Probabilistic estimation method and system for explaining settlement of face rockfill dam

Abstract

The embodiment of the application discloses a kind of faceplate rock-fill dam settlement explainable efficient probability estimation method and system, comprising: the spatial variability of rock-fill material parameters is simulated using multi-parameter-multiple partition random field, and sample data set is obtained by single-output random finite element calculation;The mapping relationship model between rock-fill material parameters and dam settlement probability distribution is constructed based on single-output sample data set;The hyperparameters of mapping relationship model are fine-tuned by prediction interval multi-objective optimization PIMO method, to obtain the final settlement probability estimation model;New sample data set is obtained by faceplate rock-fill dam Monte Carlo random finite element calculation, and the effectiveness of settlement probability estimation model is verified using the data set;The working mechanism of settlement probability estimation model is explained using SHAP method, to obtain the contribution mode of each feature to model output.The application can not only improve the probability prediction accuracy of model, but also analyze and explain the internal mechanism of model in depth.

Description

Technical Field

[0001] This invention belongs to the technical field of dam settlement uncertainty analysis, specifically relating to an interpretable and efficient probability estimation method and system for settlement of panel rockfill dams. Background Technology

[0002] Finite element analysis of settlement in rockfill dams with concrete panels is a crucial basis for evaluating dam deformation safety, with the values ​​of dam material parameters directly impacting the settlement calculation results. However, due to inherent uncertainties in the rockfill material itself and insufficient control over dam construction conditions, the actual rockfill material at the construction site often deviates from the design and exhibits spatial variability. Studies show that the spatial variability of rockfill material significantly affects dam settlement analysis, and its statistical characteristics are subject to sampling limitations and inherent uncertainties. Therefore, it is necessary to consider the spatial variability of the rockfill material in the finite element analysis of dam settlement to achieve a probabilistic estimate of dam settlement.

[0003] Stochastic finite element method (SEM) calculations for panel rockfill dams, considering the spatial variability of material parameters, require significant computational resources, severely limiting the inversion and updating of the spatial variability of rockfill material parameters. While some scholars have attempted to reduce computation by constructing surrogate models for stochastic finite element calculations using machine learning methods, these surrogate models still suffer from limitations such as the curse of input dimensionality, high training sample generation costs, inability to estimate uncertainties, and inability to be used for inversion calculations. The NGBoost model, a machine learning model based on the gradient boosting algorithm, enables uncertainty estimation. It updates model parameters through natural gradient descent, solving the reparameterization problem of traditional gradient descent used in probability calculations, and has gained widespread acceptance in various engineering probability studies. However, these studies only optimize the accuracy of the prediction mean when selecting hyperparameters for the NGBoost model, without considering the uncertainty of the model output; further refinement of hyperparameter optimization for probabilistic models is needed. Compared to finite element models, data-driven machine learning models suffer from a lack of physical meaning. Therefore, it is necessary to develop an efficient probabilistic estimation method for the settlement of panel rockfill dams that can interpret the model. Summary of the Invention

[0004] One objective of this invention is to address the shortcomings of existing technologies by providing an interpretable and efficient probabilistic estimation method for settlement of panel rockfill dams. This method not only improves the prediction accuracy of the model but also enables in-depth analysis and explanation of the internal mechanisms of the model.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: An interpretable and efficient probabilistic estimation method for settlement of panel rockfill dams includes the following steps: Step 1: The spatial variability of the parameters of the riprap material is simulated using a multi-parameter-multi-partition random field, and the sample dataset is obtained by single-output random finite element calculation. Step 2: Construct a mapping model between the parameters of the rockfill material and the probability distribution of dam settlement based on the single-output sample dataset; Step 3: Fine-tune the hyperparameters of the mapping relationship model using the prediction interval multi-objective optimization PIMO method to obtain the final settlement probability estimation model. Step 4: A new sample dataset is obtained through Monte Carlo stochastic finite element analysis of the panel rockfill dam, and the effectiveness of the settlement probability estimation model is verified using this dataset. Step 5: The SHAP method is used to explain the working mechanism of the settlement probability estimation model and to obtain the contribution of each feature to the model output.

[0006] Furthermore, in step 1, when simulating the spatial variability of the rockfill material parameters, the Duncan-Chang-EB constitutive model is adopted for the rockfill material constitutive model. A global sensitivity analysis considering the synergistic effect of the primary and secondary rockfill zones is carried out. The k material parameters with the highest impact on the dam settlement sensitivity are selected as random variables, while other material parameters are regarded as constants.

[0007] Furthermore, the spatial variability of material parameters is simulated using a multi-parameter, multi-partition random field. This random field uses the center point method based on the Cholesky decomposition to realize the random field discretization process, considering the cross-correlation between multiple material parameters, while each material partition is independent of the others.

[0008] Furthermore, in step 1, only one random finite element calculation is performed for the random field with fixed characteristics. That is, random sampling is used to obtain a random material parameter mean combination sample. The settlement calculation value of the dam body measuring point corresponding to the mean combination sample is obtained by carrying out single-output random finite element calculation. The random material parameter mean and the corresponding measuring point settlement calculation value together constitute the single-output sample dataset used for the construction of the mapping relationship model. Furthermore, in step 2, the mean value of the random material parameters of the rockfill is used as input, and the corresponding settlement probability distribution of the measuring points is used as input. The NGBoost algorithm is used to construct a mapping relationship model between the rockfill material parameters and the dam settlement probability distribution.

[0009] Furthermore, the multi-objective function expression in the model hyperparameter fine-tuning process based on multi-objective optimization of the prediction interval in step 3 is as follows: (1) in, The threshold is used; PICP represents the predicted interval coverage, and its expression is: (2) (3) in, and These represent the upper and lower bounds of the prediction confidence interval, respectively; M is the total number of samples. PIARW represents the average relative bandwidth of the prediction interval, and its expression is: (4) in, c i Indicates the first i The mean of the predicted settlement for each sample.

[0010] Furthermore, the hyperparameters of the mapping relationship model in step 3 include learning_rate, n_estimators, max_depth, minibatch_frac, and col_sample. The search intervals of these parameters are set based on experience, and then the five-fold cross-validation grid search method is used to perform multi-objective optimization of the prediction interval to obtain the optimal combination of model hyperparameters as the parameter settings for the settlement probability estimation model.

[0011] Furthermore, the model verification process in step 4 is as follows: first, the probability distribution of dam settlement is obtained by Monte Carlo random finite element calculation, and then the accuracy is compared and analyzed with the prediction results of the settlement probability estimation model in terms of prediction mean and prediction uncertainty to determine its prediction accuracy.

[0012] Furthermore, the Shapley value summary plot and feature importance plot of the settlement probability estimation model are obtained by using the SHAP method. The influence of the feature inputs of the settlement probability estimation model on the output is analyzed, thereby realizing the physical verification of the proposed model.

[0013] Another object of the present invention is to provide a system for implementing the above-described method for interpretable and efficient probabilistic estimation of settlement in panel rockfill dams, comprising: The sample calculation module is used to simulate the spatial variability of rockfill material parameters using multi-parameter-multi-partition random fields, and to obtain the sample dataset through single-output random finite element calculation. The mapping relationship model building module is used to build a mapping relationship model between the parameters of rockfill material and the dam settlement probability distribution based on a single output sample dataset; The settlement probability estimation model is established and used to fine-tune the hyperparameters of the mapping relationship model through the prediction interval multi-objective optimization PIMO method to obtain the final settlement probability estimation model. The model validation module is used to obtain a new sample dataset through Monte Carlo stochastic finite element calculation of panel rockfill dams, and to use this dataset to validate the effectiveness of the settlement probability estimation model. The model interpretation module is used to interpret the working mechanism of the settlement probability estimation model using the SHAP method, and to obtain the contribution of each feature to the model output.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention obtains material parameters that have a significant impact on dam settlement by considering the global sensitivity analysis under the synergistic effect of multiple material zones, and proposes a multi-parameter-multi-zone cross-correlation random field simulation method to realize the spatial variability characterization of the rockfill material parameters of the panel rockfill dam.

[0015] 2. This invention addresses the challenge of traditional stochastic finite element surrogate models being unable to estimate the uncertainty of model outputs by introducing the NGBoost algorithm. Furthermore, this model offers advantages such as low input dimensionality, low training sample construction cost, and applicability for uncertainty parameter inversion calculations.

[0016] 3. This invention achieves hyperparameter fine-tuning of the NGBoost probability estimation model by performing dual-objective optimization on two evaluation metrics, PICP and PIARW, within the model's prediction interval, effectively improving the model's prediction accuracy.

[0017] 4. This invention achieves in-depth analysis of the internal mechanism of the PIMO-NGBoost model through the SHAP method, further verifying the reliability of the model. Attached Figure Description

[0018] Figure 1 A flowchart illustrating an efficient probabilistic estimation method for interpretable settlement of panel rockfill dams provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of a panel rockfill dam finite element model provided in an embodiment of the present invention; Figure 3 The results of global sensitivity analysis of rockfill material parameters provided in the embodiments of the present invention; Figure 4 This is a schematic diagram of random field simulation of riprap material provided in an embodiment of the present invention; Figure 5 This is a PIMO-NGBoost model settlement prediction result using a specific measuring point as an example, provided in an embodiment of the present invention. Figure 6 A comparison of PICP and PIARW on the validation set for the NGBoost, GPR and GBQR models provided in this embodiment of the invention after hyperparameter optimization; Figure 7 The prediction results of the PIMO-NGBoost model provided in this embodiment of the invention on the test set; Figure 8The prediction results of the PIMO-GPR model provided in this embodiment of the invention on the test set; Figure 9 The prediction results of the PIMO-GBQR model provided in this embodiment of the invention on the test set; Figure 10 The PIMO-NGBoost model prediction interpretation results provided in this embodiment of the invention, taking a certain measurement point as an example. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0021] The present invention will be further described below with reference to specific embodiments, but these are not intended to limit the scope of the invention.

[0022] Step 1, Data Collection. The spatial variability of rockfill material parameters is simulated using a multi-parameter, multi-partition random field model, and a sample dataset is obtained through single-output random finite element analysis. In this step, a finite element model of the rockfill dam with a concrete panel is established. The constitutive models of the rockfill, cushion layer, and transition layer materials are based on the Duncan-Chang-EB constitutive model, while the concrete panel and foundation are considered as elastic materials. Based on this finite element model, the Sobol exponent method is used to conduct a global sensitivity analysis of the rockfill material parameters. Highly sensitive material parameters are selected as random variables, and their spatial variability is considered. Other material parameters are treated as constants, and their spatial variability is ignored. Based on engineering experience, it is assumed that the random variables of the rockfill material parameters are cross-correlated and all follow a log-normal distribution. A multi-parameter, multi-partition cross-correlated random field is constructed for the rockfill material parameters using the center-point method based on the Cholesky decomposition. This random field is then used as the material input to the finite element model to achieve stochastic finite element calculation of the rockfill dam with a concrete panel.

[0023] By randomly sampling a combination of mean random material parameters, and assuming the spatial variation characteristics of a certain rockfill material, single-output stochastic finite element analysis is performed to obtain the corresponding settlement calculation values ​​at the dam body measuring points. Finally, the mean random material parameters and the corresponding settlement calculation values ​​at the measuring points together constitute the single-output sample dataset.

[0024] Step 2, Model Building. A mapping model between the parameters of the rockfill material and the dam's settlement probability distribution is constructed based on the single-output sample dataset. In this embodiment, the base learner of the NGBoost probability estimation model is a decision tree model, the parameter probability distribution is a Gaussian distribution, and the scoring rule is a log score. Then, the single-output sample dataset generated in step 1 is divided into a sample training set and a sample validation set. The NGBoost model is trained using the sample training set, and the sample validation set is used to illustrate the prediction performance of the NGBoost model.

[0025] Step 3, Model Optimization. The hyperparameters of the NGBoost model are fine-tuned using a multi-objective optimization method for the prediction interval to obtain the final PIMO-NGBoost settlement probability estimation model.

[0026] The Predicted Interval Coverage (PICP) and Predicted Interval Mean Relative Width (PIARW) of the NGBoost model on the validation set were calculated. The model hyperparameters were optimized with the goal of achieving the baseline PICP and minimizing PIARW. The main hyperparameters of the NGBoost model include learning_rate, n_estimators, max_depth, minibatch_frac, and col_sample. Search intervals for these parameters were defined, and a cross-validation grid search method was used for multi-objective optimization of the predicted intervals to obtain a set of optimal model hyperparameters as the parameter settings for the PIMO-NGBoost settlement probability estimation model.

[0027] Step 4, Model Validation. A new sample dataset is obtained through Monte Carlo stochastic finite element method calculations for panel rockfill dams, and the effectiveness of the PIMO-NGBoost model is validated using this dataset.

[0028] A new set of random variable mean samples of rockfill material was randomly generated. Monte Carlo stochastic finite element analysis was performed on each sample to obtain the corresponding dam settlement probability distribution. The optimized PIMO-NGBoost model was then used to predict the settlement mean and interval for this dataset. Mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R²) were used to calculate the predicted settlement. 2 To evaluate the accuracy of the model's prediction of the mean settlement, the average PICP and average PIARW were used to evaluate the model's interval predictions, and the effectiveness of the model in estimating settlement uncertainty was explained based on the average absolute error of the PIARW predictions.

[0029] Step 5, Model Interpretation. The SHAP method is used to interpret the working mechanism of the proposed PIMO-NGBoost model, obtaining the contribution of each feature to the model output.

[0030] The contribution of each feature of the PIMO-NGBoost model to each sample is calculated using the SHAP method, and the corresponding Shapley value summary plot and feature importance plot are obtained to analyze the global and local effects of each material parameter on the model output settlement.

[0031] Example The present invention proposes an efficient probabilistic estimation method for settlement of a face-panel rockfill dam that considers the spatial variability of material parameters. The method is used to probabilistically estimate the settlement of a face-panel rockfill dam. The specific implementation steps are as follows: Step 1, Data Collection. The spatial variability of rockfill material parameters is simulated using a multi-parameter, multi-partition random field model, and a sample dataset is obtained through single-output random finite element analysis.

[0032] A finite element calculation model of the panel rockfill dam is established based on the engineering design data, such as... Figure 2 As shown, the constitutive models of the rockfill, cushion layer, and transition layer materials adopt the Duncan-Chang-EB constitutive model, and the model parameters are described in Table 1. The panel and foundation are considered as elastic materials with Young's moduli of 30 GPa and 12 GPa, respectively, and Poisson's ratios of 0.3 and 0.167, respectively. Based on this finite element model, the Sobol exponent method is used to conduct a global sensitivity analysis of the rockfill material parameters. Considering the synergistic effect of primary and secondary rockfill materials, the parameters of the primary rockfill material (…) are analyzed. K , R f , φ 0, K b , m , n Δ φ ) and secondary rockfill material parameters ( K ', R f ', φ 0', K b ', m ', n ',Δ φ Sensitivity analysis was performed on a total of 14 material parameters, and the results for each material parameter were obtained. S 1 and S T Value, such as Figure 3 As shown. Selecting parameters for highly sensitive materials. K , R f , φ 0, K b , K ', R f ', φ 0',K b 'Treat the materials as random variables and consider their spatial variability; treat other material parameters as constants and ignore their spatial variability.' To determine the spatial variability characteristics of the rockfill material, refer to Table 2. The coefficients of variation (COV) of the primary and secondary rockfill materials were 0.05 and 0.15, respectively, and the horizontal correlation distance of the rockfill materials was ( ) and vertical correlation distance ( As shown in Table 2, the correlation function chosen is a Gaussian correlation function. Based on engineering experience, it is assumed that the random variables of the rockfill material parameters all follow a log-normal distribution and are cross-correlated. A multi-parameter, multi-partition cross-correlated random field is constructed for the rockfill material parameters using the central point method based on Choleski decomposition. The simulation diagram of the random field is shown below. Figure 4 As shown, the random field is input as material into the finite element model to realize the stochastic finite element calculation of the panel rockfill dam. The mean baseline values ​​of the material parameters of the rockfill body are shown in Table 2. The mean sampling range is set to be 20% above or below the baseline value. Then, random sampling is used to obtain random material parameter mean combination samples. Finally, the settlement calculation values ​​of the dam body measuring points corresponding to the mean combination samples are obtained by performing single-output stochastic finite element calculations. The random material parameter mean values ​​and the corresponding measuring point settlement calculation values ​​together constitute the single-output sample dataset, which is used to construct the PIMO-NGBoost model.

[0033] Table 1. Parameters and cross-correlation of the Duncan-Zhang-EB constitutive model

[0034] Table 2 Material Parameters of Face-Panel Rockfill Dams

[0035] Step 2, Model Building. Based on the single-output sample dataset, the NGBoost natural gradient boosting algorithm is used to construct a mapping model between the parameters of the rockfill material and the dam settlement probability distribution.

[0036] This embodiment uses the mean of the random material parameters of the rockfill as input and the corresponding settlement probability distribution at the measurement points as input. It employs the NGBoost algorithm to construct a mapping model between the rockfill material parameters and the dam's settlement probability distribution. The base learner is a decision tree model, the output parameter probability distribution is a Gaussian distribution, and the scoring rule is logarithmic scores. Then, the sample dataset generated in step 1 is divided into a training set and a validation set in a 4:1 ratio using five-fold cross-validation. The NGBoost model is trained using the training set data, and the validation set is used to demonstrate the predictive performance of the NGBoost model. The pseudocode for the NGBoost algorithm training process is shown in Table 3.

[0037] Table 3. Pseudocode for the training process of the NGBoost algorithm

[0038] Step 3, Model Optimization. The hyperparameters of the NGBoost model are fine-tuned using a multi-objective optimization method for the prediction interval to obtain the final PIMO-NGBoost settlement probability estimation model; The Prediction Interval Coverage (PICP) and Prediction Interval Mean Relative Width (PIARW) of the NGBoost model on the sample validation set were calculated. The model hyperparameters were optimized with the objectives of achieving 95% baseline PICP and minimizing PIARW. The main hyperparameters of the NGBoost model include learning_rate, n_estimators, max_depth, minibatch_frac, and col_sample. The search intervals for these parameters were set empirically (see Table 4). A five-fold cross-validation grid search method was used for multi-objective optimization of the prediction intervals to obtain the optimal combination of model hyperparameters, which served as the parameter settings for the PIMO-NGBoost settlement probability estimation model. The parameters of the settlement estimation model at multiple dam measurement points were optimized, and the optimal hyperparameter combination is shown in Table 4. The prediction results of the optimized PIMO-NGBoost model on the entire dataset are as follows: Figure 5 As shown, approximately 95% of the sample points fall within the 95% confidence level. Regarding the prediction intervals, the coverage of different confidence levels and their corresponding prediction intervals remained largely consistent. Meanwhile, Gaussian process regression (GPR) and gradient boosting quantile regression (GBQR) models were used for performance comparison. After the same hyperparameter optimization process, the optimal hyperparameter combinations for the PIMO-GPR and PIMO-GBQR models are shown in Table 4. The prediction interval optimization results for the three models are as follows: Figure 6 As shown, the PICP of all three models reached 0.95 at all measurement points, with the PIMO-GPR model showing a larger PICP at some measurement points. The PIMO-GBQR model exhibited significantly larger PIARW values ​​at all measurement points, while the PIMO-NGBoost and PIMO-GPR models had similar PIARW values. Therefore, the NGBoost model showed the best optimization performance.

[0039] Table 4. Model hyperparameter optimization results

[0040] Step 4, Model Validation. A new sample dataset is obtained through Monte Carlo stochastic finite element analysis of panel rockfill dams, and this dataset is used to validate the effectiveness of the settlement probability estimation model. In this step, a new set of random variable mean samples of rockfill material parameters are randomly generated. Monte Carlo stochastic finite element analysis is performed on each sample to obtain the corresponding dam settlement probability distribution. The optimized PIMO-NGBoost model is then used to predict the settlement of this dataset, yielding the corresponding settlement prediction mean and interval, as shown below. Figure 7 As shown. The mean and interval of settlement predictions for the PIMO-GPR and PIMO-GBQR models are as follows. Figure 8 and Figure 9 As shown. Mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R²) are used. 2 The accuracy of the evaluation models in predicting the mean settlement was assessed. The average PICP and average PIARW were used to evaluate the models' interval prediction performance, and the model's effectiveness in estimating settlement uncertainty was explained based on the model's PIARW prediction mean absolute error. The prediction evaluation results of the three models are shown in Table 5. The R-squared values ​​of the PIMO-NGBoost, PIMO-GPR, and PIMO-GBQR models for predicting the mean settlement are shown in Table 5. 2 All values ​​are greater than 0.99, indicating high accuracy in mean prediction. The ideal value for prediction interval coverage is 0.95, and the actual average relative width of the dam settlement interval for the generated samples is 0.087. Table 5 shows that the PIMO-NGBoost model's prediction interval is wider and has a larger interval coverage than the actual interval, indicating a conservative approach to interval estimation. However, the prediction interval error is less than 0.8 times the actual interval estimate, suggesting the interval estimation results are effective. The PIMO-NGBoost model's PIARW mean absolute error is 0.065, which is lower than the interval estimation errors of the PIMO-GPR and PIMO-GBQR models. Therefore, the PIMO-NGBoost model can obtain effective and relatively good interval estimation results.

[0041] Table 5 Model Prediction Evaluation Results

[0042] Step 5, Model Interpretation. The SHAP method is used to interpret the working mechanism of the proposed settlement probability estimation model, obtaining the contribution of each feature to the model output; In this embodiment, the contribution of each feature of the PIMO-NGBoost model to the model output on each sample is calculated using the SHAP method, thereby obtaining the corresponding Shapley value summary plot (scatter plot) and feature importance plot (blue bar chart), as shown below. Figure 10 As shown in the figure. It can be seen from the figure that for measuring point ES5-7 located in the main rockfill area, the material parameters of the main rockfill (i.e., K , R f , φ 0,K b ) Comparison of secondary rockfill material parameters (i.e. K ', R f ', φ 0', K b The ') plays a dominant role in the settlement at the measuring point, while the secondary rockfill material parameters have almost no impact. Furthermore, when the parameters K , φ 0, K b When the value of is large, the corresponding Shapley value is negative, indicating a negative impact on the dam settlement; when the value is small, the corresponding Shapley value is positive, indicating a positive impact on the dam settlement. R f The opposite is true. This indicates that the parameter K , φ 0, K b It is negatively correlated with dam settlement, while the parameter R f The correlation with dam settlement is positive, consistent with the physical meaning of these parameters. Furthermore, the ranking of the importance of these material parameters to dam settlement differs from the sensitivity analysis results in step 1, indicating that spatial variability of materials affects the magnitude of the sensitivity of material parameters.

[0043] This invention also provides a system for implementing the above-described method for interpretable and efficient probabilistic estimation of settlement in panel rockfill dams, comprising: The sample calculation module is used to simulate the spatial variability of rockfill material parameters using multi-parameter-multi-partition random fields, and to obtain the sample dataset through single-output random finite element calculation. The mapping relationship model building module is used to build a mapping relationship model between the parameters of rockfill material and the dam settlement probability distribution based on a single output sample dataset; The settlement probability estimation model is established and used to fine-tune the hyperparameters of the mapping relationship model through the prediction interval multi-objective optimization PIMO method to obtain the final settlement probability estimation model. The model validation module is used to obtain a new sample dataset through Monte Carlo stochastic finite element calculation of panel rockfill dams, and to use this dataset to validate the effectiveness of the settlement probability estimation model. The model interpretation module is used to interpret the working mechanism of the settlement probability estimation model using the SHAP method, and to obtain the contribution of each feature to the model output.

[0044] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made based on the content of this specification should be included within the protection scope of the present invention.

Claims

1. A method for interpretable and efficient probabilistic estimation of settlement in a panel rockfill dam, characterized in that, Includes the following steps: Step 1: The spatial variability of the parameters of the riprap material is simulated using a multi-parameter-multi-partition random field, and the sample dataset is obtained by single-output random finite element calculation. Step 2: Construct a mapping model between the parameters of the rockfill material and the probability distribution of dam settlement based on the single-output sample dataset; Step 3: Fine-tune the hyperparameters of the mapping relationship model using the prediction interval multi-objective optimization PIMO method to obtain the final settlement probability estimation model. Step 4: A new sample dataset is obtained through Monte Carlo stochastic finite element analysis of the panel rockfill dam, and the effectiveness of the settlement probability estimation model is verified using this dataset. Step 5: The SHAP method is used to explain the working mechanism of the settlement probability estimation model and to obtain the contribution of each feature to the model output. The multi-objective function expression in the model hyperparameter fine-tuning process based on multi-objective optimization of the prediction interval in step 3 is as follows: (1) in, The threshold is used; PICP represents the predicted interval coverage, and its expression is: (2) (3) in, and These represent the upper and lower bounds of the prediction confidence interval, respectively; M is the total number of samples. PIARW represents the average relative bandwidth of the prediction interval, and its expression is: (4) in, c i Indicates the first i The mean of the predicted settlement for each sample.

2. The efficient probabilistic estimation method for settlement of panel rockfill dams according to claim 1, characterized in that, In step 1, when simulating the spatial variability of the rockfill material parameters, the Duncan-Chang-EB constitutive model is adopted for the rockfill material constitutive model. A global sensitivity analysis considering the synergistic effect of the primary and secondary rockfill zones is carried out. The k material parameters with the highest impact on the dam settlement sensitivity are selected as random variables, while other material parameters are regarded as constants.

3. The efficient probabilistic estimation method for settlement of panel rockfill dams according to claim 1, characterized in that, The spatial variability of material parameters is simulated using a multi-parameter, multi-partition random field. This random field uses the center point method based on the Cholesky decomposition to realize the random field discretization process, considering the cross-correlation between multiple material parameters, while each material partition is independent of the others.

4. The efficient probabilistic estimation method for settlement of panel rockfill dams according to claim 1, characterized in that, In step 1, only one random finite element calculation is performed for the random field with fixed characteristics. That is, random sampling is used to obtain a sample of random material parameter mean values. The settlement calculation value of the dam body measuring point corresponding to the sample of mean values ​​is obtained by performing single-output random finite element calculation. The random material parameter mean values ​​and the corresponding settlement calculation value of the measuring point together constitute a single-output sample dataset for the construction of the mapping relationship model.

5. The efficient probabilistic estimation method for settlement of panel rockfill dams according to claim 1, characterized in that, In step 2, the mean value of the random material parameters of the rockfill is used as input, and the corresponding settlement probability distribution of the measuring points is used as input. The NGBoost algorithm is used to construct a mapping relationship model between the rockfill material parameters and the dam settlement probability distribution.

6. The efficient probabilistic estimation method for settlement of panel rockfill dams according to claim 1, characterized in that, In step 3, the hyperparameters of the mapping relationship model include learning_rate, n_estimators, max_depth, minibatch_frac, and col_sample. The search interval of the above parameters is set based on experience, and then the five-fold cross-validation grid search method is used to perform multi-objective optimization of the prediction interval to obtain the optimal combination of model hyperparameters as the parameter settings of the settlement probability estimation model.

7. The efficient probabilistic estimation method for settlement of panel rockfill dams according to claim 1, characterized in that, The model verification process in step 4 is as follows: First, the probability distribution of dam settlement is obtained by Monte Carlo random finite element calculation. Then, the accuracy of the distribution is compared with that of the settlement probability estimation model in terms of the prediction mean and the magnitude of prediction uncertainty.

8. The efficient probabilistic estimation method for settlement of panel rockfill dams according to claim 1, characterized in that, The Shapley summaries and feature importance plots of the settlement probability estimation model are obtained by using the SHAP method. The influence of the feature inputs on the output of the settlement probability estimation model is analyzed, thereby verifying the proposed model in a physical sense.

9. A system for implementing the efficient probabilistic estimation method for interpretable settlement of panel rockfill dams as described in any one of claims 1-8, characterized in that, include: The sample calculation module is used to simulate the spatial variability of rockfill material parameters using multi-parameter-multi-partition random fields, and to obtain the sample dataset through single-output random finite element calculation. The mapping relationship model building module is used to build a mapping relationship model between the parameters of rockfill material and the dam settlement probability distribution based on a single output sample dataset; The settlement probability estimation model is established and used to fine-tune the hyperparameters of the mapping relationship model through the prediction interval multi-objective optimization PIMO method to obtain the final settlement probability estimation model. The model validation module is used to obtain a new sample dataset through Monte Carlo stochastic finite element calculation of panel rockfill dams, and to use this dataset to validate the effectiveness of the settlement probability estimation model. The model interpretation module is used to interpret the working mechanism of the settlement probability estimation model using the SHAP method, and to obtain the contribution of each feature to the model output. The multi-objective function expression in the hyperparameter fine-tuning process of the model based on multi-objective optimization of the prediction interval is as follows: (1) in, The threshold is used; PICP represents the predicted interval coverage, and its expression is: (2) (3) in, and These represent the upper and lower bounds of the prediction confidence interval, respectively; M is the total number of samples. PIARW represents the average relative bandwidth of the prediction interval, and its expression is: (4) in, c i Indicates the first i The mean of the predicted settlement for each sample.

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