Risk control method for inter-basin water diversion system

Abstract

The application discloses a kind of interbasin water transfer system risk control methods, comprising: obtaining the inflow scenario data of system to be analyzed, water demand scenario data and preconfigured water transfer scheme set;Water quantity scheduling simulation is carried out based on water transfer scheme set to scenario data, determine the water shortage risk index and water abandonment risk index of each spatial node in system under different schemes;Based on the above two types of risk indicators, the risk response function that the risk level evolves with the relationship of water transfer quantity is fitted;Based on the risk response function, the risk transfer marginal substitution index that the risk replacement efficiency between each spatial node is represented is calculated;The efficient balanced water transfer interval of system is determined in combination with risk transfer marginal substitution index and preconfigured risk space equilibrium criterion.The application can scientifically quantify the risk transfer efficiency of cross spatial unit, realize the double-target collaborative optimization decision of system total risk optimization and risk space equilibrium.

Description

Technical Field

[0001] This invention relates to the field of water resource allocation and risk management technology, specifically to a risk control method for inter-basin water transfer systems. Background Technology

[0002] In real-time water allocation, the system faces multiple uncertainties, including natural runoff and regional user water demand. Cross-regional physical allocation of water resources not only alters the spatial distribution of physical water volume but also profoundly changes the distribution of water shortage and water wastage risks across different watersheds. Therefore, scientifically quantifying the risk evolution mechanism during the allocation process and formulating multi-objective coordinated allocation strategies are of significant technical importance for ensuring the operational safety and allocation efficiency of complex water resource systems.

[0003] Current research on multi-objective water resource scheduling mainly focuses on constructing conventional multi-objective optimization scheduling models. This typically employs heuristic methods such as evolutionary algorithms to search for the Pareto front under specific hydrological boundaries, or compares the risk probabilities of different scheduling rules through large-scale Monte Carlo simulations. However, when dealing with cross-basin scheduling networks with strong spatial coupling characteristics, these existing technologies often rely on discrete simulation schemes for statistical observation, making it difficult to directly and continuously quantify the marginal impact of incremental water transfer on risk fluctuations in different spatial units. Furthermore, because different types of risks, such as the risk of water abandonment measured by volume and the risk of water shortage measured by ratio, exhibit significant asymmetric responses at the underlying physical mechanisms, existing methods struggle to accurately analyze the specific efficiency of risk replacement between different regions in multi-dimensional risk interaction scenarios. This can easily lead to high overall system risk or severe spatial imbalances when pursuing local objectives.

[0004] In summary, existing methods struggle to accurately measure the nonlinear evolution efficiency of different types of risks across time and space when dealing with complex hydrological uncertainties. Furthermore, they lack effective technical means to define the boundaries between the overall optimal system and spatial equilibrium in multi-agent game scenarios. Therefore, it is necessary to investigate a water regulation method that can effectively quantify the spatiotemporal transfer patterns of multidimensional risks and support efficient collaborative decision-making under complex physical constraints. Summary of the Invention

[0005] Therefore, this application provides a risk control method for inter-basin water transfer systems in order to solve the above-mentioned problems existing in the prior art.

[0006] According to one aspect of this application, a risk control method for an inter-basin water transfer system includes:

[0007] Obtain inflow and demand scenario data for the inter-basin water transfer system to be analyzed, and obtain a set of pre-configured water transfer schemes;

[0008] Based on the water transfer scheme set, water volume scheduling simulation is performed on inflow scenario data and water demand scenario data to determine the water shortage risk index and water abandonment risk index of each spatial node in the inter-basin water transfer system under different water transfer schemes.

[0009] Based on water shortage risk indicators and water abandonment risk indicators, a risk response function is fitted to characterize the relationship between risk level and water transfer volume.

[0010] Based on the risk response function, the marginal substitution index of risk transfer, which characterizes the efficiency of risk replacement among spatial nodes, is calculated.

[0011] Based on the risk transfer marginal substitution index and the pre-configured risk space equilibrium criterion, the efficient and balanced water transfer interval of the inter-basin water transfer system is determined.

[0012] According to another aspect of this application, a computer program product is provided, including computer instructions that, when executed by a processor, implement a risk control method for an inter-basin water transfer system proposed in this invention.

[0013] Based on the above technical solutions, this invention can scientifically quantify the risk transfer efficiency across spatial units, and achieve dual objectives of optimal total system risk and risk space equilibrium, thus enabling effective decision-making. Attached Figure Description

[0014] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0015] Figure 1 This is a schematic diagram of a risk control method for an inter-basin water transfer system provided in this application.

[0016] Figure 2 This is a schematic diagram of the process for calculating the marginal substitution index for risk transfer, which characterizes the efficiency of risk substitution between spatial nodes, provided in this application.

[0017] Figure 3 This is a schematic diagram of the process for determining the efficient and balanced water transfer interval of an inter-basin water transfer system based on the risk transfer marginal substitution index and the pre-configured risk space equilibrium criterion provided in this application.

[0018] Figure 4 This is a schematic diagram of the process for pre-acquiring water inflow scenario data and water demand scenario data provided in this application.

[0019] Figure 5 This application provides a schematic diagram of the process for extracting the optimal point of total system risk, representing the minimum value of the total weighted risk of the inter-basin water transfer system, when the risk response function is in the form of a power function containing a scale coefficient and a shape exponent. Detailed Implementation

[0020] Example 1 describes the global framework for risk control of inter-basin water transfer systems and the core link of outputting scheduling decisions and converting them into physical commands.

[0021] In one possible implementation, a risk control method for inter-basin water transfer systems, such as... Figure 1 As shown, it may include the following steps:

[0022] Step 101: Obtain the inflow scenario data and demand scenario data of the inter-basin water transfer system to be analyzed, and obtain the pre-configured set of water transfer schemes.

[0023] In this embodiment, an inter-basin water transfer system typically refers to a complex engineering system involving two or more river basins, which redistributes water resources spatially through artificial water transfer channels. For example, taking a specific inter-basin water transfer project as an example, the system mainly includes two key storage nodes: a first storage node serving as a storage hub in the source area, and a second storage node serving as a storage hub in the receiving area. Correspondingly, the inflow scenario data includes the predicted local natural inflow sequences of the two storage lakes; the demand scenario data includes the water demand sequences supplied by the first storage node (such as surrounding agricultural and industrial water users) and the second storage node.

[0024] Furthermore, the pre-configured water diversion scheme set can refer to the state domain of various combinations of external and internal water diversion volumes set by the system within a given scheduling period, based on the upper limit of the engineering water conveyance capacity. For example, the external replenishment water diversion volume from an external water source to the first storage node and the internal water diversion volume from the first storage node to the second storage node can be set. By discretizing water diversion volume combination schemes of different scales, a gridded water diversion scheme set covering various engineering boundary conditions can be formed.

[0025] Step 102: Based on the water transfer scheme set, perform water volume scheduling simulation on the inflow scenario data and the demand scenario data to determine the water shortage risk index and water abandonment risk index of each spatial node in the inter-basin water transfer system under different water transfer schemes.

[0026] For the multiple sets of uncertain scenario data and discrete water transfer schemes obtained in step 101, time-period water volume extrapolation calculations are performed. During the simulation, physical boundary constraints such as the flood control limit water level, normal storage water level, and dead storage capacity of the lake are comprehensively considered. For example, for the inter-basin water transfer system, the dynamic requirements of the upper limit of storage capacity during the flood season (usually June to September) and the non-flood season (usually October to May of the following year) are considered, and the actual water supply and storage status of each spatial node in each time period are calculated.

[0027] It should be clearly stated that this embodiment distinguishes between the dimensional definitions of water shortage risk indicators and water abandonment risk indicators. Water shortage risk indicators are specifically defined as dimensionless ratios, such as the weighted average water shortage rate, which is the percentage of water shortage relative to total water demand. Water abandonment risk indicators are defined as the volumetric value of a physical body containing water, for example, using a ratio of 10... 8 m 3 The weighted average water discharge is calculated per unit. The difference in dimensions is because water shortage events have relatively independent impacts on users of different sizes, while water discharge events are constrained by the absolute boundaries of the lake's physical storage capacity.

[0028] Step 103: Based on the water shortage risk index and the water abandonment risk index, fit a risk response function that characterizes the relationship between the risk level and the water transfer volume.

[0029] In this step, the system collects discrete risk index results under various water diversion scheme combinations and uses mathematical methods such as nonlinear regression to transform the discrete simulation point set into a continuously differentiable function surface. This transformation process reveals the marginal change patterns of risk indicators at each spatial node when the water diversion volume is increased or decreased. For example, through fitting, it was found that increasing the internal water diversion volume from the first storage node to the second storage node reduces the water abandonment risk of the first storage node itself, but increases the water shortage risk for its users, and simultaneously increases the water abandonment risk of the second storage node in the receiving area. The risk curve exhibits obvious nonlinear characteristics (such as rapid response in the early stage and slowing down or saturation in the later stage).

[0030] Step 104: Based on the risk response function, calculate the risk transfer marginal substitution index, which characterizes the risk substitution efficiency between spatial nodes.

[0031] To address the technical challenge of comparing the absolute values ​​of water shortage risk and water abandonment risk due to their different dimensions, this invention employs differentiation and ratio calculation. Specifically, for a given water transfer path (such as an internal water transfer path from the first storage node to the second storage node), the continuous risk response function generated in step 103 is used to calculate the partial derivatives of the risk indicators of the beneficiary node and the undertaking node with respect to the water transfer variable. Then, the absolute values ​​of these partial derivatives are taken as a ratio. This ratio eliminates the interference of the original indicator's absolute dimension, yielding a purely dynamic value representing efficiency. That is, for every unit of risk sacrificed by the undertaking node, how many units of risk reduction can be achieved by the beneficiary node? This provides a standardized quantitative basis for water rights exchange and risk negotiation across watersheds.

[0032] Step 105: Based on the risk transfer marginal substitution index and the pre-configured risk space equilibrium criterion, determine the efficient and balanced water transfer interval of the inter-basin water transfer system.

[0033] By combining the optimal state of overall system risk reflected by the aforementioned marginal substitution indicators with the optimal equilibrium state of risk space reflected by statistical methods such as the spatial variation coefficient, the system extracts the overlap or compromise range between the two. Determining this range avoids extreme scheduling decisions that might result from a single objective. For example, pursuing only the extreme reduction of water shortage risk in one lake could lead to another lake bearing a higher risk of water wastage with lower marginal efficiency, resulting in ineffective water diversion or even flood control hazards.

[0034] By jointly defining the water diversion range with the optimal point of total system risk and the spatial equilibrium point, any water diversion decision within the range can simultaneously ensure that the marginal improvement of the risk beneficiary is greater than the marginal cost of the risk bearer (efficiency guarantee) when increasing the water diversion volume, while the risk level of each node remains relatively balanced (equilibrium guarantee), which can effectively suppress the extreme concentration of risk at a certain node caused by the optimization of a single objective.

[0035] Optionally, after determining the efficient and balanced water transfer zone of the inter-basin water transfer system, the following may also be included:

[0036] Step 106: Select the target water transfer decision value within the efficient and balanced water transfer range.

[0037] Once the system calculates and outputs the aforementioned efficient and balanced water transfer range, the dispatch decision center can select the final deterministic water transfer volume within this safety constraint boundary, taking into account non-hydrological factors such as annual electricity price cost fluctuations.

[0038] Step 107: The target water transfer decision value is converted into a physical control signal and sent to the physical pumping station or reservoir gate corresponding to the inter-basin water transfer system to execute the actual water dispatching instructions.

[0039] After selecting the target water diversion decision value, the system scheduling module breaks it down into physical execution parameters for each time period and each engineering node, and generates electronic control signals. For example, if the target water diversion decision value determines that 20*10 water will be replenished to the first storage node from an external water source. 8 The control system translates the instruction into specific instructions on the number of units to be started and the duration of operation of the external replenishment pumping station hub, as well as instructions on the opening degree of the control gates along the line. These instructions are then sent to the front-line engineering nodes for execution through the automated control network or manually, thereby realizing the closed-loop transformation of the cross-basin water transfer risk control algorithm into the actual engineering regulation and storage actions.

[0040] According to another aspect of this application, a computer program product is also provided, including computer instructions that, when executed by a processor, implement the risk control method for an inter-basin water transfer system proposed in this invention.

[0041] Example 2, as a prerequisite data preparation support for Example 1, elaborates in detail the construction mechanism of inflow scenario data and demand scenario data in offline state, as well as the discretization generation process of water transfer scheme set.

[0042] One possible implementation, such as Figure 4 As shown, the inflow and demand scenario data are pre-acquired through the following offline construction steps:

[0043] Step 201: Obtain the pre-stored historical data of runoff prediction error and water demand prediction error for each spatial node.

[0044] In this embodiment, before performing online scheduling simulation, the system pre-constructs a set of probabilistic scenarios covering both extreme and conventional boundary conditions. Using historical observation data to drive deterministic forecasting models such as multi-process coupled runoff prediction models, it obtains the runoff prediction time series for source area and receiving area reservoirs, as well as the corresponding water demand prediction time series for users. The numerical deviation between the predicted time series and the actual observation series for the same period is calculated, and the corresponding historical runoff prediction error data and water demand prediction error data are extracted and pre-stored in the underlying database as basic input variables for subsequent probabilistic modeling.

[0045] Step 202: Marginal distribution fitting is performed on the historical data of runoff prediction error and the historical data of water demand prediction error, and the joint probability correlation structure among multiple variables is constructed using the vine structure co-system model.

[0046] Specifically, marginal distribution fitting is performed on historical data of runoff prediction error and historical data of water demand prediction error to obtain the marginal distribution function corresponding to each error variable; based on the marginal distribution function, probability integral transformation is performed on each error variable to obtain uniformly distributed variables distributed in the closed interval from zero to one; and a vine structure co-correlation model is used to construct a joint probability correlation structure among multiple variables for the uniformly distributed variables.

[0047] For the acquired multidimensional error time series, marginal distribution fitting was performed independently on the historical runoff prediction error data and water demand prediction error data acquired at each time step and spatial node. A candidate distribution family containing various statistical distribution patterns was established, specifically including normal distribution, skewed normal distribution, Student's t-distribution, and generalized extreme value distribution. The Akaike information content criterion value corresponding to each candidate distribution was calculated, and the candidate distribution with the smallest criterion value was selected as the optimal marginal distribution for the corresponding error variable.

[0048] After selecting the optimal marginal distribution using the Akaike information content criterion, a probability integral transformation is performed on each error variable to map it into a uniformly distributed variable within the 0-1 interval. A multidimensional joint probability dependency structure is then established for these uniformly distributed variables using the Vine Copula model. Specifically, the maximum spanning tree algorithm is used to determine the tree-like connection topology of the vine structure based on the calculated empirical Kendall correlation coefficient. For each binary copula node in the vine structure topology, the matching binary copula function is selected again from the Gaussian, Clayton, Gombbel, Frank, and Jo functions families based on the Akaike information content criterion.

[0049] In some embodiments, to ensure that the subsequent family of parameterized functions operates in a dimensionless space, before performing curve fitting, the water transfer volume variable of each spatial node is normalized by dividing it by the corresponding maximum engineering design water conveyance capacity, thus constraining the independent variable's value range to the dimensionless interval of 0 to 1. In this application, the water transfer volume variable in subsequent steps refers to the normalized dimensionless value, and all parameter fitting and calculation are performed in a dimensionless space.

[0050] Step 203: Perform equal probability random sampling based on the joint probability correlation structure (where the probability of each scenario is set to 1 / L) to generate pre-constructed water inflow scenario data and water demand scenario data.

[0051] After constructing the aforementioned joint probability correlation structure, a Monte Carlo simulation algorithm was used to conduct joint random sampling. A target sampling quantity parameter was set, for example, 1000 groups, and the probability of occurrence of each group's multivariate error scenario was determined to be equal, i.e., the discrete occurrence probability of a single group was 1 / 1000. The time series of random errors generated by the joint sampling were then superimposed and fused onto the original deterministic prediction sequence, resulting in 1000 groups of inflow and demand scenario data covering a combination of uncertainties in multi-source hydrological and meteorological data. This data, generated on an offline server, was packaged into a static scenario dataset and provided for batch processing in the online water allocation simulation.

[0052] In some optional implementations, in addition to constructing the scenario data described above, the system simultaneously constructs a set of water diversion schemes during this offline phase. A pre-stored historical average water diversion process sequence is acquired as a reference baseline, and two independent dimensionless scaling coefficients are configured for the system, defined as the first scaling coefficient and the second scaling coefficient. The first scaling coefficient is used to linearly scale the external water supply volume, and the second scaling coefficient is used to linearly scale the internal inter-regional water transfer volume. The search range for both the first and second scaling coefficients is set to be distributed within a closed interval of 0 to 1, and equidistant offset lengths are configured. For example, setting the offset length to 0.05, a set of water diversion schemes containing 441 different water diversion scale configuration matrices is generated by traversing all parameter node combinations through a double-layer loop. This set of water diversion schemes covers the entire control operation space from zero water supply to full-load water transfer, providing a complete sample for subsequent extraction of the nonlinear laws of the risk response function.

[0053] It should be noted that the above parameters are exemplary configurations for this embodiment, and those skilled in the art can adaptively adjust them using conventional methods according to actual accuracy requirements and computing resources.

[0054] Example 3 further describes the spatiotemporal extrapolation mechanism and the underlying physical state mutual exclusion logic in the water allocation simulation process.

[0055] In this embodiment, the inter-basin water transfer system typically consists of multiple hydraulically connected spatial nodes. Before performing water volume estimation, the topology network of each spatial node is pre-analyzed to extract the engineering water transfer direction, thereby establishing a pre-configured series topology sequence of water transfer lines. For example, in the target inter-basin water transfer system model, the system determines the node responsible for receiving external water sources, pumping water, or performing primary water transfer as the first storage node, and the node receiving water from the preceding node and participating in subsequent storage and allocation as the second storage node. The estimation process strictly follows the order of calculating the first storage node first, followed by the second storage node. In the time dimension, the entire scheduling period is discretized into continuous calculation periods, for example, setting the step size of the calculation period to a natural month or natural day, and advancing forward along the time axis within each spatial node.

[0056] One possible implementation involves simulating water allocation based on inflow and demand scenario data using a set of water transfer schemes. This simulation determines the water shortage and water abandonment risk indicators for each spatial node within the inter-basin water transfer system under different water transfer schemes, including:

[0057] For any spatial node, the following scheduling simulation steps are executed time-by-time according to the pre-configured series topology of the water diversion lines:

[0058] Step 301: Combine the pre-configured initial water storage status or the end-of-period water storage status of the previous period, and determine the available water volume for the current period based on the inflow scenario data and the water transfer scheme set.

[0059] When calculating available water volume, the system extracts the node's own historical water storage and the incremental water storage from external interactions. For the first calculation period of the scheduling period, the system reads the pre-configured initial water storage status; for subsequent periods, it extracts the end-of-period water storage status of the previous period. The system extracts the local natural inflow component from the inflow scenario data and extracts the planned inflow and planned outflow water volumes corresponding to the current period from the water transfer scheme set, performing linear summation calculations based on the water balance principle.

[0060] W i，t l =V i，t-1 l +I i，t l +Q i，t，in -Q i，t，out ;

[0061] Among them, W i，t l Let V be the available water volume of spatial node i in time period t under scenario l. i，t-1 l Let I represent the water storage state of spatial node i at the end of time period t-1 under scenario l. i，t l For the local natural inflow of spatial node i in time period t under scenario l, Q i，t，in Q is the planned water inflow. i，t，out This is the planned amount of water to be diverted.

[0062] Step 302: Combine the pre-configured dead storage capacity constraint and available water volume to determine the maximum available water volume for the current period.

[0063] Due to the physical design limitations of hydraulic structures, there exists water within spatial nodes that cannot be utilized through gravity flow or conventional pumping; this is defined as a pre-configured dead storage capacity constraint. The difference between the available water volume for the current period and the dead storage capacity constraint is calculated. If the difference is less than zero, it is forcibly set to zero; if the difference is greater than zero, it is retained as the maximum available water volume for the current period. The calculation process is as follows:

[0064] S i，t l ，max =max(0, W) i，t l -V dead );

[0065] Among them, S i，t l ，maxLet W be the maximum available water volume for spatial node i in time period t under scenario l, where max is the function that takes the maximum value. i，t l Let V be the available water volume of spatial node i in time period t under scenario l. dead For the dead storage capacity constraint of spatial node i.

[0066] Step 303: Compare the water demand scenario data with the maximum available water volume to determine the actual water supply and the water shortage status data that characterizes the degree of water shortage.

[0067] Obtain the target water demand from the current water demand scenario data, compare it with the calculated maximum available water volume, and extract the smaller value as the actual water supply. Further, calculate the difference between the target water demand and the actual water supply, and record this difference as water shortage status data characterizing the degree of water shortage.

[0068] S i，t l =min(D i，t l S i，t l ，max );

[0069] WD i，t l =D i，t l -S i，t l ;

[0070] Among them, S i，t l Let D be the actual water supply of spatial node i in time period t under scenario l, and min be the function that takes the minimum value. i，t l S represents the water demand scenario data for user corresponding to spatial node i in scenario l during time period t. i，t l ，max For maximum available water volume, WD i，t l Water shortage status data to characterize the degree of water shortage.

[0071] Step 304: Calculate the temporary water storage volume after deducting the actual water supply from the available water volume, and compare the temporary water storage volume with the pre-configured seasonal water storage upper limit constraint to determine the water abandonment status data representing the over-storage overflow and the end-of-period water storage status of the current period.

[0072] Because reservoirs need to undertake different flood control or water conservancy tasks in different seasons, the corresponding seasonal water storage upper limit constraint is dynamically applied based on the monthly attribute of the current calculation period. For example, when the current period is in the flood season, the flood limit capacity is used as the upper limit; when it is not in the flood season, the normal water storage capacity is used as the upper limit. The difference between the available water volume and the actual water supply is calculated to obtain the temporary water storage volume. The difference between this temporary water storage volume and the seasonal water storage upper limit constraint is calculated. If the difference is greater than zero, it is determined that over-storage has occurred, and the positive difference is recorded as water abandonment status data; if the difference is less than or equal to zero, the water abandonment status data is set to zero. The temporary water storage volume is subtracted from the water abandonment status data to obtain the updated end-of-period water storage status.

[0073] V i，t l ，temp =W i，t l -S i，t l ;

[0074] SP i，t l =max(0, V) i，t l ，temp -V i，t upper );

[0075] V i，t l =V i，t l ，temp -SP i，t l ;

[0076] Among them, V i，t l ，temp For temporary water storage, W i，t l S represents the available water volume. i，t l SP represents the actual water supply. i，t l For water discharge status data, max is the function to maximize the value, V i，t upper V represents the upper limit constraint for seasonal water storage corresponding to time period t. i，t l This represents the water storage status at the end of the current period.

[0077] Based on this, the water shortage status data and water abandonment status data of each spatial node during the entire scheduling period are statistically analyzed, and corresponding water shortage risk indicators and water abandonment risk indicators are generated respectively.

[0078] After completing the simulations for all time periods, the discrete state data under each single scenario are aggregated, and the expected value is calculated by combining the occurrence probability of each scenario. For water shortage risk, the ratio of the total water shortage state data to the total water demand data for the entire scheduling period under each scenario is calculated, then multiplied by the occurrence probability of that scenario and summed across scenarios to obtain a dimensionless water shortage risk index. For water abandonment risk, the system directly performs probability-weighted summation on the total water abandonment state data for the entire scheduling period under each scenario to obtain a water abandonment risk index with physical volume dimensions.

[0079] WD data on water shortage status in various scenarios and time periods i，t l (The water deficit of the entity) is normalized to a water deficit rate, and then weighted and summed with the scenario probability to obtain the dimensionless water deficit risk index SR. i :

[0080] SR i =∑(p l *R l );

[0081] Among them, SR i p is the water shortage risk index for spatial node i. l Let be the probability of the l-th scenario occurring.

[0082] R l =∑ t (WD i，t l ) / ∑ t (D i，t l ), which is the ratio of the total water shortage status data to the total water demand data during the entire scheduling period under the l-th scenario, i.e., the water shortage rate under the l-th scenario, and ∑ is the cross-scenario summation operation.

[0083] The following formula is used to summarize and calculate the risk indicators for water abandonment:

[0084] SP i =∑(p l ×SP total，i l );

[0085] Among them, SP i p is the water abandonment risk index for spatial node i. l Let SP be the probability of the l-th scenario occurring. total，i l =∑ t (SP i，t l ), where is the total water abandonment status data of spatial node i during the entire scheduling period under the l-th scenario, and ∑ is the cross-scenario summation operation.

[0086] In one possible implementation, during the process of determining water shortage status data and water abandonment status data, a water supply priority criterion is used to limit spatial nodes to one of the following three mutually exclusive states at any given time period.

[0087] The above steps are based on a water supply priority scheduling rule, meaning that the system always prioritizes using all available water to meet water demand scenarios at any given time. Only after the water demand is fully met will the remaining water be converted into storage or further overflowed and discarded. This mechanism mathematically ensures the monotonic response of available water and guarantees that the system can only be in one of the three mutually exclusive states: water shortage, water discard, or equilibrium. This effectively reduces the risk of computational divergence caused by overlapping states.

[0088] 1. Water shortage status: When the actual water supply is less than the water demand scenario data, the effective water shortage is determined as the water shortage status data, and the water abandonment status data is forcibly reset to zero.

[0089] In this state, the system's available water volume is insufficient to meet the user's water demand. Based on the sequential deduction logic of steps 303 and 304, the temporary water storage volume at this time is equal to zero or reaches the dead storage capacity boundary, which is far below the seasonal water storage upper limit constraint. Therefore, physically, there will be no over-storage overflow. The water abandonment volume is forcibly reset to zero, and only the calculated effective water shortage volume is retained for input into the subsequent risk assessment stage.

[0090] Second, water abandonment status: When the water demand scenario data is fully met by the actual water supply, and the temporary water storage is greater than the seasonal water storage upper limit constraint, the effective water abandonment is determined as the water abandonment status data, and the water shortage data in the water shortage status data is forcibly reset to zero.

[0091] In this state, the system has a relatively abundant supply of water. On the one hand, the large volume of water covers the target water demand, so the actual water supply equals the water demand scenario data, and the calculated water shortage is zero and is forcibly locked by the system. On the other hand, after fully meeting the water supply needs, the remaining water volume still exceeds the physical capacity limit of the reservoir or the flood control safety boundary. The excess water is discharged through physical facilities such as spillways, generating non-zero water discharge status data.

[0092] Third, equilibrium state: When the water demand scenario data is fully met by the actual water supply and the temporary water storage does not exceed the seasonal water storage limit, the water shortage data in the water shortage state data and the water abandonment data in the water abandonment state data are both forcibly reset to zero.

[0093] The equilibrium state is the ideal operating condition for water resource allocation. At this state, the available water volume is sufficient to cover all water demand, preventing water shortages, while the remaining water volume can be fully accommodated by the reservoir's current available capacity, avoiding unnecessary waste of water resources. In the equilibrium state, when the system receives an increase in available water volume from external water transfers, it converts this into an increase in the final storage level. This increased storage volume will be re-allocated by the system in subsequent periods, ultimately transforming into additional water supply or additional water release, ensuring the overall material conservation of the system.

[0094] In some alternative implementations, if the system does not adopt the simple scheduling principle of supplying water first and then storing it, but instead employs a complex scheduling strategy that includes hedging rules or multi-period look-ahead optimization, then the state mutual exclusion logic needs to be adjusted. Specifically, in step 303, the system no longer simply takes the smaller value between the demand and the maximum available water volume, but instead introduces a pre-configured water shortage penalty factor and a water storage benefit factor for joint optimization. Under the hedging rule, the system may proactively reduce the current actual water supply before the available water volume is exhausted, transferring some water to the water storage state in advance to prevent the risk of more severe drought in the future. In such alternatives, the coupled calculation logic of water shortage state data and water abandonment state data is updated by determining whether there is an instruction variable for actively restricting water supply in the current period.

[0095] Example 4 details how to convert discrete water volume scheduling simulation output data into a continuous differentiable function surface with physical mechanism significance.

[0096] In one possible implementation, fitting a risk response function that characterizes the relationship between risk level and water transfer volume specifically includes:

[0097] Step 401: Based on the regulation and storage mechanism and supply and demand characteristics of each spatial node in the inter-basin water transfer system during the water transfer process, determine a family of parameterized functions with preset convexity and concavity characteristics; the preset convexity and concavity characteristics are determined based on the differences in the storage capacity of each spatial node.

[0098] In this application, a concave response refers to the characteristic that the rate of risk change decreases as the water transfer volume increases (i.e., the marginal response decreases), while a convex response refers to the characteristic that the rate of risk change increases as the water transfer volume increases (i.e., the marginal response increases).

[0099] In some embodiments, a family of parameterized functions with corresponding convex-concave characteristics is determined based on pre-configured storage capacity parameters and supply-demand characteristic parameters of each spatial node.

[0100] In this embodiment, the water shortage risk index and water abandonment risk index output by the water allocation simulation are both discrete data points on a multi-dimensional grid. In order to perform analytical differentiation calculation on the risk transfer marginal substitution index between spatial nodes, the above discrete points are converted into a continuous function surface.

[0101] Specifically, the convexity / concavity of the response function is defined based on the absolute size difference of the reservoir's storage capacity. Source lakes possess large storage capacity; in the initial stage of increased outflow, their risk of water abandonment decreases rapidly, but then levels off in the later stage, exhibiting an overall concave physical characteristic. Receiving lakes have relatively smaller storage capacity; as the inflow continues to increase, their receiving capacity rapidly approaches physical saturation, leading to a sharp increase in the risk of water abandonment in the later stage, exhibiting an overall convex physical characteristic. The above physical storage mechanism is extracted, and a mathematical formula base satisfying the corresponding convexity / concavity conditions is pre-selected. In some embodiments, the situation of the source area increasing with the inflow also needs to be considered. Determining a family of parameterized functions with preset convexity / concavity characteristics includes at least one of the following function form construction steps: selecting the following function forms according to the storage role of the spatial nodes:

[0102] Step 4011: For the water release risk index determined based on the pre-configured storage capacity parameters, which exhibits a concave response characteristic with decreasing rate of decrease or a convex response characteristic with increasing rate of decrease as the amount of water released increases, a power function form with scale coefficient, shape index, and base water release level parameter is selected as the first type of sub-function family.

[0103] Specifically, the first type of sub-function family uniformly adopts a power function structure with scale coefficient, shape index and base water abandonment level parameter. Depending on the role of the spatial node, it is applicable to the source area node where the risk of water abandonment decreases with the increase of the outflow of water, and the receiving area node where the risk of water abandonment increases with the increase of the inflow of water.

[0104] Furthermore, a dedicated mathematical analytical model is constructed to address the risk of water wastage. For source region spatial nodes exhibiting concave response characteristics, the following equation is used for parameter extraction:

[0105] SP H =-a H *Q N gH +h H ;

[0106] Among them, SP H The calculated value of the water spillover risk index for spatial nodes in the source region, a HQ represents the scale factor corresponding to the spatial nodes of the source region. The scale factor is obtained by fitting discrete water transfer simulation data using a nonlinear parameter estimation method. Its value has absorbed the conversion of water transfer volume measurement units. Those skilled in the art can directly determine the appropriate value through curve fitting based on actual data. N g represents the water diversion variable within the system. H Let g be the shape index corresponding to the spatial nodes of the source region, and g H The range of values ​​is constrained to 0. <g H <1,h H The baseline water discharge level parameters of the spatial nodes in the source region.

[0107] For nodes where the risk of water wastage decreases with increasing outflow volume (such as source areas), a power function in negative form (i.e., SP) is used. H =-a H ×Q N gH +h H The risk of water abandonment is characterized by a power function (SP) in positive form. For nodes where the risk of water abandonment increases with the amount of water transferred in (such as water receiving areas), the risk is represented by a power function (SP) in positive form. L =a L ×Q N gL +h L ) is characterized.

[0108] For spatial nodes in the water-receiving area that exhibit convex response characteristics, the following form of equation is used for parameter extraction:

[0109] SP L =a L *Q N gL +h L ;

[0110] Among them, SP L For the calculated value of the water abandonment risk index of the spatial nodes in the water receiving area, a L Q represents the scale factor corresponding to the spatial nodes of the water-receiving area. N g represents the water diversion variable within the system. L Let g be the shape index corresponding to the spatial nodes of the water-receiving area, and g L The range of values ​​for g is constrained. L >1,h L The baseline water discharge level parameters of the spatial nodes in the water-receiving area.

[0111] Both forms are parameterized instances of the first type of sub-function family under different physical conditions. They both satisfy the power function structure characteristics with scale coefficient, shape index and base water discharge level parameters. Those skilled in the art can select the corresponding function form according to the storage physical characteristics of the spatial nodes.

[0112] Step 4012: For the convex decreasing response characteristics of the water shortage risk index, which is determined based on the pre-configured supply and demand characteristic parameters and decreases with the increase of the amount of water transferred in and the rate of decrease, a negative exponential function form with the maximum amount of risk that can be improved, the risk decay rate and the residual water shortage parameter is selected as the second type of sub-function family.

[0113] In situations of system water shortage, the mitigation effect of incremental water diversion on drought relief exhibits a diminishing marginal utility law. Specifically, in the initial stage with low water inflow, a small amount of additional water diversion can significantly improve water shortage conditions in most scenarios, causing a rapid decrease in water shortage risk indicators. However, once the water inflow increases to a certain scale, water demand under most conventional scenarios is largely met, and the remaining water shortage risk is mainly concentrated in a few extreme drought or high water demand scenarios. At this point, the effect of further increasing water diversion on reducing water shortage risk indicators gradually weakens and tends to converge. The process of increasing water inflow in the source area or receiving area can be represented as follows:

[0114] SR i =A i *exp(-b i *Q in )+c i ;

[0115] Among them, SR i A is the calculated value of the water shortage risk index for the target spatial node. i To maximize the amount of risk that can be improved, exp is an exponential function operation with the natural constant as the base, and b i To characterize the rate of risk decay of the diminishing marginal utility, Q in The variable representing the amount of water transferred to the target spatial node (taking numerical values), i.e., the normalized value of the total water transferred during the scheduling period, is the generalized water transfer volume, c. i This refers to residual water shortage parameters that cannot be eliminated simply by increasing the amount of available water due to physical boundary conditions such as bottlenecks in the regional water supply network.

[0116] It should be noted that in some embodiments, normalization may be performed for dimensional consistency, such as Q. in Q can be used in / Q ref To simplify the calculation, Q is... ref When the unit is 1, it can be compared with a single Q. in The numerical calculation results are consistent. Or use b. i Dimension of absorption. That is, b. i The dimensions of the water volume Q in The units of measurement for Q are reciprocals of each other. in With 10 8 m 3 If we consider it as a unit, then b iThe corresponding unit is (10 8 m 3 ) -1 b i The values ​​are determined from the data by nonlinear curve fitting, and the values ​​implicitly include the conversion information of the measurement unit of water transfer volume, ensuring that the independent variables of the formula maintain dimensionless consistency in numerical calculation.

[0117] In some embodiments, it is also necessary to consider the increased risk of water shortage in the source area as the amount of water diverted increases.

[0118] For spatial nodes in the source region, an increasing water shortage risk response function is constructed with the internal water transfer volume variable as the independent variable. This function reflects the physical process of the source region experiencing a decline in local water supply capacity and an increase in water shortage risk due to increased water transfer volume. An increasing exponential function with the maximum deterioration risk, risk accumulation rate, and basement water shortage parameters is selected as the sub-function family for water shortage risk in the source region. Together with the decreasing function in the receiving region, this forms a family of parameterized functions for water shortage risk with the internal water transfer volume variable as the unified independent variable.

[0119] Specifically, the water shortage risk response function of the spatial nodes in the source region can be expressed as:

[0120] SR H =A H ×(1-exp(-b H ×Q N ))+c H ;

[0121] Among them, SR H A is the calculated value of the water shortage risk index for spatial nodes in the source region. H For the maximum deterioration risk, exp is an exponential function operation with the natural constant as the base, and b H Q represents the rate of risk accumulation. N c represents the water diversion variable within the system. H This represents the basement water shortage parameter in the source region. This function, together with the decreasing function in the receiving region, constitutes a family of water shortage risk parameterization functions with the internal water transfer volume variable as the unified independent variable.

[0122] Step 4013: Treat the first type of sub-function family and / or the second type of sub-function family as a parameterized function family.

[0123] During configuration, the first type of sub-function family, which has passed verification, is stored in the underlying water abandonment characteristic calculation module, and the second type of sub-function family is stored in the underlying water shortage characteristic calculation module. These two types of modules are then combined to form the system's parameterized function family instance library, which is then called by the subsequent global parameter optimization and estimation program.

[0124] Step 402: Based on the discrete water transfer volume data in the water transfer scheme set, as well as the corresponding water shortage risk indicators and water abandonment risk indicators, the parameterized function family is curve-fitted using a nonlinear parameter estimation method to generate a parameterized risk response function.

[0125] In some optional implementations, the nonlinear parameter estimation method specifically employs a damped least squares algorithm to perform matrix iterative solutions. The feature matrix of the multidimensional discrete data points obtained from the previous gridded simulation is extracted and substituted into the continuous equation base determined in the previous steps. After a predetermined number of numerical approximation iterations, the discrete data array is transformed into a continuously differentiable analytical object, generating the risk response function.

[0126] One possible implementation involves curve fitting of a family of parameterized functions using a nonlinear parameter estimation method, including:

[0127] Step 4021: With the optimization objective of minimizing the deviation between the simulated observed values ​​of water shortage risk indicators and water abandonment risk indicators and the calculated values ​​output by the parameterized function family, the undetermined parameters are optimized; the optimized undetermined parameters are substituted into the parameterized function family to generate a parameterized risk response function.

[0128] The root mean square error (RMSE) index is used as the core criterion for internal iterative convergence. The index values ​​at each discrete water regulation state node are extracted, and the sum of squared residuals between these residuals and the function values ​​output by the current iterative parameters are calculated. When the change in the sum of squared residuals generated in two consecutive iterations is lower than a preset convergence threshold, the global parameter optimization calculation is considered to have converged, matrix iterative updates are stopped, and the current sequence of undetermined parameters is fixed.

[0129] Step 4022, wherein the shape index determined by optimization is used to characterize the difference in the degree of nonlinearity of the risk response of water abandonment between pairs of spatial nodes, and the risk decay rate determined by optimization is used to characterize the risk mitigation efficiency characteristics affected by the combined influence of reservoir regulation capacity and user water demand elasticity.

[0130] Extracting and retaining the aforementioned set of optimization parameters can imbue the black-box model with specific physical engineering semantics. For example, based on the equation structure of step 402, the shape exponential constraint of the source region spatial nodes is 0. <g H <1, combined with the power function structure in negative form, its risk response function exhibits a concave decreasing response that decreases with increasing water diversion volume, and the rate of decrease decreases progressively; the shape exponential constraint condition of the spatial nodes in the water-receiving area is g. L>1, combined with a power function structure in positive form, makes its risk response function exhibit a convex increasing response that rises with increasing water diversion volume at an accelerating rate. By calculating and comparing the numerical differences between the two shape indices mentioned above, the system can directly quantify and assess the degree of asymmetric distribution of the engineering storage capacity. Similarly, the higher the risk decay rate calculated and extracted for the water-receiving area, the stronger the sensitivity of industrial and agricultural users in that area to the replenishment water volume. When planning annual dispatch instructions, the system can prioritize allocating initial available water to spatial nodes with high risk decay rates to achieve higher system-level water shortage mitigation efficiency.

[0131] For example, in a target inter-basin water transfer system, the storage capacity of the first storage node is much larger than that of the second storage node. By fitting, the shape exponent of the water release risk response of the first storage node can be obtained as g. H ∈(0,1) (convex / concave features on the surface), indicating that the risk of water abandonment decreases at a decreasing rate as the amount of water discharged increases; the shape index of the water abandonment risk response of the second storage node satisfies g L A value >1 (convex surface / convex shape) indicates that the risk of water abandonment increases at an increasing rate with the amount of water transferred in. The difference between the two shape indices directly reflects the asymmetry of the two lakes' water storage capacity, providing a physical basis for subsequent calculations of marginal substitution indicators.

[0132] Example 5 further describes the analytical evaluation process of risk permutation efficiency across spatial units, and the algorithm derivation mechanism for establishing the optimal point of total system risk through the ratio of partial derivatives.

[0133] One possible implementation involves calculating a risk transfer marginal substitution index that characterizes the risk permutation efficiency between spatial nodes, such as... Figure 2 As shown, it includes:

[0134] Step 501: For two spatial nodes that are associated by predetermined water transfer variables in the water transfer scheme set, determine the increasing or decreasing trend of their risk levels based on the risk response function; the risk level is the corresponding water shortage risk level or water abandonment risk level. The specific type depends on the type of water transfer variables being analyzed.

[0135] In the spatial allocation of water resources, water transfer operations establish a strong physical coupling relationship between the source area and the receiving area. The system obtains the continuously differentiable risk response function generated in Example 4, sets the external water supply or the internal water transfer volume as the independent variable, and calculates the first-order partial derivative of the risk response function for each spatial node within the domain of the independent variable. The sign of the first-order partial derivative is determined; if the first-order partial derivative is less than 0, the risk level of the spatial node is determined to be decreasing; if the first-order partial derivative is greater than 0, the risk level of the spatial node is determined to be increasing.

[0136] Step 502: Spatial nodes whose risk level decreases as the water transfer variable increases are identified as risk beneficiaries, and spatial nodes whose risk level increases as the water transfer variable increases are identified as risk bearers.

[0137] Based on the trend direction extracted in step 501, spatial nodes are categorized by role. Regarding water shortage risk, receiving areas that receive transferred water typically experience a decreasing risk due to the increased available water volume within the region, and are logically labeled as risk beneficiaries. Conversely, source areas that receive transferred water typically experience an increasing risk due to the reduction in local available water volume or increased flood control pressure caused by the outflow of physical water, and are logically labeled as risk bearers. Regarding water abandonment risk, source areas that receive transferred water experience a decreasing risk of water abandonment because the water transfer operation frees up storage capacity, and are logically labeled as beneficiaries of water abandonment risk; however, as external water continues to flow in, receiving areas face storage saturation pressure, and the risk of water abandonment increases, and are logically labeled as bearers of water abandonment risk. By establishing the above technical mapping relationships, a directed graph for risk transfer calculation is established.

[0138] Step 503: Obtain the risk change rate of the water transfer variable for the risk beneficiary and the risk bearer, respectively.

[0139] Call the memory module to concurrently obtain the risk change rate data output by the risk beneficiary and the risk bearer under the current computing clock tick.

[0140] Optionally, when obtaining the rate of change of risk, the specific steps are as follows:

[0141] Step 5031: For the risk response functions corresponding to the risk beneficiary and the risk bearer, respectively, solve the analytical partial derivatives with respect to the specific water diversion variable to generate the corresponding continuous marginal change functions.

[0142] An analytical differentiation operation is performed on the extracted power function or negative exponential function. Since the fitted risk response function is a definite mathematical analytical expression, the differential operator is directly used to differentiate the independent variable of water transfer volume in the above equation, generating a continuous marginal change function characterizing the sensitivity of the dependent variable to the independent variable. This function physically characterizes the marginal impact of unit increases or decreases in water transfer volume on local node risk indicators.

[0143] Step 5032: Substitute the examined water transfer volume values ​​into the continuous marginal change function for calculation to obtain the risk change rate characterizing the instantaneous rate of change. That is, substitute the water transfer volume values ​​to be evaluated in the water transfer scheme set into the continuous marginal change function for calculation to obtain the risk change rate characterizing the instantaneous rate of change.

[0144] When evaluating a specific water diversion scheme, the corresponding water diversion volume is extracted and substituted into the generated continuous marginal change function to perform numerical calculations. The calculated output is the risk change rate under that specific scheduling condition. The higher the change rate, the more drastic the risk indicator fluctuations will be caused by even a small increase in water diversion when the system is in that water diversion state.

[0145] Step 504: Calculate the ratio of the risk change rate of the risk beneficiary to the risk change rate of the risk bearer, and determine the absolute value of the obtained ratio as the marginal substitution indicator for risk transfer.

[0146] To eliminate the dimensional conflict between measuring water abandonment risk by volume and water shortage risk by ratio, a ratio mapping operation is performed. The risk change rate of the beneficiary is used as the numerator, and the risk change rate of the bearer is used as the denominator for division. The absolute value of the result is then extracted. For the water abandonment risk index, analytical calculation is performed using the following formula:

[0147] RTMR SP =(a H *g H ) / (a L *g L )*Q N (gH-gL) ;

[0148] Among them, RTMR SP a is a marginal substitution indicator for the risk transfer of water abandonment risk. H g is the scaling factor corresponding to the risk beneficiary. H a is the shape index corresponding to the risk beneficiary. L g represents the scaling factor corresponding to the risk-bearing party. L Q represents the shape index corresponding to the risk-bearing party. N This refers to the water diversion variable within the system.

[0149] For the water shortage risk indicator, the absolute value of the marginal deceleration rate of the water shortage risk in the water-receiving area with respect to the variable of water transfer within the system, and the absolute value of the marginal growth rate of the water shortage risk in the source area with respect to the variable of water transfer within the system are obtained respectively. The ratio of the former to the numerator and the latter to the denominator is calculated to obtain the marginal substitution index of water shortage risk transfer.

[0150] In one possible implementation, when dealing with water shortage risk indicators, the pre-configured transfer efficiency threshold is determined in the following way:

[0151] Obtain the pre-stored first water demand data corresponding to the risk beneficiary, and the pre-stored second water demand data corresponding to the risk bearer.

[0152] In water shortage risk scenarios, the difference in physical water demand directly affects the boundary for determining the optimal risk point. The system accesses the static engineering attribute database, extracts constants representing the water demand characteristics of the risk beneficiaries as the first water demand scale data, and extracts constants representing the water demand characteristics of the risk bearers as the second water demand scale data.

[0153] Furthermore, the ratio of the second water demand data to the first water demand data is calculated to obtain a pre-configured transfer efficiency threshold used to determine the optimal point of the total risk of the system.

[0154] The calculation involves dividing the second water demand (water demand of the risk-bearing party) by the first water demand (water demand of the risk-beneficiary). The constant output of this division is then assigned to a pre-configured transfer efficiency threshold. This process transforms the asymmetry in user volume into a physical compensation factor for determining the equilibrium state of cross-regional risk game.

[0155] Optionally, when determining the efficient and balanced water transfer interval of an inter-basin water transfer system by combining the risk transfer marginal substitution indicator and the pre-configured risk spatial equilibrium criterion, the following may also be included:

[0156] The marginal substitution index for risk transfer is dynamically compared with the pre-configured transfer efficiency threshold.

[0157] An iterator module is used to extract the corresponding risk transfer marginal substitution index point by point for the discretely increasing water transfer volume sequence, and a comparison operator is used to subtract or determine the magnitude of this index with a pre-configured transfer efficiency threshold. For water abandonment risk, the pre-configured transfer efficiency threshold is set to a constant 1. This setting is based on the premise that the water abandonment risk indicators have the same physical dimensions (all measured in water volume units) and are assigned equal weights to each spatial node within the system. Under these conditions, the transfer efficiency threshold that minimizes the total water abandonment risk at each node is exactly 1. In application scenarios where different weights need to be assigned to different spatial nodes (such as based on lake storage area or regional importance), those skilled in the art can refer to the method for determining the water shortage risk threshold and set the threshold as the corresponding weight ratio.

[0158] Furthermore, the water transfer volume feature point corresponding to when the risk transfer marginal substitution index equals the pre-configured transfer efficiency threshold is extracted as the optimal point of the system's total risk, representing the minimum value of the overall risk-weighted total amount of the inter-basin water transfer system. This optimal point of the system's total risk serves as the second boundary water transfer volume feature point for determining the efficient and balanced water transfer interval.

[0159] When the risk transfer marginal substitution index equals the transfer efficiency threshold, it is determined that further increasing or decreasing the water transfer volume at this point will not be sufficient to compensate for the risk marginal loss borne by the beneficiary, meaning the overall weighted total risk of the system has reached a functional minimum. The values ​​of the independent variables on the horizontal axis that satisfy this equation are recorded and output as the water transfer volume characteristic points of the optimal point for the overall system risk to the decision-making level.

[0160] In some embodiments, the same solution approach is used for water shortage risk indicators: The marginal substitution index for water shortage risk transfer is set equal to the transfer efficiency threshold. The derivatives of the increasing exponential function in the source region and the decreasing exponential function in the receiving region are substituted into the ratio expression. The logarithm of the exponential structure is then used for algebraic solution to obtain the water transfer characteristic point corresponding to the optimal point of total risk in the water shortage risk system. This characteristic point is jointly determined by the maximum deterioration or improvement risk in both the source and receiving regions, the risk accumulation rate or risk decay rate, and the transfer efficiency threshold. When the risk response function is a power function containing a scale coefficient and a shape exponent, the optimal point of total system risk, representing the minimum weighted total risk of the inter-basin water transfer system, is extracted. Figure 5 As shown, the specific steps include the following:

[0161] 1a. Obtain the first scale coefficient and first shape index of the risk beneficiary, and the second scale coefficient and second shape index of the risk bearer, respectively.

[0162] For the mathematical analytical optimization logic, instead of using a step-by-step approximation method, the power function feature parameters obtained from the fitting in Example 4 are directly called. Two sets of four parameter feature values ​​are accurately located and extracted from the function parameter matrix.

[0163] 1b, multiply the first scale coefficient by the first shape index to obtain the first product, and multiply the second scale coefficient by the second shape index to obtain the second product.

[0164] The parameters are combined using a multiplication operator. The product described above mathematically and geometrically represents the initial gradient tendency of the original risk surface at the characteristic scale.

[0165] 1c, based on the ratio of the first product to the second product, and combined with the numerical difference characteristics of the second shape index and the first shape index, the water diversion characteristic point corresponding to the optimal point of the total risk of the system is obtained through analytical calculation.

[0166] Calculate the fundamental ratio using the first product as the numerator and the second product as the denominator. Calculate the difference between the second shape index and the first shape index. Using the reciprocal of this difference as the exponent, perform a power operation on the fundamental ratio to directly output the analytical solution.

[0167] Q N_opt=((a H *g H ) / (a L *g L )) (1 / (gL-gH)) ;

[0168] Among them, Q N_opt To determine the optimal water transfer volume corresponding to the optimal point of total system risk, a H g is the first scaling factor. H a is the first shape index. L For the second scaling factor, g L This is the second shape index.

[0169] The above analytical formula directly bypasses the complex gradient descent search algorithm, replacing iterative calculations with parameter matrix multiplication, division, and exponentiation, thus improving the overall risk optimization efficiency of the underlying hardware execution system. Those skilled in the art can substitute the fitted actual engineering parameters into the above formula to directly calculate the optimal water diversion characteristic point without any creative effort.

[0170] In some embodiments, the feasible intervals for water diversion can be independently derived based on the marginal substitution analyses of water abandonment risk and water shortage risk, respectively. When the feasible intervals corresponding to the two types of risks overlap, the intersection of the two intervals is taken as the joint feasible water diversion interval; when the two intervals do not overlap, the compromise water diversion amount is determined between the adjacent endpoints of the two intervals based on the criterion of minimizing the weighted total system risk of the two types of risks.

[0171] Example 6 describes how to quantify the dispersion of risk distribution at spatial nodes in a cross-basin water transfer system, and the process of extracting physical feature points that characterize the spatial equilibrium state of risk.

[0172] One possible implementation involves determining the efficient and balanced water transfer interval of an inter-basin water transfer system by combining risk transfer marginal substitution indicators and pre-configured risk space equilibrium criteria, including:

[0173] Step 601: Based on the water shortage risk index and water abandonment risk index corresponding to each spatial node, calculate the risk variation coefficient, which characterizes the relative dispersion of spatial risks; that is, calculate the water shortage risk variation coefficient based on the water shortage risk index corresponding to each spatial node, and calculate the water abandonment risk variation coefficient based on the water abandonment risk index. The variation coefficients are calculated independently for water shortage risk and water abandonment risk, without mixing them.

[0174] In some embodiments, the risk variation coefficient, which characterizes the relative dispersion of spatial risk, is calculated based on the water shortage risk index and water abandonment risk index corresponding to each spatial node and the water transfer volume sequence in the water transfer scheme set.

[0175] In the multi-objective scheduling of inter-basin water transfer systems, in addition to assessing the total weighted risk of the system as a whole, it is also necessary to quantify the relative differences in risk borne by different physical regions. The coefficient of variation is introduced as a statistical measure of dispersion. Specifically, the risk index values ​​of the source region spatial nodes and the water receiving region spatial nodes output from previous steps under a specific water transfer volume are obtained. The standard deviation of these risk index values ​​is calculated, and the arithmetic mean of these risk index values ​​is also calculated. The ratio of the standard deviation to the arithmetic mean is calculated to obtain the risk coefficient of variation. To prevent abnormal interruptions due to a zero denominator during the calculation process, a pre-configured minimal positive number is introduced into the denominator term for numerical constraints.

[0176] CV=|r H -r L | / (r H +r L +2*ε);

[0177] Where CV is the calculated risk coefficient of variation, r H r represents the risk indicator value corresponding to the spatial nodes in the source region. L ε represents the risk index value corresponding to the spatial node in the water-receiving area, and ε is a pre-configured, extremely small positive number used to prevent division-by-zero bias.

[0178] In the above formula, the risk indicator value can specifically refer to the water shortage risk indicator, or it can independently refer to the water abandonment risk indicator. The pre-configured minimum positive number can be set to 10. -6 The above calculations map the risk differences at the absolute numerical level to a dimensionless relative dispersion index.

[0179] Step 602: Extract the water transfer volume feature point corresponding to the minimum value when the risk variation coefficient reaches a minimum value as the water transfer volume evolves, and determine it as the spatial equilibrium point characterizing the system risk distribution tending to be in equilibrium.

[0180] The water transfer volume feature point corresponding to the minimum value when the risk variation coefficient evolves with the water transfer volume sequence is extracted, and it is determined as the spatial equilibrium point characterizing the system risk distribution tending to be balanced. The spatial equilibrium point is used as the first boundary water transfer volume feature point to determine the efficient and balanced water transfer interval.

[0181] A traversal calculation module is constructed to calculate the corresponding risk variation coefficient point by point along the independent variable axis of increasing water transfer volume. The generated continuous data array is then input into the extreme point search algorithm. The extreme point search algorithm extracts the global minimum point in the risk variation coefficient data sequence by comparing the numerical gradients of adjacent sampling points. This global minimum point represents a relatively fair state of risk sharing between the source area and the water receiving area within the system. The independent variable value corresponding to this global minimum point is extracted, stored, and defined as the spatial equilibrium point.

[0182] One possible implementation involves extracting the water transfer volume characteristic point corresponding to the minimum value of the risk variation coefficient as the water transfer volume evolves, and determining this point as the spatial equilibrium point characterizing the system risk distribution tending towards equilibrium. Specifically:

[0183] Step 6021: Based on the mathematical relationship that a risk variation coefficient of zero is equivalent to the absolute level of risk indicators of two related spatial nodes being equal, dynamically compare the numerical differences of water shortage risk indicators and water abandonment risk indicators between spatial nodes.

[0184] In some optional implementations, to reduce the computational resources consumed by the global traversal search, a method of directly comparing the intersection states of the risk response curves is adopted. The risk response function curves of the risk beneficiary and the risk bearer are loaded in parallel. As the water diversion variable value monotonically increases, the indicator value of the risk beneficiary monotonically decreases, while the indicator value of the risk bearer monotonically increases. The reduction state of the absolute difference between the two sets of values ​​under the same water diversion variable coordinates is dynamically monitored, and the coordinates of the intersection point of the two curves on the geometric plane are located.

[0185] Step 6022 involves determining the water diversion scheduling state point where the absolute levels of water shortage risk indicators or water abandonment risk indicators are equal between at least two associated spatial nodes as a spatial equilibrium point based on the simultaneous equations of the risk response function.

[0186] Based on the mathematical structure of the risk coefficient of variation described above, the risk coefficient of variation theoretically reaches its absolute minimum of zero if and only if the absolute values ​​of the risk indicators of the two spatial nodes contained in the system are completely equal, that is, when the numerator in the above linear formula reaches an absolute zero value. Based on this mathematical equivalence relation, the complex statistical minimum search problem is reduced in dimensionality and transformed into an analytical problem of solving the intersection of two nonlinear function equations.

[0187] The risk response function equations for the spatial nodes in the source region and the water-receiving region are established simultaneously. Assuming the dependent variable values ​​are equal for both, the numerical roots of the independent variables are obtained by solving this system of equations using numerical root-finding methods (such as the bisection method or Newton's iteration method). Since the two curves are monotonically decreasing and monotonically increasing respectively, their intersection point is unique and can be determined using conventional single-variable numerical root-finding methods in this field. The numerical value of this analytical root is extracted and identified as the corresponding spatial equilibrium point. This alternative to analytical determination avoids the extreme point location deviation caused by insufficient discrete grid precision, ensuring the mathematical rigor of the spatial equilibrium point extraction process.

[0188] Example 7 describes the decision-making mechanism for delineating single-objective efficient water diversion intervals and dual-objective efficient equilibrium water diversion intervals based on the optimal point of total system risk and spatial equilibrium point.

[0189] In one possible implementation, after determining the optimal point for total system risk, the following steps are also included:

[0190] Step 701: Define the range of continuous water transfer volume corresponding to the risk transfer marginal substitution index being greater than or equal to the pre-configured transfer efficiency threshold as the single-target high-efficiency water transfer interval. The single-target high-efficiency water transfer interval serves as an auxiliary decision-making output for the dispatch decision-making center to refer to.

[0191] After analyzing and locating the optimal point for overall system risk, a single-objective constraint boundary considering only overall risk efficiency is constructed. The global water transfer variable space is extracted, and conditional filtering is performed. For water abandonment risk scenarios, the pre-configured transfer efficiency threshold is forcibly set to a constant of 1. The set of water transfer volumes with risk transfer marginal substitution indicators greater than or equal to a constant of 1 is retained. This set mathematically constitutes a continuous numerical interval. The above filtering logic can be expressed by the following formula:

[0192] Q eff ={Q: RTMR(Q)≥1};

[0193] Among them, Q eff Let Q be the single-objective high-efficiency water transfer range, Q be the continuous water transfer volume variable, and RTMR(Q) be the risk transfer marginal substitution index function with respect to the water transfer volume variable.

[0194] Step 702, wherein, within the single-objective high-efficiency water transfer range, increasing the water transfer volume makes the total risk weighted amount of the system decrease monotonically, and the extreme boundary of the single-objective high-efficiency water transfer range is controlled by the optimal point of the total risk of the system, that is, determined by the water transfer volume corresponding to the optimal point of the total risk of the system.

[0195] The single-objective, high-efficiency water diversion range physically defines an undisputed gain operating domain. As long as the actual water diversion volume falls within this range, any instruction to increase the water diversion volume will ensure that the risk reduction gained by the beneficiary exceeds the risk increase borne by the risk bearer, macroscopically driving the overall risk-weighted total of the system to exhibit a monotonically decreasing trend. The system determines that this monotonically decreasing trend terminates at the critical state where the risk transfer marginal substitution index equals the transfer efficiency threshold. Therefore, the extreme boundary of the single-objective, high-efficiency water diversion range directly corresponds to the previously obtained optimal point of the system's total risk. If the actual water diversion volume exceeds this extreme boundary, continued water diversion will cause the overall risk-weighted total of the system to reverse from decreasing to increasing, resulting in ineffective resource waste.

[0196] One possible implementation involves determining the efficient and balanced water transfer interval of the inter-basin water transfer system based on risk transfer marginal substitution indicators and pre-configured risk spatial equilibrium criteria, such as... Figure 3 As shown, it includes the following steps:

[0197] ① Based on the pre-configured risk space equilibrium criterion, the first boundary water transfer volume characteristic point representing the equilibrium state of spatial risk distribution is determined.

[0198] Furthermore, based on the pre-configured risk spatial equilibrium criterion and the water shortage risk index and water abandonment risk index, the first boundary water transfer volume characteristic point, which represents the spatial risk distribution tending to be in equilibrium, is determined. The first boundary water transfer volume characteristic point corresponds to the spatial equilibrium point.

[0199] In addition to the single objective of total risk control, a multi-objective coordinated decision-making mechanism can be introduced, which can be implemented using existing methods and will not be described in detail here. The spatial equilibrium determination module is invoked to read the spatial equilibrium point data located based on the minimum value of the coefficient of variation. The water transfer volume value corresponding to this spatial equilibrium point is instantiated as the first boundary water transfer volume feature point. This feature point represents a specific scheduling scale where the source area reservoir and the receiving area reservoir achieve a state of equivalence in absolute risk-bearing value.

[0200] ② Based on the risk transfer marginal substitution index, determine the second boundary water transfer volume characteristic point that represents the overall total risk of the inter-basin water transfer system reaching a minimum.

[0201] Furthermore, based on the risk transfer marginal substitution index and the transfer efficiency threshold, a second boundary water transfer volume characteristic point is determined to represent the minimum total risk of the inter-basin water transfer system. The second boundary water transfer volume characteristic point corresponds to the optimal point of the total risk of the system.

[0202] Simultaneously, the risk efficiency determination module is invoked to read the system's overall risk optimum data determined by analyzing the partial derivative ratio relationship. The water diversion volume value corresponding to this overall risk optimum is instantiated as the second boundary water diversion volume feature point. Due to the asymmetric distribution characteristics of the reservoir's physical storage capacity, the first boundary water diversion volume feature point and the second boundary water diversion volume feature point usually do not coincide on the numerical coordinate axis, and there is an objective distance deviation between them.

[0203] ③ The first boundary water diversion feature point and the second boundary water diversion feature point are used as boundary constraints for joint comparison, and the overlapping range of water diversion between the two is extracted as the efficient and balanced water diversion interval.

[0204] To address the aforementioned objectively existing coordinate distance deviation, a compromise decision domain is extracted using set intersection operations. The feature points of the first and second boundary water diversion volumes are then reconstructed as the left and right endpoints of the closed interval, respectively. Internally, the system compares the absolute values ​​of these two endpoints to ensure that the lower limit of the interval is the smaller of the two values, and the upper limit is the larger of the two values. This logic can be expressed by the following formula:

[0205] Q opt =[min(Q N_opt QN_eq ), max(Q N_opt Q N_eq )];

[0206] Among them, Q opt For efficient and balanced water regulation intervals, min is the function to find the minimum value, max is the function to find the maximum value, and Q is... N_opt Q represents the second boundary water diversion characteristic point corresponding to the optimal point of total system risk. N_eq This is the first boundary water diversion characteristic point corresponding to the spatial equilibrium point.

[0207] Within the efficient and balanced water transfer zone, the adjustment of system scheduling commands can achieve dynamic coordination and trade-offs between two independent dimensions: overall system risk control and regional risk spatial balance. If the actual executed water transfer volume exceeds the maximum upper limit of the efficient and balanced water transfer zone, it will simultaneously face a double deterioration state of increased overall risk and exacerbated spatial imbalance. The efficient and balanced water transfer zone is used as the output of scheduling decision suggestions, allowing the scheduling decision center to select the final target water transfer volume within its boundary constraints.

[0208] Taking a cross-basin water transfer project as an example, assuming that the optimal water transfer volume corresponding to the optimal point of the total risk of the water abandonment risk system is obtained through analytical calculation, and the equilibrium water transfer volume corresponding to the spatial equilibrium point is higher than this scale, then the range between the two is the efficient equilibrium water transfer interval; within this interval, the scheduling decision ensures that the water abandonment risk transfer efficiency for each additional unit of water transfer is not lower than the marginal efficiency critical value (total risk efficiency guarantee), and also keeps the water abandonment risk level of each node within a relatively balanced range (spatial fairness guarantee).

[0209] Example 8: Taking a series of lake systems connected to a cross-basin water transfer project as an example, a risk transfer analysis model is constructed. The system has two levels of regulating lakes, and there are bidirectional water flow channels between the lakes for both water transfer and water discharge.

[0210] In this scenario, inter-basin water transfer systems typically consist of two types of water sources: local water sources and externally transferred water sources. The composition of local water sources is usually quite complex; in this application, local water sources refer to reservoirs (lakes), while externally transferred water is the portion transferred into the system from outside via water transfer channels. The main risk sources considered in this application are the prediction errors of local water inflow and user water demand forecasts, i.e., the deviation between predicted and observed values ​​in real-time forecasting and scheduling, which are described and simulated using a stochastic process.

[0211] Let the inflow of water from any water source i in time period t, and the water demand supplied by that water source to users in time period t be respectively denoted as deterministic predictions. and Then the random process can be represented as:

[0212] ;

[0213] ;

[0214] In the formula, and Let be the predicted water inflow value and the prediction error for the i-th water source in time period t, respectively. and Let be the predicted water demand and the prediction error for the i-th water source user during time period t, respectively.

[0215] For each time period, each water source's inflow error, and each user's water demand error, their marginal distributions are fitted. After obtaining the optimal marginal distribution, a vine-structure coherence model is used to describe the correlation and dependency structure among multiple variables. Combined with Monte Carlo sampling, L sets of error scenarios are generated and superimposed with the corresponding deterministic prediction process of inflow or demand to obtain L random inflow-demand scenarios, which constitute the inflow-demand scenario set.

[0216] Due to unavoidable discrepancies between runoff and water demand forecasts, water allocation decisions often face a dilemma: over-allocation of water and under-allocation. While the former can reduce the probability of water shortages, it may lead to excessively high reservoir and lake levels, resulting in water wastage when combined with abundant local inflows, thus increasing ineffective water allocation. Conversely, while the latter can reduce water wastage, it also increases the risk of water shortages, creating two types of water allocation risks. Therefore, based on the above mechanisms, this invention primarily considers the following two types of risks within the framework of inter-basin water transfer systems:

[0217] (1) Water shortage risk. For a certain water-using area (user), an event in which the water supply is less than the water demand is defined as a water shortage event, which is quantitatively described by the weighted average water shortage rate:

[0218] ;

[0219] In the formula, D i，t l Let S be the water demand of the local user of the i-th reservoir in the l-th scenario during time period t. i，t l Let SR be the water supply directly provided by the i-th reservoir to its local users during time period t under the l-th scenario. i p is the weighted average water shortage rate (water shortage risk index of spatial node i) for local users of the i-th reservoir. l The probabilities of different water inflow-water demand scenarios. The scenario set is generated through Monte Carlo sampling, with each scenario randomly generated from the corresponding random variable distribution. , , Where I, T, and L represent the number of reservoirs, time periods, and combined water inflow-water demand scenarios, respectively.

[0220] (2) Water Abandonment Risk. A risk event is defined as an event where the reservoir's storage capacity exceeds its upper limit at the end of a given period, leading to water abandonment. This risk event is quantitatively described using a weighted average water abandonment volume.

[0221] ;

[0222] In the formula, SP i，t l Let SP be the amount of water discharged from the i-th reservoir in time period t under the l-th scenario. i Let be the weighted average water discharge of the i-th reservoir.

[0223] The risk assessment model for inter-basin water transfer system scheduling can be expressed in the following form:

[0224] ;

[0225] In the formula, Φ represents the unified scheduling model for inter-basin water transfer from multiple water sources. For the local inflow of the i-th reservoir in time period t under the l-th scenario, Let be the planned water inflow to the i-th reservoir during time period t. Let be the planned water release volume of the i-th reservoir during time period t.

[0226] As shown in the above formula, under any scenario, the water supply and discharge of each reservoir and the water shortage of each user are jointly determined by the planned water inflow and outflow from each reservoir. These two factors influence risk by altering the available water volume of the reservoirs. To fully reveal the mechanism of system risk change and its spatial transfer pattern with water transfer, this paper conducts the following derivation based on the water balance formula:

[0227] During the entire scheduling period, assuming the reservoir's ending storage equals its beginning storage and ignoring reservoir losses, inter-basin water transfer changes the available water volume of the reservoir. Under scenario l, the water balance of the i-th reservoir can be expressed as:

[0228] (a)

[0229] The above formula indicates that, under given scenario l, the sum of the total water supply and total water abandonment of the entire system during the entire scheduling period is equal to the sum of the total local runoff (including transit water) and the total change in available water volume brought about by inter-basin water transfer.

[0230] The discussion will focus on changes in the planned water inflow. Changes over time Changes in the planned water inflow At this point, the planned water outflow remains unchanged, i.e., the change in the planned water outflow... The local runoff of the reservoir is not affected by changes in water diversion, i.e., the change in local inflow. The amount of water discharged from the reservoir and the amount of water supplied to users will change accordingly, and the degree of change can be expressed as follows: and Substituting the perturbed variables into equation (a) and subtracting from the original equation, we can obtain the following relationship between the increments:

[0231] ;

[0232] Throughout the entire scheduling period, let: , , Then the above formula can be further expressed as:

[0233] ;

[0234] For reservoir i and its supplying users, under any inflow-demand scenario l, one of three mutually exclusive states can occur during time period t, or the reservoir may release water. , Or, the reservoir may be short of water for its users. , Or, if the reservoir neither releases water nor experiences a shortage of water for its users, then... , Therefore, under the established scheduling rules, the increase in the available water volume of the reservoir can only be allocated as additional water supply and / or additional water discharge during the water allocation process. Thus, the total water supply and total water discharge of the reservoir will not decrease as the available water volume increases. Therefore, the above formula shows that, under scenario l, when the planned water inflow to reservoir i during the scheduling period increases, its increment can be decomposed into two parts: one part is converted into additional water supply, and the other part is converted into additional water discharge. Therefore, as the planned water inflow increases, i.e., the change in planned water inflow... Changes in water supply Changes in water discharge It can be expressed in derivative form as:

[0235] ;

[0236] ;

[0237] Furthermore, under scenario l, the water shortage rate supplied by reservoir i to users can be expressed as:

[0238] ;

[0239] exist Under the premise of remaining unchanged, Only follow Change, its following The rate of change is:

[0240] ;

[0241] Reservoir water shortage rate Total water supply The function, and Another planned water diversion The function is such that it can be expressed using the chain rule as follows:

[0242] ;

[0243] because And the previous derivation has already been obtained. Therefore That is, the water shortage rate of reservoir i to users decreases as the planned water inflow increases.

[0244] By taking the average of the weighted sums of the scenarios, the relationship between the planned water diversion volume and the risk can be derived as follows:

[0245] ;

[0246] ;

[0247] Therefore, as the planned water inflow increases, the risk of water shortage in reservoir i will decrease, while the risk of water abandonment will increase.

[0248] When investigating the impact of planned water outflow on the risks of reservoir i and its supply users, the same reasoning applies if the planned water inflow is fixed. It can be concluded that as the planned water outflow increases, the water shortage risk of reservoir i will increase, while the risk of water wastage will decrease.

[0249] Inter-basin water transfer not only alters the spatial distribution of water volume but also causes a redistribution of water abandonment and water shortage risks among different reservoirs and receiving areas. To quantitatively assess the impact of changes in water transfer scale on the spatial aggregation and distribution pattern of system risks, this application uses the coefficient of variation (CV) to characterize the risk distribution characteristics under different water transfer levels. Specifically, taking the water abandonment and water shortage risks of each spatial unit within the system as the objects, the corresponding coefficients of variation for water abandonment and water shortage risks are calculated. The calculation process can be expressed as follows: ;

[0250] In the formula, μ is the mean risk. σ represents the overall standard deviation of risk. When calculating the coefficient of variation of water abandonment risk, r i SP for each reservoir i When calculating the coefficient of variation of water shortage risk, r i Take each user's SP iε is a very small positive number to avoid a denominator of 0. The closer the coefficient of variation (CV) is to 0, the closer the risk levels of each spatial unit (reservoir / user) are, and the more spatially balanced the risk distribution of the system tends to be. Conversely, it indicates that the risk is highly concentrated in one or a few units, showing a spatial imbalance.

[0251] By implementing the method of this invention, the risk of water abandonment in the water source area decreases in a concave manner with the increase of internal water transfer volume QN, while the risk of water abandonment in the water receiving area increases in a convex manner; the marginal ratio of the two (the risk transfer marginal substitution index RTMR) SP ) with Q N Increases and monotonically decreases; when RTMR SP When =1, the corresponding Q N That is, the optimal point of total system risk Q. N_opt When the absolute levels of water abandonment risk are equal in the source area and the receiving area, the corresponding Q is... N That is, the spatial equilibrium point Q N_eq The final determined efficient and balanced water transfer interval [min(Q] N_opt Q N_eq ), max(Q N_opt Q N_eq This provides a quantitative boundary for scheduling decisions.

[0252] Starting from the prediction of uncertainty, this application systematically characterizes the formation mechanism of water shortage risk and water abandonment risk in inter-basin water transfer scheduling, clarifies the role path of water inflow and demand uncertainty in transforming into multi-regional risks through water transfer decisions, reveals the transmission and transformation law of water shortage risk and water abandonment risk in inter-basin water transfer system with changes in water transfer scale, and constructs a risk space equilibrium evaluation method based on the coefficient of variation from the perspective of risk space redistribution, quantitatively revealing the risk concentration and diffusion characteristics under different water transfer schemes, and providing a quantitative basis for inter-basin water transfer decision-making.

[0253] It should be noted that the inter-basin water transfer system of the present invention is not limited to a two-node (source area + receiving area) secondary structure. For multi-level water storage systems containing three or more spatial nodes, the risk transfer marginal substitution index and spatial equilibrium analysis can be performed sequentially on adjacent node pairs according to the method of the present invention. The efficient and balanced water transfer intervals of each segment are determined according to the serial relationship of each water transfer path in the system topology, and the multi-dimensional water transfer optimization scheme of the whole system is comprehensively output.

[0254] According to one aspect of this application, to quantitatively characterize the risk transfer efficiency between spatial nodes in an inter-basin water transfer system, a risk transfer marginal substitution rate (risk transfer marginal substitution index) is defined as RTMR. For two spatial units connected by a water transfer volume Q, one being a risk beneficiary (risk decreases as Q increases) and the other a risk bearer (risk increases as Q increases), the RTMR for the k-th type of risk is defined as:

[0255] ;

[0256] in For the k-th type of risk of the beneficiary, This is the k-th type of risk borne by the party in charge. This indicates that the reduction in risk for the beneficiary is greater than the increase in risk for the bearer, meaning that risk transfer has a gain effect; This indicates that the risk transfer is inefficient, and the risk improvement gained by the beneficiary is less than the risk cost paid by the bearer. This is the efficiency critical point.

[0257] In this invention, the risk of water wastage is addressed by the amount of water Q transferred from the water source area. N As a variable in water diversion, the water source area is the beneficiary of water abandonment risk (water abandonment risk varies with Q). N (Increases and decreases), the water receiving area is the party bearing the risk of water abandonment (the risk of water abandonment increases with Q). N If the risk of water abandonment increases (and rises), then the RTMR is:

[0258] ;

[0259] Regarding the risk of water shortage, the water-receiving area's supply users are the beneficiaries (the risk of water shortage varies with Q). N (Increases and decreases), the water source area supply users are the bearers (water shortage risk increases with Q) N If the water shortage risk increases (and rises), then the RTMR is:

[0260] ;

[0261] In gridded numerical experiments, RTMR can be approximated using finite difference methods:

[0262] ;

[0263] in and The discrete levels of adjacent water diversion volumes.

[0264] Regarding the risk of water spillage, the total risk of water spillage in the system is defined as the sum of the risks of water spillage from each reservoir: ;

[0265] In the two-database system of this invention: ;

[0266] because , Setting the above equation to zero yields the condition for the total risk of system water wastage to reach an extreme value: ;

[0267] Right now: ;

[0268] Therefore, the water diversion level with a risk of water abandonment RTMR=1 This corresponds precisely to the optimal point where the total risk of water wastage in the system is minimized. When hour Increasing the amount of water diverted from the north can reduce the overall risk of water wastage in the system; when hour Continuing to increase the amount of water diverted to the north will only increase the total risk of water wastage in the system.

[0269] Regarding the risk of water shortage, since the risk of water shortage is measured by the water shortage rate (dimensionless ratio), and the total water demand of different users is different, the total water shortage risk of the system should be weighted by water demand: ;

[0270] in Let Q be the total water demand of the user corresponding to reservoir i during the scheduling period. Let the total weighted water shortage risk of the system be proportional to Q. N The derivative is 0: ;

[0271] Therefore, the condition for minimizing the system's water shortage is obtained: ;

[0272] Right now: ;

[0273] When the water demand of the two users is equal (D) H =D L When the system's water shortage is minimized, the condition becomes: When D H >D L Under optimal conditions, RTMR should be greater than 1, indicating that more water shortage risk should be retained on the user side of the water receiving area with lower water demand in order to minimize the total water shortage of the system.

[0274] Defining efficient water transfer zones based on RTMR: ;

[0275] Within this interval, increasing the water transfer volume can reduce the total amount of type k risk in the system. When Q exceeds this interval, the marginal efficiency of risk transfer is less than 1, and continuing water transfer will increase the total risk of the system. The upper bound of this interval is... (Solution for RTMR=1). In some scenarios, it is also necessary to normalize some parameters in the above embodiments, such as RTMR.

[0276] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A risk control method for inter-basin water transfer systems, characterized in that, include: Obtain inflow and demand scenario data for the inter-basin water transfer system to be analyzed, and obtain a set of pre-configured water transfer schemes; Based on the water transfer scheme set, water volume scheduling simulation is performed on inflow scenario data and water demand scenario data to determine the water shortage risk index and water abandonment risk index of each spatial node in the inter-basin water transfer system under different water transfer schemes. Based on water shortage risk indicators and water abandonment risk indicators, a risk response function is fitted to characterize the relationship between risk level and water transfer volume. Based on the risk response function, the marginal substitution index of risk transfer, which characterizes the efficiency of risk replacement among spatial nodes, is calculated. Based on the risk transfer marginal substitution index and the pre-configured risk space equilibrium criterion, the efficient and balanced water transfer interval of the inter-basin water transfer system is determined. When fitting the risk response function that characterizes the relationship between risk level and water transfer volume, the following are included: Based on the storage and regulation mechanism and supply and demand characteristics of each spatial node in the inter-basin water transfer system during the water transfer process, a family of parameterized functions with pre-defined convex-concave characteristics is determined. Based on the discrete water transfer volume data in the water transfer scheme set, as well as the corresponding water shortage risk indicators and water abandonment risk indicators, the parameterized function family is curve fitted by the nonlinear parameter estimation method to generate a parameterized risk response function. Determining a family of parameterized functions with predefined convexity / concavity characteristics includes at least one of the following function form construction steps: To address the concave response characteristics of the water abandonment risk index, which exhibits a decreasing rate of decline or a convex response characteristics, which exhibit an increasing rate of decline, a power function form with a scale coefficient, shape index, and base water abandonment level parameter is selected as the first type of sub-function family. In response to the convex decreasing response characteristics of water shortage risk indicators, which decrease with increasing water inflow and at a decreasing rate, a negative exponential function with the maximum amount of risk that can be improved, the risk decay rate, and the residual water shortage parameter is selected as the second type of sub-function family. Treat the first type of sub-function family and / or the second type of sub-function family as a parameterized function family; When determining the efficient and balanced water transfer interval of an inter-basin water transfer system by combining risk transfer marginal substitution indicators and pre-configured risk space equilibrium criteria, the following should be included: Based on the water shortage risk index and water abandonment risk index corresponding to each spatial node, the risk variation coefficient, which characterizes the relative dispersion of spatial risk, is calculated. Extract the water transfer volume characteristic point corresponding to the minimum value of the risk variation coefficient as the water transfer volume evolves, and determine it as the spatial equilibrium point characterizing the system risk distribution tending to be in equilibrium.

2. The method according to claim 1, characterized in that, Curve fitting of a family of parameterized functions is performed using nonlinear parameter estimation methods, including: The optimization objective is to minimize the deviation between the simulated observed values ​​of water shortage risk indicators and water abandonment risk indicators and the calculated values ​​output by the parameterized function family, and to optimize the parameters to be determined. Among them, the shape index determined by optimization is used to characterize the difference in the nonlinearity of the risk response of water abandonment between pairs of spatial nodes, and the risk decay rate determined by optimization is used to characterize the risk mitigation efficiency characteristics affected by the combined influence of reservoir regulation capacity and user water demand elasticity.

3. The method according to claim 1, characterized in that, When determining the efficient and balanced water transfer interval of an inter-basin water transfer system by combining risk transfer marginal substitution indicators and pre-configured risk spatial equilibrium criteria, the following are also included: The marginal substitution index for risk transfer is dynamically compared with the pre-configured transfer efficiency threshold; The water transfer volume feature point corresponding to the risk transfer marginal substitution index being equal to the pre-configured transfer efficiency threshold is extracted as the optimal point of the total system risk, representing the minimum value of the overall risk weighted total amount of the inter-basin water transfer system.

4. The method according to claim 3, characterized in that, When processing water shortage risk indicators, the pre-configured transfer efficiency threshold is determined in the following way: Obtain the pre-stored first water demand data corresponding to the risk beneficiary, and the pre-stored second water demand data corresponding to the risk bearer; The ratio of the second water demand data to the first water demand data is calculated to obtain a pre-configured transfer efficiency threshold used to determine the optimal point of total system risk.

5. The method according to claim 1, characterized in that, Water inflow scenario data and water demand scenario data are pre-acquired through the following offline construction steps: Acquire the pre-stored historical data of runoff prediction error and water demand prediction error for each spatial node; Marginal distribution fitting was performed on historical data of runoff prediction error and historical data of water demand prediction error, and a joint probability correlation structure among multiple variables was constructed using a vine-structure co-correlation model. Random sampling is performed based on a joint probability correlation structure to generate pre-constructed water inflow scenario data and water demand scenario data.

6. The method according to claim 1, characterized in that, After determining the efficient and balanced water transfer range of the inter-basin water transfer system, the following is also included: Select the target water transfer decision value within the efficient and balanced water transfer range; The target water diversion decision value is converted into a physical control signal and sent to the corresponding physical pumping station or reservoir gate of the inter-basin water diversion system to execute the actual water allocation instructions.

7. A computer program product comprising computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method described in any one of claims 1 to 6.

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