for warning, and red for restriction) ; provide historical same period comparison and future trend prediction; support hypothetical scenario analysis to evaluate the impact of different decisions.

[0335] According to another aspect of the present application, a water diversion project annual scheduling plan generation multi-agent evolutionary game system is provided, comprising:

[0336] At least one processor; and

[0337] A memory connected in communication with the at least one processor; wherein,

[0338] The memory stores instructions executable by the processor, and the instructions are executed by the processor to implement the multi-agent evolutionary game method for generating a water diversion project annual scheduling plan.

[0339] The above describes the preferred embodiments of the present application, but the present application is not limited to the specific details in the above embodiments, and various equivalent transformations of the technical solutions of the present application can be made within the technical concept of the present application, and these equivalent transformations all belong to the protection scope of the present application.

Claims

1. A multi-agent evolutionary game method for generating a water transfer project annual operation plan, characterized in that, include: Collect data on the study area, divide the study area into water source area and water receiving area, and formulate a set of water use planning strategies for the water receiving area; Construct a three-dimensional joint distribution function of the current water diversion volume in the water source area, the current water inflow volume in the water receiving area, and the previous water inflow volume in the water receiving area, and generate random samples of the divertable water volume and the water inflow process in the water receiving area. Random samples are extracted and combined with the water use planning strategies of the water-receiving areas. The samples are then input into the annual water volume scheduling plan compilation model of the water diversion project to obtain the water supply volume of each water-receiving area in each time period under the water use planning strategy combination. Based on the water supply, a multi-objective benefit vector of the water-receiving area under the combination of water use planning strategies is generated, the comprehensive benefit value of the water-receiving area is calculated, and the expected benefit value of the water-receiving area is calculated after traversing the combination of water use planning strategies. The water use planning strategy of the water-receiving area is adjusted and iterated until the probability of the water-receiving area choosing a specific water use planning strategy approaches 1, thus obtaining a stable decision combination of the annual water use plan of the water-receiving area corresponding to the random sample. The three-dimensional joint distribution function of the current water diversion volume of the water source area, the current water inflow volume of the water receiving area, and the previous water inflow volume of the water receiving area includes: Historical water diversion data of the water source area and historical water inflow data of the water receiving area were extracted from the data of the study area. Marginal distributions of water diversion volume in the water source area, current water inflow volume in the water receiving area, and previous water inflow volume in the water receiving area were fitted respectively. A two-dimensional Copula function is used to construct the joint distribution of water diversion from the water source area and the current water inflow from the water receiving area, so as to obtain the conditional distribution of the current water inflow from the water receiving area under the given water diversion from the water source area. Based on conditional distribution, a three-dimensional joint distribution function is constructed by connecting the water volume of the water receiving area at the previous moment using a conditional Copula function. The conditional Copula function used to connect the water inflow volume of the water receiving area at the previous moment includes: The marginal distribution of water diversion volume in the water source area and the marginal distribution of water inflow in the water receiving area at the current moment are transformed into a uniform distribution. The Kendall rank correlation coefficient is calculated and the parameters of the two-dimensional Copula function are determined. By taking the partial derivative of the two-dimensional Copula function, we can obtain the conditional distribution function of the water inflow to the water-receiving area at the current moment under the given water diversion volume from the water source area. Based on the conditional distribution function and the marginal distribution of water inflow in the water-receiving area at the previous moment, the conditional Kendall rank correlation coefficient is calculated, the parameters of the conditional Copula function are determined, and a complete three-dimensional joint distribution is constructed.

2. The method according to claim 1, wherein, The adjustment and iteration of water use planning strategies for the water-receiving areas includes: A replication dynamic equation incorporating learning ability coefficients and risk preference coefficients is used to calculate risk-adjusted utility based on the expected return of the water-receiving area. The probability of selecting each water use plan strategy in the water-receiving area is updated based on the difference between risk-adjusted utility and average expected return, combined with the learning ability coefficient. The strategy selection probability is iteratively updated until the probability of the water-receiving area selecting a specific water use plan strategy approaches 1, and the probability of selecting other strategies approaches 0, thus obtaining a stable decision combination.

3. The method according to claim 2, wherein, The calculation of the risk-adjusted utility includes: Calculate the variance of revenue from the water-receiving area's water use planning strategy, and multiply the variance of revenue by the risk preference coefficient to obtain the risk adjustment term; The risk-adjusted utility is obtained by subtracting the risk adjustment term from the expected benefit value; The updating of the probability of the water receiving area selecting each water use planning strategy comprises: The difference between the risk-adjusted utility and the average expected benefit of the water receiving area is calculated, the difference is multiplied by the learning ability coefficient and the current strategy selection probability to obtain a probability updating amount, and the strategy selection probability is adjusted according to the probability updating amount.

4. The method according to claim 2 or 3, wherein, The obtaining of the stable decision combination comprises: A convergence threshold of the strategy selection probability is set, when the probability of the water receiving area selecting a water use planning strategy exceeds the convergence threshold, the strategy is determined as the stable strategy of the water receiving area; After all the water receiving areas determine the stable strategies, a stable decision combination corresponding to the random sample is formed; According to the annual water inflow level of the water receiving area of the random sample, the stable decision combination is classified into annual water use planning strategies corresponding to wet years, normal years and dry years.

5. The method according to claim 1, wherein, The generation of the random sample of the water receiving process and the available water inflow comprises: An initial random number matrix is generated based on a three-dimensional joint distribution function, a row of the matrix represents a time period, and a column of the matrix represents a water source area and a water receiving area; A time series correlation matrix between adjacent months in the historical data is calculated, and a type correlation matrix between different water receiving areas is constructed; An improved Latin hypercube sampling method is used to reorder the initial random number matrix according to the time series correlation matrix and the type correlation matrix, and a random sample maintaining spatio-temporal correlation is generated.

6. The method according to claim 5, wherein, The calculation of the time series correlation matrix and the construction of the type correlation matrix comprise: The water inflow sequence of each month in the historical data is extracted, the Pearson correlation coefficient between adjacent months is calculated, and a 12*12 time series correlation matrix is formed; The spatial distance weight is calculated according to the geographical position of the water receiving area, and the type correlation matrix between the water receiving areas is constructed by combining the water supply feature similarity of the water receiving areas; The time series correlation matrix and the type correlation matrix are respectively subjected to Cholesky decomposition to obtain lower triangular matrices, and the initial random number matrix is multiplied by the lower triangular matrices to realize the generation of the random sample under the correlation constraint.

7. The method according to claim 1, wherein, The calculation of the comprehensive benefit value of the water receiving area comprises: The water supply guarantee target, the water use benefit target, the water transfer cost target and the fairness target of the water receiving area are calculated based on the water supply amount, a four-dimensional benefit vector is formed and normalized, and the four-dimensional benefit vector is normalized; The water supply guarantee target is measured by a water supply guarantee rate, and is calculated as the ratio of the number of time periods satisfying the water demand to the total number of time periods; The water use benefit target is calculated by weighted summation of the benefits of power generation and water supply; The water transfer cost target is calculated by the product of the actual water supply amount and the water transfer cost coefficient; The fairness target is measured by the difference between the water supply guarantee degree of the water receiving area and that of other areas; The multi-objective benefit vector set is subjected to Pareto non-dominated sorting to determine the non-dominated level of each strategy combination, and the crowding distance is calculated in the same non-dominated level; The strategy dispersion degree of the water use planning strategy combination is calculated, and the comprehensive benefit value is obtained by weighted combination of the non-dominated level, the crowding distance and the strategy dispersion degree.

8. The method according to claim 7, wherein, The calculation of the strategy dispersion degree comprises: The frequency of each strategy in the water use planning strategy combination is counted, the strategy distribution entropy is calculated, and the strategy dispersion degree is obtained by dividing the strategy distribution entropy by the maximum possible entropy value. The calculation formula of the comprehensive benefit value is: taking the reciprocal of the non-dominant level as the level score, taking the normalized congestion distance as the distance score, assigning the level score, the distance score and the strategy dispersion degree to the weight coefficients a, b and c respectively, and weighting and summing to obtain the comprehensive benefit value.

9. The method according to claim 1, wherein, The generation of the random sample of the water intake and water receiving area water inflow process adopts a master-slave calculation method, comprising: From the three-dimensional joint distribution function, first, the uniform distribution random number of the water source area water intake is generated by inverse transformation sampling; Based on the generated water source area water intake, the water receiving area current time water inflow is generated by the conditional distribution function; According to the water source area water intake and the water receiving area current time water inflow, the water receiving area last time water inflow is generated by the conditional Copula function, and the uniform distribution random number is inversely transformed to the original variable space to form a random sample that maintains the space-time correlation.

10. The method according to claim 1 or 2, wherein, It also includes classification processing of stable decision combinations: According to the annual water inflow of the water receiving area in the random sample, the stable decision combinations are divided into three categories: wet year, normal year and dry year; The frequency distribution of the water receiving area selecting each water plan strategy under each type of water inflow condition is counted, and the strategy difference degree between different water inflow conditions is calculated; When the strategy difference degree exceeds the set threshold, the stable decision combinations under different water inflow conditions are stored respectively as classified scheduling plans; otherwise, a unified stable decision combination is used as the annual scheduling plan.

11. The method according to claim 5, wherein, The improved Latin hypercube sampling method comprises: The historical water consumption sequence is seasonally-trend decomposed by using local weighted regression method, the trend item, the seasonal item and the residual item are extracted, and the water consumption benchmark range of different months is determined; An ARIMA model is used to fit the time series relationship between monthly water consumption, and a 12x12 time series correlation matrix is constructed; The Pearson correlation coefficients of the same period and different types of water consumption are calculated, and the Archimedean Copula function is used to fit the joint distribution of the linear correlation weak to obtain the inter-type correlation matrix; The marginal distribution of each month-water type dimension is divided into N equal probability intervals, and N is the sampling sample size of the random strategy and N≥50; The first month is taken as the benchmark to randomly sample from N layers, and the sampling layer of the subsequent months is constrained according to the time series correlation matrix to ensure the dependence of the sample of each month on the previous months; The current correlation matrix of each month and different types of water samples is calculated, and when the correlation deviation from the inter-type correlation matrix is greater than 5%, the target correlation matrix is embedded in the sample for correction by Cholesky decomposition.

12. A multi-agent evolutionary game system for generating a water transfer project annual operation plan, characterized in that, It comprises: At least one processor; And The memory is in communication connection with the at least one processor; wherein The memory stores instructions executable by the processor, and the instructions are executed by the processor to implement the water transfer project annual scheduling plan generation multi-agent evolutionary game method of any one of claims 1 to 11.

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