A stepped earth-rock dam reservoir group system failure probability analysis and intelligent control method

Abstract

The present application relates to the technical field of hydraulic engineering safety, especially relates to a cascade earth-rock dam reservoir group system failure probability analysis and intelligent control method, the method first acquires basic data, constructs a failure research and judgment model to calculate the failure probability of a single earth-rock dam; secondly, the static water power connection degree is calculated and the time-varying water power connection degree is obtained by using the time-varying water dynamic parameter correction, and the target weight is obtained by combining the global sensitivity index correction analytic hierarchy process weight; then the above results are solved, and the overall failure probability of the system is calculated through recursive logic; finally, a risk scheduling optimization model is constructed, taking the flood discharge flow as the decision variable and minimizing the overall failure probability as the target, to solve and generate the optimal scheduling scheme. The present application can accurately quantify the dynamic risk transmission of the cascade system, realize the accurate evaluation and intelligent control of the system risk, and ensure the flood control safety of the basin.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering safety technology, and in particular to a method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system. Background Technology

[0002] Earth-rock dams are the most widely used dam type worldwide. With the expansion of cascade development in river basins, cascade earth-rock dam reservoir groups have formed a tightly interconnected system. However, this layout also brings potential cascading risks. If an upstream reservoir fails, it can easily trigger a domino effect, causing catastrophic consequences. Therefore, accurately assessing the failure probability of the cascade reservoir system and implementing intelligent risk control are crucial for ensuring flood control safety in river basins. Currently, the relevant technical fields mainly face the following problems:

[0003] First, there are limitations to calculating the failure probability of a single earth-rock dam. Traditional deterministic analysis methods cannot quantify the risks arising from the uncertainty of soil parameters; while probabilistic analysis methods based on Monte Carlo simulations are accurate, they are computationally time-consuming and difficult to meet real-time scheduling requirements. Although neural network models introduced in recent years have improved efficiency, they often exhibit "black box" characteristics, lack physical mechanism constraints, and their prediction results may violate the laws of soil mechanics, resulting in insufficient generalization ability.

[0004] Second, the risk transmission mechanism of cascade reservoir systems remains unclear. Existing research largely focuses on the isolated safety analysis of individual dams, neglecting the complex spatiotemporal relationships between cascade reservoirs. Dam-break floods caused by the failure of an upstream reservoir significantly alter the input conditions of downstream reservoirs, and this risk transmission effect exhibits significant time-varying dynamic characteristics. Current technologies lack a quantitative description of this dynamic hydraulic connection, leading to distorted assessments of the overall system failure probability.

[0005] Third, there is a lack of intelligent control measures aimed at minimizing system risks. Existing reservoir scheduling models mostly aim to maximize power generation benefits or only use water level as a safety constraint, lacking an optimization scheduling model that directly aims at minimizing the overall system failure probability. Under extreme disaster conditions, it is difficult to effectively block the risk transmission path through proactive hydraulic control measures.

[0006] In summary, how to integrate physical mechanisms and data-driven methods to improve the computational efficiency and accuracy of single dam failure probability, and on this basis quantify the dynamic risk transmission of cascade systems, and then construct an intelligent control model oriented towards minimizing system risk, is a technical challenge that urgently needs to be solved. Summary of the Invention

[0007] Therefore, this invention provides a method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system to solve the aforementioned problems in the prior art.

[0008] To achieve the above objectives, this invention provides a method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system, comprising:

[0009] Step S1: Obtain the soil material parameters, engineering characteristic parameters, and disaster-causing condition parameters of the cascade reservoir dam to obtain basic data;

[0010] Step S2: Using the aforementioned basic data as input, a failure assessment model is constructed and trained by designing a loss function to obtain the failure probability of a single earth-rock dam.

[0011] Step S3: Calculate the static hydraulic connectivity degree based on the engineering characteristic parameters, and then correct the static hydraulic connectivity degree by introducing time-varying hydrodynamic parameters under disaster-causing conditions to obtain the time-varying hydraulic connectivity degree.

[0012] Step S4: Calculate the global sensitivity index of the basic data, and correct the eigenvector of the initial judgment matrix obtained by the analytic hierarchy process based on the global sensitivity index to obtain the target weight.

[0013] Step S5: Combine the failure probability of the single earth-rock dam, the time-varying hydraulic connectivity, and the target weight; use recursive logic to determine the failure state of the upstream reservoir; use the time-varying hydraulic connectivity to update the failure probability of the downstream reservoir level by level; and calculate and determine the overall failure probability of the cascade earth-rock dam reservoir group system.

[0014] Step S6: Construct a risk scheduling optimization model, taking the flood discharge flow of each cascade reservoir as the decision variable, minimizing the overall failure probability as the optimization objective, and using an intelligent optimization algorithm to iteratively solve the problem to generate the optimal risk scheduling scheme that meets the constraints.

[0015] Furthermore, the process of step S2 includes:

[0016] A failure assessment model is constructed, using the aforementioned basic data as the input variables of the model;

[0017] The total loss function of the failure assessment model is defined as consisting of a data loss term and a physical loss term, wherein the physical loss term is derived from the limit state equation for dam slope stability based on the simplified Bishop method.

[0018] During the model training iteration, the weight ratio of the data loss term and the physical loss term in the total loss function is dynamically adjusted based on the error feedback from the validation set.

[0019] The failure assessment model is optimized with the goal of minimizing the residual of the limit state equation in the sample space. When the model converges, a reliability index is output and converted into the failure probability of a single earth-rock dam using a standard normal distribution function.

[0020] Furthermore, the process of dynamically adjusting the weight ratio of the data loss term and the physical loss term in the total loss function based on the error feedback of the validation set includes:

[0021] Define a physical residual convergence threshold and monitor the magnitude of the physical loss term in real time during the iterative process of model training;

[0022] If the detected physical loss term value exceeds the physical residual convergence threshold, a weight adaptive adjustment strategy is triggered to increase the weight ratio of the physical loss term in the total loss function.

[0023] If the detected physical loss term value is within the physical residual convergence threshold, the weight ratio of the physical loss term in the total loss function is reduced, while the weight ratio of the data loss term is increased accordingly.

[0024] Furthermore, the process of step S3 includes:

[0025] A TOPSIS-EWM coupled model was established, and the total storage capacity of the upstream reservoir, the total storage capacity of the reservoir itself, the flood control capacity, the controlled catchment area, the distance from the upstream reservoir, and the multi-year average flow were selected as evaluation indicators. The static hydraulic connectivity was obtained by calculating the distance between each scheme and the positive and negative ideal solutions.

[0026] The time-varying hydrodynamic parameters include peak flow, flood arrival time, and river velocity.

[0027] Based on the time-varying hydrodynamic parameters, a dynamic correction coefficient is calculated, and the static hydraulic connectivity is then weighted and updated using the dynamic correction coefficient to obtain the time-varying hydraulic connectivity.

[0028] Furthermore, the process of calculating the dynamic correction coefficient based on the time-varying hydrodynamic parameters includes:

[0029] ,

[0030] in, For dynamic correction coefficients, These are the real-time peak flow, river velocity, and flood arrival time under disaster-causing conditions. The average flow rate over many years is used as the baseline value for flow rate. The historical average flow velocity of the river channel. For the time of flood arrival, These are weighting coefficients, representing the degree of influence of peak flow, river velocity, and flood arrival time on the intensity of risk transmission. If calculated... Then take This indicates that the intensity of risk transmission under the current time-varying operating conditions has not exceeded the static level.

[0031] Furthermore, the process of step S4 includes:

[0032] Using the dam soil material parameters and engineering characteristic parameters as input variables and the reliability index as the output response, calculate the first-order sensitivity index of the contribution of each input variable to the variance of the output response;

[0033] The first-order sensitivity index is normalized to obtain the sensitivity weight vector.

[0034] The target weight is obtained by multiplying and correcting the eigenvectors of the initial judgment matrix obtained by the analytic hierarchy process using the sensitivity weight vector.

[0035] Furthermore, the process of multiplying and correcting the eigenvectors of the initial judgment matrix obtained through the analytic hierarchy process based on the sensitivity weight vector to obtain the target weights includes:

[0036] ,

[0037] in, For the target weight, Let be the initial weights of the i-th cascade reservoir obtained through the analytic hierarchy process. This is the sensitivity index after normalization of the corresponding parameters.

[0038] Furthermore, the process of step S5 includes:

[0039] The actual failure probability of the upstream cascade reservoirs in the basin is initialized to the failure probability of the single earth-rock dam corresponding to it.

[0040] A recursive algorithm was used to calculate the actual failure probability of each downstream cascade reservoir along the river flow direction;

[0041] Based on the k / N system reliability model, the unit reliability components of each cascade reservoir are calculated;

[0042] The overall system reliability is obtained by multiplying the unit reliability components of all cascade reservoirs, and then the overall failure probability of the cascade earth-rock dam reservoir group system is determined.

[0043] Furthermore, the process of calculating the actual failure probability of each downstream cascade reservoir sequentially along the river flow direction using a recursive algorithm includes:

[0044] For the i-th level reservoir, where i ≥ 2, determine the failure state of its upstream (i-1)-th level reservoir, and use the time-varying hydraulic connectivity degree. As a risk transmission coefficient, the actual failure efficiency of the i-th level reservoir is updated using the following formula:

[0045] ,

[0046] in, Let be the single failure probability of the i-th level reservoir. This represents the actual failure probability of the upstream reservoir.

[0047] Furthermore, step S6 includes the following process:

[0048] A risk scheduling optimization model was constructed, with the objective function set as minimizing the overall failure probability of the cascade earth-rock dam reservoir system, and the flood discharge flow of each cascade reservoir was used as the decision variable.

[0049] The constraints of the optimization model are set, including reservoir water balance constraints, upper and lower limits of reservoir water level constraints, flood discharge capacity constraints of flood discharge facilities, and safe discharge capacity constraints of downstream river channels.

[0050] The algorithm uses an intelligent optimization algorithm to iteratively find the best solution. In each iteration, the currently generated flood discharge flow scheme is substituted into the failure judgment model and the recursive calculation process of the system failure probability. The corresponding failure probability is calculated as the fitness value, and the population is updated according to the fitness value until the algorithm converges. The optimal flood discharge flow combination that minimizes the overall failure probability is output as the risk scheduling scheme.

[0051] Compared with existing technologies, the advantages of this invention are as follows: By embedding the soil mechanics equilibrium equation into neural network training, the failure probability prediction results strictly follow the mechanical equilibrium mechanism, overcoming the shortcomings of poor physical interpretability of pure data-driven models; by using time-varying hydrodynamic parameters to correct static topological connections, the invention accurately depicts the transmission and attenuation laws of risk energy during flood evolution, avoiding the distorted description of dynamic risk transmission by static indicators; by combining parameter sensitivity correction weights, the invention objectively reveals the actual driving effect of soil parameter variations on dam stability; and by recursively coupling upstream and downstream risks, the invention realistically recreates the cascade failure response process caused by hydraulic correlation in the cascade system, ultimately reducing the system failure risk directly by adjusting the flood discharge flow to change the hydraulic boundary conditions, thus achieving deep coupling from physical mechanism characterization and risk evolution simulation to control decision generation. Attached Figure Description

[0052] Figure 1 A flowchart illustrating the failure probability analysis and intelligent control method for a cascade earth-rock dam reservoir system provided by this invention;

[0053] Figure 2 A flowchart illustrating step S2 in the method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system provided by the present invention;

[0054] Figure 3 A flowchart illustrating step S4 in the method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system provided by the present invention;

[0055] Figure 4 A schematic plan view of a group of three cascade reservoirs on the main stream of a river, provided in an embodiment of the present invention;

[0056] Figure 5 This is a model diagram of the system failure event tree provided in an embodiment of the present invention. Detailed Implementation

[0057] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0058] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0059] It should be noted that in the description of this invention, the terms "upper", "lower", "left", "right", "inner", "outer", etc., which indicate directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. This is only for the convenience of description and is not intended to indicate or imply that the device or element must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0060] Furthermore, it should be noted that, in the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0061] Please see Figure 1 As shown, this invention provides a method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system, including:

[0062] Step S1: Obtain the soil material parameters, engineering characteristic parameters, and disaster-causing condition parameters of the cascade reservoir dam to obtain basic data;

[0063] Specifically, this invention requires selecting at least two or more cascaded earth-rock dam reservoirs with hydraulic connections within the same river basin as the objects of system failure probability analysis.

[0064] Specifically, the physical and mechanical parameters of the soil for each cascade reservoir dam were obtained through geological survey data and laboratory geotechnical tests. These soil material parameters include at least: dry density, cohesion, internal friction angle φ, and permeability coefficient. Among these, cohesion and internal friction angle are key strength indicators determining the dam's anti-sliding stability, and the permeability coefficient k is a key hydraulic indicator determining the seepage field distribution within the dam body. Considering the variability of soil parameters, statistical characteristic values ​​of the above parameters, including the mean and standard deviation, were obtained to characterize the degree of uncertainty of the parameters.

[0065] Design and operation data for each cascade reservoir were collected, and engineering characteristic parameters were extracted. These parameters include: geometric parameters such as dam height, dam crest width, and upstream and downstream slope ratios, used to define the physical boundary conditions of the dam; hydraulic parameters such as water level-storage capacity curves and spillway capacity curves, used to describe the reservoir's regulation and discharge characteristics; and key threshold parameters such as normal storage level, design flood level, check flood level, and downstream safe discharge. The function of these key threshold parameters is to serve as benchmark limits for determining the dam's safety status; for example, when the calculated water level exceeds the check flood level, it is considered a surge in the risk of overtopping. The downstream safe discharge is used to constrain the downstream flow rate and prevent flooding disasters in the downstream river channel. Disaster-causing parameters were determined based on historical hydrological data and flood control scheduling plans. The disaster-causing parameters include extreme hydrological loads: design flood hydrographs with different return periods (such as 100-year return periods and 1000-year return periods) are selected as inflow inputs to simulate extreme flood disaster scenarios; wave run-up, wind-induced backwater height, and rainfall intensity are obtained under disaster-causing conditions. The wave run-up and wind-induced backwater height are used to correct the static water level and calculate whether the dam crest freeboard meets the wave protection requirements, which are important dynamic parameters for judging overtopping failure. The soil material parameters, engineering characteristic parameters, and disaster-causing parameters obtained above are subjected to data cleaning and normalization.

[0066] Specifically, for parameters of different dimensions and orders of magnitude (such as unifying the data of permeability coefficient level and dam height level), the maximum-minimum normalization method is used to map them to the [0,1] interval to eliminate the influence of dimensions and construct a basic dataset containing the sample input matrix and corresponding labels (such as stable / failure state).

[0067] Step S2: Using the aforementioned basic data as input, a failure assessment model is constructed and trained by designing a loss function to obtain the failure probability of a single earth-rock dam.

[0068] Specifically, such as Figure 2 As shown, the process of step S2 includes:

[0069] Step S21: Construct a failure assessment model, using the basic data as the input variables of the model;

[0070] Specifically, a failure assessment model based on a Physical Information Neural Network (PINN) is constructed. This model includes an input layer, several hidden layers, and an output layer. The basic data is used as the model's input variables, specifically including soil material parameters (cohesion, internal friction angle, permeability coefficient) and disaster-causing condition parameters (upstream water level, downstream water level). The model's output variable is set as the reliability index β of the earth-rock dam. The hidden layers use the hyperbolic tangent function or the ReLU function as activation functions to fit the complex nonlinear mapping relationship between the input and output variables.

[0071] Step S22: Set the total loss function of the failure assessment model to consist of a data loss term and a physical loss term. The physical loss term is derived from the limit state equation for dam slope stability based on the simplified Bishop method.

[0072] Specifically, the limit state function g(X) is established: Where X is the input variable, M_R is the anti-sliding moment, and M_S is the sliding moment. The anti-sliding moment and sliding moment are calculated using the strip method according to the simplified Bishop method, and their expressions are controlled by soil parameters and pore water pressure. The physical loss term... Defined as the mean square error of the residuals of the limit state function: The function of this loss term is to force the prediction results of the neural network to conform to the torque balance principle in soil mechanics, and to prevent the model from getting trapped in overfitting or local optima that violate physical laws.

[0073] Specifically, define the data loss term. It is used to measure the deviation between the model's predicted values ​​and the historical sample labels. ,in, As a reliable indicator of model prediction, Tag data generated based on historical monitoring data or Monte Carlo simulations. λ

[0074] Specifically, the total loss function The expression is:

[0075]

[0076] in, and These are the data loss weights and physical loss weights, which change dynamically with the number of training iterations t, respectively.

[0077] Step S23: During the model training iteration, dynamically adjust the weight ratio of the data loss term and the physical loss term in the total loss function based on the error feedback of the validation set;

[0078] Specifically, the process of dynamically adjusting the weight ratio of the data loss term and the physical loss term in the total loss function based on the error feedback of the validation set includes:

[0079] Define a physical residual convergence threshold and monitor the magnitude of the physical loss term in real time during the iterative process of model training;

[0080] Specifically, a physical residual convergence threshold is set. The value range is

[10] . -4 10 -3 ] represents the maximum tolerance allowed for the model prediction to deviate from the mechanical equilibrium equation.

[0081] If the detected physical loss term value exceeds the physical residual convergence threshold, a weight adaptive adjustment strategy is triggered to increase the weight ratio of the physical loss term in the total loss function.

[0082] Specifically, in each epoch t of model training, the current physical loss value is calculated. If detected If this indicates that the current model's prediction results severely violate physical laws, then the weight adjustment mechanism is triggered, increasing the physical loss weight by a set step size (e.g., increasing by 10%). This forces the model to prioritize satisfying physical constraints.

[0083] If the detected physical loss term value is within the physical residual convergence threshold, the weight ratio of the physical loss term in the total loss function is reduced, while the weight ratio of the data loss term is increased accordingly.

[0084] Specifically, if detected This indicates that the model has met the physical constraints, so the physical loss weights should be reduced accordingly. And increase the weight of data loss. This guides the model to focus on improving the fitting accuracy of specific sample data.

[0085] Step S24: The failure assessment model is optimized with the goal of minimizing the residual of the limit state equation in the sample space. When the model converges, a reliability index is output and converted into the failure probability of a single earth-rock dam using a standard normal distribution function.

[0086] Specifically, an adaptive moment estimation optimizer is used to iteratively train the failure assessment model. With the goal of minimizing the total loss function, the network weights and bias parameters are updated via backpropagation. Training stops and the model parameters are saved when the total loss function converges or reaches the preset maximum number of iterations. Real-time basic data is input into the trained failure assessment model, and the reliability index β is output. Based on reliability theory, the reliability index is converted into the failure probability of a single earth-rock dam using a standard normal distribution function. :

[0087]

[0088] in, Let be the cumulative distribution function of the standard normal distribution, from which the failure probability of a single earth-rock dam under the current working conditions can be obtained.

[0089] Step S3: Calculate the static hydraulic connectivity degree based on the engineering characteristic parameters, and then correct the static hydraulic connectivity degree by introducing time-varying hydrodynamic parameters under disaster-causing conditions to obtain the time-varying hydraulic connectivity degree.

[0090] Specifically, step S3 includes the following process:

[0091] A TOPSIS-EWM coupled model was established, and the total storage capacity of the upstream reservoir, the total storage capacity of the reservoir itself, the flood control capacity, the controlled catchment area, the distance from the upstream reservoir, and the multi-year average flow were selected as evaluation indicators. The static hydraulic connectivity was obtained by calculating the distance between each scheme and the positive and negative ideal solutions.

[0092] Specifically, the total storage capacity of the upstream reservoir, the total storage capacity of the reservoir itself, the flood control capacity, the controlled catchment area, the distance from the upstream reservoir, and the multi-year average flow are selected as evaluation indicators to construct an initial decision matrix. The Entropy Weight Method (EWM) is used to objectively calculate the weight vectors of each evaluation indicator, avoiding bias from subjective assignment. The TOPSIS method (Top-Side Distance Method) is used to calculate the Euclidean distance between the evaluation indicator values ​​of each cascade reservoir and the positive and negative ideal solutions. Based on the Euclidean distance, the relative proximity of each reservoir is calculated and defined as the static hydraulic connectivity degree S_static, with a numerical range of [0,1], used to characterize the inherent topological and hydraulic connectivity strength between cascade reservoirs under normal operating conditions.

[0093] The time-varying hydrodynamic parameters include peak flow, flood arrival time, and river velocity.

[0094] Specifically, based on the flood evolution simulation results under disaster-causing conditions, time-varying hydrodynamic parameters required for dynamic correction are extracted, including: real-time peak flow Q(t), real-time river velocity v(t), and flood arrival time T(t). Baseline values ​​are set for each parameter to achieve dimensional uniformity: flow baseline Q_base: the historical maximum value of the reservoir's multi-year average flow; velocity baseline v_base: the historical average river velocity; time baseline T_base: the historical average flood propagation time.

[0095] Based on the time-varying hydrodynamic parameters, a dynamic correction coefficient is calculated, and the static hydraulic connectivity is then weighted and updated using the dynamic correction coefficient to obtain the time-varying hydraulic connectivity.

[0096] Specifically, the process of calculating the dynamic correction coefficient based on the time-varying hydrodynamic parameters includes:

[0097] ,

[0098] in, For dynamic correction coefficients, These are the real-time peak flow, river velocity, and flood arrival time under disaster-causing conditions. The average flow rate over many years is used as the baseline value for flow rate. The historical average flow velocity of the river channel. For the time of flood arrival, These are weighting coefficients, representing the degree of influence of peak flow, river velocity, and flood arrival time on the intensity of risk transmission. If calculated... Then take This indicates that the intensity of risk transmission under the current time-varying operating conditions has not exceeded the static level.

[0099] Specifically, satisfy It should be noted that the peak flow and river velocity are positive incentive indicators, meaning that the larger the value, the stronger the risk transmission, so ω1 and ω2 are positive; the flood arrival time is a negative inhibition indicator, meaning that the shorter the time, the faster the risk transmission, so ω3 is negative.

[0100] Specifically, the static hydraulic connectivity S_static is updated using the dynamic correction coefficient λ(t) to obtain the time-varying hydraulic connectivity S_time(t). The update formula is:

[0101]

[0102] The time-varying hydraulic relationship S_time(t) comprehensively reflects the static topological characteristics and dynamic hydraulic response of the cascade reservoirs under the condition of disastrous floods.

[0103] Step S4: Calculate the global sensitivity index of the basic data, and correct the eigenvector of the initial judgment matrix obtained by the analytic hierarchy process based on the global sensitivity index to obtain the target weight.

[0104] Specifically, such as Figure 3 As shown, the process of step S4 includes:

[0105] Step S41: Using the dam soil material parameters and engineering characteristic parameters as input variables and the reliability index as the output response, calculate the first-order sensitivity index of the contribution of each input variable to the variance of the output response.

[0106] Specifically, the soil material parameters of the dam (cohesion, internal friction angle, permeability coefficient k) and engineering characteristic parameters (dam height, dam slope ratio m) are used as the input variable set. The reliability index β calculated in step S2 is used as the output response. An input sample matrix is ​​generated using Monte Carlo sampling or Latin hypercube sampling, and the variance decomposition principle is used to calculate each input variable. First-order sensitivity index :

[0107]

[0108] in, The total variance of the output response. For only input variables The expected variance of the resulting output response. The first-order sensitivity index reflects the contribution rate of the uncertainty of a single parameter to the uncertainty of dam reliability; the larger the value, the more significant the impact of that parameter on the dam's safety status.

[0109] Step S42: Normalize the first-order sensitivity index to obtain the sensitivity weight vector;

[0110] Specifically, the calculated first-order sensitivity index is normalized and mapped to weighting coefficients. The specific calculation formula is as follows:

[0111]

[0112] in, Let be the normalized sensitivity index of the i-th input parameter. A sensitivity weight vector is constructed by combining the sensitivity indices corresponding to the key characteristic parameters of each cascade reservoir. This vector objectively reflects the sensitivity of the properties of each cascade reservoir to its failure probability.

[0113] Step S43: The initial judgment matrix eigenvectors obtained by the analytic hierarchy process are multiplied and corrected according to the sensitivity weight vector to obtain the target weight.

[0114] Specifically, the Analytic Hierarchy Process (AHP) is used to construct a judgment matrix for the importance of cascade reservoirs. Based on qualitative indicators such as the reservoir capacity, the importance of the protected objects, and the installed capacity of each cascade reservoir, pairwise comparisons are performed using expert scoring to construct and calculate the judgment matrix. The maximum eigenvalue λ_max and its corresponding normalized eigenvector are analyzed, and a consistency check is performed, requiring a consistency ratio CR < 0.1 to ensure the consistency of the expert judgment logic. The eigenvector... It represents the subjective initial weights of each cascade reservoir based on empirical knowledge.

[0115] Specifically, the process of multiplying and correcting the eigenvectors of the initial judgment matrix obtained by the analytic hierarchy process (AHP) based on the sensitivity weight vector to obtain the target weights includes:

[0116] ,

[0117] in, For the target weight, Let be the initial weights of the i-th cascade reservoir obtained through the analytic hierarchy process. This is the sensitivity index after normalization of the corresponding parameters.

[0118] Specifically, the introduction of regulatory factors If the parameters of a certain reservoir are highly sensitive ( If the target weight is relatively large, its target weight is enhanced based on the initial weight; otherwise, it remains unchanged or decreases. The denominator ensures that the sum of the target weights of all cascade reservoirs is 1. The target weights include both the experts' subjective consideration of the socio-economic importance of the reservoirs and the objective mechanism of the impact of engineering physical parameters on structural safety, and are used to calculate the overall failure probability of the system in the subsequent step S5.

[0119] Step S5: Combine the failure probability of the single earth-rock dam, the time-varying hydraulic connectivity, and the target weight; use recursive logic to determine the failure state of the upstream reservoir; use the time-varying hydraulic connectivity to update the failure probability of the downstream reservoir level by level; and calculate and determine the overall failure probability of the cascade earth-rock dam reservoir group system.

[0120] Specifically, step S5 includes the following process:

[0121] The actual failure probability of the upstream cascade reservoirs in the basin is initialized to the failure probability of the single earth-rock dam corresponding to it.

[0122] Specifically, the topological structure of the cascade reservoirs in the basin is determined, and the upstreammost cascade reservoir (designated as level 1) is located. Since there is no risk of upstream water transmission to the upstreammost reservoir, the failure probability of its corresponding single earth-rock dam is directly initialized to the actual failure probability.

[0123] A recursive algorithm was used to calculate the actual failure probability of each downstream cascade reservoir along the river flow direction;

[0124] Specifically, the process of using a recursive algorithm to calculate the actual failure probability of each downstream cascade reservoir along the river flow direction includes:

[0125] For the i-th level reservoir, where i ≥ 2, determine the failure state of its upstream (i-1)-th level reservoir, and use the time-varying hydraulic connectivity degree. As a risk transmission coefficient, the actual failure efficiency of the i-th level reservoir is updated using the following formula:

[0126] ,

[0127] in, Let be the single failure probability of the i-th level reservoir. This represents the actual failure probability of the upstream reservoir.

[0128] Specifically, firstly, the time-varying hydraulic connectivity between the i-th level reservoir and the upstream (i-1)-th level reservoir is obtained. This characterizes the intensity of risk transmission from upstream dam-break floods to downstream areas. Secondly, it obtains the single failure probability of the i-th level reservoir itself. and the calculated actual failure probability of the upstream (i-1)th level reservoir. Finally, the actual failure probability of the i-th level reservoir is updated using the risk superposition formula.

[0129] Specifically, the actual risk of a downstream reservoir is a linear superposition of its inherent risk (single failure probability) and the risk transmitted from upstream (the product of the actual failure probability of the upstream reservoir and the time-varying hydraulic connectivity). It should be noted that if the calculation results... If the value is forced to be 1, it indicates that the reservoir is in a completely ineffective state.

[0130] Based on the k / N system reliability model, the unit reliability components of each cascade reservoir are calculated;

[0131] Specifically, based on the k / N system reliability model, the cascade earth-rock dam reservoir group is considered as a series system, meaning that the failure of any reservoir is considered a system failure, corresponding to the k=N model. The reliability of each reservoir is weighted and corrected using target weights to calculate the unit reliability components of the i-th level reservoir. : The failure probability is converted into a reliability component, while also taking into account the impact of the reservoir's importance on the overall system safety.

[0132] The overall system reliability is obtained by multiplying the unit reliability components of all cascade reservoirs, and then the overall failure probability of the cascade earth-rock dam reservoir group system is determined.

[0133] Specifically, based on the probability product rule for cascade systems, the unit reliability components of all cascade reservoirs are multiplied together to obtain the overall reliability of the cascade earth-rock dam reservoir system: Therefore, the overall failure probability of the cascade earth-rock dam reservoir system is determined. .

[0134] Step S6: Construct a risk scheduling optimization model, taking the flood discharge flow of each cascade reservoir as the decision variable, minimizing the overall failure probability as the optimization objective, and using an intelligent optimization algorithm to iteratively solve the problem to generate the optimal risk scheduling scheme that meets the constraints.

[0135] Specifically, step S6 includes the following process:

[0136] A risk scheduling optimization model was constructed, with the objective function set as minimizing the overall failure probability of the cascade earth-rock dam reservoir system, and the flood discharge flow of each cascade reservoir was used as the decision variable.

[0137] Specifically, the decision variable is defined as the flood discharge flow process of each cascade reservoir during the scheduling period, that is, the flood discharge flow of the i-th reservoir in time period t. The objective function is set as minimizing the overall failure probability of the cascade earth-rock dam reservoir system. The objective function expression is:

[0138]

[0139] in, The overall failure probability is dynamically updated as the flood discharge flow rate decision variable changes.

[0140] The constraints of the optimization model are set, including reservoir water balance constraints, upper and lower limits of reservoir water level constraints, flood discharge capacity constraints of flood discharge facilities, and safe discharge capacity constraints of downstream river channels.

[0141] Specifically, the set of physical and security constraints that must be satisfied during construction includes:

[0142] Reservoir water balance constraints: ,in, For storage capacity, For inbound flow, To lose water, The duration of the time period;

[0143] Reservoir water level boundary constraints: ,in, Dead water level To verify the flood level or the current maximum allowable water level;

[0144] Flood discharge capacity constraints: This means that the flood discharge flow cannot exceed the maximum discharge capacity of the flood discharge facility corresponding to the current water level;

[0145] Downstream channel safety discharge constraints: That is, the sum of the downstream discharge and the confluence of the intervals must not exceed the downstream river channel's flood control safety discharge capacity.

[0146] For solutions that do not meet the above constraints, a penalty function method is used to apply a penalty term during fitness calculation, so that the solution is eliminated during the optimization process.

[0147] The algorithm uses an intelligent optimization algorithm to iteratively find the best solution. In each iteration, the currently generated flood discharge flow scheme is substituted into the failure judgment model and the recursive calculation process of the system failure probability. The corresponding failure probability is calculated as the fitness value, and the population is updated according to the fitness value until the algorithm converges. The optimal flood discharge flow combination that minimizes the overall failure probability is output as the risk scheduling scheme.

[0148] Specifically, a genetic algorithm or particle swarm optimization algorithm is selected as the intelligent optimization algorithm to perform an iterative optimization process: an initial population is randomly generated within the feasible region of the decision variables, with each individual representing a flood discharge scheduling scheme. For each individual in the population, the reservoir water level process is first calculated based on the water balance equation; then, the water level and corresponding operating parameters are input into the failure assessment model to calculate the single failure probability of each reservoir; the target weight and the recursive calculation model of step S5 are called to solve for the overall system failure probability corresponding to the scheme, which is used as the fitness value. Based on the fitness value, selection, crossover, and mutation operations are performed to generate a new generation of population. The above fitness evaluation and population update process is repeated until the maximum number of iterations is reached or the fitness value convergence accuracy meets the preset requirements. The optimal individual at the time of algorithm convergence is output, and it is decoded into the flood discharge sequence of each cascade reservoir at each time period. This sequence is the optimal risk scheduling scheme that satisfies the constraints and minimizes the overall failure probability of the system.

[0149] In this embodiment, a group of three cascade reservoirs (A, B, and C) planned sequentially from top to bottom on the main stream of a river is used as an example, and their planar locations are shown in the figure. Figure 4 Dam C is a key cascade in the river section where the three cascades are located.

[0150] 1) Basic data collection and determination

[0151] Based on geological surveys, laboratory tests, and design data, the soil material parameters, engineering characteristic parameters, and disaster-causing condition parameters of each reservoir's dam were obtained, as shown in Tables 1 and 2, respectively. Two typical disaster-causing conditions were selected: super-standard flood (recurrence period of 10,000 years) and earthquake (peak acceleration of 0.2g).

[0152] Table 1. Soil Material Parameters for Each Reservoir

[0153]

[0154] Note: If the intensity is a Mohr-Coulumb linear intensity, take c and f; if the intensity is a Duncan logarithmic mode nonlinear intensity, take c and f. and Where c is in kPa, f has no unit. and The unit is (°), and the unit of density is kN / m3.

[0155] Table 2 Engineering characteristic parameters of each reservoir

[0156]

[0157] 2) Construction of Failure Assessment Model

[0158] A Physical Information Neural Network (PINN) is constructed with 10 nodes in the input layer, corresponding to the key parameters affecting dam slope stability listed in Tables 1 and 2 (including dam height, cohesion c, internal friction angle φ, unit weight, slope ratio, upstream and downstream water levels, horizontal seismic coefficient, and permeability coefficient). The hidden layer consists of 3 layers with 50 neurons each, using the hyperbolic tangent function (tanh) as the activation function. The output layer has one node, directly outputting the reliability index β.

[0159] 3) Loss Function Design

[0160] The total loss function consists of the data loss term. and physical loss item composition:

[0161] in, The mean square error between the β value predicted by the model and the label value calculated by the first second moment method (FORM); The limit state equations derived based on the simplified Bishop method Mean square error of residuals:

[0162]

[0163] and These are dynamic weights that are adaptively adjusted during training.

[0164] 4) Training data generation

[0165] 10,000 sets of input parameter samples were generated using Latin hypercube sampling. Of these, 5,000 sets were used as label data based on the corresponding reliability indices calculated using FORM, while the remaining 5,000 sets were used solely for physical loss calculation. All input and output data were normalized.

[0166] 5) Training process and adaptive weight adjustment

[0167] Using the Adam optimizer, with an initial learning rate of 0.001, a batch size of 128, and 2000 iterations. A physical residual convergence threshold is set. Every 50 training epochs, calculate the physical loss on the validation set. :like Then Increase by 10%, and decrease accordingly. ,Keep ;like Then Reduce by 10%, and increase accordingly. .

[0168] 6) Calculation of single failure probability

[0169] The input parameters of each reservoir were substituted into the trained PINN model to obtain the reliability index β, which was then converted into the failure probability through the standard normal distribution function. The calculation results are shown in Table 3.

[0170] Table 3 Calculation results for a single-stage reservoir

[0171]

[0172] 7) Calculation of static hydraulic compatibility

[0173] Six evaluation indicators were selected: total upstream reservoir capacity (C1, benefit-oriented), total reservoir capacity (C2, cost-oriented), flood control capacity (C3, cost-oriented), controlled catchment area (C4, cost-oriented), distance from upstream reservoir (C5, cost-oriented), and multi-year average flow (C6, benefit-oriented). A decision matrix M was constructed based on the data in Table 2.

[0174]

[0175] Standardization was performed using the range method, and benefit indicators were categorized as follows: Cost-related indicators Calculate and obtain the standardized matrix. .

[0176] The weights of each indicator are calculated using the entropy weight method: first, the information entropy is calculated. Then determine the weights. The calculation result is: Determine the positive and negative ideal solutions, calculate the relative closeness, i.e., the static hydraulic connectivity, and the connectivity of Reservoir B. The connectivity of Reservoir C .

[0177] 8) Time-varying hydraulic connectivity correction

[0178] Taking the case of floods exceeding standard levels as an example, time-varying hydrodynamic parameters are obtained through flood evolution simulation: real-time peak flow. Flow baseline value Real-time river flow velocity Flow velocity reference value Flood arrival time Time base value Set the weighting coefficients: (Positive impact of peak flood flow) (Positive effect of flow velocity) (Arrival time has a negative impact; the shorter the arrival time, the greater the risk). Calculate the dynamic correction factor: ,because This indicates that the risk transmission intensity exceeds the static level under the current operating conditions. Therefore, the time-varying hydraulic connectivity is, and the connectivity of Reservoir B is... When the calculation result is greater than 1, it is set to 1 (indicating complete risk transmission). This represents the connectivity of Reservoir C. Take 1. Under seismic conditions, if there is no significant flood evolution, take 1. The time-varying correlation degree is equal to the static value.

[0179] 9) Initial weight calculation for the analytic hierarchy process (AHP)

[0180] Using dam height, total reservoir capacity, controlled drainage area, and average slope ratio of upstream and downstream dam slopes as criteria, a judgment matrix (expert scoring) was constructed, and eigenvectors were calculated. After a consistency test (CR < 0.1), the initial weights of each reservoir were obtained.

[0181] 10) Calculation of global sensitivity index

[0182] Using soil material parameters (cohesion c, internal friction angle φ, etc.) of each reservoir as input variables and the reliability index β of a single earth-rock dam as the output, the first-order sensitivity index is calculated using the variance-based Sobol method. Monte Carlo simulation (sample size 10000) is used to obtain the contribution rate of each parameter to the output variance. Then, for each reservoir, the sensitivity indices of its relevant parameters are weighted and averaged to obtain the normalized sensitivity index of that reservoir. Using formula After normalization, the target weights are obtained: .

[0183] 11) Recursive calculation of the overall system failure probability

[0184] Taking the above-standard flood condition as an example, the single failure probability of each reservoir is taken from Table 3, the time-varying hydraulic connectivity degree is taken as the corrected value (all taken as 1), and the target weight is taken as... Recursively calculate the actual failure probability: Reservoir B: C Reservoir: .

[0185] Based on the connectivity and the comprehensive weight of each reservoir, the actual failure probability of a single reservoir is obtained. See the system failure event tree below. Figure 5Based on the k / N system reliability model, and according to the golden ratio principle, taking 61.8% of the total as the value of k, and using the 2 / 3 system model for analysis, the system failure probability is calculated by combining the above data: For the super-standard flood condition: System failure probability. Earthquake conditions: System failure probability .

[0186] 12) Solving the risk scheduling optimization model

[0187] The flood discharge flow of each reservoir during the scheduling period (24 hours, 1 hour period) Decision variables. The objective function is to minimize the overall system failure probability. The constraints include: water balance. Water level constraints: (Specific values: Reservoir A upper limit 231m, Reservoir B upper limit 130m, Reservoir C upper limit 312m); Discharge capacity constraints: Downstream safe discharge: ,(Pick m³ / s, m³ / s).

[0188] A genetic algorithm was used with the following parameters: population size 100, crossover probability 0.8, mutation probability 0.1, and a maximum number of iterations 200. The fitness function was the calculated system failure probability. A penalty term (with the fitness value set to a maximum) was applied to individuals that violated the constraints. After 200 generations of evolution, the optimal flood discharge process was obtained. After optimization, the system failure probability under the super-standard flood condition decreased by approximately 31.8%, verifying the effectiveness of the proposed method.

[0189] Specifically, this invention embeds the soil mechanics equilibrium equations into neural network training, ensuring that the failure probability prediction results strictly follow the mechanical equilibrium mechanism, thus overcoming the poor physical interpretability of purely data-driven models. It utilizes time-varying hydrodynamic parameters to correct static topological connections, accurately depicting the transmission and attenuation of risk energy during flood evolution, avoiding distorted descriptions of dynamic risk transmission by static indicators. Combined with parameter sensitivity correction weights, it objectively reveals the actual driving effect of soil parameter variations on dam stability. By recursively coupling upstream and downstream risks, it realistically recreates the cascade failure response process caused by hydraulic correlation in a cascade system. Ultimately, by adjusting the flood discharge flow to change the hydraulic boundary conditions, it directly reduces the system failure risk, achieving deep coupling from physical mechanism characterization and risk evolution simulation to control decision generation.

[0190] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0191] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system, characterized in that, include: Step S1: Obtain the soil material parameters, engineering characteristic parameters, and disaster-causing condition parameters of the cascade reservoir dam to obtain basic data; Step S2: Using the aforementioned basic data as input, a failure assessment model is constructed and trained by designing a loss function to obtain the failure probability of a single earth-rock dam. Step S3: Calculate the static hydraulic connectivity degree based on the engineering characteristic parameters, and then correct the static hydraulic connectivity degree by introducing time-varying hydrodynamic parameters under disaster-causing conditions to obtain the time-varying hydraulic connectivity degree. Step S4: Calculate the global sensitivity index of the basic data, and correct the eigenvector of the initial judgment matrix obtained by the analytic hierarchy process based on the global sensitivity index to obtain the target weight. Step S5: Combine the failure probability of the single earth-rock dam, the time-varying hydraulic connectivity, and the target weight; use recursive logic to determine the failure state of the upstream reservoir; use the time-varying hydraulic connectivity to update the failure probability of the downstream reservoir level by level; and calculate and determine the overall failure probability of the cascade earth-rock dam reservoir group system. Step S6: Construct a risk scheduling optimization model, taking the flood discharge flow of each cascade reservoir as the decision variable, minimizing the overall failure probability as the optimization objective, and using an intelligent optimization algorithm to iteratively solve the problem to generate the optimal risk scheduling scheme that meets the constraints.

2. The method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system according to claim 1, characterized in that, The process of step S2 includes: A failure assessment model is constructed, using the aforementioned basic data as the input variables of the model; The total loss function of the failure assessment model is defined as consisting of a data loss term and a physical loss term, wherein the physical loss term is derived from the limit state equation for dam slope stability based on the simplified Bishop method. During the model training iteration, the weight ratio of the data loss term and the physical loss term in the total loss function is dynamically adjusted based on the error feedback from the validation set. The failure assessment model is optimized with the goal of minimizing the residual of the limit state equation in the sample space. When the model converges, a reliability index is output and converted into the failure probability of a single earth-rock dam using a standard normal distribution function.

3. The method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system according to claim 2, characterized in that, The process of dynamically adjusting the weight ratio of the data loss term and the physical loss term in the total loss function based on the error feedback of the validation set includes: Define a physical residual convergence threshold and monitor the magnitude of the physical loss term in real time during the iterative process of model training; If the detected physical loss term value exceeds the physical residual convergence threshold, a weight adaptive adjustment strategy is triggered to increase the weight ratio of the physical loss term in the total loss function. If the detected physical loss term value is within the physical residual convergence threshold, the weight ratio of the physical loss term in the total loss function is reduced, while the weight ratio of the data loss term is increased accordingly.

4. The method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system according to claim 3, characterized in that, The process of step S3 includes: A TOPSIS-EWM coupled model was established, and the total storage capacity of the upstream reservoir, the total storage capacity of the reservoir itself, the flood control capacity, the controlled catchment area, the distance from the upstream reservoir, and the multi-year average flow were selected as evaluation indicators. The static hydraulic connectivity was obtained by calculating the distance between each scheme and the positive and negative ideal solutions. The time-varying hydrodynamic parameters include peak flow, flood arrival time, and river velocity. Based on the time-varying hydrodynamic parameters, a dynamic correction coefficient is calculated, and the static hydraulic connectivity is then weighted and updated using the dynamic correction coefficient to obtain the time-varying hydraulic connectivity.

5. The method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system according to claim 4, characterized in that, The process of calculating the dynamic correction coefficient based on the time-varying hydrodynamic parameters includes: ， in, For dynamic correction coefficients, These are the real-time peak flow, river velocity, and flood arrival time under disaster-causing conditions. The average flow rate over many years is used as the baseline value for flow rate. The historical average flow velocity of the river channel. For the time of flood arrival, These are weighting coefficients, representing the degree of influence of peak flow, river velocity, and flood arrival time on the intensity of risk transmission. If calculated... Then take This indicates that the intensity of risk transmission under the current time-varying operating conditions has not exceeded the static level.

6. The method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system according to claim 5, characterized in that, The process of step S4 includes: Using the dam soil material parameters and engineering characteristic parameters as input variables and the reliability index as the output response, calculate the first-order sensitivity index of the contribution of each input variable to the variance of the output response; The first-order sensitivity index is normalized to obtain the sensitivity weight vector. The target weight is obtained by multiplying and correcting the eigenvectors of the initial judgment matrix obtained by the analytic hierarchy process using the sensitivity weight vector.

7. The method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system according to claim 6, characterized in that, The process of multiplying and correcting the eigenvectors of the initial judgment matrix obtained by the analytic hierarchy process based on the sensitivity weight vector to obtain the target weight includes: ， in, For the target weight, Let be the initial weights of the i-th cascade reservoir obtained through the analytic hierarchy process. This is the sensitivity index after normalization of the corresponding parameters.

8. The method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system according to claim 7, characterized in that, The process of step S5 includes: The actual failure probability of the upstream cascade reservoirs in the basin is initialized to the failure probability of the single earth-rock dam corresponding to it. A recursive algorithm was used to calculate the actual failure probability of each downstream cascade reservoir along the river flow direction; Based on the k / N system reliability model, the unit reliability components of each cascade reservoir are calculated; The overall system reliability is obtained by multiplying the unit reliability components of all cascade reservoirs, and then the overall failure probability of the cascade earth-rock dam reservoir group system is determined.

9. The method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system according to claim 8, characterized in that, The process of calculating the actual failure probability of each downstream cascade reservoir sequentially along the river flow direction using a recursive algorithm includes: For the i-th level reservoir, where i ≥ 2, determine the failure state of its upstream (i-1)-th level reservoir, and use the time-varying hydraulic connectivity degree. As a risk transmission coefficient, the actual failure efficiency of the i-th level reservoir is updated using the following formula: ， in, Let be the single failure probability of the i-th level reservoir. This represents the actual failure probability of the upstream reservoir.

10. The method for failure probability analysis and intelligent control of a cascade earth-rock dam reservoir system according to claim 9, characterized in that, The process of step S6 includes: A risk scheduling optimization model was constructed, with the objective function set as minimizing the overall failure probability of the cascade earth-rock dam reservoir system, and the flood discharge flow of each cascade reservoir was used as the decision variable. The constraints of the optimization model are set, including reservoir water balance constraints, upper and lower limits of reservoir water level constraints, flood discharge capacity constraints of flood discharge facilities, and safe discharge capacity constraints of downstream river channels. The algorithm uses an intelligent optimization algorithm to iteratively find the best solution. In each iteration, the currently generated flood discharge flow scheme is substituted into the failure judgment model and the recursive calculation process of the system failure probability. The corresponding failure probability is calculated as the fitness value, and the population is updated according to the fitness value until the algorithm converges. The optimal flood discharge flow combination that minimizes the overall failure probability is output as the risk scheduling scheme.

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