A method for predicting dam-break probability of earth-rock dam

Abstract

The application relates to the technical field of hydraulic engineering, and discloses a soil and rock dam dam-break probability prediction method, which comprises the following steps: acquiring basic cause variables and state conversion variables leading to soil and rock dam dam-break, adopting a fixed threshold method to perform discretization processing, and generating discretization standards of the variables; a one-dimensional dam-break flow simulation model is constructed; based on the discretization standards, a data set covering multiple grades of flood scenarios is generated; a three-layer Bayesian network model is constructed; the data set is input into the three-layer Bayesian network model for training; a Bayesian smoothing method is adopted to calculate the conditional probability of each node in the three-layer Bayesian network model, so as to correct model parameters; finally, the trained three-layer Bayesian network model is input into the variable data of a to-be-tested soil and rock dam, so as to realize dam-break probability prediction and risk grade evaluation; through fusion of a physical mechanism and statistical learning, the dam-break prediction probability is quantified and improved, and high-precision dam-break risk prediction is realized.

Description

Technical Field

[0001] This invention relates to the field of hydraulic engineering technology, specifically to a method for predicting the probability of dam failure in earth-rock dams. Background Technology

[0002] Dam failure is one of the most destructive natural disasters in the field of water conservancy engineering. Due to the dam height, large reservoir capacity, and complex watershed hydrological conditions, the risk assessment of large earth-rock dams at high altitudes is significantly more difficult than that of conventional projects. Traditional dam failure risk assessment methods, including deterministic analysis methods, empirical statistical methods, and simplified probabilistic methods, have many shortcomings: deterministic analysis methods are unable to quantify the system uncertainties such as watershed hydrology and dam material parameters, resulting in low dam failure prediction accuracy; empirical statistical methods lack physical mechanism support for dam types with high altitude and deep overburden, resulting in low dam failure prediction accuracy; and simplified probabilistic methods cannot accurately reflect the interaction between the dam body and water flow under complex hydraulic conditions, resulting in low dam failure prediction accuracy. Summary of the Invention

[0003] To address the aforementioned shortcomings in existing technologies, this invention provides a method for predicting the probability of dam failure in earth-rock dams. By integrating physical mechanisms and statistical learning, the method quantifies and improves the probability of dam failure prediction, thereby solving the problem of low accuracy in dam failure risk assessment methods.

[0004] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0005] A method for predicting the probability of earth-rock dam failure includes the following steps:

[0006] Obtain the fundamental causal variables and state transition variables that lead to the failure of earth-rock dams;

[0007] The fixed threshold method is used to discretize the basic causal variables and state transition variables, generating a discretization standard that includes the discrete state, value range and threshold of each variable.

[0008] A one-dimensional dam-break flow simulation model was constructed, and a dataset covering multiple flood scenarios was generated based on the discretization standard.

[0009] By treating the discrete states of each variable as network nodes, a three-layer Bayesian network model is constructed, which includes a basic cause layer, a state transition layer, and a failure mode layer, and the dependencies between each node are determined.

[0010] The dataset is input into a three-layer Bayesian network model for training. The conditional probability of each node in the three-layer Bayesian network model is calculated using the Bayesian smoothing method to correct the model parameters and generate a trained three-layer Bayesian network model.

[0011] The fundamental causal variables and state transition variables of the earth-rock dam to be tested are obtained, discretized, and then input into a trained three-layer Bayesian network model to predict the dam failure probability, generate dam failure probability values, and determine the dam failure risk level.

[0012] The present invention has the following beneficial effects:

[0013] 1. The proposed method for predicting the probability of dam failure in earth-rock dams integrates physical mechanisms and statistical learning to quantify the probability of dam failure and improve the probability of dam failure prediction. It solves the problem of low accuracy in dam failure risk prediction in existing dam failure risk assessment methods, and breaks through the dependence of traditional methods on measured flood data.

[0014] 2. The three-layer Bayesian network model constructed in this invention conforms to the physical logic of risk transmission. Combined with the Bayesian smoothing method, it improves the prediction accuracy and reliability of the three-layer Bayesian network model. It can not only identify high-risk state combinations, but also provide effective technical support for the safety management of earth-rock dams. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a method for predicting the probability of earth-rock dam failure proposed in this invention.

[0016] Figure 2 This is a schematic diagram of the three-layer Bayesian network model in the embodiment;

[0017] Figure 3 This is a schematic diagram comparing the dam failure probabilities under the test set and the validation set in the embodiment;

[0018] Figure 4 This is a schematic diagram of the dam failure probability prediction results under 15 simulated flood scenarios in the example. Detailed Implementation

[0019] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0020] like Figure 1 As shown, a method for predicting the probability of earth-rock dam failure includes the following steps:

[0021] Obtain the fundamental causal variables and state transition variables that lead to the collapse of the earth-rock dam.

[0022] Specifically, the fundamental causal variables include peak flow, process curve shape, gate operation time, gate operation rate, and channel roughness.

[0023] Specifically, the state transition variables include water level status, duration of water level exceeding warning level, impact of water flow on the dam body, and dam body stability status.

[0024] In this embodiment, the aforementioned basic causal variables and state transition variables are collected to construct a complete risk transmission technology chain from external inducements to intermediate physical responses and ultimately to failure. Specifically, the basic causal variables serve as input driving factors for the subsequently constructed three-layer Bayesian network model, covering three core sources of uncertainty: flood characteristics, scheduling operations, and river environment, providing source-level risk parameters for dam failure probability prediction. The state transition variables are used to quantify the key physical responses and state evolution of the dam system under the aforementioned causal effects, transforming the continuous physical process into discrete states that can be processed by the three-layer Bayesian network model. This serves as a bridge connecting the initial inducement and the final dam failure conclusion, thereby ensuring that the method proposed in this invention has both clear physical mechanism support and can achieve effective probabilistic reasoning and risk prediction.

[0025] The fixed threshold method is used to discretize the basic causal variables and state transition variables, generating a discretization standard that includes the discrete states, value ranges, and thresholds of each variable.

[0026] In this embodiment, this step is the process of setting discretization standards for each variable. Specifically, it involves using a fixed threshold method to discretize the basic causal variables and state transition variables, clarifying the discrete state, value range, and division threshold of each variable. The division thresholds are determined with reference to the following standards: "Technical Specification for Safety Monitoring of Earth-Rock Dams" (SL551-2012), "Design Specification for Rolled Earth-Rock Dams" (SL274-2001), "Guidelines for Risk Assessment and Emergency Response Plan Preparation for Water Conservancy and Hydropower Projects" (SL / Z 714-2015), and "Guidelines for Risk Assessment of Reservoirs and Dams" (NB / T 35049-2015). The discretization process is as follows:

[0027] Specifically, the process of discretizing the fundamental dependent variables is as follows:

[0028] Based on the design value of the flood return period, flood flow thresholds are defined, and the peak flow is discretized into multiple flow level states.

[0029] In this embodiment, flood flow thresholds are defined based on the flood return period design value, including low flow thresholds, medium flow thresholds, and high flow thresholds. Then, based on the flood flow thresholds, the peak flow is discretized to generate discrete states of the peak flow, including low flow state, medium flow state, high flow state, and extremely high flow state. Table 1 shows the discretization criteria for the peak flow, as follows:

[0030] Table 1 Discretization Standard Table of Peak Flood Discharge

[0031]

[0032] Based on the characteristics of flood rise and fall duration, flood rise and fall duration thresholds are defined, and the process line shape is discretized into two states: flat and steep.

[0033] In this embodiment, based on the characteristics of flood rise and fall durations, flood rise and fall duration thresholds are defined, including steep rise duration thresholds and steep fall thresholds. Then, based on the flood rise and fall duration thresholds, the process line shape is discretized to generate discrete states of the process line shape, including steep states and flat states. Table 2 shows the discretization criteria for the process line shape, as follows:

[0034] Table 2 Discretization Criteria for Process Line Shape

[0035]

[0036] Based on the time offset of gate operation relative to the flood process, operation time thresholds are defined, and the gate operation time is discretized into multiple operation timing states.

[0037] In this embodiment, based on the time offset of the gate operation relative to the flood process, operation time thresholds are defined, including advance discharge thresholds, regular operation thresholds, and delayed operation thresholds. Then, based on the operation time thresholds, the gate operation time is discretized to generate discrete states of the gate operation time, including advance discharge state, regular advance operation state, on-time operation state, and delayed operation state. Table 3 shows the discretization criteria of the gate operation time, as follows:

[0038] Table 3 Discretization Standard Table of Gate Operation Time

[0039]

[0040] Based on the gate opening and closing rate characteristics, the operating rate threshold is divided, and the gate operating rate is discretized into multiple operating rate level states.

[0041] In this embodiment, based on the gate opening and closing rate characteristics, operation rate thresholds are defined, including extremely slow rate thresholds, normal rate thresholds, and fast rate thresholds. Then, based on the operation rate thresholds, the gate operation rate is discretized to generate discrete states of the gate operation rate, including extremely slow state, relatively slow state, normal state, and fast state. Table 4 shows the discretization criteria of the gate operation rate, as follows:

[0042] Table 4 Discretization Standard Table of Gate Operating Rate

[0043]

[0044] Based on the river channel resistance characteristics, the river channel roughness threshold is defined, and the river channel roughness is discretized into multiple resistance level states.

[0045] In this embodiment, based on the river channel resistance characteristics, river channel roughness thresholds are defined, including a very smooth threshold, a normal roughness threshold, and a very roughness threshold. Then, based on these thresholds, the river channel roughness is discretized to generate discrete states of roughness, including a very smooth state, a relatively smooth state, a normal state, and a very roughness state. Table 5 shows the discretization criteria for river channel roughness, as follows:

[0046] Table 5 Discretized Standard Table of Channel Roughness

[0047]

[0048] Specifically, the process of discretizing the state transition variables is as follows:

[0049] Based on the design safety water level threshold of the dam, the water level threshold is divided, and the water level status is discretized into multiple warning levels.

[0050] In this embodiment, based on the dam's designed safe water level threshold, water level thresholds are divided, including safe water level threshold, warning water level threshold, and critical water level threshold. Then, based on the water level thresholds, the water level state is discretized to generate discrete states of the water level state, including safe water level state, warning water level state, critical water level state, and dangerous water level state. Table 6 shows the discretization criteria of the water level state, as follows:

[0051] Table 6 Discretized Standard Table of Water Level Status

[0052]

[0053] Based on the duration of the water level in front of the dam exceeding the warning level, thresholds for the duration of exceeding the warning level are defined, and the duration of the water level exceeding the warning level is discretized into multiple duration levels.

[0054] In this embodiment, based on the duration of the water level in front of the dam exceeding the warning level, thresholds for the duration of exceeding the warning level are defined, including a zero-hour threshold, a short-term threshold, and a long-term threshold. Then, based on the thresholds for the duration of exceeding the warning level, the time-based state is discretized to generate discrete states of the time-based state, including a non-warning-level state, a short-term warning-level state, a moderate-duration warning-level state, and a long-term warning-level state. Table 7 shows the discretization criteria for the time-based state of exceeding the warning level, as follows:

[0055] Table 7 Discretized Standard Table of Duration of Water Level Exceeding Warning Level

[0056]

[0057] Based on the degree of influence of water flow velocity on the dam body, flow velocity thresholds are defined, and the impact state of water flow on the dam body is discretized into multiple impact levels.

[0058] In this embodiment, based on the degree of influence of water flow velocity on the dam body, flow velocity thresholds are defined, including low flow velocity threshold, medium flow velocity threshold, and high flow velocity threshold. Then, based on the flow velocity thresholds, the impact state is discretized to generate discrete states of the impact state, including low flow velocity state, medium flow velocity state, relatively high flow velocity state, and high flow velocity state. Table 8 shows the discretization criteria of the water flow impact state on the dam body, as follows:

[0059] Table 8 Discretization Standard Table of Water Flow Impact State on Dam Body

[0060]

[0061] Based on the comparison between the dam stability calculation index and the allowable safety margin, stability thresholds are defined, and the dam stability state is discretized into multiple stability levels.

[0062] In this embodiment, based on the comparison between the dam stability calculation index and the allowable safety margin, stability thresholds are defined, including very stable threshold, relatively stable threshold, and critically stable threshold. Then, based on the stability thresholds, the stable state is discretized to generate discrete states of the stable state, including very stable state, relatively stable state, critically stable state, and unstable state. Table 9 shows the discretization criteria for the dam stability state, as follows:

[0063] Table 9 Discretization Standard Table for Dam Stability State

[0064]

[0065] In summary, the above steps categorize the variables into two types: fundamental causal variables and state transition variables. By clarifying the core variables and discretization criteria, the discrete logic and engineering relevance are enhanced. Furthermore, each discrete state is determined in conjunction with the earth-rock dam design parameters, operational characteristics, and risk thresholds, ensuring alignment with actual engineering conditions. Simultaneously, the introduction of a stability index enables the quantitative discretization of the structural stable state, providing accurate input for the subsequent training of the three-layer Bayesian network model and improving the model's risk capture capability.

[0066] A one-dimensional dam-break flow simulation model is constructed, and a dataset covering multiple flood scenarios is generated based on the discretization standard.

[0067] In this embodiment, a one-dimensional dam-break flow simulation model is built using HEC-RAS software. By integrating engineering design data, watershed hydrological observation data, and historical flood records, a dataset covering multiple flood scenarios is generated. The operation process is as follows:

[0068] The engineering topographic and hydrological data were acquired to construct a one-dimensional dam-break flow simulation model. The engineering topographic data was used to define the physical space of the one-dimensional dam-break flow simulation model, which included digital elevation model, river cross-sectional geometric data, and dam structural dimensions. The hydrological data was used to define the initial hydraulic conditions and boundary properties of the one-dimensional dam-break flow simulation model, which included historical flood records, design flood hydrographs, and water level-discharge relationship data.

[0069] Specifically, the process of acquiring engineering topographic and hydrological data and constructing a one-dimensional dam-break flow simulation model is as follows:

[0070] The computational domain of the one-dimensional dam-break flow simulation model is defined based on engineering topographic data. This computational domain extends from the upstream tributary confluence to the downstream dam hydrological station, and the length of the computational domain does not exceed a set threshold, covering the upstream inflow convergence section, the backwater section in front of the dam, and the downstream energy dissipation and evolution section.

[0071] Meanwhile, based on hydrological data, a flow process line input is set at the upstream boundary of the computational domain, and a water level and flow relationship control is set at the downstream boundary. The dam structure is also used as an internal boundary module, and the dam's water-retaining structure parameters and scheduling rules are entered and defined.

[0072] In this embodiment, a one-dimensional dam-break flow simulation model is constructed in HEC-RAS software. First, the simulation range (computational domain) and boundary conditions need to be determined. The upstream of the simulation range begins at the confluence of tributaries in the basin, and the downstream extends to the hydrological station on the dam body, with a total simulation length of no less than 80 km, covering the upstream confluence section, the impoundment section in front of the dam, and the downstream energy dissipation and evolution section. The upstream boundary uses a flow process line boundary, the downstream boundary uses a water level and flow relationship boundary, and the dam body boundary uses the dam structure as an internal boundary module, defining it by inputting dam water-retaining structure parameters and scheduling rules, specifically: based on the process line shape (steep or flat) in the discretized standard corresponding to each flood scenario, the corresponding number of flood process lines is generated. According to the above, the upstream boundary is the input basis; the downstream boundary adopts the water level and flow relationship boundary, which is determined in advance by hydraulic principles based on the geometric data of the downstream river section, the gradient, and a benchmark Manning coefficient representing the normal state of the river roughness; the dam body boundary is defined by calling the structure-dam module in the software and inputting the dam body size, flood discharge structure parameters, and scheduling rules; and the upstream flow process line boundary, the downstream water level and flow relationship boundary, and the dam body boundary are all standard boundary types supported by one-dimensional flow simulation software (such as HEC-RAS software). Their specific data are all generated and input into the software based on the aforementioned engineering topographic data, hydrological data, and discretization standards, without the need to define custom hydraulic control equations.

[0073] Based on the discretization standard, flood levels are classified according to the flood return period. A one-to-one mapping is established between the flood levels and the discrete states of peak discharge, generating multiple flood scenarios, specifically:

[0074] Obtain flood flow rates for the flood recurrence interval and classify flood levels, including frequent floods, moderate floods, rare floods, and extreme floods.

[0075] By mapping the discrete states of flood levels to peak flows, multiple flood scenarios are generated, including flood scenarios with low flow rates corresponding to frequent floods, flood scenarios with medium flow rates corresponding to moderate floods, flood scenarios with high flow rates corresponding to rare floods, and flood scenarios with extremely high flow rates corresponding to extreme floods.

[0076] For each type of flood scenario, a preset parameter generation standard is adopted to generate peak flow rate, process line shape type, gate operation time, gate operation rate and channel roughness value that match the discrete state mapped by the flood scenario. Finally, several sets of scenario parameters matching the discrete state of the flood scenario are obtained.

[0077] In this embodiment, based on the dam design documents and hydrological analysis, the correspondence between the return period and the peak flow is established. For example, the flood flows with a return period of 1 year, 5 years, 20 years, 50 years, and 100 years are approximately 2200, 4000, 7000, 11800, and 14500 m³ / s, respectively. Based on this, the return period range is determined, including 1-5 years, 5-20 years, 20-50 years, and more than 50 years. Simultaneously, the flood class within the return period range is determined, including frequent floods (1-5 years), moderate floods (5-20 years), rare floods (20-50 years), and extreme floods (more than 50 years). Subsequently, this return period range (or flood class) is correlated with the discrete state of the peak flow determined in the above steps. A one-to-one mapping is performed to generate multiple flood scenarios: frequent floods (1-5 years) correspond to low flow conditions, moderate floods (5-20 years) correspond to moderate flow conditions, rare floods (20-50 years) correspond to high flow conditions, and extreme floods (over 50 years) correspond to extra-high flow conditions, resulting in four flood scenario categories. Then, for each flood scenario, a preset parameter generation standard (i.e., a parameter generation standard determined by statistical distribution methods) is used to generate peak flow values, process curve shape types, gate operation time values, gate operation rate values, and channel roughness values ​​that match the discrete state mapped to that flood scenario. This results in several sets of scenario parameters matching the discrete state of the flood scenario, specifically:

[0078] The peak flow parameters are adopted using a truncated normal distribution. The generation process begins by determining the threshold range based on the discrete states corresponding to the current flood level. Then calculate the distribution parameters. and distribution parameters Finally, the truncated normal distribution Randomly generate specific peak flow values This is directly used as the peak flow parameter for this type of flood scenario; The minimum allowable peak flow for the discrete state of the current target flood is derived from the threshold lower limit explicitly set for the discrete state of the peak flow in the above steps; The maximum allowable peak flow for the discrete state of the current target flood is derived from the upper limit of the threshold explicitly set for the discrete state of the peak flow in the above steps.

[0079] The process line shape parameter describes the morphological characteristics of the flood discharge over time. In this invention, it is simplified to two states: steep and flat. The process line shape parameter is generated using a conditional probability allocation method based on historical statistics. Specifically: First, based on the discrete state (small flow, medium flow, etc.) to which the generated peak flow value belongs, the conditional probability table shown in Table 10 is consulted. The probability relationships in this table are determined based on statistical analysis of historical flood data in the basin. Then, according to the obtained probability distribution (e.g., P_steep = 0.2, P_flat = 0.8), a random number uniformly distributed within the interval [0, 1) is generated for determination. If the random number is less than the steep probability, it is assigned to the steep state; otherwise, it is assigned to the flat state. The final assigned steep or flat state serves as the discrete input parameter for the process line shape of this flood scenario. The conditional probability table is shown in Table 10.

[0080] Table 10 Conditional Probability Table

[0081]

[0082] The gate operation time parameter is the time offset (in hours) of the gate opening and closing action relative to the arrival of the flood, reflecting the timeliness of dispatching. This gate operation time parameter is generated using a discrete distribution. Specifically, based on the discrete states and time ranges of the variables defined in the above steps, sampling weights are assigned to each state according to the urgency of the current flood level. Finally, the operation time state is randomly selected according to this weighted discrete distribution. This operation time state is the gate operation time parameter determined by the flood scenario, as shown in Table 11.

[0083] Table 11 Gate Operation Time Parameter Table

[0084]

[0085] The gate operation rate parameter refers to the relative amplitude (between 0 and 1) of gate opening and closing per unit time, reflecting the intensity of operation. This gate operation rate parameter is generated using a Beta distribution, and the favorable characteristics of the Beta distribution enable it to accurately simulate the probability distribution characteristics of the operation rate under different levels of urgency, ensuring that the generated parameter is both random and reasonable. Specifically, the distribution parameter is set according to the flood level, and after generating a random number R, it is mapped to the corresponding discrete state according to the threshold defined in the above steps. This discrete state is the gate operation rate parameter determined by the flood scenario, as shown in Table 12.

[0086] Table 12 Gate Operation Rate Parameters

[0087]

[0088] The river roughness parameter is determined by setting a reasonable standard deviation based on the median value of the normal state as defined in Table 5, and truncating sampling within the effective roughness range. Finally, the generated values ​​are divided into corresponding discrete states according to the threshold, and these discrete states are the river roughness parameters determined for the flood scenario.

[0089] The initial water level parameters in front of the dam are set to a normal distribution based on the daily operating water level range of the dam. The mean of this distribution is set as the statistical average of the normal storage water level or the daily operating water level of the dam, and the standard deviation is determined based on the daily fluctuation range calculated from long-term water level observation data. The range of the distribution is truncated to the upper and lower limits of the daily operating water level allowed by the dam design. The random water level value generated in this way is used as the initial water level parameters in front of the dam for this flood scenario.

[0090] Therefore, the generation of scenario parameters in the above steps combines statistical distribution and discretization standards to ensure that the values ​​of each scenario parameter conform to probability laws and match discrete states. Among them, the peak flow parameter adopts a truncated normal distribution and the gate operation rate parameter adopts a Beta distribution, which conforms to the characteristics of parameter engineering distribution and makes the flood scenario physically realistic. At the same time, the initial water level and roughness distribution cover both normal and extreme scenarios, providing comprehensive sample support for dam prediction with scarce data.

[0091] Each set of scenario parameters is used as input data for a one-dimensional dam-break flow simulation model. The model is run automatically, and the system monitors in real time whether each set of scenario parameters meets its corresponding discrete state threshold. If so, the system extracts the peak flood level in front of the dam, the flow velocity through the dam, the duration of the water level exceeding the warning level, the river channel shear stress, and the dam-break state from each set of simulation results to generate a dataset covering multiple levels of flood scenarios. Otherwise, the flow simulation process continues.

[0092] In this embodiment, based on a predefined discretization standard, a parameterized random generation algorithm is used to generate at least 8,000 sets of specific scenario parameters that conform to physical reality and state consistency according to the probability distributions corresponding to the discrete state categories (truncated normal distribution, Beta distribution, and conditional probability tables based on historical statistics). These scenario parameter sets are input into a one-dimensional dam-break flow simulation model to iteratively simulate the physical response of the dam under various scenarios. In each iteration, based on the discrete state determined in the above steps, it calls the specified probability distribution to generate specific values ​​for each basic causal variable, ensuring that the generated values ​​fall within the range of the target discrete state. If any scenario parameter generated in real time does not meet its discrete state threshold, the entire set of parameters is automatically discarded and regenerated immediately. Only when all parameters strictly conform to their target state range will the set of scenario parameters be approved and automatically submitted to the one-dimensional dam-break flow simulation model for batch processing simulation, from which state transition variables such as the flood peak level in front of the dam and the flow velocity, as well as the dam-break state results, are extracted. Finally, all data are automatically integrated to form a complete dataset covering multiple levels of flood scenarios.

[0093] In summary, the above steps, through the construction and parameter configuration of a one-dimensional dam-break flow simulation model, can simulate the hydraulic response characteristics of earth-rock dams without requiring a large amount of measured flood data. Secondly, by combining flood scenario design with discretization standards, accurate matching of parameters and discrete states for each scenario is achieved. At the same time, automated data generation improves efficiency, enabling large-scale datasets to cover various risk scenarios, meeting the training and validation needs of the model, providing sufficient sample support for data-scarce earth-rock dams, and ensuring the model's accuracy and generalization ability.

[0094] By treating the discrete states of each variable as network nodes, a three-layer Bayesian network model is constructed, comprising a basic cause layer, a state transition layer, and a failure mode layer, and the dependencies between each node are determined.

[0095] In this embodiment, the process of constructing a three-layer Bayesian network model comprising a basic causation layer, a state transition layer, and a failure mode layer, thereby clarifying the dependencies between basic causation variables, state transition variables, and dam-break states, is as follows:

[0096] The discretized peak flow, process curve shape, gate operation time, gate operation rate, and river roughness are used as network input nodes to construct the basic causal layer.

[0097] In this embodiment, the discretized peak flow, process curve shape, gate operation time, gate operation rate, and river roughness are used as network input nodes to construct the basic causal layer, thereby providing the initial driving factors for dam failure risk.

[0098] The discretized water level status, the duration of water level exceeding the warning level, the impact of water flow on the dam body, and the dam body stability status are used as intermediate nodes in the network to construct a state transition layer. The discretized water level status nodes and the duration of water level exceeding the warning level status nodes depend on the discretized peak flow nodes, process line shape nodes, gate operation time nodes, and gate operation rate nodes in the basic causal layer. The discretized water flow impact on the dam body status nodes depend on the discretized peak flow nodes, process line shape nodes, and channel roughness nodes in the basic causal layer. The discretized dam body stability status nodes depend on the discretized water flow impact on the dam body status nodes in the state transition layer.

[0099] The failure mode layer is constructed by taking the dam failure state as the network output node; and the dam failure state node depends on the discretized water level state node, the water level exceeding the warning level duration state node, the water flow impact on the dam body state node, and the dam body stability state node in the state transition layer.

[0100] In this embodiment, the dam failure state is used as the network output node to construct a failure mode layer. The dam failure state node depends on the water level state node, the water level exceeding the warning level duration state node, the water flow impact on the dam body state node, and the dam body stability state node in the state transition layer, which can reflect the comprehensive impact of the four factors on the probability of dam failure.

[0101] In summary, the three-layer Bayesian network model described above clearly presents the transmission path from risk causation to failure using a three-layer topology, closely aligning with the dam-break mechanism. Variable dependencies are based on engineering physics logic, ensuring a scientifically sound network structure. The basic causation layer covers core driving factors, the state transition layer quantifies hydraulic and structural responses, and the failure mode layer focuses on the dam-break outcome. This progressive design enhances the logical consistency of probabilistic reasoning and quantifies the influence weights of each factor.

[0102] The dataset is input into a three-layer Bayesian network model for training. The conditional probability of each node in the three-layer Bayesian network model is calculated using the Bayesian smoothing method to correct the model parameters and generate a trained three-layer Bayesian network model.

[0103] Specifically, the process of calculating the conditional probability of each node in a three-layer Bayesian network model using the Bayesian smoothing method is as follows:

[0104] Calculate the conditional probability of each network output node in the failure mode layer, i.e.:

[0105]

[0106] in, This represents the conditional probability of a network output node failing under various combinations of states of its parent node in the failure mode layer. This represents the number of samples corresponding to each combination of states of the parent node of the network output node. This represents the number of samples where the network output node is in a dam failure state, considering all possible combinations of the parent node's state. The parameter... The integer 4 in the parameter represents the total number of pseudo-samples, including 2 invalid pseudo-samples and 2 safe pseudo-samples, used to balance the probability estimation of small sample combinations; The integer 2 in the formula represents two invalid pseudo-samples.

[0107] Calculate the conditional probabilities of each intermediate node in the state transition layer, i.e.:

[0108]

[0109] in, This represents the conditional probability that each intermediate node in the state transition layer is in a certain discrete state, given the combined states of the parent node of each intermediate node. This represents the number of samples corresponding to each combination of states of the parent node of each intermediate node in the network. This represents the number of samples where each intermediate node is in a discrete state, given all possible combinations of the parent node's states. The parameter... decimals in This represents the number of pseudo-samples, specifically adding 0.5 pseudo-samples for each state. (Parameter) The integer 2 represents the total number of pseudo-samples, thus avoiding the extreme case where the probability is 0.

[0110] In this embodiment, a Bayesian smoothing method is employed to address probability estimation biases in small sample state combinations by introducing spurious samples, thus avoiding extreme probabilities and improving the reliability of the conditional probability table. Both the failure mode layer and the state transition layer utilize differentiated smoothing formulas to adapt to their respective sample distribution characteristics, ensuring accurate probability calculations. Furthermore, this method rapidly constructs conditional probability tables based on simulated datasets, providing a reliable foundation for probabilistic inference in Bayesian networks.

[0111] Furthermore, in the specific implementation process, the dataset can be divided into a validation set and a training set in a 3:7 ratio for model training and validation. This process does not require the introduction of a large amount of measured flood data, thus ensuring the accuracy and generalization ability of the model.

[0112] The fundamental causal variables and state transition variables of the earth-rock dam to be tested are obtained, discretized, and then input into a trained three-layer Bayesian network model to predict the dam failure probability, generate dam failure probability values, and determine the dam failure risk level.

[0113] In this embodiment, the dam failure risk levels include extremely low risk (<1%), low risk (1%-5%), low-to-medium risk (5%-10%), medium risk (10%-30%), medium-to-high risk (30%-50%), high risk (50%-70%), extremely high risk (70%-90%), and extreme risk (>90%). By determining which dam failure risk level the probability value falls into, the dam failure risk level of the earth-rock dam under test is obtained.

[0114] To verify the effectiveness of the proposed method for predicting the probability of earth-rock dam failure in this invention, the following experiment was conducted:

[0115] Taking the Lianghekou earth-rock dam (gravel-soil core rockfill dam, maximum dam height 295m, elevation 2875m, normal water level 2865m, wave wall crest elevation 2873m) in the Yalong River basin as the research object, this dam lacks a large number of measured flood records, making it suitable for the prediction needs of the data-scarce scenario in this invention. The operation process is as follows:

[0116] I. Establishing Discretization Criteria for Each Variable

[0117] Based on dam design documents, hydrological observation specifications, and safety assessment standards, a fixed threshold method was used to discretize each variable, eliminating the need to rely on measured flood data. Furthermore, the discretization was based on the "Technical Specification for Safety Monitoring of Earth-Rock Dams" (SL551-2012), combined with flood design values ​​and basin-wide rainfall statistics, ensuring a high degree of alignment between the discretization standard and actual engineering conditions. Specifically:

[0118] (a) Discretization of basic dependent variables

[0119] Discrete state of peak flow: according to (Low flow) (Medium flow) (High flow rate) (Extra-large flow rates) are divided into categories corresponding to the dam's design values ​​for floods with return periods of 1-5 years, 5-20 years, 20-50 years, and over 50 years. Specifically, the flow rate for a 1-year flood is 2200 m³ / s, for a 50-year flood is 11800 m³ / s, and for a 100-year flood is 14500 m³ / s. Indicates flow rate.

[0120] Discrete states of process line shape: flat process lines (flood rise duration > 12h or flood recede duration > 24h) and steep process lines (flood rise duration ≤ 12h and flood recede duration ≤ 24h). Based on the statistical analysis of rainstorm observation data in the same basin from 1980 to 2020, it was found that the proportion of steep flood process lines caused by short-duration heavy rainstorms reached 89%.

[0121] Discrete states of gate operation time: (Pre-release) (Standard advance procedures) (Timely operation) (Delayed operation) to match the time node requirements of pre-discharge scheduling, routine scheduling, and emergency scheduling in the dam's "Flood Discharge Scheduling Regulations"; among which, Indicates the operation time.

[0122] Discrete states of gate operating rate: (Extremely slow, equipment under maintenance) (Slower, normal and stable operation) (Normal, recommended for flood control) (Fast, emergency operation) Based on the safety operation test data provided by the gate equipment manufacturer, the maximum safe opening rate is 0.92, and the recommended flood control rate is 0.6-0.85; among which, Indicates the operating rate.

[0123] Discrete state of channel roughness: (Very smooth, after river dredging) (Relatively smooth, typical hydrological year) (Normal, baseline state) (Very rough, siltation or high-sediment-laden flood), determined based on watershed hydrological characteristics analysis, requiring no actual flood calibration; among which, This represents the roughness coefficient.

[0124] (ii) Discretization of state transition variables

[0125] Discrete states of water level: (Safe water level: normal water level + 5m) (Warning water level) (Critical water level, top elevation of the wave wall -0.5m) (Dangerous water level, above the top of the wave wall), where the normal water level of 2865m and the top elevation of the wave wall of 2873m are both parameters clearly defined in the dam's design documents; among them, Indicates water level.

[0126] Discrete states of the water level exceeding the warning level over time: (Not exceeding the warning level) (Briefly exceeding the warning level) (Medium duration above warning level) (Exceeding warning level for an extended period); among them, Indicates the duration of exceeding the warning level.

[0127] Discrete states of the impact of water flow on the dam body: (Low flow rate) (Medium flow rate) (Higher flow rate) (High flow velocity, exceeding the scour threshold of the rockfill body): Based on the scour test results of the rockfill body of this dam, the maximum allowable scour velocity for the rockfill body is 7 m / s; exceeding this velocity can easily lead to dam surface scour. Indicates flow rate.

[0128] Discrete states of dam stability: (Very stable) (Relatively stable) (Critical stability) (Unstable), among which , For the shear stress of the dam body, , is the allowable shear stress of the rockfill mass, determined according to the shear strength standard of the rockfill mass in the "Code for Design of Earth-Rockfill Dams" (SL274-2001); among which, This indicates a stability index.

[0129] Therefore, the discretization criteria for the fundamental causal variables and the discretization criteria for the state transition variables of high-altitude earth-rock dams are shown in Tables 13-14:

[0130] Table 13 Discretized Standard Table of Fundamental Causative Variables for High-Altitude Earth-Rock Dams

[0131]

[0132] Table 14 Discretization Standard Table of State Transition Variables for High-Altitude Earth-Rock Dams

[0133]

[0134] Tables 13 and 14 above clearly show the discrete states, thresholds, and engineering significance of the basic causal variables and state transition variables, providing a unified standard for subsequent steps such as dataset generation and model training.

[0135] II. Construction of a One-Dimensional Dam-Break Flow Simulation Model and Generation of Datasets

[0136] Using HEC-RAS software, a one-dimensional dam-break flow simulation model was constructed. By integrating dam design data, hydrological data, and historical flood records, a dataset covering multiple flood scenarios was generated according to the aforementioned discretization standard. No actual flood data was required, ensuring the physical authenticity and engineering representativeness of the data. Specifically:

[0137] (I) Construction of a one-dimensional dam-break flow simulation model

[0138] The simulation range extends from the tributary confluence to the downstream hydrological station, covering the inflow convergence, dam backwater, and downstream energy dissipation evolution. The upstream boundary is located at the tributary confluence and uses the flow process line boundary built into the HEC-RAS software, with data directly accessed from the flood process lines generated in each simulation of the flood scenario. The downstream boundary uses the water level-discharge relationship boundary built into the HEC-RAS software, generating a unified boundary curve through hydraulic methods. The Manning roughness required for the calculation is taken from the median value of the discretized normal state, i.e. The flow rate range was set from 500 to 16000 m³ / s to fully cover all flood scenarios in the steps. Based on the downstream standard cross-section geometry and river slope, the Manning formula was applied to calculate a complete boundary table of water level and flow rate relationship, which was then input into the one-dimensional dam-break flow simulation model, along with dam structure parameters. Topographic data was based on a 1:10000 DEM and geological survey data, with a total of 127 cross-sections laid out, spaced 500m apart at key river sections, including parameters such as elevation, river width, and slope. Table 15 shows some data from the water level and flow rate relationship boundary table, as shown below:

[0139] Table 15 Boundary Table of Water Level and Flow Rate Relationship

[0140]

[0141] (II) Flood Scenario Design and Dataset Generation

[0142] Scenario Classification: Based on the flood return period and the discretization criteria shown in Tables 13-14, the correspondence between the return period and peak flow is established according to the dam design documents and hydrological analysis (the flood flows for 1-year, 5-year, 20-year, 50-year, and 100-year floods are approximately 2200, 4000, 7000, 11800, and 14500 m³ / s, respectively). Subsequently, this return period range is mapped to the discrete state of the peak flow—frequent floods (1-5 years) correspond to low flow state, moderate floods (5-20 years) correspond to moderate flow state, rare floods (20-50 years) correspond to high flow state, and extreme floods (more than 50 years) correspond to extra-large flow state.

[0143] Scenario parameter generation:

[0144] Peak flow parameters: values ​​ranging from 2000 to 15000 m³ / s are set for floods of various levels, covering all flood scenarios from the minimum to the maximum probability, and a truncated normal distribution is adopted. generate, , , , The minimum peak flow allowed for the current target flood discrete state is derived from the lower limit of the threshold explicitly set for this discrete state in the above steps; The maximum allowable peak flow for the current target flood discrete state is derived from the upper limit of the threshold explicitly set for this discrete state in the above steps.

[0145] Process curve shape parameters: Based on the size of the previous flood peak flow, steep / flat types are assigned by conditional probability. The steep probability of an extremely large flow flood is 1, the steep probability of a large flow flood is 0.9, the steep probability of a medium flow flood is 0.7, and the steep probability of a small flow flood is 0.2. The flat probability of an extremely large flow flood is 0, the flat probability of a large flow flood is 0.1, the flat probability of a medium flow flood is 0.3, and the flat probability of a small flow flood is 0.8.

[0146] Gate operation time parameters: The operation time adopts a discrete distribution. The corresponding weight column is selected according to the current flood level. According to the weight ratio, an operation time state is selected. The specific time value is generated by uniformly sampling within the time range corresponding to the state: advance release: [-6, -4] hours; regular advance operation: (-4, -1] hours; on-time operation: (-1, 1] hours; delayed operation: (1, 3] hours.

[0147] Gate operation rate parameters: The operation rate adopts a Beta distribution, with an average of 0.68 for extreme floods and an average of 0.60 for other floods; the corresponding Beta distribution parameter is selected according to the flood level, and random numbers are generated based on the Beta distribution, i.e., the operation rate. ∈ (0, 1), will the operation rate Values ​​mapped to their defined discrete states: extremely slow. Slower: ;normal: ;fast: .

[0148] River channel environmental parameters: River channel roughness is set to (Truncation to [0.7, 1.3]), initial water level set to It fits the daily operating range.

[0149] Then, automated data generation is performed: through the linkage of Python scripts and HEC-RAS batch processing, the one-dimensional dam-break flow simulation model automatically generates 8,000 sets of scenario parameters and executes the simulation. After extracting key hydraulic parameters, the status is marked according to the dam-break judgment criteria, such as water level > 2873m and exceeding the warning level for more than 24 hours or flow velocity > 10m / s. After data cleaning, 8,000 valid records are retained and divided into a validation set (2,400 records) and a training set (5,600 records) in a 3:7 ratio, without the need for actual flood data.

[0150] III. Construction and Training of a Three-Layer Bayesian Network Model

[0151] Based on discretized variables and the generated dataset, a three-layer Bayesian network model is constructed. The dependencies between variables are clarified, and the conditional probability table is calculated using the Bayesian smoothing method. The training and optimization of the three-layer Bayesian network model are then completed to ensure its high-accuracy predictive capability even without measured flood data. Specifically:

[0152] (I) Construction of a three-layer Bayesian network model

[0153] like Figure 2 As shown, a Bayesian network is constructed with a three-layer structure, and the discrete states and dependencies of each node are labeled to reflect the physical logic from the fundamental cause to the intermediate state and finally to the failure. Specifically:

[0154] 1. Basic Cause Layer → State Transition Layer:

[0155] Peak flow rate → water level status, duration status, impact status; process curve shape → water level status, duration status, impact status; gate operation time → water level status, duration status; gate operation rate → water level status, duration status; roughness → impact status;

[0156] 2. Within the state transition layer: shock state → steady state;

[0157] 3. State transition layer → Failure mode layer:

[0158] Water level status → Dam break status; Duration status → Dam break status; Impact status → Dam break status; Stable status → Dam break status.

[0159] (ii) Calculation of conditional probability tables

[0160] The peak flow rate, process curve shape, gate operation time, gate operation rate, and roughness are used as network input nodes; the water level status, duration status, impact status, and steady state are used as network intermediate nodes; and the dam break status is used as network output nodes.

[0161] Calculate the conditional probability of each network output node in the failure mode layer, i.e.:

[0162]

[0163] in, This represents the conditional probability of a network output node failing under various combinations of states of its parent node in the failure mode layer. This represents the number of samples corresponding to each combination of states of the parent node of the network output node. This represents the number of samples where the network output node is in a dam failure state, considering all possible combinations of the parent node's state. The parameter... The integer 4 in the parameter represents the total number of pseudo-samples, including 2 invalid pseudo-samples and 2 safe pseudo-samples, used to balance the probability estimation of small sample combinations; The integer 2 in the formula represents two invalid pseudo-samples.

[0164] Calculate the conditional probabilities of each intermediate node in the state transition layer, i.e.:

[0165]

[0166] in, This represents the conditional probability that each intermediate node in the state transition layer is in a certain discrete state, given the combined states of the parent node of each intermediate node. This represents the number of samples corresponding to each combination of states of the parent node of each intermediate node in the network. This represents the number of samples where each intermediate node is in a discrete state, given all possible combinations of the parent node's states. The parameter... decimals in This represents the number of pseudo-samples, specifically adding 0.5 pseudo-samples for each state. (Parameter) The integer 2 represents the total number of pseudo-samples, thus avoiding the extreme case where the probability is 0.

[0167] (III) Training and Validation of Three-Layer Bayesian Network Model

[0168] Based on the above dataset, the three-layer Bayesian network model was trained and validated, and the results are as follows: Figure 3 As shown, the probability distribution of the Bayesian network is consistent on the training and validation sets, with average dam failure probabilities of 0.1705 and 0.1761, respectively, differing by only 0.0056, indicating no overfitting. The probability density is highly concentrated in the low-risk region (0-0.1), consistent with the characteristics of normal operating conditions. The probability is divided into 8 risk levels, and the failure rate of the training set for each level is highly consistent with the predicted probability of the test set, proving that the risk stratification is accurate.

[0169] IV. Dam Failure Probability Prediction for Individual Flood Scenarios

[0170] Based on the trained three-layer Bayesian network model, 15 diverse flood scenarios are input, and the dam failure probability is output as shown in Table 16:

[0171] Table 16: Diverse Flood Scenarios

[0172]

[0173] And from Figure 4As can be seen, extreme risk scenarios (Scenarios 1-3, 14) all exhibit typical dangerous combinations, such as the extremely large flow rate in Scenario 1 combined with extremely slow gate operation and a rough river channel; high-risk scenarios (Scenarios 6, 10, 13, etc.) show a reasonable risk gradient, with the risk in Scenario 6 reduced to 0.618 due to advance pre-release of large flow rates, while in Scenario 10, the risk remains high at 0.613 due to the steep hydrograph; medium-risk (Scenarios 8, 15) and low-to-medium-risk scenarios (Scenario 5) both have favorable combinations, such as the probability of a flat hydrograph with small flow rates in Scenario 5 being only 0.098. The probabilities of each scenario strictly correspond to the engineering parameters, with a continuous distribution from 0.098 to 1.0000 without anomalies. The 26.7% extreme risk proportion objectively reflects the severity of the risk in high-altitude areas, proving the reliability of the dam failure probability prediction method proposed in this invention.

[0174] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0175] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for predicting the probability of dam failure in earth-rock dams, characterized in that, Includes the following steps: Obtain the fundamental causal variables and state transition variables that lead to the failure of earth-rock dams; The fixed threshold method is used to discretize the basic causal variables and state transition variables, generating a discretization standard that includes the discrete state, value range and threshold of each variable. A one-dimensional dam-break flow simulation model was constructed, and a dataset covering multiple flood scenarios was generated by combining discretization standards. By treating the discrete states of each variable as network nodes, a three-layer Bayesian network model is constructed, which includes a basic cause layer, a state transition layer, and a failure mode layer, and the dependencies between each node are determined. The dataset is input into a three-layer Bayesian network model for training. The conditional probability of each node in the three-layer Bayesian network model is calculated using the Bayesian smoothing method to correct the model parameters and generate a trained three-layer Bayesian network model. The fundamental causal variables and state transition variables of the earth-rock dam to be tested are obtained, discretized, and then input into a trained three-layer Bayesian network model to predict the dam failure probability, generate dam failure probability values, and determine the dam failure risk level.

2. The method for predicting the probability of earth-rock dam failure according to claim 1, characterized in that, The fundamental causal variables include peak flow, process curve shape, gate operation time, gate operation rate, and channel roughness.

3. The method for predicting the probability of earth-rock dam failure according to claim 2, characterized in that, The state transition variables include water level status, duration of water level exceeding the warning level, impact of water flow on the dam body, and dam body stability status.

4. The method for predicting the probability of earth-rock dam failure according to claim 3, characterized in that, The process of discretizing the fundamental dependent variables is as follows: Based on the design value of the flood return period, flood flow thresholds are defined, and the peak flow is discretized into multiple flow level states; Based on the characteristics of flood rise and fall duration, flood rise and fall duration thresholds are defined, and the process line shape is discretized into two states: flat and steep. Based on the time offset of gate operation relative to the flood process, operation time thresholds are defined, and the gate operation time is discretized into multiple operation timing states. Based on the characteristics of the gate opening and closing rate, the operating rate threshold is divided, and the gate operating rate is discretized into multiple operating rate level states. Based on the river channel resistance characteristics, the river channel roughness threshold is defined, and the river channel roughness is discretized into multiple resistance level states.

5. The method for predicting the probability of earth-rock dam failure according to claim 4, characterized in that, The process of discretizing the state transition variables is as follows: Based on the design safety water level threshold of the dam, the water level threshold is divided, and the water level status is discretized into multiple warning levels. Based on the duration of the water level in front of the dam exceeding the warning level, the threshold for the duration of exceeding the warning level is divided, and the duration of the water level exceeding the warning level is discretized into multiple duration levels. Based on the degree of influence of water flow velocity on the dam body, flow velocity thresholds are defined, and the impact state of water flow on the dam body is discretized into multiple impact levels. Based on the comparison between the dam stability calculation index and the allowable safety margin, stability thresholds are defined, and the dam stability state is discretized into multiple stability levels.

6. The method for predicting the probability of earth-rock dam failure according to claim 5, characterized in that, The process of constructing a one-dimensional dam-break flow simulation model and generating a dataset covering multiple flood scenarios by combining discretization criteria is as follows: Acquire engineering topographic and hydrological data to construct a one-dimensional dam-break flow simulation model. The engineering topographic data is used to define the physical space of the one-dimensional dam-break flow simulation model, which includes digital elevation model, river channel cross-sectional geometric data, and dam structure dimensions. The hydrological data is used to define the initial hydraulic conditions and boundary properties of the one-dimensional dam-break flow simulation model, which includes historical flood records, design flood hydrographs, and water level-discharge relationship data. Based on the discretization standard, flood levels are classified according to the flood return period, and the flood levels are mapped one-to-one with the discrete state of the peak flow to generate multiple flood scenarios. For each type of flood scenario, a preset parameter generation standard is adopted to generate peak flow value, process line shape type, gate operation time value, gate operation rate value and river roughness value that match the discrete state mapped by the flood scenario. Finally, several sets of scenario parameters matching the discrete state of the flood scenario are obtained. Each set of scenario parameters is used as input data for a one-dimensional dam-break flow simulation model. The model is run automatically, and the system monitors in real time whether each set of scenario parameters meets its corresponding discrete state threshold. If so, the system extracts the peak flood level in front of the dam, the flow velocity through the dam, the duration of the water level exceeding the warning level, the river channel shear stress, and the dam-break state from each set of simulation results to generate a dataset covering multiple levels of flood scenarios. Otherwise, the flow simulation process continues.

7. The method for predicting the probability of earth-rock dam failure according to claim 6, characterized in that, The process of acquiring engineering topographic and hydrological data and constructing a one-dimensional dam-break flow simulation model is as follows: The computational domain of the one-dimensional dam-break flow simulation model is defined based on engineering topographic data. This computational domain extends from the upstream tributary confluence to the downstream dam hydrological station, and the length of the computational domain does not exceed a set threshold, covering the upstream inflow convergence section, the backwater section in front of the dam, and the downstream energy dissipation and evolution section. Meanwhile, based on hydrological data, a flow process line input is set at the upstream boundary of the computational domain, and a water level and flow relationship control is set at the downstream boundary. The dam structure is also used as an internal boundary module, and the dam's water-retaining structure parameters and scheduling rules are entered and defined.

8. The method for predicting the probability of earth-rock dam failure according to claim 7, characterized in that, Based on the discretization standard, flood levels are classified according to the flood return period. The process of mapping the flood level to the discrete state of the peak flow to generate multiple flood scenarios is as follows: Obtain flood flow rates during the flood recurrence interval and classify flood levels, including frequent floods, moderate floods, rare floods, and extreme floods; By mapping the discrete states of flood levels to peak flows, multiple flood scenarios are generated, including flood scenarios with low flow rates corresponding to frequent floods, flood scenarios with medium flow rates corresponding to moderate floods, flood scenarios with high flow rates corresponding to rare floods, and flood scenarios with extremely high flow rates corresponding to extreme floods.

9. The method for predicting the probability of earth-rock dam failure according to claim 8, characterized in that, The process of constructing a three-layer Bayesian network model, consisting of a basic causation layer, a state transition layer, and a failure mode layer, by treating the discrete states of each variable as network nodes, and determining the dependencies between nodes, is as follows: The discretized peak flow, process curve shape, gate operation time, gate operation rate, and river roughness are used as network input nodes to construct the basic causal layer; The discretized water level status, the duration of water level exceeding the warning level, the impact of water flow on the dam body, and the stability of the dam body are used as intermediate nodes in the network to construct a state transition layer. The discretized water level status nodes and the duration of water level exceeding the warning level status nodes depend on the discretized peak flow nodes, process line shape nodes, gate operation time nodes, and gate operation rate nodes in the basic causal layer. The discretized water flow impact on the dam body status nodes depend on the discretized peak flow nodes, process line shape nodes, and channel roughness nodes in the basic causal layer. Furthermore, the discretized dam stability state nodes depend on the discretized water flow impact state nodes on the dam in the state transition layer. The failure mode layer is constructed by taking the dam failure state as the network output node; and the dam failure state node depends on the discretized water level state node, the water level exceeding the warning level duration state node, the water flow impact on the dam body state node, and the dam body stability state node in the state transition layer.

10. The method for predicting the probability of earth-rock dam failure according to claim 9, characterized in that, The process of calculating the conditional probability of each node in a three-layer Bayesian network model using the Bayesian smoothing method is as follows: Calculate the conditional probability of each network output node in the failure mode layer, i.e.: in, This represents the conditional probability of a network output node failing under various combinations of states of its parent node in the failure mode layer. This represents the number of samples corresponding to each combination of states of the parent node of the network output node. This represents the number of samples where the network output node is in a dam failure state, given all possible combinations of the parent node's state. Calculate the conditional probabilities of each intermediate node in the state transition layer, i.e.: in, This represents the conditional probability that each intermediate node in the state transition layer is in a certain discrete state, given the combined states of the parent node of each intermediate node. This represents the number of samples corresponding to each combination of states of the parent node of each intermediate node in the network. This represents the number of samples in a discrete state of each intermediate node in the network, given the combined states of the parent node of each intermediate node.

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