A two-stage method for determining dam deformation characteristics using fused parameter inversion

Abstract

This invention provides a two-stage method for determining dam deformation characteristics through fusion parameter inversion, relating to the field of dam safety monitoring. S1 involves collecting historical dam monitoring data and related design information; S2 constructing a finite element proxy model based on multi-output support vector regression, combined with a multi-objective gray wolf optimization algorithm for multi-measuring point parameter inversion; S3 calculating physical driving factors, introducing spatial information, and constructing an initial high-dimensional feature set; S4 employing a two-stage feature selection strategy to obtain the optimal factor set; and S5 constructing a deformation analysis model using the optimal feature factor set selected in S4. This method achieves a deep integration of the dam's mechanical evolution mechanism and machine learning models, fundamentally improving the physical interpretability, statistical robustness, and modeling efficiency of the optimized feature set.

Description

Technical Field

[0001] This invention relates to the field of dam safety monitoring, and in particular to a two-stage method for determining dam deformation characteristics using fused parameter inversion. Background Technology

[0002] Dam deformation is a key indicator reflecting its structural safety and operational status. Traditional deformation prediction models are often constructed independently for single measuring points, making it difficult to effectively characterize the multi-point correlated deformation features of the dam's overall structure under coordinated load-bearing. While the introduction of spatial coordinates of measuring points and complex multi-source environmental factors can reflect differences in measuring point locations and significantly enhance the characterization of multi-point dam deformation with the advancement of dam safety monitoring technology, the resulting high-dimensional input leads to severe feature redundancy. A large number of irrelevant or weakly correlated redundant features not only drastically increase model complexity but also easily trigger the curse of dimensionality and model overfitting.

[0003] Existing feature selection methods typically employ fixed step sizes, making it difficult to balance selection efficiency and accuracy. Furthermore, single evaluations are highly susceptible to random disturbances and lack statistical stability, resulting in insufficient generalization ability of the selected factor set when facing complex working conditions. On the other hand, existing methods often rely solely on pure data-driven approaches, lacking the integration of physical information such as dam material parameters, leading to weak interpretability of the features.

[0004] Therefore, a two-stage dam deformation characteristic determination method based on fused parameter inversion is needed to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a two-stage method for determining dam deformation characteristics by integrating parameter inversion. By constructing a finite element surrogate model, combining a multi-output support vector regression (MTSVR) surrogate model with a multi-objective gray wolf optimization algorithm (MOGWO) to invert monitoring point parameters and construct physical driving factors, a two-stage feature selection strategy is proposed to determine the optimal feature subset that balances prediction performance and model simplicity. This method effectively integrates physical driving and data driving, significantly improving the interpretability, robustness, and modeling efficiency of the feature set.

[0006] To achieve the above objectives, this invention provides a two-stage method for determining dam deformation characteristics through fusion parameter inversion, comprising the following steps: S1: Collect historical monitoring data and relevant design information of the dam, establish a finite element model of the dam, and record the plane coordinates of the monitoring points. ; S2: Construct an MTSVR finite element proxy model and combine it with the MOGWO optimization algorithm to invert the mechanical parameters of the dam materials and obtain the optimal material parameters; S3: Calculate the physical driving factors, introduce spatial information, and construct an initial high-dimensional feature set; S4: Use a two-stage feature selection strategy to obtain the optimal feature factor set; S5: Construct a deformation analysis model using the optimal set of feature factors selected in S4.

[0007] Preferably, the monitoring data in S1 includes environmental quantities, specifically including: upstream of the dam. Water level at any time , No. Displacement monitoring values ​​at each monitoring point and temperature monitoring data , , This represents the number of measurement points. Relevant design data includes the range of dam material parameters. 1. Geometric dimensions and related design data of the dam section Number the parameters to be inverted. m The number of parameters to be inverted is determined, and a finite element model of the dam is established.

[0008] Preferably, in S2, the trained multi-output support vector regression model MTSVR is used as a finite element surrogate model. The specific process of constructing the finite element surrogate model is as follows: Latin hypercube sampling is used to generate samples within the material parameter range. N Group of parameters combined samples, let the first group of parameters be the sample. The sample vector of material parameters is Combined with the water level in front of the dam Forming input samples Subsequently, these N sets of input samples are successively substituted into the dam finite element model for forward analysis to obtain the corresponding... The displacement response values ​​at each measuring point form a parameter displacement sample set. A nonlinear mapping from input parameters to the displacement of monitoring points is established using the MTSVR finite element proxy model: ; in Indicates the relationship with the first The support vector sub-model corresponding to each monitoring point is specifically represented as follows: in and They are respectively with the first Each monitoring point corresponds to a weight vector and bias term in the support vector sub-model; For kernel function mapping; Corresponding to the The support vector sub-models corresponding to each monitoring point are obtained by solving a convex quadratic programming problem: ; Add constraints: ; and These are slack variables; For the first The sample at the th Displacement values ​​simulated by the finite element model at each monitoring point; For the first One input sample; This is a regularization parameter that controls the balance between model complexity and training error; For insensitive loss parameters; This is a kernel function mapping.

[0009] Preferably, in S2, the multi-objective gray wolf optimization algorithm (MOGWO) is used for parameter inversion. The specific process is as follows: S21: Constructing a multi-objective function: ; in The parameters to be inverted, m The number of parameters to be inverted. Let be the objective function. The number of measuring points; if the measured water level in front of the dam at time t is... Input for constructing parameter inversion for: ; The first result is obtained based on the finite element proxy model. t Time of the first j Predicted displacement corresponding to each monitoring point for: ; objective function Defined as the first Normalized mean square error between the calculated and monitored displacement values ​​at each monitoring point: ; In the formula: for t The time corresponding to the water level below the first The monitored displacement values ​​corresponding to each monitoring point; Total number of monitoring moments; S22: The MOGWO algorithm is used for parameter optimization. An external archive is introduced to store non-dominated solutions, and an alpha wolf is selected from the archive through a leader selection mechanism. Guiding population renewal: ; in: ; coefficient vector Decrease linearly from 2 to 0. for Random variables whose intervals are all distributed; In the formula For the first The individual position of a generation; They are respectively The wolf's position vector; and Let be the coefficient vector, respectively by Calculated; for The distance vector between the wolf and the alpha wolf; The convergence factor decreases linearly with iteration; S23: Iterate until the maximum algebraic number or convergence condition is reached, and select the optimal material parameter set. .

[0010] Preferably, the specific process in S3 is as follows: Based on the optimal material parameter set obtained in S23 Substitute the data into the finite element proxy model to calculate the monitoring date. Corresponding physical driving factors Construct an initial high-dimensional feature set: ; ; ; ; in For monitoring points exist The surrogate model calculates the value at time 1. To monitor the day before The average temperature of the day The value is set as follows: ; The time-dependent characteristics of the dam, The cumulative duration from the initial monitoring day to the current day, Low-dimensional feature set, For the introduced nonlinear power parameter, This indicates that a Cartesian operation is performed on the set of physical factors and the set of spatial features.

[0011] Preferably, in the first stage of S4, the BorutaShap algorithm is used to generate shadow features for initial feature screening, and irrelevant and redundant features are removed to obtain the first stage feature set; in the second stage, an enhanced incremental feature selection mechanism based on multi-round random seed perturbation is introduced, and incremental verification is performed according to the stability ranking of feature importance, and finally the optimal feature factor set for each monitoring point is determined.

[0012] Preferably, the first-stage feature selection process specifically includes the following steps: S41: For the initial feature set primitive features The shadow features are generated by randomly rearranging the sample order. Combined to form an extended feature set ; in , where 'a' is the number of features. h For feature index; S42: Based on extended feature set Train the gradient boosting decision tree model and calculate features. Shapley value of marginal contribution : ; in, Features Shapley value; For features not included Any subset of features; and These represent the number of features in the corresponding feature subset and the expanded feature set, respectively. This is the prediction utility function of the model under a specific subset of features; S43: The maximum Shapley value among all shadow features is... ,satisfy and ; The significance probability value is used for the statistical significance test. Features with a Shapley value greater than a certain threshold are retained based on the statistical significance test, forming the first-stage feature set. .

[0013] Preferably, in the second-stage incremental feature selection mechanism Voting-IFS, the specific calculation of stability ranking includes the following steps: A41: Set the number of independent random seed perturbation rounds to... For the first s wheel( The regression model is trained using the corresponding random seed, and the first-stage feature set is calculated. The Shapley values ​​of each feature in the corresponding round; A42: Calculate features by combining all rounds and all samples. Global cumulative absolute average score : ; A43: According to Sort all features in descending order to obtain a stable sorted list: ; in The total number of samples in the training set. ; Indicates the first In the wheel disturbance model, the first Features corresponding to each monitoring point The Shapley value.

[0014] Preferably, a stable sorted list is used. Perform incremental feature selection to determine the optimal feature factor set The specific process is as follows: Initialize empty feature subset ,according to Prioritize features by performing forward incremental selection, adding features one by one to construct nested feature subset sequences. ; through feature subset sequences Train the model and calculate the mean squared error on the validation set. Record the global minimum mean square error generated during all incremental processes. Introducing tolerance parameters Find the minimum feature subset index that satisfies the accuracy compromise condition. : Before selection The set of features constitutes the optimal feature factor set. ;in .

[0015] Therefore, the present invention employs the above-mentioned two-stage dam deformation characteristic determination method based on fusion parameter inversion, and the technical effects are as follows: (1) This invention innovatively integrates physical driving and data driving. By constructing a finite element proxy model and combining the multi-output support vector regression (MTSVR) proxy model with the multi-objective gray wolf optimization algorithm (MOGWO) to invert the monitoring point parameters, a physical driving factor is constructed, which effectively solves the problem of lack of physical interpretability in traditional pure data-driven methods.

[0016] (2) This invention abandons the limitations of independent modeling of a single measurement point or early feature splicing, and innovatively proposes a two-stage robust feature selection strategy: the first stage uses the BorutaShap algorithm for global robust initial screening, and eliminates noise and redundant features through shadow feature comparison and statistical test; the second stage introduces the enhanced incremental feature selection Voting-IFS mechanism based on multi-round random seed perturbation, and determines the optimal feature subset that takes into account both model performance and feature parsimony performance based on feature importance stability ranking and forward incremental strategy, which significantly overcomes the redundant interference caused by high-dimensional spatiotemporal features, the low efficiency of traditional fixed step size screening, and the random instability of feature evaluation mechanism.

[0017] (3) This invention utilizes the selected optimal feature factor set to construct a deformation analysis model, which can fully explore the local spatial heterogeneity and global collaborative bearing evolution law among various measuring points of the dam, providing high-quality feature input for subsequent high-precision prediction of dam deformation. It is suitable for multi-measuring point deformation analysis of concrete dams that consider complex spatial coordinates and multi-source environmental information. Attached Figure Description

[0018] Figure 1 This is a flowchart of a two-stage dam deformation characteristic determination method based on fused parameter inversion according to the present invention; Figure 2 These are the environmental effect monitoring values ​​in the embodiments of the present invention; Figure 3 This is the finite element model in the embodiments of the present invention; Figure 4 This is a flowchart of the MTSVR-MOGWO multi-point inversion process in an embodiment of the present invention; Figure 5 This is a schematic diagram of the two-stage feature selection in an embodiment of the present invention; Figure 6 This is a graph showing the change in quantity of features in the screening process in an embodiment of the present invention. Detailed Implementation

[0019] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0021] Example 1 like Figure 1 As shown, this invention provides a two-stage method for determining dam deformation characteristics through fusion parameter inversion, comprising the following steps: S1: Collect historical monitoring data and relevant design information of the dam, and establish a finite element model of the dam, such as Figure 2 and Figure 3As shown, record the plane coordinates of the monitoring points. The monitoring data in S1 includes environmental quantities, specifically: upstream of the dam. Water level at any time , No. Displacement monitoring values ​​at each monitoring point and temperature monitoring data , , This represents the number of measurement points. Relevant design data includes the range of dam material parameters. 1. Geometric dimensions and related design data of the dam section Number the parameters to be inverted. m The number of parameters to be inverted is determined, and a finite element model of the dam is established.

[0022] S2: Construct an MTSVR finite element proxy model and combine it with the MOGWO optimization algorithm to invert the mechanical parameters of the dam materials and obtain the optimal material parameters; In S2, the trained multi-output support vector regression model MTSVR is used as a finite element proxy model. The specific process of constructing the finite element proxy model is as follows: Latin hypercube sampling is used to generate samples within the material parameter range. N Group of parameters combined samples, let the first group of parameters be the sample. The sample vector of material parameters is Combined with the water level in front of the dam Forming input samples Subsequently, these N sets of input samples are successively substituted into the dam finite element model for forward analysis to obtain the corresponding... The displacement response values ​​at each measuring point form a parameter displacement sample set. A nonlinear mapping from input parameters to the displacement of monitoring points is established using the MTSVR finite element proxy model: ; in Indicates the relationship with the first The support vector sub-model corresponding to each monitoring point is specifically represented as follows: in and They are respectively with the first Each monitoring point corresponds to a weight vector and bias term in the support vector sub-model; For kernel function mapping; Corresponding to the The support vector sub-models corresponding to each monitoring point are obtained by solving a convex quadratic programming problem: ; Add constraints: ; and These are slack variables; For the first The sample at the th Displacement values ​​simulated by the finite element model at each monitoring point; For the first One input sample; This is a regularization parameter that controls the balance between model complexity and training error; For insensitive loss parameters; This is a kernel function mapping.

[0023] In S2, the multi-objective gray wolf optimization algorithm (MOGWO) is used for parameter inversion, such as... Figure 4 The specific process is as follows: In S2, the multi-objective gray wolf optimization algorithm (MOGWO) is used for parameter inversion. The specific process is as follows: S21: Constructing a multi-objective function: ; in The parameters to be inverted, m The number of parameters to be inverted. Let be the objective function. The number of measuring points; if the measured water level in front of the dam at time t is... Input for constructing parameter inversion for: ; The first result is obtained based on the finite element proxy model. t Time of the first j Predicted displacement corresponding to each monitoring point for: ; objective function Defined as the first Normalized mean square error between the calculated and monitored displacement values ​​at each monitoring point: ; In the formula: for t The time corresponding to the water level below the first The monitored displacement values ​​corresponding to each monitoring point; Total number of monitoring moments; S22: The MOGWO algorithm is used for parameter optimization. An external archive is introduced to store non-dominated solutions, and an alpha wolf is selected from the archive through a leader selection mechanism. Guiding population renewal: ; in: ; coefficient vector Decrease linearly from 2 to 0. for Random variables whose intervals are all distributed; In the formula For the first The individual position of a generation; They are respectively The wolf's position vector; and Let be the coefficient vector, respectively by Calculated; for The distance vector between the wolf and the alpha wolf; The convergence factor decreases linearly with iteration; S23: Iterate until the maximum algebraic number or convergence condition is reached, and select the optimal material parameter set. .

[0024] S3: Calculate the physical driving factors, introduce spatial information, and construct an initial high-dimensional feature set; the specific process in S3 is as follows: based on the optimal material parameter set obtained in S23... Substitute the data into the finite element proxy model to calculate the monitoring date. Corresponding physical driving factors Construct an initial high-dimensional feature set: ; ; ; ; in For monitoring points exist The surrogate model calculates the value at time 1. To monitor the day before The average temperature of the day The value is set as follows: ; The time-dependent characteristics of the dam, The cumulative duration from the initial monitoring day to the current day, Low-dimensional feature set, For the introduced nonlinear power parameter, This indicates that a Cartesian operation is performed on the set of physical factors and the set of spatial features.

[0025] S4: A two-stage feature selection strategy is adopted to obtain the optimal feature factor set. In the first stage of S4, the BorutaShap algorithm is used to generate shadow features for initial feature screening, and irrelevant and redundant features are removed to obtain the first stage feature set. In the second stage, an enhanced incremental feature selection mechanism based on multi-round random seed perturbation is introduced, and incremental verification is performed according to the stability ranking of feature importance to finally determine the optimal feature factor set for each monitoring point.

[0026] like Figure 5 As shown, the first-stage feature selection process specifically includes the following steps: S41: For the initial feature set primitive features The shadow features are generated by randomly rearranging the sample order. Combined to form an extended feature set ; in , where 'a' is the number of features. h For feature index; S42: Based on extended feature set Train the gradient boosting decision tree model and calculate features. Shapley value of marginal contribution : ; in, Features Shapley value; For features not included Any subset of features; and These represent the number of features in the corresponding feature subset and the expanded feature set, respectively. This is the prediction utility function of the model under a specific subset of features; S43: The maximum Shapley value among all shadow features is... ,satisfy and ; The significance probability value is used for the statistical significance test. Features with a Shapley value greater than a certain threshold are retained based on the statistical significance test, forming the first-stage feature set. .

[0027] In the second-stage incremental feature selection mechanism Voting-IFS, the specific calculation of stability ranking includes the following steps: A41: Set the number of independent random seed perturbation rounds to... For the first s wheel( The regression model is trained using the corresponding random seed, and the first-stage feature set is calculated. The Shapley values ​​of each feature in the corresponding round; A42: Calculate features by combining all rounds and all samples. Global cumulative absolute average score : ; A43: According to Sort all features in descending order to obtain a stable sorted list: ; in The total number of samples in the training set. ; Indicates the first In the wheel disturbance model, the first Features corresponding to each monitoring point The Shapley value.

[0028] By stable sorting list Perform incremental feature selection to determine the optimal feature factor set The specific process is as follows: Initialize empty feature subset ,according to Prioritize features by performing forward incremental selection, adding features one by one to construct nested feature subset sequences. ; through feature subset sequences Train the model and calculate the mean squared error on the validation set. Record the global minimum mean square error generated during all incremental processes. Introducing tolerance parameters Find the minimum feature subset index that satisfies the accuracy compromise condition. : Before selection The set of features constitutes the optimal feature factor set. ;in The number of features changes during the final screening process as follows: Figure 6 As shown S5: Construct a deformation analysis model using the optimal set of feature factors selected in S4. This model can fully explore the local spatial heterogeneity and global collaborative bearing evolution law among various measuring points of the dam, providing high-quality feature input for high-precision prediction of dam deformation. It is extremely suitable for multi-measuring-point deformation analysis and feature determination of concrete dams considering complex spatial coordinates and multi-source environmental information.

[0029] Therefore, the present invention adopts the above-mentioned two-stage dam deformation feature determination method based on fusion parameter inversion, which realizes the deep integration of dam mechanical evolution mechanism and machine learning model, fundamentally improving the physical interpretability, statistical robustness and modeling efficiency of the optimized feature set.

[0030] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A two-stage method for determining dam deformation characteristics using fused parameter inversion, characterized in that, Includes the following steps: S1: Collect historical monitoring data and relevant design information for the dam, and record the plane coordinates of the monitoring points. Establish a finite element model of the dam; S2: Construct an MTSVR finite element proxy model and combine it with the MOGWO optimization algorithm to invert the mechanical parameters of the dam materials and obtain the optimal material parameters; S3: Calculate the physical driving factors, introduce spatial information, and construct an initial high-dimensional feature set; S4: Use a two-stage feature selection strategy to obtain the optimal feature factor set; S5: Construct a deformation analysis model using the optimal set of feature factors selected in S4.

2. The method for determining the deformation characteristics of a two-stage dam based on fused parameter inversion according to claim 1, characterized in that, The monitoring data in S1 includes environmental quantities, specifically: upstream of the dam. Water level at any time , No. Displacement monitoring values ​​at each monitoring point and temperature monitoring data , , This represents the number of measurement points. Relevant design data includes the range of dam material parameters.

1. Geometric dimensions and related design data of the dam section Number the parameters to be inverted. m The number of parameters to be inverted is determined, and a finite element model of the dam is established.

3. The method for determining the deformation characteristics of a two-stage dam based on fused parameter inversion according to claim 1, characterized in that, In S2, the trained multi-output support vector regression model MTSVR is used as a finite element proxy model. The specific process of constructing the finite element proxy model is as follows: Latin hypercube sampling is used to generate samples within the material parameter range. N Group of parameters combined samples, let the first group of parameters be the sample. The sample vector of material parameters is Combined with the water level in front of the dam Forming input samples ; Subsequently, these N sets of input samples were successively substituted into the dam finite element model for forward analysis to obtain the corresponding... The displacement response values ​​at each measuring point form a parameter displacement sample set. A nonlinear mapping from input parameters to the displacement of monitoring points is established using the MTSVR finite element proxy model: ； in Indicates the relationship with the first The support vector sub-model corresponding to each monitoring point is specifically represented as follows: in and They are respectively with the first Each monitoring point corresponds to a weight vector and bias term in the support vector sub-model; For kernel function mapping; Corresponding to the The support vector sub-models corresponding to each monitoring point are obtained by solving a convex quadratic programming problem: ； Add constraints: ； and These are slack variables; For the first The sample at the th Displacement values ​​simulated by the finite element model at each monitoring point; For the first One input sample; This is a regularization parameter that controls the balance between model complexity and training error; For insensitive loss parameters; This is a kernel function mapping.

4. The method for determining the deformation characteristics of a two-stage dam based on fused parameter inversion according to claim 1, characterized in that, In S2, the multi-objective gray wolf optimization algorithm (MOGWO) is used for parameter inversion. The specific process is as follows: S21: Constructing a multi-objective function: ; in The parameters to be inverted, m The number of parameters to be inverted. Let be the objective function. The number of measuring points; if the measured water level in front of the dam at time t is... Input for constructing parameter inversion for: ； The first result is obtained based on the finite element proxy model. t Time of the first j Predicted displacement corresponding to each monitoring point for: ； objective function Defined as the first Normalized mean square error between the calculated and monitored displacement values ​​at each monitoring point: ； In the formula: for t The time corresponding to the water level below the first The monitored displacement values ​​corresponding to each monitoring point; Total number of monitoring moments; S22: The MOGWO algorithm is used for parameter optimization. An external archive is introduced to store non-dominated solutions, and an alpha wolf is selected from the archive through a leader selection mechanism. Guiding population renewal: ； in: ； coefficient vector Decrease linearly from 2 to 0. for Random variables whose intervals are all distributed; In the formula For the first The individual position of a generation; They are respectively The wolf's position vector; and Let be the coefficient vector, respectively by Calculated; for The distance vector between the wolf and the alpha wolf; The convergence factor decreases linearly with iteration; S23: Iterate until the maximum algebraic number or convergence condition is reached, and select the optimal material parameter set. .

5. The method for determining the deformation characteristics of a two-stage dam based on fused parameter inversion according to claim 4, characterized in that, The specific process in S3 is as follows: Based on the optimal material parameter set obtained in S23... Substitute the data into the finite element proxy model to calculate the monitoring date. Corresponding physical driving factors Construct an initial high-dimensional feature set: ； ； ； ； in For monitoring points exist The surrogate model calculates the value at time 1. To monitor the day before The average temperature of the day The value is set as follows: ; The time-dependent characteristics of the dam, The cumulative duration from the initial monitoring day to the current day, Low-dimensional feature set, For the introduced nonlinear power parameter, This indicates that a Cartesian operation is performed on the set of physical factors and the set of spatial features.

6. The method for determining the deformation characteristics of a two-stage dam based on fused parameter inversion according to claim 1, characterized in that, In the first stage of S4, the BorutaShap algorithm is used to generate shadow features for initial feature screening, eliminating irrelevant and redundant features to obtain the first-stage feature set. In the second stage, an enhanced incremental feature selection mechanism based on multi-round random seed perturbation is introduced, and incremental verification is performed according to the stability ranking of feature importance to finally determine the optimal feature factor set for each monitoring point.

7. The method for determining the deformation characteristics of a two-stage dam based on fused parameter inversion according to claim 6, characterized in that, The first-stage feature selection process includes the following steps: S41: For the initial feature set primitive features The shadow features are generated by randomly rearranging the sample order. Combined to form an extended feature set ; in , where 'a' is the number of features. h For feature index; S42: Based on extended feature set Train the gradient boosting decision tree model and calculate features. Shapley value of marginal contribution : ； in, Features Shapley value; For features not included Any subset of features; and These represent the number of features in the corresponding feature subset and the expanded feature set, respectively. This is the prediction utility function of the model under a specific subset of features; S43: The maximum Shapley value among all shadow features is... ,satisfy and ; The significance probability value is used for the statistical significance test. Features with a Shapley value greater than a certain threshold are retained based on the statistical significance test, forming the first-stage feature set. .

8. The method for determining the deformation characteristics of a two-stage dam based on fused parameter inversion according to claim 6, characterized in that, In the second-stage incremental feature selection mechanism Voting-IFS, the specific calculation of stability ranking includes the following steps: A41: Set the number of independent random seed perturbation rounds to... For the first s wheel( The regression model is trained using the corresponding random seed, and the first-stage feature set is calculated. The Shapley values ​​of each feature in the corresponding round; A42: Calculate features by combining all rounds and all samples. Global cumulative absolute average score : ； A43: According to Sort all features in descending order to obtain a stable sorted list: ； in The total number of samples in the training set. ; Indicates the first In the wheel disturbance model, the first Features corresponding to each monitoring point The Shapley value.

9. The method for determining the deformation characteristics of a two-stage dam based on fused parameter inversion according to claim 8, characterized in that, By stable sorting list Perform incremental feature selection to determine the optimal feature factor set The specific process is as follows: Initialize empty feature subset ,according to Prioritize features by performing forward incremental selection, adding features one by one to construct nested feature subset sequences. ; through feature subset sequences Train the model and calculate the mean squared error on the validation set. Record the global minimum mean square error generated during all incremental processes. Introducing tolerance parameters Find the minimum feature subset index that satisfies the accuracy compromise condition. : Before selection The set of features constitutes the optimal feature factor set. ;in .

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