Chain risk analysis method for reservoir group flood resource utilization

Abstract

This invention discloses a chain-based risk analysis method for flood resource utilization in reservoir groups, comprising: fitting an error probability distribution based on meteorological no-rain forecast data to generate a set of probability forecast scenarios for the receding water level; inputting the set of probability forecast scenarios for the receding water level and employing a dynamic allocation method considering the spatial distribution and real-time status of floods to determine the probability samples of the reservoir's initial regulation water level; using graph neural networks to learn the topological association features of the reservoir group based on historical flood data to optimize the spectral clustering process, and using a neural gas algorithm to generate a design flood hydrograph scenario; fusing the probability samples of the initial regulation water level and the design flood hydrograph scenario to construct a chain-based risk decision tree for the entire flood control process; and establishing a dual-threshold risk early warning mechanism based on CVaR and VRR through full-path scheduling simulation and risk contribution backtracking analysis. This invention achieves chain-based coupling of multi-source uncertainties, improving the accuracy of risk assessment and the reliability of decision-making.

Description

Technical Field

[0001] This invention relates to flood analysis and prediction, and in particular to a chain-based risk analysis method for flood resource utilization in reservoir groups. Background Technology

[0002] Floods during the flood season are the main cause of flood disasters, but they also contain a huge amount of freshwater resources. Therefore, under the premise of ensuring flood control safety, scientifically utilizing the flood control capacity of reservoir groups to appropriately impound and regulate floods, and realizing the resource utilization of floods, has become an inevitable requirement for alleviating the contradiction between water supply and demand and ensuring sustainable development. However, the process of flood resource utilization is a dynamic game between flood control risks and beneficial effects, making the accurate quantification and scientific assessment of potential risks in this process a top priority of research.

[0003] Currently, extensive research has been conducted on reservoir flood control scheduling and risk analysis. Regarding uncertainty quantification, researchers often employ statistical models and probability distribution fitting methods to analyze the error characteristics of meteorological and hydrological forecasts (such as rainfall forecasts) and input them into hydrological models to generate probabilistic runoff forecasts. In terms of flood scenario generation, multivariate statistical methods such as the Copula function are commonly used to construct the joint distribution of flood elements (such as peak flow and volume), or traditional clustering algorithms such as K-means are used to classify historical floods to generate typical flood processes for simulation. However, in terms of reservoir group scheduling and water allocation, existing research largely focuses on allocation methods based on static flood control capacity ratios or empirical rules.

[0004] However, existing technologies still face several in-depth and specific technical challenges in addressing the complex issue of flood resource utilization in reservoir groups. These mainly focus on the fragmented nature of risk transmission, the static nature of water allocation, and the one-sidedness of scenario generation. Existing risk analyses are generally single-stage or isolated, failing to effectively couple the uncertainties of initial conditions and encountered events. Specifically, the probability distribution of the initial adjustment water level caused by weather forecast uncertainties and the probability distribution of the design flood caused by the spatiotemporal variability of floods are two independent risk sources, but traditional methods lack a framework for fusing these two probabilistic inputs and analyzing their chain transmission effects. Existing methods for allocating excess storage capacity largely rely on static flood control capacity ratios, resulting in spatially blind allocations that cannot dynamically adjust the flood control responsibilities of each reservoir based on the spatial distribution characteristics of flood forecasts (e.g., the location of the rainstorm center), leading to low relevance and efficiency in allocation schemes. Traditional flood scenario generation methods (such as K-means) only focus on numerical similarity and ignore the physical topological relationships within the reservoir system (such as upstream and downstream confluence relationships). This results in scenarios that may be statistically valid but are not reasonable in terms of physical transmission, thus reducing the authenticity of risk assessment. Summary of the Invention

[0005] The purpose of this invention is to provide a chain-based risk analysis method for the utilization of flood resources in reservoir groups, in order to solve at least one of the aforementioned problems in the existing technology.

[0006] Technical solution: A chain-based risk analysis method for flood resource utilization in reservoir groups, comprising:

[0007] Read and fit the error probability distribution based on meteorological no-rain forecast data to generate a set of probability forecast scenarios for the receding water section flow.

[0008] Based on the probability forecast scenario set of the flow rate in the receding section, the dynamic allocation method of excess water storage in the reservoir group is adopted to determine the probability sample of the starting water level.

[0009] Based on pre-stored historical flood data, a clustering process optimized by graph neural networks and a neural gas algorithm are used to generate a design flood process line scenario.

[0010] By integrating the probability samples of water level regulation with the design flood process line scenario, a flood control chain risk decision tree is constructed, and the risk analysis results are output through risk contribution retrospective analysis.

[0011] Beneficial effects: This invention achieves chain coupling of multi-source uncertainties, improving the accuracy of risk assessment and the reliability of decision-making. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the overall process of the chain-based risk analysis method for flood resource utilization in reservoir groups.

[0013] Figure 2 A schematic diagram illustrating the process for calculating the equivalent flood control capacity of the system to determine the deterministic excess water storage capacity of the entire system.

[0014] Figure 3 A schematic diagram illustrating the initial allocation of the overall deterministic excess water storage capacity of the system to each reservoir.

[0015] Figure 4 A schematic diagram of the process for generating a deterministic final allocation scheme for excess water storage.

[0016] Figure 5 This is a schematic diagram of a chain-like risk analysis method for the utilization of flood resources in reservoir groups that integrates meteorological no-rain forecasting and simulation of the spatial composition of design floods. Detailed Implementation

[0017] Example 1 describes the overall framework of a chain-based risk analysis method for flood resource utilization in reservoir groups, such as... Figure 1 As shown.

[0018] Step 101: Read the pre-stored no-rain forecast data, and based on the no-rain forecast data, fit the error probability distribution to generate a set of probability forecast scenarios for the receding water section flow. This step is used to quantify the uncertainty of weather forecasts.

[0019] Specifically, meteorological no-rain forecast data refers to the prediction by meteorological models that there will be no rainfall within a certain period of time (e.g., 0-120 hours). However, precipitation may still occur in reality, and deviation is one of the sources of risk. This step collects historical forecast-measured data pairs and establishes a statistical model to fit the probability distribution characteristics of this no-rain forecast error. Based on this, a large number of rainfall scenarios considering uncertainty errors are generated through random sampling (e.g., Latin hypercube sampling). The rainfall scenario set is input into the hydrological forecast model to simulate various possible inflow processes in the watershed during the recession phase, forming a probability forecast scenario set for the recession phase flow. This scenario set is the key probabilistic input for subsequent calculations of reservoir excess storage.

[0020] In some alternative implementations, the hydrological forecasting model can be the Xin'anjiang model, HEC-HMS model, or SWAT model, which are well-known in the art. The specific model can be adapted to the actual runoff generation and confluence characteristics of the target watershed.

[0021] Step 102: Input the probability forecast scenario set of the receding section flow, and use the dynamic allocation method of excess water storage in the reservoir group to determine the probability sample of the starting water level, so as to determine the initial conditions and uncertainties of the flood control scheduling stage.

[0022] Specifically, this step receives multiple possible receding flow processes generated in step 101, i.e., a set of probabilistic forecast scenarios for receding flow. On one hand, using the pre-storage and pre-discharge method, the probability distribution of the actual excess water volume that the reservoir can absorb is calculated based on the probabilistic inflow process. On the other hand, this invention employs a dynamic allocation method for excess water volume in a reservoir group. This method is based on deterministic rainfall and flood forecasting, comprehensively considering the spatial distribution of floods, the real-time status of each reservoir (such as the current water level), and static flood control capacity, to calculate a set of deterministic final allocation schemes for excess water volume. By fusing the probabilistic actual excess water volume with the deterministic allocation schemes, a set of reservoir starting water levels with different probabilities of occurrence is finally obtained, i.e., a probability sample of starting water levels.

[0023] Furthermore, the preferred implementation of the dynamic allocation method for excess water storage capacity in a reservoir group includes: calculating scenario weighting factors based on the spatial distribution of flood forecasts, and constructing the equivalent flood control capacity of the system accordingly; and constructing a comprehensive decomposition weighting system with multi-factor coupling, supplemented by a secondary allocation rule, to achieve spatial optimization of water allocation. The specific implementation of this method will be detailed in subsequent embodiments.

[0024] Step 103: Read the pre-stored historical flood data. Based on the historical flood data, use a graph neural network-optimized clustering process and a neural gas algorithm to generate a design flood process line scenario.

[0025] This step is used to generate a set of external disturbances or risk encounters during the flood control scheduling phase. It aims not only to generate floods that conform to historical statistical patterns but also to ensure their representativeness and distinguishability in spatiotemporal distribution. Specifically, key risk source factors, such as upstream flood volume, inter-regional flood volume, and external river water levels, are first identified from historical flood data. To characterize the complex correlations between factors, especially the tail correlations under extreme conditions, a VineCopula model is preferably used to construct their joint probability distribution. This invention introduces a Graph Neural Network (GNN) to learn the correlation between the topology of the reservoir system and the spatiotemporal characteristics of floods, and utilizes the node embeddings learned by the GNN to optimize the traditional spectral clustering process, enabling the clustering results to better distinguish floods with different risk transmission characteristics. Based on the clustering results, the Neural Gas Algorithm (NG) is used to construct a scene tree, and combined with a proportional scaling method, a series of design flood process line scenarios with spatiotemporal distribution characteristics and corresponding probabilities are generated.

[0026] In some embodiments, to ensure a sufficient representation of extreme events, an extreme event-enhanced sampling strategy is preferably incorporated when generating risk source factor samples. The specific implementation of this method will be detailed in subsequent embodiments.

[0027] Step 104: Integrate the probability samples of the water level adjustment with the design flood process line scenario to construct a flood control chain risk decision tree, and output the risk analysis results through risk contribution retrospective analysis.

[0028] This step probabilistically couples the output of step 102 (N probabilistic samples of starting water levels, representing initial conditions) with the output of step 103 (M design flood hydrograph scenarios, representing encountered events). Specifically, a decision tree structure can be constructed, containing N×M complete risk transmission paths from initial conditions to encountered events to final risk. The invention then performs a full-path flood control scheduling simulation for each risk path, calculating its final risk index, such as the maximum water level exceeding the flood control limit. Based on the simulation results of all paths, an empirical probability distribution of the maximum flood control limit can be constructed, and advanced risk measurement indicators such as Conditional Value at Risk (CVaR) and Value at Risk (VRR) can be calculated. Through risk contribution retrospective analysis, such as analyzing which starting water level intervals contribute most to the overall CVaR, key risk transmission paths and key starting water level intervals are identified, and the final risk analysis results are output, providing decision-makers with a scientific basis for early warning and control.

[0029] Preferably, the risk warning mechanism established in this step is a dual-threshold warning mechanism based on CVaR and VRR, which can simultaneously monitor the absolute level of risk and the fat-tailed characteristics of the risk distribution. The specific implementation of this method will be detailed in subsequent embodiments.

[0030] Optionally, a chain-based risk analysis method for flood resource utilization in reservoir groups, integrating meteorological no-rain forecasting and simulation of the spatial composition of design floods, is provided. Figure 5 As shown, it may also include the following steps:

[0031] A rainfall forecast-measurement database is constructed based on multi-source data of the target watershed. The probability distribution of no-rain forecast error is fitted and random error samples are generated to form a multi-predictability rainfall scenario set. The set of probability forecast scenarios for the discharge section is then input into the hydrological model.

[0032] Input the probability forecast scenario set of the receding section flow, calculate the series of values ​​of the reservoir's pre-discharge excess water volume for beneficial purposes based on the pre-storage and pre-release method, realize the spatial optimization configuration of excess water volume based on the dynamic allocation method of excess water volume of the reservoir group system considering the spatial distribution and real-time status of floods, and determine the probability sample of the starting water level.

[0033] Based on historical flood data, a joint probability distribution of risk source factors is constructed using the VineCopula model. Combined with an extreme event-enhanced sampling strategy, a graph neural network is used to learn the spatiotemporal characteristics of floods in the topological association of reservoir groups to optimize the spectral clustering process. A neural gas algorithm is used to generate design flood process line scenarios, in which the generated scenarios have discriminative characteristics in terms of risk transmission.

[0034] By integrating the probability samples of the starting water level with the design flood process line scenario, a chain-like risk decision tree for flood control throughout the entire process is constructed. Through full-path scheduling simulation and risk contribution retrospective analysis, key risk transmission paths are identified, and a dual-threshold risk early warning mechanism based on CVaR and VRR is established.

[0035] Example 2 details the generation process of the probability forecast scenario set for the receding water section flow, describing how to start from the original meteorological forecast data, through a series of statistical modeling and simulations, to finally quantify the uncertainty of the meteorological forecast and generate the probability forecast scenario set for the receding water section flow as the source of chain risk analysis.

[0036] Step 201: Integrate measured rainfall samples from meteorological stations with high-resolution deterministic rainfall forecast data to construct a forecast-measured dual-source database.

[0037] In this embodiment, data preparation is the foundation for subsequent statistical analysis. Specifically, it is necessary to systematically collect historical data of the target study area. Meteorological station measured rainfall samples refer to quality-controlled historical daily or periodic rainfall data from hydrological monitoring stations and watershed management agencies within the basin. High-resolution deterministic rainfall forecast data can preferably come from the forecast products of the European Centre for Medium-Range Weather Forecasts (ECMWF) within the global multi-model forecasting system TIGGE. When collecting forecast data, it is necessary to simultaneously collect forecast results for different lead times, such as forecasts for the next 0-120 hours, i.e., forecasts for the next 1-5 days. By matching the forecast values ​​for predetermined dates and stations with the measured values, a forecast-measured dual-source database is constructed. This database is the core basis for subsequent analysis of forecast error characteristics.

[0038] Step 202: Analyze the actual precipitation under different forecast periods of no rainfall in the forecast-measured dual-source database, extract the forecast error sequence and perform probability distribution modeling to determine the forecast error probability distribution.

[0039] This invention focuses on a no-rain forecast scenario, where weather forecasts indicate no future precipitation (e.g., forecast precipitation less than 0.1 mm), but precipitation actually occurs. This error of reporting no precipitation is the direct cause of reservoirs erroneously exceeding their storage capacity during the receding water phase. Specifically, this step filters all data pairs forecasting no precipitation from the forecast-measured dual-source database and statistically analyzes the actual precipitation for different forecast periods (e.g., 24 hours, 48 ​​hours, etc.) to form a forecast error sequence.

[0040] Furthermore, a probability distribution model is performed on the forecast error sequence. Various candidate marginal distribution functions can be used for fitting, such as the generalized extreme value distribution function (GEV), the normal distribution function, the exponential distribution function, the gamma distribution function, and the log-normal distribution function. To select the optimal distribution model, statistical indicators such as the root mean square error (RMSE), the KS test, or the AIC / BIC information criterion can be used for optimization. For example, the candidate distribution function with the smallest RMSE value is selected as the marginal distribution function of the error sequence. This optimal distribution is the forecast error probability distribution.

[0041] Step 203: Based on the probability distribution of forecast errors, a random sample of forecast errors is generated using a sampling method, and the random sample is superimposed on the deterministic rainfall forecast to generate a set of forecast rainfall scenarios for the receding water period.

[0042] After determining the probability distribution of the error, this step generates a large number of possible error scenarios. Specifically, the sampling method preferably employs the Latin hypercube sampling method (LHS). Using LHS ensures stratification and uniform coverage across the entire probability distribution range while maintaining sample randomness, achieving high sampling efficiency with a smaller sample size (e.g., N = 1000 samples). Based on the prediction error probability distribution determined in step 202, N random samples of prediction errors can be generated through LHS sampling.

[0043] After obtaining error samples, these samples are superimposed onto an existing single deterministic rainfall forecast process. For example, if the currently obtained 24-hour deterministic rainfall forecast P... deterministic (t), then the superimposed error sample E sample_i After (t), the i-th rainfall scenario P is generated. scenario_i (t):

[0044] P scenario_i (t)=P deterministic (t)+E sample_i (t).

[0045] By repeating this process on N error samples, a set of predicted rainfall scenarios for the receding water section containing N rainfall events can be generated.

[0046] Step 204: Input the predicted rainfall scenario set for the receding section into the hydrological forecasting model to simulate and obtain the probability forecast scenario set for the receding section flow. This step is used to realize the physical simulation process of the transfer from rainfall uncertainty to flow uncertainty.

[0047] The hydrological forecasting model is a calibrated rainfall-runoff model applicable to the study area, such as the Xin'anjiang model, the HEC-HMS model, or other hydrological models suitable for a specific watershed. This step uses the N predicted rainfall scenarios for the receding water sections generated in step 203 as N independent inputs to run the hydrological forecasting model separately, simulating and forecasting the flow in the receding water sections.

[0048] Accordingly, the model will output N possible flow processes in the receding section, which together constitute a probability forecast scenario set for the receding section flow. This scenario set (e.g., 1000 flow process lines) is the direct input for determining the probability sample of the starting water level, and also the basis for subsequent calculations of the uncertainty of the reservoir's starting water level.

[0049] Example 3 describes the generation process of the reservoir's initial water level probability sample, and elaborates on how to couple uncertainty analysis with a dynamic allocation method that considers spatiotemporal distribution, so as to finally determine the key initial state before flood control scheduling, namely the initial water level probability sample.

[0050] Step 301: Based on the probability forecast scenario set of the discharge section flow, calculate the series of actual excess water storage values ​​using the pre-storage and pre-discharge method.

[0051] Receive a set of probabilistic forecast scenarios for the receding water flow, for example, N=1000 flow processes. The pre-storage and pre-discharge method involves using the reservoir's flood control capacity to store an excess of water during the predicted rainless receding water period, and then gradually dissipating it through beneficial water supply (such as power generation and irrigation) so that the water level can be lowered to the flood limit level before the next flood.

[0052] Due to forecast uncertainties, the actual inflow rate Q tilde_in (t) is a random variable, resulting in the actual absorbable excess water storage capacity W. tilde It is also a random variable. Consider the forecast error ε(t) = Q(t) - Q hat (t) (where Q(t) is the actual flow rate, Q) hat (t) represents the predicted flow rate, and the actual excess water storage capacity W tilde It can be represented as:

[0053] W tilde =Σ[(q m -Q tilde_in [(t)+ε(t))×Δt],

[0054] Where q m To utilize the water flow rate, Δt is the time step.

[0055] By substituting each of the 1000 flow scenarios into the formula, 1000 possible excess water storage volumes can be obtained, forming a series of actual excess water storage volumes. Preferably, statistical analysis can be performed on this series of values, using methods such as the KS test, AIC, and BIC criteria to fit its probability distribution function for subsequent fusion.

[0056] Step 302: Read the pre-stored deterministic rainfall and flood forecast data, and execute the dynamic allocation method for excess water storage of the reservoir system based on the deterministic rainfall and flood forecast data. This method includes: calculating the equivalent flood control capacity of the system to determine the overall deterministic excess water storage of the system, such as... Figure 2 As shown.

[0057] This step is to calculate a planned, deterministic excess water storage allocation scheme. Deterministic rainfall and flood forecast data refers to a single flood forecast process and its corresponding rainfall forecast process used for decision-making, such as a typical flood and rainfall process or the latest forecast.

[0058] Extract the surface average forecast rainfall from deterministic rainfall forecast data and calculate the scenario weighting factor α, which characterizes the spatial distribution differences of floods. iSpecifically, the average forecast rainfall P for each reservoir i controlled sub-basin is extracted from the rainfall and flood forecast for this event. i Calculate the average areal rainfall P across the entire watershed. bar =[1 / I]*ΣP i Let I be the total number of reservoirs. Then the scenario weighting factor α for reservoir i is... i '=P i / P bar And normalize it, for example, so that Σα i =I. If the forecast rainfall for a reservoir's controlled watershed is much greater than the average (α) i >1), indicating that the reservoir is a key focus of this flood control effort, and its weight should be increased accordingly.

[0059] Furthermore, using the scenario weighting factor α i The static flood control capacity of each reservoir is dynamically weighted to construct a scenario-adaptive system equivalent flood control capacity V. eff In traditional methods, the total flood control capacity of the system is the static capacity V of each reservoir. i,f The sum. This invention uses formula V eff =Σ(α i *V i,f The calculation is performed using this formula. This transforms the system's flood control capacity from a static attribute to a scenario-adaptive attribute: the reservoir at the center of the storm (α) i The higher the storage capacity, the greater the weight, making V... eff It can dynamically reflect the system's actual flood control capacity under the current flood conditions.

[0060] The system's equivalent flood control capacity is represented as a virtual reservoir, and the safe discharge at the downstream flood control point is used as the core constraint. The deterministic excess storage capacity W of the entire system is obtained through flood regulation calculations. This step equates the entire reservoir group system to a virtual reservoir with V... eff A virtual reservoir with a storage capacity. The safe discharge Q at the downstream flood control point. safe As the core constraint, and to ensure that the simulated highest flood level Z of the equivalent reservoir is... max Not exceeding its flood control high water level Z f By performing flood control calculations on the equivalent reservoir, a maximum W value is obtained, which represents the total reservoir capacity that the entire system needs to release before the flood season.

[0061] Step 303: Construct a comprehensive decomposition weight of the coupled scenario weight factor, flood control factor, urgency factor, and efficiency factor to initially allocate the overall deterministic excess water storage capacity of the system to each reservoir. Obtain the initial excess water storage capacity; perform feasibility verification and secondary allocation on the initial excess water storage capacity to generate the final deterministic excess water storage capacity allocation scheme.

[0062] This step is used to reasonably and initially allocate the total system volume W calculated in step 302 to each reservoir. The flood control factor, representing the static flood control capacity of the reservoirs, the urgency factor, representing the real-time urgency, and the efficiency factor, representing the pre-release efficiency, are calculated separately. A weighted geometric average method is used to couple the flood control factor, urgency factor, efficiency factor, and scenario weight factor to determine the normalized comprehensive decomposition weights. These comprehensive decomposition weights are then used to decompose the deterministic excess storage capacity of the entire system, obtaining the preliminary excess storage capacity of each reservoir, such as... Figure 3 As shown.

[0063] This invention constructs a multi-factor coupled comprehensive decomposition weight ω i Except for the scenario weighting factor α in step 302. i In addition, it also includes:

[0064] Flood control factor β i1 This characterizes the static flood control capacity of a reservoir. Specifically, β i1 =V i,f / ΣV i,f This refers to the proportion of the static flood control capacity of reservoir i to the total capacity of the system.

[0065] Urgency factor β i2 This characterizes the urgency level of the reservoir's real-time status. Specifically, the current water level Z is first calculated. i,c With flood control limit water level Z i,fL The difference d i =Z i,c -Z i,fL . d i The smaller the value, the higher the water level, and the greater the need for emergency pre-release. To prevent the denominator from being too small, β can be used. i2 =1 / log(e+d) i Calculate and normalize to obtain β i2 .

[0066] Efficiency factor β i3 This characterizes the contribution efficiency of reservoir pre-discharge to downstream flood control points. It can be simplified to the time t it takes for the reservoir discharge to propagate to the downstream flood control point. i The reciprocal of β i3 =1 / t i And normalize to obtain β i3 Propagation time t i The shorter the length, the higher the efficiency.

[0067] After obtaining the above four factors, the weighted geometric mean method is used for coupling to calculate the unnormalized comprehensive decomposition weights:

[0068] ω i '=(β i1 w1 *β i2w2 *β i3 w3 *α i w4 ) (1 / (w1+w2+w3+w4)) ;

[0069] Where w1, w2, w3, and w4 are the importance weights of each factor, satisfying w1+w2+w3+w4=1. The weight values ​​are determined by expert experience or historical optimization data. For example, in scenarios where flood control safety is emphasized, the weights of w1 (flood control factor) and w4 (scenario factor) can be increased.

[0070] For ω i The final comprehensive decomposition weight ω is obtained by performing normalization. i =ω i ' / Σω i '.

[0071] Using this weight, the total system volume W is decomposed to obtain the preliminary excess storage capacity W of each reservoir. i =ω i *W.

[0072] Step 304: Perform feasibility verification and secondary allocation on the preliminary allocation results to generate a deterministic final allocation plan for excess water storage.

[0073] This step is a correction to the preliminary allocation results of step 303, ensuring the feasibility of the plan.

[0074] like Figure 4 As shown, specifically, based on the maximum allowable discharge flow and pre-discharge period of each reservoir, the feasibility of the initial excess water storage is verified; the set of infeasible reservoirs whose allocated water exceeds their maximum discharge capacity is identified, and the excess water is determined as the water to be allocated; based on the preset secondary allocation rules, the water to be allocated is redistributed to other reservoirs with surplus discharge capacity; the secondary allocation rules are: priority is given to reservoirs that have both high scenario weight factors and large surplus discharge capacity, so as to generate a deterministic final allocation scheme for excess water storage.

[0075] Conduct a feasibility verification. Set a uniform pre-release period T (e.g., 48 hours) and check the initial allocation volume W for each reservoir i. i Whether it exceeds its maximum discharge capacity during that period, i.e., the constraint condition:

[0076] W i ≤Q i,max *T;

[0077] Among them, Q i,max This represents the maximum allowable discharge flow rate for reservoir i.

[0078] Identify all reservoirs that do not meet this constraint, forming the infeasible reservoir set S. inf Calculate the excess water volume to obtain the water volume to be allocated. The total excess water volume of these reservoirs is then determined as the water volume to be allocated, ΔW.

[0079] ΔW=Σ(W j -Q j,max *T)(j∈S inf );

[0080] Among them, W j Q is the initial discharge volume of infeasible reservoir j determined in the optimization or scheduling scheme (without considering the maximum discharge flow constraint). j,max The maximum allowable discharge flow for an infeasible reservoir is given by [reference to a specific reservoir name].

[0081] At the same time, the allocation of infeasible reservoir j is adjusted to its maximum discharge capacity W. j,n =Q j,max *T.

[0082] Furthermore, a secondary allocation is performed. Other sets of reservoirs S with surplus discharge capacity are identified. f The secondary allocation rule of this invention is: to preferentially allocate the water volume to be allocated ΔW to those with a higher scenario weighting factor α. i Reservoirs with a relatively large surplus discharge capacity.

[0083] Specifically, the secondary allocation weight γ is calculated. i :

[0084] γ i =[α i *(Q i,max TW i )] / Σ[α k *(Q k,max TW k (where i, k∈S) f ).

[0085] The numerator α of this weight i *(Q i,max *TW i It incorporates contextual importance (α) i The above allocation rules are implemented through the use of surplus capacity (in parentheses) and excess capacity.

[0086] Using this weight γ i Reallocate ΔW and update the final excess capacity W of the feasible reservoir. i,f =W i +γ i *ΔW.

[0087] The allocation of the infeasible reservoir is W. j,nThe feasible reservoir allocation is W. i,f Together, these two constitute the final, executable, deterministic allocation scheme for excess water storage. f}

[0088] Step 305: Integrate the actual excess water storage series values ​​with the deterministic final allocation scheme of excess water storage, and combine them with the pre-stored water level-reservoir capacity relationship to generate a probability sample of the starting water level.

[0089] Let V x_i Let f(•) be the reservoir storage capacity corresponding to the design flood control limit water level of reservoir i, and let f(•) be the water level-reservoir capacity relationship function. Then, considering uncertainties, the starting water level Z... tilde_i The calculation formula is:

[0090] Z tilde_i =f(V x_i +W f_i -W tilde_i );

[0091] Among them, W f_i W is the allocation value in the deterministic final allocation scheme of excess water storage for reservoir i. tilde_i This is a series of actual excess water storage values ​​for reservoir i (e.g., 1000 samples). W tilde_i By substituting each of the 1000 sample values ​​into the formula, the 1000 corresponding Z values ​​can be calculated. tilde_i value.

[0092] This series containing 1000 water level values ​​is the starting water level probability sample sought in this invention, reflecting the dynamic allocation strategy W. f It also carries the uncertainty of weather forecasts. tilde , which are the N initial condition inputs for chain risk analysis.

[0093] For example, a numerical calculation case of dynamic allocation of a reservoir group is provided. Assume a reservoir group system includes three reservoirs, A, B, and C, with a downstream flood control point safe discharge capacity Q. safe 5000m 3 / s. Under a certain deterministic rainfall and flood forecast scenario, the parameters of each reservoir are shown in Table 1:

[0094] Table 1

[0095]

[0096] Calculate the average areal rainfall P across the entire watershed bar =(120+90+60) / 3=90mm.

[0097] Calculate the scenario weighting factor α i α A=120 / 90=1.33, α B =90 / 90=1.00,α C =60 / 90=0.67.

[0098] The equivalent flood control capacity V of the calculation system eff =(1.33*2.0+1.00*1.0+0.67*0.5)=4.0 billion m 3 .

[0099] Based on V eff =4.0 and Q safe =5000, based on flood control calculations, the overall deterministic excess storage capacity of the system is determined to be W = 0.8 billion m³. 3 .

[0100] Calculate each factor (β) i1 ,β i2 ,β i3 And assume the weights w1=0.4, w2=0.2, w3=0.1, w4=0.3.

[0101] Calculate the comprehensive decomposition weight ω i :ω A =0.50,ω B =0.30,ω C =0.20.

[0102] Calculate the initial allocation W i :W A =0.50 * 0.8 = 0.40, W B =0.30 * 0.8 = 0.24, W C =0.20 * 0.8 = 0.16 billion m 3 .

[0103] Feasibility verification, assuming a pre-release period of T = 72h = 259200s:

[0104] W A_max =1000 * 259200 = 259 million m 3 W A <W A_max (feasible).

[0105] W B_max =800 * 259200 = 207 million m 3 W B <W B_max (feasible).

[0106] W C_max =500 * 259200 = 130 million m 3 W C =0.16 billion m3 >W C_max =0.13 billion m 3 (Not feasible)

[0107] Identify the set of infeasible reservoirs S inf ={C}. Calculate the amount of water to be allocated ΔW:

[0108] ΔW=W C -W C_max =0.16 - 0.13 = 0.03 billion m 3 .

[0109] Fix W C,f =W C_max =0.13 billion m 3 .

[0110] Secondary allocation: S f ={A,B}. Calculate the surplus capacity (W) of A and B. A_max -W A ) and (W B_max -W B ), and combined with α A and α B Calculate the secondary allocation weight γ A and γ B Assume γ A =0.7,γ B =0.3.

[0111] Final allocation:

[0112] W A,f =W A +γ A *ΔW=0.40+0.7*0.03=0.421 billion m 3 .

[0113] W B,f =W B +γ B *ΔW=0.24+0.3*0.03=0.249 billion m 3 .

[0114] Final solution {W f}={W A,f 0.421,W B,f 0.249,W C,f 0.13 billion m 3 .

[0115] Example 4 describes the implementation of the design flood hydrograph scenario. It details how flood patterns are extracted from historical data and how a graph neural network (GNN) is used to optimize the clustering process to generate a design flood hydrograph scenario with high discriminative power in terms of risk transmission characteristics.

[0116] Step 401: Identify and extract risk source factors from historical flood data and construct a graph structure.

[0117] This step requires identifying the key driving factors that lead to historical flood events, i.e., risk source factors. In this embodiment, three types of factors are preferably identified: upstream inflow into the reservoir, inflow into the lake within the region, and the highest water level of the outer river.

[0118] The factors are quantified. For example, the annual maximum value method is used to select the largest flood event in each year and calculate its corresponding upstream inflow, inter-regional inflow into the lake, and highest water level of the outer river. The calculation formula is as follows:

[0119] x 1h =ΣΣQU h i,t ;

[0120] Where, x 1h For the historical flood data of year h, the upstream inflow volume is QU h i,t The historical upstream inflow of the i-th reservoir in year h during period t;

[0121] x 2h =ΣQL h t ;

[0122] Where, x 2h QL represents the inflow volume into the lake within the historical flood data for year h. h t The inflow to the lake during the historical interval of year h in time period t;

[0123] x 3h =maxZ R,t h ;

[0124] Where, x 3h Z represents the highest water level of the outer river in the historical flood data of year h. R,t h The water level of the outer river in the h-th year during the t-th period is the historical water level of the outer river.

[0125] Specifically, three types of risk source factors are used as nodes in the graph. Spatial edges are constructed based on the physical topological connections of the reservoir group; statistical edges are constructed based on the Pearson correlation coefficient or mutual information between factors; and even time-varying dependencies at different flood stages (such as rise and peak flood) can be considered to construct dynamic edges. Finally, an adjacency matrix and a node feature matrix (containing historical observations of each factor) are formed, which serve as inputs to the subsequent graph neural network.

[0126] Step 402: Based on the risk source factors, generate probability samples of the risk source factors using the VineCopula model and an extreme event-enhanced sampling strategy. This step is used to construct the joint probability distribution of the factors and generate samples. Specifically:

[0127] For each type of risk source factor (x) quantified in step 401 1h ,x 2h ,x 3h Fit an adaptive marginal distribution function, for example: u n =F n (x n ), where x n Let F be the observed vector of the nth type of risk source factor. n Let u be the corresponding marginal distribution function. n It is a closed interval containing the marginal distribution function value, which ranges from 0 to 1.

[0128] To characterize the complex high-dimensional correlation structure among the three types of factors, this embodiment preferably employs the VineCopula model. This model utilizes a layer-by-layer nested two-dimensional Copula function (C... n,k ) and conditional Copula functions (C n|1 ...) to flexibly construct the joint distribution C(...). This structure excels at capturing the tail correlation between variables, that is, the probability of extreme events (such as extremely large floods and extremely high water levels in external rivers) occurring simultaneously, which is crucial for risk analysis.

[0129] Samples are generated based on the constructed VineCopula model. To ensure that extreme cases of flood events (usually low-probability events) are adequately represented, this embodiment preferably incorporates an extreme event enhanced sampling strategy. By selecting an appropriate auxiliary distribution, the sampling frequency in the extreme flood event area is intentionally increased. A large number of probability samples (u1, u2, u3) are obtained through sampling, their joint probability Pv is calculated, and samples that meet the design flood probability threshold P are selected. w The sample (i.e., Pv) <P w The probability samples that meet the conditions are transformed by the inverse marginal distribution X. n =F n -1 (u nThe transformation ultimately yields the probability samples of risk source factors.

[0130] In other words, steps 401 and 402 can also be summarized as: generating probability samples of risk source factors based on historical flood data, using the VineCopula model and an extreme event-enhanced sampling strategy.

[0131] Step 403: A graph neural network is used to learn the spatiotemporal characteristics of flood topological associations of reservoir groups, and the spatiotemporal characteristics are used to optimize the spectral clustering process to cluster the probability samples of risk source factors, thereby obtaining cluster groups and node embeddings.

[0132] Specifically, a graph convolutional network is used to learn the features of the probability sample nodes of the risk source factors, and the spatiotemporal correlation features of flood events are extracted through the neighborhood aggregation mechanism. The node embeddings learned and output by the graph neural network are used as the input of the spectral clustering algorithm, and cluster analysis is performed on the Laplacian matrix feature vectors to form cluster groups corresponding to the topology of the reservoir group.

[0133] Traditional clustering methods (such as K-means) only consider the distance between sample points in the feature space, ignoring the potential spatiotemporal correlations between flood events. For example, the flood peak of reservoir A always precedes that of reservoir B. This invention utilizes graph neural networks (GNNs) to address this problem.

[0134] Specifically, the risk source factor probability samples generated in step 402 are used as nodes of the graph, and the graph structure (adjacency matrix) constructed in step 401 is used as edges. Graph neural network models such as Graph Convolutional Network (GCN) or Graph Attention Network (GAT) are used to learn features from the nodes. Through a neighborhood aggregation mechanism, GNNs can fuse the representation of each node with information from its neighboring nodes (i.e., other flood events that are related in the spatiotemporal topology), extracting node embeddings that contain the spatiotemporal correlation features of floods.

[0135] A similarity matrix is ​​constructed based on the probability samples of risk source factors, and the corresponding Laplace matrix is ​​calculated.

[0136] In traditional spectral clustering, the algorithm needs to perform eigenvalue decomposition on the Laplacian matrix of the graph and then cluster the resulting eigenvectors. This invention uses node embeddings rich in spatiotemporal topological information learned by GNNs as input to the spectral clustering algorithm to guide and optimize the clustering process.

[0137] In other words, GNN-assisted spectral clustering addresses the problem of how to ensure that clustering results not only reflect the similarity of risk factor values, but also the similarity of flood patterns in the topological structure of reservoir groups.

[0138] The number of clusters, R (i.e., the number of groups), can be adaptively determined using the elbow rule. The final output of clustering is R clusters and the node embeddings of all samples.

[0139] Step 404: Based on clustering groups and node embedding, a scene tree is constructed using the neural gas algorithm, and a flood scene is generated based on the scene tree.

[0140] This step is used to generate representative scenarios within the already clustered groups. This embodiment preferably employs the Neural Gas Algorithm (NG), a robust clustering algorithm that adaptively adjusts cluster centers through a competitive learning mechanism. Optimized scenario tree nodes are obtained, which are used to generate the design flood scenario, which exhibits discriminative characteristics in terms of risk transmission.

[0141] The neural gas algorithm is used to construct the scene tree, including: using a batch loading mechanism to progressively train the cluster groups and prioritizing the learning of sample distribution in high-risk areas; during the training process, the node embedding representation is dynamically updated based on the graph neural network to maintain the topological continuity of flood event features; and the cluster centers are adaptively adjusted through a competitive learning mechanism to ensure that the generated design flood scene has discriminative characteristics in terms of risk transmission.

[0142] In this embodiment, a separate scene tree is constructed for each cluster group output in step 403. To improve training efficiency and accuracy, a batch loading mechanism is preferably used for progressive training.

[0143] During the iterative training of the Neural Gas Algorithm (NG algorithm), it doesn't just use static risk factor samples, but dynamically updates node embeddings based on a graph neural network. In other words, as the NG algorithm adjusts the cluster centers, the GNN simultaneously optimizes its representation of flood event features. This dual optimization approach ensures the topological continuity between node embeddings and clustering results, enabling the final generated scene to clearly distinguish its impact on the excessive risk at the end of the decision tree.

[0144] In the specific iterative update process of the neural gas algorithm, Δs p,q (r) It is the adjustment amount of the node value, which is jointly controlled by the step size function ε(l), the local step size function λ(l), and the fitness function (also known as the neighborhood function) h[...], and the formula is:

[0145] Δs p,q (r) =ε(l)·h[O p (r),λ(l)]·(X k,q (r) -s p,q (r) );

[0146] Where ε(l) is the step size function, h is the fitness function, and X k,q(r) Let s be the q-th component of the k-th risk source factor sample in the r-th group. p,q (r) This is the value of the current node.

[0147] After iteration, the probability P(S) of each scene (cluster center) is calculated based on the distance and number of its nearest samples. p (r) The formula is:

[0148] P(S p (r) )=P(S p (r) |r,w)P(r|w)P w ;

[0149] Wherein, P(S) p (r) |r,w) represents the conditional probability of the scenario occurring under the conditions of the design flood event and group r, and P(r|w) represents the conditional probability of group r occurring under the conditions of the design flood event. w This is used to design a probability threshold for flood events. The formula is an application of the total probability formula or Bayesian chain decomposition, used to assign a probability threshold to each cluster center (i.e., scenario S). p (r) A probability of occurrence is given, making it a probabilistic design flood scenario.

[0150] Cluster centers with probability are used to design flood scenarios.

[0151] Step 405: Scale the design flood scenario and the pre-stored historical flood process line by the same factor to generate the design flood process line scenario.

[0152] The design flood scenario generated in step 404 is a static total flood volume (e.g., upstream total flood volume X billion m³). 3 However, flood control scheduling requires a dynamic process line, that is, the change of flow over time. This step aims to address this issue.

[0153] This embodiment uses the same scaling method, taking the collected historical flood process line (e.g., the measured flow process of a typical flood) as a template, and the design flood scenario (total flood volume value) generated in step 404 as the control total.

[0154] Specifically, scale the outflow process line of the outer river, the upstream inflow process line, and the inflow process line of the lake in the interval.

[0155] For example, the design flood hydrograph calculation formula Q Ui,tr,p =S p,2 (r) *Q Ui,th / (coeff*ΣΣQ Ui,th In ), S p,2 (r) Q is the total flood of scenes generated by the NG algorithm. Ui,th This is a historical flood hydrograph template, and coeff is the unit conversion factor. This formula makes the generated design flood hydrograph Q... Ui,tr,p Its total amount is exactly equal to the scene value S generated by the NG algorithm. p,2 (r) Meanwhile, its process shape (peak, peak type) inherits the dynamic evolution characteristics of historical floods. Outer river water level Z R,t r,p =S p,1 (r) ×Z R,t h / maxΣ T t=1 Z R,t h Z R,t r,p For the p-th design flood scenario in the r-th round of clustering, S is the external river water level in time period t. p,1 (r) The highest water level of the outer river is generated by the NG algorithm, Z. R,t h It is the historical water level of the outer river in the hth year during the tth period.

[0156] A flood hydrograph with probability, controlled total amount and time dynamics constitutes the design flood hydrograph scenario, which serves as the input for M encounter events in subsequent embodiments, where M = P × R.

[0157] In some preferred embodiments, an evaluation step can be added to ensure the quality of the generated scene. For example, after step 404, the modularity or silhouette coefficient of the graph is preferably used to quantitatively evaluate the clustering effect. In addition, based on the node embeddings generated by the GNN, centrality analysis (such as eigenvector centrality) can be used to identify risk source factors that play a key role in the propagation of flood risk.

[0158] Example 5 describes the specific implementation of decision tree fusion and chain-based risk assessment, detailing how to fuse the two generated uncertain inputs (initial water level and flood scenario) to construct a risk decision tree for the entire process, and ultimately achieve quantitative assessment, early warning and retrospective analysis of risks.

[0159] Step 501: Set the initial water level probability sample as the first-level decision state variable, and the design flood hydrograph scenario as the second-level risk encounter variable. Construct a full-process flood control risk decision tree containing N×M risk paths through probabilistic coupling. Where N is the number of initial water level probability samples, and M is the total number of design flood hydrograph scenarios;

[0160] In this embodiment, the initial water level probability samples are from N possible initial states, for example, N=1000 water level samples, and each state corresponds to an occurrence probability P. n The flood hydrograph scenario is designed with M possible external disturbances (e.g., M=500 flood scenarios), each scenario corresponding to an occurrence probability P. m .

[0161] Specifically, the decision-making stage of pre-storage and pre-release for beneficial purposes (outputting the starting water level) is considered the first-level decision-making stage; the flood control scheduling execution stage (encountering the design flood) is considered the second-level risk encounter stage. By combining N states with M scenarios through Cartesian products, a full-process flood control risk decision tree is constructed, containing N×M complete initial conditions-encounter events-final risk transmission links. The joint occurrence probability P(n,m) of each risk path (n,m) is P... n *P m (Assume the two phases are independent).

[0162] Step 502: Perform a full-process scheduling simulation for each risk path, calculate the maximum scheduling water level exceeding the flood control limit for each risk path, and construct an empirical probability distribution based on the joint probability of all paths.

[0163] The system simulates and calculates the risks for N×M risk paths to obtain the risk results. Specifically, for each risk path (n, m), the system uses Z0 as the starting value, and its corresponding starting water level Z... tilde_i,n Assuming initial conditions before the flood, simulate the hydrograph Q of the design flood. in The entire process of flood control scheduling is carried out at time (m). After the simulation, the highest flood level Z is calculated. max (n,m) and flood control high water level Z MF The difference is used to obtain the highest flood control level exceeding the flood control limit for this route:

[0164] D(n,m)=max(0,Z max (n,m)-Z MF ).

[0165] After obtaining the flood control elevation values ​​D(n,m) and their joint probabilities P(n,m) for all N×M paths, this step statistically analyzes the results. All D(n,m) are sorted in ascending order, resulting in an ordered sequence D(1)≤D(2)≤...≤D(N×M). The empirical cumulative probability F(D(k)) corresponding to the k-th flood control elevation value D(k) is equal to the sum of the joint probabilities of all paths whose flood control elevation values ​​do not exceed D(k), i.e., F(D(k))=ΣP(j) (where j=1...k). Thus, an empirical probability distribution for quantifying risk is constructed.

[0166] Step 503: Based on the empirical probability distribution, calculate the conditional value of risk at different confidence levels, and calculate the value-at-risk ratio based on the ratio of conditional value of risk at different confidence levels to diagnose fat-tailed risk.

[0167] Traditional Value at Risk (VaR) only represents the loss quantile at a certain confidence level, for example:

[0168] VaR α =inf{D|F(D)≥α}, but cannot measure the severity of loss exceeding this quantile.

[0169] Therefore, this embodiment preferably calculates the conditional value of risk (CVaR). α This refers to losses exceeding VaR. α The average flood control peak value during extreme events. Its calculation formula is:

[0170] CVaR α =[1 / (1-α)]*Σ[D(j)*P(j)] (where j satisfies D(j)>VaR) α ).

[0171] In this embodiment, multiple confidence levels are preferably calculated, such as CVaR. 90% CVaR 95% and CVaR 99% To comprehensively depict the risks.

[0172] Furthermore, to diagnose whether the risk distribution exhibits fat-tailed characteristics—that is, events with extremely low probability of occurrence but extremely high destructive potential—this embodiment further calculates the Value at Risk (VRR). This indicator is defined as the ratio of the high quantile CVaR to the low quantile CVaR, for example, VRR = CVaR. 99% / CVaR 90% The higher the VRR value, the more pronounced the fat-tail risk characteristics of the system.

[0173] Step 504: Establish a dual-threshold early warning mechanism based on conditional value of risk and value-at-risk ratio. When an early warning is triggered, locate and output the key risk path whose risk contribution meets the preset threshold.

[0174] Specifically, this embodiment establishes a dual-threshold early warning mechanism:

[0175] Absolute risk threshold: set based on CVaR 95% Threshold CVaR t When CVaR 95% ≥CVaR t This indicates that the average level of extreme risks faced by the system has exceeded the acceptable safety baseline.

[0176] Relative Risk Structure Threshold: Set a threshold based on VRR (Risk Ratio). t (For example, VRR) t =1.5). When VRR ≥ VRR t This indicates a deterioration in the system's risk structure and an increased risk of black swan events.

[0177] When any of the above conditions are met, the system will immediately trigger an early warning.

[0178] After an alert is triggered, the system automatically identifies critical risk paths. The contribution of each path (n,m) to the tail risk, RC(n,m), can be calculated as follows:

[0179] RC(n,m)=max(D(n,m)-VaR 95% ,0)*P(n,m).

[0180] The system sorts the RC(n,m) of all paths and selects the top K paths with the highest contribution as critical risk paths. The selection of K can be based on the cumulative contribution criterion, that is, the proportion of the sum of the risk contributions of the top K paths to the total tail risk exceeds a preset threshold θ. For example, preferably, θ = 0.7, that is, locating the critical path combinations that contribute 70% of the extreme risk.

[0181] Step 505: Based on the range of values ​​of the starting water level probability samples, the risk paths are grouped into several consecutive starting water level intervals according to their corresponding starting water level status.

[0182] Specifically, this step divides the continuous range of starting water levels (e.g., the range of 1000 water level samples output in Example 3) into K continuous starting water level intervals Z. k For example, if the initial water level range is 98.0m to 100.0m, it can be divided into K=4 equal intervals:

[0183] Z1=[98.0,98.5), Z2=[98.5,99.0), Z3=[99.0,99.5), Z4=[99.5,100.0].

[0184] The N×M risk paths in step 501 are arranged according to their starting adjustment level Z. tilde_i,n The interval to which it belongs is classified into K different path subsets.

[0185] Step 506: Quantitatively calculate the product of the flood control peak value and the joint occurrence probability of the risk path within each starting water level interval, and determine the risk contribution of each interval to the overall conditional risk value.

[0186] Specifically, for each starting water level interval k divided in step 505, its risk contribution RC to the overall CVaR is calculated.k The calculation formula is as follows:

[0187] RC k =[Σmax(D(n,m)-VaR α ,0)*P(n,m)] / [Σ all max(D-VaR α ,0)*P]. Among them, the summation term (n,m) in the numerator only applies to all paths where the starting water level belongs to interval k, while the denominator applies to all paths.

[0188] The indicator RC k This reflects the share of the k-th starting water level interval in all extreme risks. RC k The larger the value, the greater the contribution of the initial water level range to the extreme risk of the system, and the more dangerous the initial state.

[0189] Step 507: Sort the starting water level intervals based on risk contribution, identify and output the key starting water level intervals whose cumulative contribution exceeds the preset ratio, as the source of risk transmission.

[0190] After calculating the risk contribution RC for all K intervals k Afterwards, regarding RC k Sort in descending order.

[0191] This step uses path backtracking analysis to identify the key starting water level ranges that contribute the most to the overall risk. For example, cumulative contribution can be calculated to identify those ranges where the total cumulative contribution exceeds, for example, 70%.

[0192] As a preferred implementation, the set K of critical risk paths identified in step 504 for each interval k can also be calculated. path The share that it occupies, namely:

[0193] KRC k =[ΣRC(n,m),(n,m)∈Z k ∩K path ] / [ΣRC(n,m),(n,m)∈K path ];

[0194] Among them, Z k Let K be the set of paths belonging to the k-th water level interval. path This is a set of key risk paths.

[0195] via KRC k Sorting can more accurately pinpoint the key sources of high risk in the driving system, providing targeted guidance for flood control scheduling decisions (e.g., avoiding water levels falling into the Z3 and Z4 ranges).

[0196] For example, a simplified case of risk backtracking calculation is provided.

[0197] Assuming N=5 water level samples, M=3 flood scenarios, and a total of 15 paths, the simulation shows VaR... 95% =0.8m. Assume water level intervals Z1 (low water level), Z2 (medium water level), and Z3 (high water level). Calculate the tail risk contribution RC(n,m)=max(D(n,m)-0.8,0)*P(n,m) for each path, as shown in Table 2.

[0198] Table 2

[0199]

[0200] Assume the sum of RC(n,m) for all 15 paths (i.e., the denominator of the CVaR calculation) is 0.050.

[0201] Assume that the sum of RC(n,m) of all paths belonging to the Z1 interval is 0.002.

[0202] Assume that the sum of RC(n,m) of all paths belonging to the Z2 interval is 0.010.

[0203] Assume that the sum of RC(n,m) of all paths belonging to the Z3 interval is 0.038.

[0204] The risk contribution RC of each interval k for:

[0205] RC Z1 =0.002 / 0.050=4%; RC Z2 =0.010 / 0.050=20%; RC Z3 =0.038 / 0.050=76%.

[0206] The Z3 (high water level) range contributed 76% of the extreme risks and was identified as the key starting water level range, which is the final output of the risk backtracking.

[0207] Example 6 provides a preferred and specific implementation of Graph Neural Networks (GNN) and related algorithms.

[0208] In a preferred embodiment of the present invention, the following exemplary configuration can be adopted to specifically implement the graph neural network used to optimize the spectral clustering process. The GNN preferably adopts a graph convolutional network (GCN) architecture. The number of layers in the GCN network is preferably set to 2 to 3 layers of graph convolutional layers. Too few layers make it difficult to capture complex topological relationships, while too many layers may lead to oversmoothing. The node feature dimension of the input GCN is preferably 3, corresponding to three types of risk source factors, including upstream flood volume, inter-regional flood volume, and external river water level. The node embedding dimension of the output GCN can preferably be set to 64 or 128 to balance computational overhead while retaining sufficient information. ReLU is preferably used as the activation function between the convolutional layers of the GCN. The Adam optimizer is preferably used when training the GNN. The loss function can be flexibly selected according to the task objective. For example, if there are historical flood risk level labels, cross-entropy loss for node classification can be used; if there are no labels, a contrastive loss function can be used to make flood events that are similar in topology and features closer in the embedding space.

[0209] Furthermore, to address the computational efficiency issue of spectral clustering when processing large-scale data (e.g., a very large number of historical flood samples), this invention preferably employs an approximate eigenvalue decomposition method. Specifically, when performing spectral decomposition on the Laplacian matrix of the graph, instead of complete eigenvalue decomposition, a combination of the Lanczos algorithm or stochastic eigenvalue decomposition methods is used to efficiently calculate the required small number of primary eigenvectors, thereby significantly improving computational efficiency while ensuring clustering effectiveness.

[0210] Furthermore, to reduce the computational complexity of the N×M full-path decision tree, this invention preferably adds an optimization step to the generated scenario tree after generating the design flood scenario. Specifically, graph compression and multi-level graph optimization are used to reduce the number of scenarios M in the final output. For example, redundant scenario nodes can be identified and merged by calculating the similarity between nodes; or community detection algorithms (such as the Louvain method) can be used to merge highly similar scenarios into super nodes, effectively reducing the order of magnitude of M without sacrificing accuracy, thereby reducing the computational complexity and memory requirements of subsequent full-path enumeration.

[0211] Example 7 describes in detail the process of generating a flood process line scenario, specifically describing how to construct a joint probability distribution of risk source factors based on the VineCopula model.

[0212] In this invention, chain risk refers to a complex risk formed by the sequential transmission and accumulation of multiple stages of uncertainty sources. This risk is characterized by the fact that the output state of the previous stage constitutes the input condition of the next stage, and the risk evolves step-by-step along the link from the initial conditions to the encountered event and then to the final consequence. In the reservoir group flood resource utilization scenario addressed by this invention, the first stage is the probability distribution of the initial regulating water level caused by the uncertainty of meteorological forecasts, and the second stage is the probability distribution of the flood process caused by the spatiotemporal variability of the design flood. The uncertainties of the two stages are coupled in a chain through a decision tree structure.

[0213] In the identification and quantification of risk source factors, the probability threshold of the design flood event must first be determined. This invention employs the return period analysis method, setting the return period TE according to flood control standards or risk management requirements, and the probability threshold P of the design flood event. w The calculation formula is:

[0214] P w =1 / TE;

[0215] Here, TE represents the return period, set based on historical flood data and flood control specifications, in years. When the return period is set to 100 years, the corresponding probability threshold is 0.01. Based on this probability threshold, historical design flood events with a probability less than this threshold can be selected.

[0216] When fitting marginal distribution functions for each type of risk source factor, this invention employs maximum likelihood estimation for parameter estimation. The candidate marginal distribution function set includes generalized extreme value distribution functions, normal distribution functions, exponential distribution functions, gamma distribution functions, and log-normal distribution functions. For each type of risk source factor, the above candidate functions are used for fitting, and the statistical significance of the fit is determined by the Kolmogorov-Smirnov test (KS test). Simultaneously, the Akaike information criterion is used for model selection. The candidate function that passes the KS test and has the smallest Akaike information criterion value is selected as the marginal distribution function for that risk source factor. The expression for the marginal distribution function of the nth type of risk source factor is:

[0217] u n =F n (x n );

[0218] Where, x n Let F be the observed vector of the nth type of risk source factor. n Let u be the corresponding marginal distribution function. n It is a closed interval containing the marginal distribution function value, which ranges from 0 to 1.

[0219] When constructing a two-dimensional Copula function, the Kendall rank correlation coefficient τ between various risk source factors needs to be calculated first. This coefficient measures the rank correlation between two variables, and its value ranges from -1 to a closed interval of 1. Based on the Kendall rank correlation coefficient and the marginal distribution function values, the optimal function is selected from a candidate set of two-dimensional Copula functions. The candidate set includes the Clayton Copula function, the Frank Copula function, and the Gumbel Copula function.

[0220] The ClaytonCopula function is suitable for variable pairs with lower-tail correlation, the GumbelCopula function is suitable for variable pairs with upper-tail correlation, and the FrankCopula function is suitable for symmetric correlation structures.

[0221] The Bayesian information criterion is used to evaluate the fitting effect of each candidate function, and the function with the smallest Bayesian information criterion value is selected as the optimal two-dimensional Copula function. The expression for the two-dimensional Copula function between the nth and kth risk source factors is as follows:

[0222] C n,k (u n ,u k );

[0223] Among them, C n,k The two-dimensional Copula function representing the joint distribution of risk source factors of type n and type k, u n and u k These are the marginal distribution function values ​​of the corresponding risk source factors.

[0224] In constructing the conditional Copula function, this invention uses existing marginal distribution functions and two-dimensional Copula functions, obtaining the conditional distribution through partial derivative operations. The conditional Copula function is used to calculate the conditional distribution of a given risk factor, given all other risk factors. Taking three types of risk factors as an example, given the first and second types of risk factors, the formula for calculating the conditional Copula function of the third type of risk factor is:

[0225] C 3|1,2 (u3|u1,u2)=dC 1,2,3 (u1,u2,u3) / (du1du2);

[0226] Among them, C 1,2,3 is a joint Copula function of the three types of risk source factors, and the partial derivative operation d is used to obtain the conditional distribution.

[0227] This invention employs the VineCopula structure to characterize the high-dimensional correlation of three types of risk source factors. The VineCopula structure constructs a high-dimensional joint distribution by nesting two-dimensional Copula functions and conditional Copula functions layer by layer, which can flexibly capture the tail correlation between variables. This invention preferably uses a C-Vine structure, which constructs a tree structure centered on a core variable. In this embodiment, the highest water level of the outer river is used as the root node variable, and two-dimensional Copulas are constructed sequentially with the upstream inflow flood volume and the inter-regional inflow flood volume. The overall expression of the VineCopula function is:

[0228] C(u1,u2,...,u n )=∏ n=1 N-1 ∏ k=n+1 N C n,k|Dn,k (u n ,u k |D n,k );

[0229] Among them, C n,k|Dn,k This indicates that, given the set of condition variables D n,k The conditional Copula function for the nth and kth risk source factors, with the chain multiplication symbol representing the iterative combination of the hierarchical structure.

[0230] When calculating the joint probability of risk source factor probability samples, this invention is based on the VineCopula structure and the principle of probabilistic mutual exclusion. For the three types of risk source factors, the formula for calculating their joint transcendence probability is:

[0231] P v (u*1,u*2,u*3)=1-C(u*1,1,1)-C(1,u*2,1)-C(1,1,u*3)+C(u*1,u*2,1)+C(u*1,1,u*3)+C(1,u*2,u*3)-C(u*1,u*2,u*3);

[0232] Among them, P v Let u*1, u*2, and u*3 represent the joint exceedance probability, where u*1, u*2, and u*3 are the sampled values ​​of the marginal distribution functions of the three risk source factors, respectively. This formula calculates the probability that the three factors simultaneously exceed their respective thresholds based on the inclusion-exclusion principle. The design flood probability threshold P is determined above. w Filter to satisfy P v Less than P w The probability samples of the conditions are used as the probability samples of risk source factors corresponding to the design flood event.

[0233] Example 8 describes an enhanced sampling strategy for extreme events.

[0234] When generating probability samples of risk source factors based on the VineCopula model, since extreme flood events are low-probability events, traditional uniform sampling or Latin hypercube sampling cannot guarantee sufficient sample representation for these key areas. Therefore, this invention employs an extreme event-enhanced sampling strategy, which increases the sampling frequency of low-probability areas by selecting an appropriate auxiliary distribution.

[0235] The specific implementation of this strategy includes the following steps: First, determine the target joint probability distribution based on historical flood data. This distribution is the joint distribution of risk source factors described by the aforementioned VineCopula model. Second, select an auxiliary distribution based on the distribution characteristics of extreme flood events at the tail of the marginal distribution. Optional auxiliary distribution types include the Weibull distribution and the Gumbel distribution, which can generate higher sampling density in the tail region.

[0236] During the sampling process, after generating samples based on the auxiliary distribution, it is necessary to calculate the importance weight of each sample:

[0237] w i =p(x i ) / q(x i );

[0238] Among them, w i p(x) represents the importance weight of the i-th sample. i Let q(x) be the probability density of the target distribution at this sample point. i The probability density of the auxiliary distribution at this sample point is denoted by . By adjusting the weights, it can be ensured that the final sample set is statistically equivalent to the result of direct sampling from the target distribution, while having more adequate sample coverage in extreme event regions.

[0239] The regular samples generated by Latin hypercube sampling, the importance-based samples from auxiliary distributions, and the enhanced samples for extreme scenarios are merged and weighted according to the importance weights of each sample. Through this process, the resulting probability sample set of risk source factors can fully characterize the extreme situations of flood events, providing reliable input data for chain risk analysis.

[0240] Example 9 provides a supplementary explanation of the specific implementation of the graph neural network optimization spectral clustering process.

[0241] Traditional spectral clustering algorithms only consider the Euclidean distance or similarity of sample points in the feature space, neglecting the potential spatiotemporal correlations between flood events. In reservoir systems, the flood peak of upstream reservoirs often precedes that of downstream reservoirs, and there are clear topological dependencies in the flood responses of different reservoirs. This invention introduces a graph neural network to learn these topological correlation features and utilizes the learned node embeddings to optimize the spectral clustering process.

[0242] When constructing the graph structure, probability samples of risk source factors are used as nodes. The graph edges are constructed based on three types of relationships. The first type is spatial edges, established according to the physical topological connections of the reservoir group. When there is a direct upstream-downstream hydraulic connection between two reservoirs, a spatial edge is established between the corresponding nodes. The second type is statistical edges, constructed based on the Pearson correlation coefficient between risk source factors. A statistical edge is established when the correlation coefficient between the corresponding factors of two sample points exceeds a preset threshold, which can be set to 0.6. The third type is dynamic edges, considering the time-varying dependence of different stages of flooding, dynamically adjusting the edge weights based on the correlation differences between the flood rise and flood fall periods. Through the comprehensive construction of these three types of edges, a graph structure reflecting the spatiotemporal correlation of flood events is formed, and an adjacency matrix and node feature matrix are generated accordingly.

[0243] This invention employs a graph convolutional network (GCNN) as the specific implementation architecture of the graph neural network. The GCNN has two layers, with an input node feature dimension of 3, corresponding to three types of risk source factors, and an output node embedding dimension of 64. The ReLU activation function is used between the graph convolutional layers. The GCNN performs feature learning through a neighborhood aggregation mechanism, allowing the embedding representation of each node to incorporate information from its neighboring nodes. After multiple layers of graph convolution operations, the output node embedding not only contains the node's own risk factor features but also information about other flood events topologically related to it.

[0244] In optimizing the spectral clustering process, this invention replaces the similarity matrix calculated directly based on the original features in traditional spectral clustering with node embeddings learned by a graph neural network. Specifically, cosine similarity between samples is calculated based on node embedding vectors to construct a new similarity matrix. Then, eigenvalue decomposition is performed on the Laplacian matrix corresponding to this matrix to obtain the main eigenvectors. The K-means algorithm is then applied to these eigenvectors to complete clustering. The number of clusters can be adaptively determined using the elbow rule, which identifies the optimal number of clusters by analyzing the relationship between the number of clusters and the sum of squared errors within each group.

[0245] For large-scale data scenarios, performing full eigenvalue decomposition directly on the Laplacian matrix incurs significant computational overhead. To improve computational efficiency, this invention combines the Lanczos algorithm with approximate eigenvalue decomposition. This algorithm can efficiently compute the required small number of key eigenvectors, reducing computational complexity while maintaining clustering effectiveness.

[0246] According to one aspect of this application, a detailed description is provided of a specific implementation of the neural gas algorithm for constructing scene trees.

[0247] Unlike the hard allocation mechanism of the K-means algorithm, the neural gas algorithm allows each sample to have varying degrees of influence on multiple cluster centers. By controlling the range of influence through an adaptation function, the neural gas algorithm can generate smoother and more robust clustering results, making it suitable for generation tasks that require maintaining topological continuity.

[0248] In this invention, a separate scenario tree is constructed for each cluster group. The scenario tree adopts a hierarchical structure, starting from the root node and gradually branching out to the leaf nodes, with each leaf node corresponding to an independent design flood scenario. The tree structure is determined based on the variance characteristics of the three types of risk source factors, with the factor with the smallest variance serving as the root node and the factor with the largest variance serving as the leaf node.

[0249] Scene trees can be represented in matrix form, where the r-th scene tree is represented as S. (r) The columns of the matrix correspond to nodes at different levels, with each column representing a type of risk source factor. The number of rows in the matrix corresponds to the number of scenarios contained in the scenario tree. The value of the q-th node in the p-th scenario of the scenario tree is represented as s. p,q (r) The r-th scene tree can be represented as:

[0250] ;

[0251] In this matrix, the columns correspond to different nodes (i.e., root node, intermediate nodes, and leaf nodes), each column node corresponds to a type of risk source factor, and the number of rows in the matrix corresponds to the number of leaf nodes in the scenario, that is, each row represents one scenario, S (r) S represents the r-th scene tree. p (r) s represents the p-th scene in the r-th scene tree. p,q (r) q represents the node value of the r-th scene tree; p is the number of scenes in the scene tree; q is the number of nodes contained in each scene.

[0252] The neural gas algorithm employs a batch loading mechanism for progressive training. In the initialization phase, initial cluster centers are determined based on the node embeddings output by the graph neural network. In the iterative update phase, the Euclidean distance from the scene tree node values ​​to the risk source factor samples is first calculated, and these distances are then sorted in descending order to form a sorted sequence O. p (r) The node values ​​are adjusted according to the neural gas learning rules. The formula for calculating the adjustment amount is as follows:

[0253] Δs p,q (r) =ε(l)·h[O p (r),λ(l)]·(X k,q (r) -sp,q (r) );

[0254] Where ε(l) is the step size function, h is the fitness function, and X k,q (r) Let s be the q-th component of the k-th risk source factor sample in the r-th group. p,q (r) This is the value of the current node.

[0255] The step size function ε(l) decreases with the number of iterations, ε(l) = ε0·(ε f / ε0) (l / lm) ;

[0256] Where ε0 is the initial step size, its value is set to 5, ε f The final step size is set to 1, and l is the current iteration number. m This is the maximum number of iterations, and its value is set to 10000.

[0257] The fitness function h provides fitness values ​​based on the distance between node values ​​and samples, and its calculation formula is as follows:

[0258] h(O p (r) ,λ(l))=exp(-O p (r) / λ(l));

[0259] Where λ(l) is the local step size function, λ(l) = λ0·(λ f / λ0) (l / lp) ;

[0260] Where λ0 and λ f These are the initial and final values ​​of the local step size, respectively.

[0261] In each iteration, the node values ​​of the scene tree are updated according to the above formula, which is:

[0262] S p,q (r,l+1) =s p,q (r,l) +Δs p,q (r) .

[0263] The iterations are repeated until the maximum number of iterations is reached. During training, the graph neural network synchronously updates the node embedding representations to maintain the topological continuity of the flood event features.

[0264] After iteration, the probability of each scenario in the scenario tree is calculated. This probability is determined based on the ratio of the number of risk source factor samples closest to each scenario to the total number of samples in the group, calculated using the following formula:

[0265] P(S p (r) =count(k|D p,k (r) =min p (D p,k (r) )) / K r ;

[0266] The `count` function calculates the number of samples that meet the conditions, D. p,k (r) Let K be the Euclidean distance from the p-th scene node value to the k-th sample. r Let be the total number of samples in the r-th group.

[0267] Based on the scenario tree constructed from all groups, design the flood scenario S. p (r) The final probability is calculated using the following formula:

[0268] P(S p (r) )=P(S p (r) |r,w)·P(r|w)·P w ;

[0269] Wherein, P(S) p (r) |r,w) represents the conditional probability of the scenario occurring under the conditions of the design flood event and group r, and P(r|w) represents the conditional probability of group r occurring under the conditions of the design flood event. w To design the probability threshold for flood events.

[0270] To reduce the computational complexity of the subsequent full-path decision tree, this invention performs optimization processing after the scene tree is constructed. Redundant scenes are identified by calculating the similarity between scene nodes, and a community detection algorithm is used to merge scenes with extremely high similarity into super nodes, effectively reducing the number of scenes in the final output without sacrificing accuracy.

[0271] This invention introduces Value at Risk (VaR) and Conditional Value at Risk (CVR) into the flood control risk analysis of reservoir groups. The difference between the two lies in their different abilities to characterize extreme risks.

[0272] Value at Risk (VaR) represents the maximum loss quantile at a given confidence level. Taking confidence level α as an example, VaR... α Value at Risk (VaR) indicates that there is an α percent chance that the loss will not exceed this value in the probability distribution; its mathematical definition is the α quantile of the cumulative distribution function. However, VaR only provides information about a critical point and cannot measure the severity of the loss when it exceeds that critical point.

[0273] Conditional Value at Risk (CVaR) addresses this deficiency by calculating the average loss after the loss exceeds a certain threshold, serving as a tail expectation indicator. In the flood risk analysis of this invention, CVaR represents the average depth by which the reservoir's highest water level exceeds the flood control high water level under extreme conditions. At a confidence level of 95%, the CVaR is... 95% This represents the average depth of overrun under the most unfavorable 5% scenario.

[0274] The Value at Risk (VRR) is an indicator constructed in this invention for diagnosing fat-tail risk. It is defined as the ratio of the high-quantile conditional value at risk to the low-quantile conditional value at risk. In this embodiment, VRR is defined as CVaR. 99% With CVaR 90% The ratio of VRR to VRR is used to determine the risk distribution. When the ratio is close to 1, it indicates that the risk distribution is relatively uniform and there is no obvious fat-tailed characteristic. When the ratio is significantly greater than 1, it indicates the existence of extreme events with extremely low probability of occurrence but extremely high destructive power, and the system faces fat-tailed risk. Experience shows that when VRR exceeds 1.5, the system should be considered to have obvious fat-tailed risk characteristics, and extreme scenarios need to be given attention.

[0275] The pre-storage and pre-release method is a dynamic reservoir management strategy based on meteorological forecasts. Its idea is to improve water resource utilization efficiency by fully utilizing forecast information while ensuring flood control safety. This method divides reservoir management into two interconnected processes: a pre-storage phase and a pre-release phase.

[0276] During the pre-storage phase, when weather forecasts indicate no rainfall or minimal rainfall in the near future, reservoirs can temporarily raise their water levels above the flood control limit, storing a certain amount of water within their flood control capacity to enhance their beneficial effects. This portion of water stored above the flood control limit is called excess storage.

[0277] During the pre-release phase, the reservoir gradually absorbs the excess water through various water utilization methods. These methods include power generation, irrigation, and ecological replenishment. The pre-release aims to lower the water level to the flood control limit before the next flood arrives, ensuring the reservoir's flood control capacity remains intact and usable.

[0278] The flood control limit level is the highest water level a reservoir is allowed to hold during the flood season when there is no flood, and it is clearly stipulated in the reservoir operation regulations. The flood control high water level is the highest water level a reservoir is allowed to reach when encountering a design flood, and this water level is determined by the dam safety standards. The reservoir capacity between the flood control limit level and the flood control high water level is the flood control capacity, which is an important resource for reservoir flood regulation.

[0279] The risk of the pre-storage and pre-discharge method lies in the uncertainty of weather forecasts. When the forecast indicates no rain but precipitation actually occurs, the excess water storage may not be able to absorb it before the flood arrives, resulting in the starting water level being higher than the flood limit level, thus reducing the available flood control capacity. This invention generates a probability sample of the starting water level by quantifying the probability distribution of weather forecast errors, thereby achieving a quantitative assessment of this risk source.

[0280] In summary, this application does not analyze any risk source in isolation. Instead, it generates two key probabilistic inputs through two independent but interconnected steps: first, by modeling the error of no-rain forecasts, it generates N possible initial water level probability samples (representing the uncertainty of initial conditions); second, by deeply mining historical floods, it generates M possible design flood process line scenarios (representing the uncertainty of the encountered event). This invention explicitly fuses the two independent probability sets by constructing an N×M full-path flood control chain risk decision tree. This fusion allows the system to simulate (N×M) possible risk combinations, chaining together the previously separate stages. Based on this coupling, the scheme further calculates the conditional value of risk (CVaR) and risk value ratio (VRR), and can accurately identify high-risk paths caused by a certain initial water level and a certain flood scenario combination through risk contribution backtracking, overcoming the limitations of single-stage analysis.

[0281] This invention provides a highly dynamic and scenario-adaptive allocation method. This method abandons allocation methods that rely solely on static storage capacity ratios. It introduces a scenario weighting factor α. i This factor is calculated based on the spatial distribution of the current deterministic flood forecast (i.e., the area-average forecast rainfall). This factor is used to dynamically construct the system's equivalent flood control capacity V. eff This transforms the system's flood control capacity assessment from a static value into a dynamic value related to the location of the storm center. Based on this, the method also constructs a comprehensive decomposition weight ω that includes flood control, urgency, efficiency, and scenario weights. i Initial allocation was performed. A secondary allocation rule was further designed, which, after verifying feasibility (e.g., not exceeding the maximum discharge flow), prioritizes allocating the water to be allocated to reservoirs with high scenario weights and large surplus capacity. This multi-step, multi-factor dynamic allocation mechanism ensures that the allocation scheme for excess storage is both spatially intelligent (responding to the center of the rainstorm and adapting in real time, taking into account the current water level) and physically feasible (verifying discharge capacity).

[0282] This invention proposes a clustering method based on Graph Neural Networks (GNNs). A reservoir group is a physical topological system, not a collection of independent data points. Therefore, this invention constructs a graph structure that reflects the upstream and downstream relationships between reservoirs. A GNN (such as a Graph Neural Network) is used to learn the spatiotemporal correlation features of flood events on the graph structure. The output of the GNN, i.e., the node embedding, is a low-dimensional vector rich in topological information. This invention uses the node embedding (rather than the original flood data) as input to the spectral clustering algorithm, using topological information to guide the clustering process. In the subsequent training of the neural gas algorithm, these embedding representations are also dynamically updated using GNNs. This ensures that the final generated design flood hydrograph scenario is not only numerically representative but also maintains a high degree of rationality in terms of physical topology (such as the timing of upstream and downstream confluence), improving the quality and authenticity of the input data used for risk assessment.

[0283] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in 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 chain-based risk analysis method for flood resource utilization in a reservoir group, characterized in that, include: Read and fit the error probability distribution based on meteorological no-rain forecast data to generate a set of probability forecast scenarios for the receding water section flow. Based on the probability forecast scenario set of the flow rate in the receding section, the dynamic allocation method of excess water storage in the reservoir group is adopted to determine the probability sample of the starting water level. Based on pre-stored historical flood data, a clustering process optimized by graph neural networks and a neural gas algorithm are used to generate a design flood process line scenario. By integrating the probability samples of water level regulation with the design flood process line scenario, a flood control chain risk decision tree is constructed, and the risk analysis results are output through risk contribution retrospective analysis. This involves integrating probabilistic samples of water level regulation with design flood hydrograph scenarios to construct a flood control chain-like risk decision tree. Through risk contribution retrospective analysis, the risk analysis results are output, including: The probability sample of the starting water level is set as the first-level decision state variable, and the design flood hydrograph scenario is set as the second-level risk encounter variable. A full-process flood control risk decision tree containing N×M risk paths is constructed through probabilistic coupling, where N is the number of probability samples of the starting water level and M is the number of design flood hydrograph scenarios. For each risk path, a full-process scheduling simulation is performed to calculate the corresponding highest scheduling water level exceeding the flood control limit, and an empirical probability distribution is constructed based on the joint probability of all paths. Based on empirical probability distributions, the conditional value of risk at different confidence levels is calculated, and the value-at-risk ratio is calculated based on the ratios to diagnose fat-tailed risks. Establish a dual-threshold early warning mechanism based on conditional value of risk and value of risk ratio. When an early warning is triggered, locate and output the key risk path whose risk contribution meets the preset threshold. Input the probability forecast scenario set of the receding water section flow, and use the dynamic allocation method of excess water storage in the reservoir group to determine the probability sample of the starting water level, including: Based on the probability forecast scenario set of the receding section flow, the series of actual excess water storage volume values ​​are calculated using the pre-storage and pre-release method. A dynamic allocation method for excess water storage in a reservoir group is implemented based on deterministic rainfall and flood forecast data. This method includes: calculating the equivalent flood control capacity of the system to determine the overall deterministic excess water storage of the system; constructing a comprehensive decomposition weight of coupled scenario weight factors, flood control factors, urgency factors, and efficiency factors to initially allocate the overall deterministic excess water storage of the system to each reservoir; and performing feasibility verification and secondary allocation on the preliminary allocation results to generate the final allocation scheme for the deterministic excess water storage. By integrating the actual excess water storage series values ​​with the deterministic final allocation scheme of excess water storage, and combining the water level and reservoir capacity relationship, a probability sample of the starting water level is generated.

2. The method according to claim 1, characterized in that, Through retrospective analysis of risk contribution, the risk analysis results are output, including: Risk paths are grouped into several consecutive starting water level intervals according to their corresponding starting water level status. The product of the flood control peak value and the probability of joint occurrence of the risk path within each starting water level interval is quantitatively calculated to determine the risk contribution of each interval to the overall conditional risk value. The starting water level intervals are sorted based on their risk contribution, and key starting water level intervals with cumulative contribution exceeding a preset ratio are identified and output as sources of risk transmission.

3. The method according to claim 1, characterized in that, The equivalent flood control capacity of the system is calculated based on deterministic rainfall and flood forecast data to determine the overall deterministic excess water storage of the system, including: Extract the surface average forecast rainfall from deterministic rainfall forecast data and calculate the scenario weighting factor characterizing the spatial distribution differences of floods; By using scenario weighting factors to dynamically weight the static flood control capacity of each reservoir, a scenario-adaptive system equivalent flood control capacity is constructed. The equivalent flood control capacity of the system is represented as a virtual reservoir, and the safe discharge of the downstream flood control control point is taken as the core constraint. The deterministic excess water storage of the entire system is obtained by flood regulation calculation.

4. The method according to claim 3, characterized in that, A comprehensive decomposition weighting system is constructed, comprising coupled scenario weighting factors, flood control factors, urgency factors, and efficiency factors, to initially allocate the overall deterministic excess storage capacity of the system to each reservoir, including: Calculate the flood control factor characterizing the static flood control capacity of the reservoir, the urgency factor characterizing the real-time urgency, and the efficiency factor characterizing the pre-release efficiency, respectively. The weighted geometric mean method is used to couple the above three factors and the scenario weight factor to determine the normalized comprehensive decomposition weight; The deterministic excess water volume of the entire system is decomposed using comprehensive decomposition weights to obtain the preliminary excess water volume of each reservoir.

5. The method according to claim 1, characterized in that, The preliminary allocation results are then subjected to feasibility verification and secondary allocation to generate a deterministic final allocation plan for excess water storage, including: Based on the maximum allowable discharge flow and pre-discharge period of each reservoir, a feasibility verification of the initial excess water storage capacity is conducted. Identify an infeasible set of reservoirs whose allocated water volume exceeds their maximum discharge capacity, and determine the excess water volume as the water volume to be allocated. Based on the preset secondary allocation rules, the water volume to be allocated is redistributed to other reservoirs with surplus discharge capacity. The secondary allocation rule is: priority is given to reservoirs that have both high scenario weight factors and large surplus discharge capacity, so as to generate a deterministic final allocation scheme for excess water storage. Secondary weight allocation γ i Calculation formula: c i =[a i *(Q i,max TW i )] / Σ[a k *(Q k,max TW k )],i,k∈S f ; Where, α i Q is the scenario weighting factor. i,max Where is the maximum allowable discharge flow of reservoir i, T is the pre-discharge period, and W is the maximum discharge flow of reservoir i. i For the initial excess water storage capacity, (Q) i,max TW i S represents surplus capacity. f This refers to a collection of other reservoirs with surplus discharge capacity.

6. The method according to claim 1, characterized in that, Based on pre-stored historical flood data, a clustering process optimized by graph neural networks and a neural gas algorithm are used to generate a flood hydrograph scenario, including: Based on historical flood data, a probability sample of risk source factors is generated using the VineCopula model and an extreme event-enhanced sampling strategy. A graph neural network is used to learn the spatiotemporal characteristics of flood topological associations in a reservoir group, and the spatiotemporal characteristics are used to optimize the spectral clustering process to cluster the probability samples of risk source factors, thereby obtaining cluster groups and node embeddings. Based on clustering groups and node embedding, a neural gas algorithm is used to construct a scene tree and generate a design flood scene. The design flood scenario is scaled up by the same factor as the historical flood process line to generate the design flood process line scenario.

7. The method according to claim 6, characterized in that, A graph neural network is used to learn the spatiotemporal characteristics of flood topological associations in a reservoir group, and these spatiotemporal characteristics are then used to optimize the spectral clustering process, including: A graph convolutional network is used to learn features from the probability sample nodes of risk source factors, and the spatiotemporal correlation features of flood events are extracted through a neighborhood aggregation mechanism. The node embeddings learned and output by the graph neural network are used as input to the spectral clustering algorithm. Cluster analysis is performed on the eigenvectors of the Laplacian matrix to form cluster groups corresponding to the topological structure of the reservoir group.

8. The method according to claim 6, characterized in that, The scene tree is constructed using a neural gas algorithm, including: A batch loading mechanism is used to progressively train the cluster groups, prioritizing the learning of sample distribution in high-risk areas; During training, node embedding representations are dynamically updated based on graph neural networks to maintain the topological continuity of flood event features; By adaptively adjusting the cluster centers through a competitive learning mechanism, the generated design flood scenarios are guaranteed to have distinctiveness in risk transmission characteristics.

Images