A Modeling Method for Dam Risk Bayesian Network Model Incorporating Machine Learning

Abstract

The present invention discloses a method for modeling a dam risk Bayesian network model that integrates machine learning. The method comprises the following steps: S1. removing outliers from an original dataset containing historical data to obtain a dam accident dataset and extracting feature information from it; S2. selecting key risk factors from the dam accident dataset using a boosted regression tree algorithm; S3. constructing a network structure for the dam risk model based on the key risk factors using a structural learning algorithm; S4. determining the network parameters of the dam risk model using a parameter learning algorithm based on the network structure; and S5. evaluating the performance of the dam risk model. The present invention solves the problem in the prior art of using Bayesian networks to construct dam risk models, which requires manual selection of risk factors based on domain knowledge and manual network construction, resulting in high modeling difficulty, strong subjectivity, and poor reliability.

Description

Technical Field

[0001] The present invention belongs to the field of dam risk, and specifically relates to a dam risk Bayesian network modeling method integrating machine learning. Background Art

[0002] While dams provide benefits through water storage, they also carry significant safety risks. Establishing an objective and reasonable dam risk model is crucial for enhancing dam breach preparedness and improving dam risk management. Bayesian networks (BNs), combining the strengths of graph theory and probability theory, have become an effective tool for dam risk analysis thanks to their intuitive network structure and efficient probabilistic reasoning.

[0003] The BN-based dam risk modeling process presents two challenges: variable selection and network construction. Dam safety status is often influenced by a combination of multiple risk factors. However, some risk factors contribute little to model performance and may even increase the risk of overfitting. Therefore, accurately selecting key risk factors from a variety of risk factors is a prerequisite for ensuring modeling quality. Furthermore, complex correlations exist between dam risk factors, and constructing a complete dam risk network requires considering a wide variety of network structures and determining a large number of network parameters. Therefore, a reasonable network construction method is key to improving modeling efficiency and model rationality.

[0004] Currently, the dam risk field mainly uses a domain knowledge-based approach to implement the modeling process. This approach has the following shortcomings: (1) The accuracy of variable selection is affected by the subjectivity of experts, and the conflicting opinions of different experts also increase the difficulty of variable selection; (2) Manual network construction is difficult and inefficient, and the constructed network is difficult to fully explore and accurately quantify the interaction between variables. As my country's water conservancy industry continues to transform towards modernization, informatization, and intelligence, traditional domain knowledge-based modeling methods are difficult to meet the requirements of dam risk management at this stage. Summary of the Invention

[0005] The purpose of the present invention is to provide a Bayesian network modeling method for dam risk that integrates machine learning, so as to solve the problem that when the existing technology uses BN to construct a dam risk model, it is necessary to manually select risk factors based on domain knowledge and manually construct the network, which leads to high modeling difficulty, strong subjectivity and poor reliability.

[0006] To solve the above technical problems, the technical solution of the present invention is: a dam risk Bayesian network modeling method integrating machine learning, comprising the following steps:

[0007] S1. Eliminate outliers from the original data set containing historical data, obtain the dam accident data set, and extract feature information from it;

[0008] S2, using the boosted regression tree algorithm to select key risk factors from the dam accident dataset;

[0009] S3. Based on key risk factors, a network structure of the dam risk model is constructed using a structural learning algorithm;

[0010] S4. Based on the network structure, determine the network parameters of the dam risk model through parameter learning algorithm;

[0011] S5. Evaluate the performance of the dam risk model.

[0012] As a preferred technical solution of the present invention, S1 is specifically:

[0013] S11. Remove outliers from the original data set to obtain a dam accident data set containing N samples;

[0014] S12. Extract the response variable Y and the complete set of predictor variables X containing all risk factors from the dam accident data set = {x1, x2, ..., x n The response variable Y is the dam safety state variable, and the safety state includes at least the accident state and the non-accident state.

[0015] As a preferred technical solution of the present invention, S2 is specifically:

[0016] S21, the dam accident data set is randomly divided into K data subsets of the same size using the K-fold cross-validation method, and the λth data subset is based on the complete prediction variable set X={x1,x2,...,x n Fit the BRT model and obtain the initial predicted value of the response variable corresponding to the jth data sample

[0017] S22, using binary cross entropy to calculate the initial prediction deviation D of the λth data subset λ0 , take the average of K data subsets to obtain the initial prediction deviation D0 of the BRT model;

[0018] S23, from the complete set of predictor variables X = {x1, x2, ..., x n Eliminate single risk factor x i , get the predictor variable subset X i =X\{x i}, based on X i Fit the new BRT model to get the new prediction deviation D i , for the complete set of predictor variables X={x1,x2,...,x n}, and the prediction deviation D corresponding to each risk factor is obtained. i, and then integrate the contribution of each risk factor to the BRT model prediction deviation ΔD i ;

[0019] S24, from the complete set of predictor variables X = {x1, x2, ..., x n}, gradually eliminate t risk factors, and the elimination order is determined by the contribution of each risk factor to the prediction deviation ΔD i Determine, where ΔD i The smallest risk factor is eliminated first, thus obtaining the change of BRT model prediction deviation with the number of variables eliminated ΔD t ;

[0020] S25. According to the noise threshold criterion, when the criterion is met, the corresponding t is the number of risk factors that need to be eliminated. At this time, the prediction variable set X={x1,x2,...,x n The remaining risk factors in} are key risk factors, and their number is nt.

[0021] As a preferred technical solution of the present invention, the BRT model is based on the initial prediction value of the jth sample in the λth data subset given by the complete prediction variable set X. for:

[0022]

[0023] Where M is the number of tree models in the BRT model, T(x;γ m ) represents the mth tree model, γ m 、ω m are the number and weight of split points corresponding to the m-th tree model respectively;

[0024] The initial prediction deviation D of the λth data subset λ0 And the initial prediction deviation D0 of the BRT model is:

[0025]

[0026]

[0027]

[0028] Where y λj is the observed value of the jth sample in the λth data subset, is the initial prediction deviation corresponding to the jth sample in the λth data subset;

[0029] The BRT model is based on a subset of predictor variables X i =X\{x i}'s prediction deviation D i , and each risk factor xi Contribution to BRT model prediction bias ΔD i They are:

[0030]

[0031]

[0032] Where D λi To remove risk factor x i The prediction deviation corresponding to the last λ data subset;

[0033] The change of the BRT model prediction deviation with the number of variables removed t ΔD t for:

[0034]

[0035]

[0036] Where D λt D is the prediction deviation corresponding to the λth data subset after removing t risk factors, t is the average prediction deviation after removing t risk factors;

[0037] The noise threshold criterion is as follows:

[0038] ΔD t >SE(D0)

[0039]

[0040] Where SE(D0) is the standard error of the initial prediction deviation D0.

[0041] As a preferred technical solution of the present invention, S3 is specifically:

[0042] S31. Randomly divide the dam accident dataset into a training set and a validation set, with the training set accounting for 70% and the validation set accounting for 30%;

[0043] S32. The dam safety status and the selected key risk factors are used as nodes of the dam risk model, and the status of each node is divided;

[0044] S33. Based on the training set, the Peter-Clark algorithm is used to construct the network structure of the dam risk model.

[0045] As a preferred technical solution of the present invention, the steps of constructing the network structure of the dam risk model using the Peter-Clark algorithm are as follows:

[0046] (1) All nodes are fully connected to obtain a fully connected undirected graph;

[0047] (2) Given a set of constraints Z, for each pair of connected nodes C i and C j Iteratively perform conditional independence tests, where the constraint set Z consists of the r common adjacent nodes of the pair of nodes, with r increasing from zero to the number of adjacent edges of the pair of nodes; conditionally independent connections are deleted through the independence test, and the entire iterative process is carried out until all conditionally independent connections are deleted, thereby obtaining the network skeleton;

[0048] (3) Search for a V-shaped structure in the network skeleton and orient the remaining connections between nodes according to the principle of not generating any loops and preventing the generation of new V-shaped structures; a V-shaped structure is a connection structure in which two nodes point to the same node.

[0049] As a preferred technical solution of the present invention, the independence test includes: given the original hypothesis H0, C i and C j Conditional independence on the constraint set Z; calculate the likelihood ratio test statistic L and find its χ2 under the condition of (r-1)×(s-1)×v degrees of freedom. 2 The corresponding p-value on the distribution, if the p-value is greater than the significance level α CI , then the original hypothesis H0 is established, and the connection between the pair of nodes is deleted, where r, s and v are the nodes C i and C j and the number of states in the constraint set; the statistic L is calculated as follows:

[0050]

[0051] Where: Indicates that C is satisfied in the training set i with C j The state values of are a and b respectively, and the state combination of constraint set Z is the number of samples of c; To satisfy C in the training set i The number of samples whose state value is a and whose state combination of constraint set Z is c; To satisfy C in the training set j The number of samples whose state value is b and whose state combination of constraint set Z is c; Indicates the number of samples in the training set whose state combination is c and satisfies the constraint set Z.

[0052] As a preferred technical solution of the present invention, S4 specifically comprises: determining the network parameters of the dam risk model, i.e., the conditional probability table, using the expectation maximum algorithm based on the training set and the network structure; the iterative process of determining the network parameters using the expectation maximum algorithm is:

[0053] (1) Arbitrarily set the initial network parameters θ 0 , let θ t =θ 0 ;

[0054] (2) Through steps (3) and (4), at θ t Based on this, the network parameters are updated to θ t+1 ;

[0055] (3) The specific steps for calculating the expectation are as follows: a) Using θ t Calculate the conditional probability distribution P(e*|e,θ) of the missing value e* of the sample t ); b) P(e*|e,θ t ) is assigned as a weight to the missing value e* to obtain a supplementary sample, which is added to the original dataset to obtain a complete dataset;

[0056] (4) The maximization step is specifically to solve the network parameters that maximize the likelihood estimate of the complete data set in step (3) b), which is the new parameter θ t+1 ;

[0057] (5) If convergence is achieved and stable parameter estimates are obtained, the algorithm stops; if not, let θ t =θ t+1 , return to step (2).

[0058] As an optimal technical solution of the present invention, the conditional probability distribution P(e*|e,θ t ) is calculated as follows:

[0059]

[0060] Where: e is the training set data, θ t are the network parameters in the iterative process.

[0061] As a preferred technical solution of the present invention, the S5 is specifically:

[0062] S51. For the dam risk model constructed based on the training set, the prediction performance of the model is evaluated using the training set and the validation set respectively. The evaluation indicators include the overall accuracy OA score and F1 score.

[0063] S52. The parsimony of the model was evaluated using the dam accident dataset. The evaluation indicators included the Akaike information criterion criterion, namely the AIC criterion, and the Bayesian information criterion criterion, namely the BIC criterion.

[0064] As a preferred technical solution of the present invention, the OA and F1 score calculation formulas are as follows:

[0065]

[0066]

[0067]

[0068]

[0069] where TP and TN are the numbers of correctly predicted failed and non-failed dams, respectively; FP is the number of non-failed dams classified as failed; FN is the number of failed dams classified as non-failed; Prec is the precision, Rec is the recall, and the harmonic mean of the two is the F1 score.

[0070] The AIC and BIC calculation formulas are as follows:

[0071]

[0072]

[0073]

[0074] Where n is the number of nodes in the Bayesian network model; q i is the i-th variable x i The number of combinations of state values of the parent node; r i is x i The number of state values; N is the number of samples in the data set; N ijk In the data set, the parent node is the jth value, and the node x i is the number of samples with the kth value; In the data set, node x i The parent node is the number of samples under the j-th value.

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] 1. Based on the noise threshold criterion, the present invention uses the enhanced regression tree algorithm to eliminate risk factors that have little contribution to model prediction. This provides a quantitative standard for automatically determining the types and numbers of key risk factors, which can effectively improve the accuracy of variable selection and solve the subjective problem in existing variable selection methods.

[0077] 2. Based on optimized variable selection, the present invention utilizes structural learning algorithms and parameter learning algorithms to comprehensively explore the correlation between variables and accurately quantify the degree of correlation between variables, providing an objective network construction method that can improve model quality and effectively reduce modeling difficulty compared with existing network construction methods.

[0078] 3. The modeling method proposed in this invention is data-driven and integrates multiple machine learning methods. It has the characteristics of quantification, integration, and intelligence. It can not only improve the reliability of the dam risk model based on the Bayesian network, but also provide a reference for risk modeling problems in other engineering fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 A schematic diagram of a basic implementation flow of an embodiment of the present invention;

[0080] Figure 2 A schematic diagram of the variable selection principle of an embodiment of the present invention;

[0081] Figure 3 A schematic diagram of the network structure construction principle of an embodiment of the present invention;

[0082] Figure 4 Schematic diagram of the network parameter determination principle according to an embodiment of the present invention. DETAILED DESCRIPTION

[0083] To make the objectives, technical solutions, and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0084] The present invention combines the statistical data of earth-rock dam accidents to provide an intelligent modeling method of dam risk Bayesian network model integrating machine learning, such as Figure 1 As shown, the method includes:

[0085] S1, obtain dam accident dataset and extract feature information;

[0086] S2, based on the dam accident dataset, uses the boosted regression tree algorithm to select key risk factors;

[0087] S3, using the selected risk factors, constructs the network structure of the model through the structure learning algorithm;

[0088] S4, based on the constructed network structure, determines the network parameters of the model through parameter learning algorithm;

[0089] S5, evaluate the performance of the constructed dam risk model.

[0090] Among them, the dam risk model is a model built based on Bayesian network.

[0091] Furthermore, the S1 specifically includes:

[0092] S11, remove outliers from the statistics of earth-rock dam accidents and obtain an earth-rock dam accident dataset containing 760 samples;

[0093] S12, extract the response variable Y (i.e., the safety status of the earth-rock dam) and the prediction variable set X containing 25 risk factors from the earth-rock dam accident data set. 25}.

[0094] like Figure 2 As shown, the S2 specifically includes:

[0095] S21, the 10-fold cross-validation method is used to randomly divide the earth-rock dam accident data set into 10 data subsets of equal size. For the λth data subset, the complete prediction variable set X={x1,x2,...,x 25 Fit the BRT model and obtain the initial predicted value of the response variable corresponding to the jth data sample

[0096] S22, based on S21, uses binary cross entropy to calculate the initial prediction deviation D of the λth data subset λ0 , take the average of K data subsets to obtain the initial prediction deviation D0 of the BRT model;

[0097] S23, from the set of predictor variables X={x1,x2,...,x 25 Eliminate single risk factor x i , get the predictor variable subset X i =X\{x i}, based on X i Fit the new BRT model to get the new prediction deviation D i , and then the contribution of each risk factor to the BRT model prediction deviation ΔD is obtained i ;

[0098] S24, from the set of predictor variables X={x1,x2,...,x 25}, gradually eliminate t risk factors, and the elimination order is determined by the contribution of each risk factor to the prediction deviation ΔD i Determine, ΔD i The smallest risk factor is eliminated first, thus obtaining the change of BRT model prediction deviation with the number of variables eliminated ΔD t ;

[0099] S25, according to the noise threshold criterion, when the criterion is met, the corresponding t is the number of risk factors that need to be eliminated. At this time, the prediction variable set X={x1,x2,...,x 25 The remaining risk factors in} are key risk factors, and their number is 25-t. In this embodiment, t=13, that is, the number of key risk factors is 12.

[0100] Specifically, the BRT model described in S21 is based on the complete set of predictor variables X, giving the initial predicted value of the j-th sample in the λ-th data subset as follows:

[0101]

[0102] Where: M is the number of tree models in the BRT model;

[0103] T(x;γ m ) represents the mth tree model;

[0104] γ m 、ω m are the number and weight of split points corresponding to the m-th tree model respectively;

[0105] Specifically, the initial prediction deviation D of the λth data subset in S22 is λ0 And the initial prediction deviation D0 of the BRT model is as follows:

[0106]

[0107]

[0108]

[0109] Where: y λj is the observation value of the jth sample in the λth data subset;

[0110] is the initial prediction deviation corresponding to the jth sample in the λth data subset;

[0111] Specifically, the BRT model described in S23 is based on the predictor variable subset X i =X\{x i}'s prediction deviation D i , and each risk factor x i Contribution to BRT model prediction bias ΔD i They are:

[0112]

[0113]

[0114] Where: D λi To remove risk factor x i The prediction deviation corresponding to the last λ data subsets.

[0115] Specifically, the change in the BRT model prediction deviation as the number of variables removed t is ΔD t for:

[0116]

[0117]

[0118] Where: D λt is the prediction deviation corresponding to the λth data subset after removing t risk factors;

[0119] D t is the average prediction deviation after removing t risk factors.

[0120] Specifically, the noise threshold criterion in S25 is as follows:

[0121] ΔD t >SE(D0)

[0122]

[0123] Where: SE(D0) is the standard error (SE) of the initial prediction deviation D0.

[0124] Furthermore, the S3 specifically includes:

[0125] S31, the earth-rock dam accident dataset is randomly divided into a training set (70%) and a validation set (30%);

[0126] S32, the safety status of earth-rock dam and the selected 12 key risk factors are used as nodes of the dam risk model, and the status of each node is divided;

[0127] S33, based on the training set, uses the Peter-Clark (PC) algorithm to build the network structure of the model

[0128] Specifically, the nodes required for constructing the model described in S32 include failure modes in addition to the dam safety status and the key risk factors selected in S2. These nodes and their status are obtained from the dam accident dataset.

[0129] like Figure 3 As shown, the process of constructing the network structure by the PC algorithm described in S33 is as follows:

[0130] (1) All nodes are fully connected to obtain a fully connected undirected graph;

[0131] (2) Given a set of constraints Z, for each pair of connected nodes (C i and C j ) Iteratively perform conditional independence (CI) testing, where the constraint set Z consists of the r common neighbors of a pair of nodes, where r increases from zero to the number of neighbors of the pair. Conditionally independent connections are deleted through the CI test, and the entire iterative process is repeated until all conditionally independent connections are deleted, thus obtaining the skeleton of the network.

[0132] (3) Search for V structures such as A→B←E in the network skeleton, and orient the remaining connections between nodes according to the principle of not generating any cycles and preventing the generation of new V structures.

[0133] Specifically, the CI test includes: given the null hypothesis H0, C i and C j Conditional independence on the constraint set Z; calculate the likelihood ratio test statistic L and find its χ2 under the condition of (r-1)×(s-1)×v degrees of freedom. 2 The corresponding p-value on the distribution, if the p-value is greater than the significance level α CI , then the original hypothesis H0 is established, and the connection between the pair of nodes is deleted, where r, s and v are the nodes C i and C j and the number of states in the constraint set. The statistic L is calculated as follows:

[0134]

[0135] Where: Indicates that the data (training set) satisfies C i with C j The state values of are a and b respectively, and the state combination of constraint set Z is the number of samples of c; To satisfy C in the training set i The number of samples whose state value is a and whose state combination of constraint set Z is c; To satisfy C in the training set j The number of samples whose state value is b and whose state combination of constraint set Z is c; Indicates the number of samples in the training set whose state combination is c and satisfies the constraint set Z.

[0136] like Figure 4 As shown, S4 specifically includes: based on the training set and the constructed network structure, using the Expectation Maximum (EM) algorithm to determine the network parameters of the model (i.e., the conditional probability table). The iterative process of the EM algorithm to determine the network parameters is as follows:

[0137] (1) Arbitrarily set the initial network parameters θ 0 , let θ t =θ 0 ;

[0138] (2) Through steps (3) and (4), at θ t Based on this, the network parameters are updated to θ t+1 ;

[0139] (3) Expectation (E) step: a) Using θ t Calculate the conditional probability distribution P(e*|e,θ) of the missing value e* of the sample t ); b) P(e*|e,θ t ) is assigned as a weight to the missing value e* to obtain a supplementary sample, which is added to the original dataset to obtain a complete dataset;

[0140] (4) Maximization (M) step: solve the network parameters that maximize the likelihood estimate of the complete data set in step (3) b), which is the new parameter θ t+1 .

[0141] (5) If convergence is achieved and stable parameter estimates are obtained, the algorithm stops; if not, let θ t =θ t+1 , return to step (2).

[0142] Specifically, the conditional probability distribution of the missing value e* is P(e*|e,θ t ) is calculated as follows:

[0143]

[0144] Where: e represents data (training set), θ t are the network parameters in the iterative process.

[0145] Furthermore, the S5 specifically includes:

[0146] S51, for the dam risk model constructed based on the training set, the prediction performance of the model is evaluated using the training set and validation set respectively. The evaluation indicators include overall accuracy (OA) and F1 score.

[0147] S52, the dam accident data set was used to evaluate the parsimony of the model, and the evaluation indicators included the Akaikeinformation criterion (AIC) criterion and the Bayesian information criterion (BIC) criterion.

[0148] Specifically, the calculation formulas for OA and F1 scores are as follows:

[0149]

[0150]

[0151]

[0152]

[0153] Where TP and TN represent the number of correctly predicted failed and non-failed dams; FP represents the number of non-failed dams classified as failed; FN represents the number of failed dams classified as non-failed; Prec is the precision, Rec is the recall, and the harmonic mean of the two is the F1 score.

[0154] Specifically, the AIC and BIC calculation formulas are as follows:

[0155]

[0156]

[0157]

[0158] Where: n is the number of nodes in the BN model; q i Represents the i-th variable x i The number of combinations of state values of the parent node; r i is x i The number of state values; N is the number of samples in the data set; N ijk Indicates that in the data set, the parent node is the jth value, and the node x i is the number of samples with the kth value; In the data set, node x i The parent node is the number of samples under the j-th value.

[0159] The above descriptions are merely embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A dam risk Bayesian network modeling method integrating machine learning, characterized in that: The following steps are involved: S1. Eliminate outliers from the original data set containing historical data, obtain the dam accident data set, and extract feature information from it; S2, using the boosted regression tree algorithm to select key risk factors from the dam accident dataset; S3. Based on key risk factors, a network structure of the dam risk model is constructed using a structural learning algorithm; S4. Based on the network structure, determine the network parameters of the dam risk model through parameter learning algorithm; S5. Evaluate the performance of the dam risk model; The S2 is specifically: S21. Use K-fold cross validation method to randomly divide the dam accident data set into K data subsets of equal size. A subset of data based on the full set of predictors Fit the BRT model and get The initial predicted value of the response variable corresponding to the data sample ; S22, using binary cross entropy to calculate the Initial prediction bias for a subset of data , take the average of K data subsets to get the initial prediction deviation of the BRT model ; S23. From the complete set of predictors Eliminating a single risk factor , and obtain a subset of predictor variables ,based on Fitting a new BRT model to obtain a new prediction bias , for the full set of predictors Eliminate each risk factor and obtain the prediction deviation corresponding to each risk factor , and then integrate the contribution of each risk factor to the BRT model prediction bias ; S24. From the complete set of predictors Gradually eliminate risk factors, and the order of elimination is determined by the contribution of each risk factor to the prediction bias. Decision, among which The smallest risk factor is eliminated first, thus obtaining the change of BRT model prediction bias with the number of variables eliminated ; S25, according to the noise threshold criterion, the corresponding is the number of risk factors that need to be eliminated, and the set of predictor variables is The remaining risk factors are key risk factors, and their number is .

2. The dam risk Bayesian network modeling method integrating machine learning according to claim 1 is characterized in that: The S1 is specifically: S11. Remove outliers from the original data set to obtain a dam accident data set containing N samples; S12. Extract the response variable Y and the complete set of predictor variables containing all risk factors from the dam accident dataset ; The response variable Y is the dam safety state variable, and the safety state includes at least the accident state and the non-accident state.

3. The dam risk Bayesian network modeling method integrating machine learning according to claim 1 is characterized in that: The BRT model is based on a complete set of predictor variables Given In the data subset The initial prediction value of the sample for: Where, is the number of tree models in the BRT model, Indicates the A tree model, 、 Respectively The number and weight of split points corresponding to each tree model; The said Initial prediction bias for a subset of data and the initial prediction bias of the BRT model for: Where, For the In the data subset The observed value of the sample, For the In the data subset The initial prediction deviation corresponding to the sample; The BRT model is based on a subset of predictor variables Prediction bias , and each risk factor Contribution to BRT model prediction bias They are: Where, To remove risk factors Later The prediction deviation corresponding to the data subset; The BRT model prediction bias changes with the number of variables removed Changes for: Where, To remove After the risk factor The prediction deviation corresponding to the data subset, To remove The average prediction bias after 3 risk factors; The noise threshold criterion is as follows: Where, is the initial prediction deviation The standard error of .

4. The dam risk Bayesian network modeling method integrating machine learning according to claim 1 is characterized in that: The S3 is specifically: S31. The dam accident dataset is randomly divided into a training set and a validation set, with the training set accounting for 70% and the validation set accounting for 30%; S32. The dam safety status and the selected key risk factors are used as nodes of the dam risk model, and the status of each node is divided; S33. Based on the training set, the Peter-Clark algorithm is used to construct the network structure of the dam risk model.

5. The dam risk Bayesian network modeling method integrating machine learning according to claim 4 is characterized in that: The steps for constructing the network structure of the dam risk model using the Peter-Clark algorithm are as follows: (1) All nodes are fully connected to obtain a fully connected undirected graph; (2) Given a set of constraints In the case of and Iteratively perform conditional independence tests, constraint set By the pair of nodes Common adjacent nodes, The number of adjacent edges of the pair of nodes is increased from zero; conditionally independent connections are deleted through independence test, and the entire iterative process is carried out until all conditionally independent connections are deleted, thereby obtaining the network skeleton; (3) Search for a V-shaped structure in the network skeleton and orient the remaining connections between nodes according to the principle of not generating any loops and preventing the generation of new V-shaped structures; a V-shaped structure is a connection structure in which two nodes point to the same node.

6. The dam risk Bayesian network modeling method integrating machine learning according to claim 5 is characterized in that: The independence test includes: given the null hypothesis H0, and About Constraint Sets Conditional independence; computing the likelihood ratio test statistic And find out its degree of freedom in obeying of The corresponding distribution Value, if The value is greater than the significance level , then the original hypothesis H0 is established, and the connection between the pair of nodes is deleted, where 、 and Node and And the number of states in the constraint set; statistics The calculation is as follows: Where: Indicates that the training set satisfies and The status values are and , and the constraint set The state combination is The number of samples; To meet the training needs The status value is And the constraint set The state combination is The number of samples; To meet the training needs The status value is And the constraint set The state combination is The number of samples; Indicates that the constraint set is satisfied in the training set The state combination is The number of samples.

7. The dam risk Bayesian network modeling method integrating machine learning according to claim 4 is characterized in that: Specifically, S4 includes: determining the network parameters of the dam risk model, i.e., the conditional probability table, using the expectation maximum algorithm based on the training set and the network structure; the iterative process of determining the network parameters using the expectation maximum algorithm is: (1) Arbitrary setting of initial network parameters ,make ; (2) Through steps (3) and (4), Based on this, the network parameters are updated as ; (3) The specific steps for calculating the expectation are: a) using Calculate missing values for samples The conditional probability distribution of ; b) Assign missing values as weights Get a supplementary sample, add the sample to the original data set and get a complete data set; (4) The maximization step is to find the network parameters that maximize the likelihood estimate of the complete data set in step (3) b), which is the new parameter ; (5) If convergence is achieved and stable parameter estimates are obtained, the algorithm stops; if not, let , return to step (2); The missing value The conditional probability distribution of The calculation method is: Where, is the training set data, are the network parameters in the iterative process.

8. The dam risk Bayesian network modeling method integrating machine learning according to claim 4 is characterized in that: The S5 is specifically: S51. For the dam risk model constructed based on the training set, the prediction performance of the model is evaluated using the training set and the validation set respectively. The evaluation indicators include the overall accuracy OA score and F1 score. S52. The parsimony of the model was evaluated using the dam accident dataset. The evaluation indicators included the Akaike information criterion criterion, i.e., the AIC criterion, and the Bayesian information criterion criterion, i.e., the BIC criterion.

9. The dam risk Bayesian network modeling method integrating machine learning according to claim 8 is characterized in that: The OA and F1 score calculation formulas are as follows: Where, and are the number of dams that failed and did not fail that were correctly predicted, respectively; is the number of non-failed dams classified as failed; is the number of failed dams classified as non-failed; Prec is precision, Rec is recall, and the harmonic mean of the two is the F1 score; The AIC and BIC calculation formulas are as follows: Where, is the number of nodes in the Bayesian network model; For the variables The number of combinations of state values of the parent node; for The number of state values; is the number of samples in the dataset; In the data set, the parent node is Under this value, the node For the The number of samples with the same value; For the data set, node The parent node is The number of samples under the given value.

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