Efficient inversion method, medium and device for rockfill dam material parameters considering target uncertainty and prior knowledge constraints

Abstract

This invention discloses an efficient inversion method, medium, and equipment for material parameters of rockfill dams that considers target uncertainty and prior knowledge constraints. The method includes steps such as determining inversion parameters and calculating measurement points, constructing a high-precision multi-output surrogate model, constructing a multi-objective function expression, performing multi-objective parameter inversion calculations, and optimizing the solution set. By constructing a multi-objective function, the solution set space of target settlement under different spatiotemporal importance trade-offs is obtained. When generating parameters, the prior relationships between material parameters are used as constraints to avoid the generation of unreasonable results. At the same time, the uncertainty of target settlement is considered and reduced by introducing an error allowable interval and a high-precision surrogate model. Finally, a relaxed and improved Bayesian multi-objective optimization algorithm is used to achieve efficient and high-quality calculation of parameter inversion.

Description

Technical Field

[0001] This invention relates to the field of dam parameter inversion calculation technology, specifically to an efficient inversion method, medium, and equipment for rockfill dam material parameters that considers objective uncertainty and prior knowledge constraints. Background Technology

[0002] The material properties of rockfill dams are a key element in the structural safety analysis of dams. However, due to errors in laboratory tests and uncertainties in construction quality, the measured material parameters often deviate from the actual material parameters on-site, leading to discrepancies between the calculated dam structural response and the actual results, thus affecting the reliability of the structural safety analysis. Using actual monitoring data to invert the dam material parameters is widely considered an effective method.

[0003] Currently, research methods for inverting dam material parameters based on monitoring data typically treat it as an optimization problem. Machine learning algorithms are used to construct a finite element method (FEM) proxy model of the dam, and intelligent optimization algorithms are employed to perform the inversion calculation of rockfill material parameters. Commonly used machine learning algorithms include Support Vector Machines (SVMs), Random Forests, and XGBoost, while commonly used intelligent optimization algorithms include Genetic Algorithms, Particle Swarm Optimization (PSO), and Bayesian optimization algorithms. With the development of artificial intelligence technology and the emergence of more and more new algorithms, the accuracy of material parameter inversion calculation results has been continuously improved. Traditional parameter inversion calculations aim to minimize the average distance between the finite element simulation values ​​and the actual monitoring values ​​at the corresponding measurement points. However, this single-objective optimization method can only obtain a solution with limited information and does not consider key locations and time periods, thus having certain limitations. According to numerous statistical analyses, there are significant correlations between some rockfill material parameters; however, traditional parameter inversion calculation processes mostly treat material parameters as discrete variables, leading to inversion results that do not conform to the prior relationship of the parameters.

[0004] Furthermore, current finite element models, surrogate models, and monitoring data for rockfill dams all contain certain errors and computational uncertainties. Given the propagation of errors from multiple sources, previous optimization methods that solely approximate deterministic monitoring data also have limitations. Therefore, considering the limitations of the aforementioned methods, it is necessary to explore a more reasonable paradigm for inverting rockfill dam parameters. Summary of the Invention

[0005] The purpose of this invention is to address the problems existing in the prior art by providing an efficient inversion method, medium, and equipment for the material parameters of rockfill dams that takes into account the uncertainty of the target and the constraints of prior knowledge.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: Firstly, an efficient inversion method for material parameters of rockfill dams, considering both objective uncertainty and prior knowledge constraints, is provided, comprising the following steps: Establish a finite element calculation model for a rockfill dam; Based on the global sensitivity analysis method, material parameters with higher sensitivity are selected as inversion parameters; based on multi-index comprehensive analysis, multiple measuring points on the rockfill dam body are scored, and measuring points with higher scores are selected as calculation measuring points. Based on the inversion parameters, a combination of correlation parameters is generated. The settlement values ​​of the measurement points are extracted as labels for the sample set through finite element calculation and combined with the obtained calculation measurement points to generate learning samples. Based on the generated learning samples, the RC-Stacking model is trained and optimized to construct a high-precision multi-output proxy model. For each type of measurement point settlement, an objective function is constructed. Considering the uncertainty of the target settlement, an error allowable interval is constructed for the target settlement of each measurement point. The prior relationship between material parameters is used as a constraint condition. The objective is to construct a multi-objective function expression with the goal of minimizing the relative distance between the calculated settlement and the target settlement interval. The search space for material parameters is determined, and the constructed multi-objective function expression is solved using the relaxation-dominated Bayesian multi-objective optimization algorithm to obtain the optimal Pareto solution set for the material parameters. The optimal Pareto solution set is substituted into the finite element calculation model of the rockfill dam to calculate the corresponding settlement value of the measuring point and the corresponding relative error score of the measuring point. According to the engineering requirements, the measuring points at different time and space locations are weighted, and the spatiotemporal weighted TOPSIS method is used to score each Pareto solution. The solution with the highest score is selected as the final parameter inversion result.

[0007] Furthermore, the sensitivity analysis process for the material parameters considers the synergistic effect of primary and secondary rockfill materials. Both primary and secondary rockfill materials adopt the Duncan-Zhang-EB constitutive model. The global sensitivity analysis method is used to calculate the sensitivity of the primary and secondary rockfill material parameters to the settlement of multiple measuring points of the dam body. The material parameters with higher comprehensive sensitivity are selected as inversion parameters.

[0008] Furthermore, when scoring multiple measuring points on the rockfill dam body through multi-index comprehensive analysis, the parameter sensitivity, settlement magnitude, and monitoring data quality of the measuring points are comprehensively considered. Parameter sensitivity refers to the sensitivity of the measuring point settlement to changes in material parameters. The monitoring data quality comprehensively considers the missing values ​​and stability of the monitoring data. After normalization processing, the mean value is obtained and used as the comprehensive evaluation value of the measuring point. The measuring points are then selected based on this comprehensive evaluation value.

[0009] Furthermore, the RC-Stacking model uses multiple diverse and high-performing machine learning models as base models, logistic regression models as meta-models, integrates models through feature stacking, and optimizes model parameters using a grid search algorithm.

[0010] Furthermore, the RC-Stacking model uses the regression chain method to consider the correlation between settlements at multiple measuring points, and uses the grey relational analysis method to obtain the correlation matrix between settlements at each measuring point. Based on this correlation matrix, the settlements at the measuring points are classified using the hierarchical clustering method, and the settlements at the measuring points with strong correlations are used as a set to construct a regression chain.

[0011] Furthermore, considering the uncertainty of the objective and the constraints of prior knowledge, the multi-objective function expression is as follows: , In the formula, p ={ p 1, p 2, ..., p S} represents the material parameter vector to be inverted, and there are a total of S One material parameter; L This is the lower bound of the material parameters. U This is the upper bound of the material parameters; f k Indicates the first k There are n objective functions, totaling n. K One objective function; N k Indicates the first k The number of measurement points considered in each objective function; E and E 'Represents the material strength of the primary and secondary rockfill zones, respectively; R(p) This represents the empirical regression relationship between material parameters; g i (p) This represents the score of the relative error at the measuring point.

[0012] Furthermore, the relative error score of the measuring points. g i (p) The expression is as follows: , in, u i * Indicates the first i Target settlement value at each measuring point; u i Indicates the first i The calculated settlement values ​​of each measuring point are obtained from a high-precision multi-output proxy model calculated by finite element method.L i * Indicates the first i The lower bound of the settlement interval of each measuring point target. U i * Indicates the first i The upper limit of the settlement interval of each measuring point target.

[0013] Furthermore, the sources of uncertainty in target settlement are considered to include fluctuations in settlement monitoring data, errors in the high-precision multi-output surrogate model, and allowable errors in the finite element calculation model of the rockfill dam. The uncertainty in target settlement is quantified by adding the fluctuation range of settlement monitoring data, the mean absolute error of the high-precision multi-output surrogate model, and the allowable error of the finite element calculation model of the rockfill dam. An allowable error interval is then constructed for the target settlement at each monitoring point. L i * , U i * ].

[0014] Furthermore, the relaxed dominance Bayesian multi-objective optimization algorithm is an improvement on the dominance relationship of the original Bayesian multi-objective optimization algorithm. The relaxation improvement method is that when the distance between the objective function values ​​corresponding to two solutions is within the range of computational uncertainty, these two solutions can dominate each other on that objective function. The expression for the computational uncertainty of the objective function value is: , Where, Δ k Indicates the first k The magnitude of the computational uncertainty of each objective function, δ i Indicates the first i The magnitude of fluctuation in settlement monitoring data at each monitoring point MAE i Indicates the first i The mean absolute error of the settlement surrogate model at each measuring point; N k Indicates the first k The number of measurement points whose settlement is considered in each objective function; r c This represents the relaxation coefficient, which reflects the degree of relaxation.

[0015] Furthermore, the solution set optimization process involves directly substituting the optimal Pareto solution set into the finite element calculation model of the rockfill dam to calculate the corresponding settlement values ​​of the measuring points. Then, higher weights are assigned to the settlement values ​​of the measuring points in the main rockfill area and the impoundment period, while lower weights are assigned to the settlement values ​​of the measuring points in the secondary rockfill area and the completion period. The solution with the highest score is obtained through the spatiotemporal weighted TOPSIS method as the final parameter inversion result.

[0016] Secondly, an efficient inversion system for rockfill dam material parameters considering objective uncertainty and prior knowledge constraints is provided. This system is used to implement the efficient inversion method for rockfill dam material parameters considering objective uncertainty and prior knowledge constraints as described above. The system includes: The first module is used to establish the finite element calculation model of the rockfill dam; The second module is used to determine the inversion parameters and calculate the measurement points; The third module is used to build a high-precision multi-output agent model; The fourth module is used to construct multi-objective function expressions; The fifth module is used to perform multi-objective parameter inversion calculations; The sixth module is used to optimize the solution set, selecting the solution with the highest score as the final parameter inversion result.

[0017] Thirdly, a computer-readable storage medium is provided, the computer-readable storage medium including a stored program that, when executed by a processor, implements the efficient inversion method for rockfill dam material parameters considering target uncertainty and prior knowledge constraints as described above.

[0018] Furthermore, an electronic device is provided, comprising at least one processor and at least one memory connected to the processor; wherein the processor is configured to invoke program instructions in the memory to execute the efficient inversion method for rockfill dam material parameters considering target uncertainty and prior knowledge constraints as described above.

[0019] Compared with existing technologies, the beneficial effects of this invention are: 1. This method focuses on the sensitivity analysis of material parameters and the comprehensive selection of measuring points for rockfill dam projects, identifying key research objects and helping to improve the effectiveness and efficiency of parameter inversion calculation; 2. This method proposes to construct a proxy model for finite element calculation of rockfill dams using the RC-Stacking machine learning algorithm, integrating multiple machine learning models through the Stacking ensemble strategy, and considering the correlation of multiple measuring points through hierarchical clustering-regression chain method to achieve multiple model outputs, effectively improving the accuracy and robustness of the proxy model, thereby reducing model error propagation in the parameter inversion calculation process; 3. This method fully considers the uncertainty of the target and the constraints of prior knowledge to construct a multi-objective function expression, and considers the uncertainty of target settlement and the prior relationship between material parameters. The system aims to obtain a higher quality and more reasonable solution space. Furthermore, this expression constructs multiple objective functions for different measuring point locations and settlement periods, enabling the acquisition of solution spaces under various spatiotemporal trade-offs, providing researchers with richer solution information. 4. This method employs the relaxed-dominated Bayesian multi-objective optimization algorithm IMOTPE to perform parameter inversion calculations, alleviating the domination resistance problem that easily arises in high-dimensional objective optimization problems. This algorithm also has advantages over other multi-objective optimization algorithms in terms of high computational efficiency and solution diversity. 5. This method proposes directly substituting the obtained Pareto solution set into the finite element model of the rockfill dam when selecting the final parameter inversion result to calculate the corresponding measuring point settlement value. This avoids the problem of suboptimal finite element calculation results caused by errors between the surrogate model and the finite element model in traditional methods. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the efficient inversion method for material parameters of rockfill dams that takes into account target uncertainty and prior knowledge constraints, as described in this invention. Figure 2 The finite element calculation model and measurement point distribution of the rockfill dam provided in Embodiment 2 of the present invention; Figure 3 The results of global sensitivity analysis of rockfill material parameters provided in Embodiment 2 of the present invention; Figure 4 This is the comprehensive evaluation result of the settlement calculation and measurement points of the rockfill dam provided in Embodiment 2 of the present invention; Figure 5 The hierarchical clustering results of the settlement at the completion period of the rockfill dam measuring points provided in Embodiment 2 of the present invention; Figure 6 The hierarchical clustering results of the settlement of the rockfill dam measuring points during the water storage period provided in Embodiment 2 of the present invention; Figure 7 The prediction results of the finite element calculation proxy model for rockfill dams provided in Embodiment 2 of the present invention on the training set and the test set; Figure 8The accuracy evaluation results of the finite element calculation proxy model of the rockfill dam provided in Embodiment 2 of the present invention at different spatiotemporal measurement points; Figure 9 The correlation diagram of the rockfill material parameter samples provided in Embodiment 2 of the present invention under the conditions of having and not having prior knowledge constraints; Figure 10 The Pareto solution set obtained by inversion calculation of riprap material parameters provided in Embodiment 2 of the present invention; Figure 11 This is the updated result of the finite element calculation of the rockfill dam provided in Embodiment 2 of the present invention. Detailed Implementation

[0021] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] In the description of this invention, it should be noted that the terms "middle", "upper", "lower", "left", "right", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0023] Example 1: A method for efficiently inverting material parameters of rockfill dams considering objective uncertainty and prior knowledge constraints is provided, combined with... Figure 1 As shown, it includes the following steps: Step 1: Establish a finite element calculation model of the rockfill dam; Step 2: Determine the inversion parameters and calculation points. Based on the global sensitivity analysis method, select the material parameters with higher sensitivity as inversion parameters. Based on multi-index comprehensive analysis, score multiple measurement points on the rockfill dam body and select the measurement points with higher scores as calculation points. Step 3: Construct a high-precision multi-output surrogate model. Generate a combination of relevant parameters based on the inversion parameters. Extract the settlement values ​​of the measurement points as labels for the sample set through finite element calculation and combined with the obtained calculation measurement points to generate learning samples. Based on the generated learning samples, train and optimize the RC-Stacking model to construct a high-precision multi-output surrogate model. Step 4: Construct a multi-objective function expression. Construct an objective function for each type of settlement at the measuring point. Considering the uncertainty of the target settlement, construct an error allowable interval for the target settlement at each measuring point. Use the prior relationship between material parameters as a constraint condition. Construct a multi-objective function expression with the objective of minimizing the relative distance between the calculated settlement and the target settlement interval. Step 5: Perform multi-objective parameter inversion calculations to determine the material parameter search space. Use the relaxation-dominated Bayesian multi-objective optimization algorithm to solve the constructed multi-objective function expression and obtain the optimal Pareto solution set of the material parameters. Step 6: Implement solution set optimization. Substitute the optimal Pareto solution set into the finite element calculation model of the rockfill dam to calculate the corresponding settlement value of the measuring point and the corresponding relative error score of the measuring point. According to the engineering requirements, weight the measuring points at different time and space locations. Use the spatiotemporal weighted TOPSIS method to score each Pareto solution and select the solution with the highest score as the final parameter inversion result.

[0024] This method constructs a multi-objective function through the above steps to obtain the solution space of target settlement under different spatiotemporal importance trade-offs. When generating parameters, the prior relationship between material parameters is used as a constraint to avoid the generation of unreasonable results. At the same time, the uncertainty of target settlement is considered and reduced by introducing an error allowable interval and a high-precision surrogate model. Finally, a relaxation-improved Bayesian multi-objective optimization algorithm is used to achieve efficient and high-quality calculation of parameter inversion.

[0025] This method focuses on the sensitivity analysis of material parameters and the comprehensive selection of measuring points for rockfill dam projects. It identifies key research objects and helps improve the effectiveness and efficiency of parameter inversion calculation.

[0026] This method fully considers the uncertainty of the target and the constraints of prior knowledge to construct a multi-objective function expression. By taking into account the uncertainty of the target settlement and the prior relationship between material parameters, it obtains a higher quality and more reasonable solution space. At the same time, the expression constructs multiple objective functions for different measurement point locations and settlement periods, which can obtain a solution space under various spatiotemporal trade-offs, providing researchers with richer solution information.

[0027] The IMOTPE multi-objective optimization algorithm of relaxed domination is used to realize parameter inversion calculation, which alleviates the problem of domination resistance that the original algorithm is prone to in high-dimensional objective optimization problems. At the same time, this algorithm has the advantages of high computational efficiency and solution set diversity compared with other multi-objective optimization algorithms.

[0028] This method proposes to directly substitute the obtained Pareto solution set into the finite element model of the rockfill dam when selecting the final parameter inversion results to calculate the corresponding settlement value of the measuring point. This avoids the problem of suboptimal finite element calculation results caused by the error between the surrogate model and the finite element model in the traditional method.

[0029] Furthermore, the sensitivity analysis process of the material parameters takes into account the synergistic effect of the primary and secondary rockfill materials. The Duncan-Zhang-EB constitutive model is used for both primary and secondary rockfill materials. The global sensitivity analysis method (Sobol method) is used to calculate the sensitivity of the primary and secondary rockfill material parameters to the settlement of multiple measuring points of the dam body. The material parameters with higher comprehensive sensitivity are selected as the inversion parameters.

[0030] Furthermore, when scoring multiple measuring points on the rockfill dam body through multi-index comprehensive analysis, the parameter sensitivity, settlement magnitude, and monitoring data quality of the measuring points are comprehensively considered, and their respective index values ​​are obtained. Parameter sensitivity refers to the sensitivity of the measuring point settlement to changes in material parameters. Monitoring data quality comprehensively considers the missing values ​​and stability of the monitoring data. Finally, these index values ​​are normalized to obtain the mean value, which is then used as the comprehensive evaluation value of the measuring point. The measuring points are then selected based on this comprehensive evaluation value.

[0031] Furthermore, the RC-Stacking model uses multiple diverse and high-performing machine learning models as base models, logistic regression models as meta-models, integrates models through feature stacking, and optimizes model parameters using a grid search algorithm.

[0032] The base models include support vector machines (SVM), random forests (RF), gradient boosting trees (GBDT), XGBoost, and extreme trees (ET) or several of these models.

[0033] Furthermore, the RC-Stacking model uses the regression chain method to consider the correlation between settlements at multiple measuring points. Here, the grey relational analysis method is first used to obtain the correlation matrix between settlements at each measuring point. Then, based on the correlation matrix, the settlements at the measuring points are classified using the hierarchical clustering method, and the settlements at the measuring points with strong correlations are used as a set to construct a regression chain.

[0034] By using the RC-Stacking machine learning algorithm to construct a proxy model for finite element calculation of rockfill dams, and by integrating multiple machine learning models through the Stacking ensemble strategy, and by considering the correlation of multiple measurement points through hierarchical clustering-regression chain method to achieve multiple outputs of the model, the accuracy and robustness of the proxy model are effectively improved, thereby reducing the propagation of model errors in the parameter inversion calculation process.

[0035] Furthermore, considering the uncertainty of the objective and the constraints of prior knowledge, the multi-objective function expression is as follows: (1), In the formula, p ={ p 1, p 2, ..., pS} represents the material parameter vector to be inverted, and there are a total of S One material parameter; L This is the lower bound of the material parameters. U This is the upper bound of the material parameters; f k Indicates the first k There are n objective functions, totaling n. K One objective function; N k Indicates the first k The number of measurement points considered in each objective function; E and E 'Represents the material strength of the primary and secondary rockfill zones, respectively; R(p) This represents the empirical regression relationship between material parameters; g i (p) This represents the score of the relative error at the measuring point.

[0036] Furthermore, the relative error score of the measuring points. g i (p) The expression is as follows: (2), in, u i * Indicates the first i Target settlement value at each measuring point; u i Indicates the first i The calculated settlement values ​​of each measuring point are obtained from a high-precision multi-output proxy model calculated by finite element method. L i * Indicates the first i The lower bound of the settlement interval of each measuring point target. U i * Indicates the first i The upper limit of the settlement interval of each measuring point target.

[0037] Furthermore, the sources of uncertainty in target settlement are considered to include fluctuations in settlement monitoring data, errors in the high-precision multi-output surrogate model, and allowable errors in the finite element calculation model of the rockfill dam. The uncertainty in target settlement is quantified by adding the fluctuation range of settlement monitoring data, the mean absolute error of the high-precision multi-output surrogate model, and the allowable error of the finite element calculation model of the rockfill dam. An allowable error interval is then constructed for the target settlement at each monitoring point. L i * , U i * ].

[0038] Furthermore, the relaxed dominance Bayesian multi-objective optimization algorithm is an improvement on the dominance relationship of the original Bayesian multi-objective optimization algorithm. The relaxation improvement method is that when the distance between the objective function values ​​corresponding to two solutions is within the range of computational uncertainty, these two solutions can dominate each other on that objective function. The expression for the computational uncertainty of the objective function value is: (3), Where, Δ k Indicates the first k The magnitude of the computational uncertainty of each objective function, δ i Indicates the first i The magnitude of fluctuation in settlement monitoring data at each monitoring point MAE i Indicates the first i The mean absolute error of the settlement surrogate model at each measuring point; N k Indicates the first k The number of measurement points whose settlement is considered in each objective function; r c This represents the relaxation coefficient, which reflects the degree of relaxation.

[0039] Furthermore, the solution set optimization process involves directly substituting the optimal Pareto solution set into the finite element calculation model of the rockfill dam to calculate the corresponding settlement values ​​of the measuring points. Then, higher weights are assigned to the settlement values ​​of the measuring points in the main rockfill area and the impoundment period, while lower weights are assigned to the settlement values ​​of the measuring points in the secondary rockfill area and the completion period. The solution with the highest score is obtained through the spatiotemporal weighted TOPSIS method as the final parameter inversion result.

[0040] Example 2: Combination Figures 1 to 11 As shown, this embodiment uses a more specific case to illustrate in detail the efficient inversion method for material parameters of rockfill dams in Embodiment 1, which considers target uncertainty and prior knowledge constraints.

[0041] First, the inversion parameters and calculation measurement points were determined. The dam material zones and corresponding material constitutive models for the rockfill dam under study were selected. Considering the correlation of material parameters, a global sensitivity analysis method was used to obtain the sensitivity of material parameters to the dam structure response under the synergistic effect of multiple material zones. Material parameters with higher sensitivity were selected as inversion parameters. Simultaneously, considering the parameter sensitivity of measurement points, the magnitude of settlement, and the quality of monitoring data, multiple measurement points on the dam were scored through multi-index comprehensive analysis, and measurement points with higher scores were selected as calculation measurement points.

[0042] Table 1: Test values ​​of parameters and their cross-correlation of riprap materials

[0043] Based on engineering data, a finite element calculation model of the largest cross-section of the Liyuan concrete rockfill dam in Yunnan Province was constructed, and the layout of measuring points was as follows: Figure 2 As shown, considering the dam body material zoning, including the face plate, cushion layer, transition layer, main rockfill zone, and secondary rockfill zone, there are 24 measuring points on the dam body cross-section, denoted as BV1 to BV24. The inversion study object is the rockfill material parameters, and the material constitutive model Duncan-Chang EB model is used. The experimental values ​​of the model parameters and the parameter correlation matrix are shown in Table 1. Considering the synergistic effect of the main and secondary rockfill materials on dam body settlement, the rockfill material parameters include the main rockfill material parameters K and R. f , φ0, K b , n, Δφ, m and secondary rockfill material parameters K', R f '、φ0'、K b '、n'、Δφ' and m'.

[0044] Considering the correlation between material parameters and between different material zones, and combining engineering experience, the value ranges of each material parameter are given. The corresponding settlement values ​​are obtained through finite element method settlement calculation of the dam as samples for sensitivity analysis. The global sensitivity analysis method, Sobol method, is used to calculate the sensitivity of the rockfill material parameters to the settlement of each measuring point in the dam body. Figure 3 As shown, the final selection of 8 parameters R with high overall sensitivity was made. f , φ0, K b , Δφ, m, R f '、φ0' and K b ' is used as the inversion parameter. Here, parameters φ0' and K are specifically chosen. b This is because they have a significant impact on some monitoring points in the secondary rockfill area, which is beneficial for the calibration of settlement at these monitoring points. A comprehensive evaluation of each monitoring point is conducted, considering three indicators: settlement magnitude, parameter sensitivity, and monitoring data quality. The settlement magnitude and parameter sensitivity of the monitoring points are normalized to obtain indicator scores. Based on the degree of missing settlement monitoring data and data volatility, the monitoring data quality scores are divided into 0, 0.8, and 1. The mean of the scores for each indicator is used as the comprehensive quality evaluation value for the monitoring point. The calculation results are as follows: Figure 4 As shown. Based on the comprehensive quality evaluation value, measurement points BV3, BV4, BV11, BV12, BV13, BV14, BV18, BV19, BV20, BV21, BV23, and BV24 were selected as calculation measurement points.

[0045] Secondly, a high-precision multi-output surrogate model is constructed. Considering the correlation between material parameters, material parameter combinations are randomly generated within a reasonable range as features of the sample set. Based on the generated material parameter combinations, the corresponding settlement values ​​of the measurement points are obtained through finite element analysis as labels for the sample set. A Stacking ensemble algorithm is used to fuse multiple machine learning models to improve the fitting accuracy of the surrogate model. Simultaneously, a regression chain is used to consider the correlation between settlements at multiple measurement points, further improving the accuracy of the surrogate model and achieving multiple outputs. Finally, a high-precision multi-output surrogate model, namely the RC-Stacking model, is obtained. The generated sample dataset is then used to train and optimize the parameters of this surrogate model.

[0046] Combining the material parameter correlation matrix in Table 1 and the parameter range in Table 2, the material parameter R to be inverted is randomly generated. f ,φ0,K b ,Δφ,m,R f ', φ0' and K b The combined samples of material parameters were input into the finite element calculation model of the rockfill dam, and the corresponding settlement values ​​of the measuring points were calculated as the model output, forming the final model sample. After multiple adjustments, the sample size was selected as 900 sets. To construct the surrogate model, the grey relational analysis method was first used to calculate the correlation degree of the settlement of the measuring points at different time periods based on these samples. Based on this correlation degree, hierarchical clustering was used to classify the measuring points. The classification results are as follows: Figures 5-8 As shown, the measuring points are hierarchically clustered with a link distance of 0.7 as the threshold. For the settlement of measuring points during the completion period, the hierarchical clustering results are as follows: measuring points BV3, BV4, BV11, BV12, BV13, BV14, and BV18 ​​belong to one class, denoted as C1-Ⅰ; measuring points BV19, BV20, BV21, BV23, and BV24 belong to another class, denoted as C2-Ⅰ. For the settlement of measuring points during the water storage period, the hierarchical clustering results are as follows: measuring points BV3, BV11, BV12, BV18, BV19, and BV24 belong to one class, denoted as C1-Ⅱ; BV4, BV13, BV14, BV20, and BV21 belong to another class, denoted as C2-Ⅱ. Then, an RC-Stacking model is constructed for each class of related measuring points, and the model is trained and its parameters are optimized. Support Vector Machine (SVM), Random Forest (RF), Gradient Boosting Tree (GBDT), XGBoost, and Extreme Tree (ET) models were selected as base models, and Logistic Regression (LR) model was selected as the meta-model. The optimization results of the model parameters are shown in Table 3. The R-squared values ​​of the surrogate model are used... 2A threshold greater than 0.9 was used to select the settlement during the completion period for measuring points BV3, BV4, BV11, BV12, BV13, BV14, BV18, BV19, BV20, BV21, BV23, and BV24, and the settlement during the water storage period for measuring points BV4, BV13, BV14, BV20, and BV21 for parameter inversion calculation. The surrogate model fitting effect and accuracy evaluation index values ​​corresponding to the spatiotemporal settlement of each measuring point are as follows: Figure 4 As shown.

[0047] Table 2: Initial values ​​and ranges of inversion parameters

[0048] Table 3: Parameter Values ​​for the Agent Model

[0049] Third, construct a multi-objective function expression. The settlement of the measured points is classified according to the dam's operating period, zone location, and correlation. An objective function is constructed for the settlement of each type of measured point. At the same time, considering the uncertainty of the target settlement, an error allowable interval is constructed for the target settlement of each measured point. The prior relationship between material parameters is used as a constraint condition. The multi-objective function expression is constructed with the goal of minimizing the relative distance between the calculated settlement and the target settlement.

[0050] Based on equations (1) and (2), the multi-objective optimization function expression in this implementation case is constructed as follows:

[0051] in, p ={ p 1, p 2, ..., p 8} represents the material parameter vector to be inverted, with a total of 8 material parameters, namely R f , φ0, K b , Δφ, m, R f '、φ0' and K b '; U and L These are the upper and lower bounds for the material parameter values, respectively. f k Indicates the first k Six objective functions were constructed, taking into account different time periods, zoning locations, and correlations of the settlement at the measuring points. The settlement at the measuring points considered by each objective function are as follows: BV3-Ⅰ, BV4-Ⅰ, BV11-Ⅰ, BV12-Ⅰ, BV13-Ⅰ, BV18-Ⅰ, BV14-Ⅰ, BV19-Ⅰ, BV23-Ⅰ, BV20-Ⅰ, BV21-Ⅰ, BV24-Ⅰ, BV4-Ⅱ, BV13-Ⅱ, BV14-Ⅱ, BV20-Ⅱ, and BV21-Ⅱ.N k This represents the number of measurement points considered in the k-th objective function; r 0 This represents a random number between 0.81 and 1.19. g i (p) The relative error score of the measuring point is expressed as follows:

[0052] in, u i * Indicates the first i The actual monitoring values ​​of each measuring point; u i Indicates the first i The calculated settlement values ​​of each measuring point are obtained from the finite element calculation proxy model. U i * and L i * They represent the first i The upper and lower bounds of the allowable error for settlement at each measuring point are defined, and the allowable error is calculated as follows: , in, ξ i Indicates the first i Allowable error in calculating settlement at each measuring point; δ i Indicates the first i The magnitude of fluctuation in settlement monitoring data at each monitoring point MAE i Indicates the first i The mean absolute error of the settlement surrogate model at each measuring point was 3%. ·u i * Indicates the first i Allowable error of the finite element calculation model for settlement at each measuring point.

[0053] Fourth, perform multi-objective parameter inversion calculations. Determine the material parameter search space, and use the relaxation-dominated Bayesian multi-objective optimization algorithm IMOTPE to solve the multi-objective function expression constructed in the previous step. Select a relaxation coefficient of 1.0 to perform parameter inversion calculations and obtain a set of optimal Pareto solutions.

[0054] The dominance relationship in the original Bayesian multi-objective optimization algorithm MOTPE is relaxed and improved. Specifically, it is assumed that when the calculated settlement values ​​of two parametric solutions with respect to a certain measuring point both fall within the allowable range of the target settlement error, these two parametric solutions are mutually dominant in terms of the settlement at that measuring point. This relaxation improvement alleviates the dominance resistance problem of the original algorithm and improves the quality of the non-dominated solution set. The improved MOTPE algorithm is used to solve the established multi-objective function expression, with 500 iterations, yielding the optimal Pareto solution set. A total of 69 Pareto solutions were obtained using the MOTPE algorithm, exhibiting a uniform distribution and diversity. Furthermore, the algorithm's running time is 0.38 hours, significantly shorter than the corresponding finite element computation time of 2.5 hours, demonstrating a significant advantage in computational efficiency.

[0055] Fifth, optimal solution set selection is achieved. The optimal Pareto solution set of material parameters is substituted into the finite element model of the rockfill dam to calculate the corresponding settlement value of the measuring point and the corresponding relative error score of the measuring point. According to the engineering requirements, the measuring points at different spatiotemporal locations are weighted, and the spatiotemporal weighted TOPSIS method is used to score each Pareto solution. The solution with the highest score is selected as the final parameter inversion result.

[0056] The Pareto solution set obtained in the previous step was substituted into the finite element model to calculate the settlement of the measuring points over multiple time periods, obtaining the updated settlement values ​​for each measuring point. Considering spatiotemporal weights, the weighting coefficients for the settlement during the water storage period at the main rockfill area measuring points, the settlement during the water storage period at the secondary rockfill area measuring points, the settlement at the completion period at the main rockfill area measuring points, and the settlement at the completion period at the secondary rockfill area measuring points were given as 3:2:2:1. Furthermore, the distance between the inversion results and the experimental results was used as an evaluation index, with a weighting coefficient of 3. Finally, the TOPSIS method was used to select the solution with the highest score as the final parameter inversion result. The corresponding finite element forward calculation results are shown below. Figure 11 .Depend on Figure 11 It is evident that the proposed parameter inversion method can effectively improve the accuracy of the finite element model, with a cumulative relative improvement of 69.9% in settlement during the completion period and a cumulative relative improvement of 46.8% in settlement during the water storage period.

[0057] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An efficient inversion method for material parameters of rockfill dams considering objective uncertainty and prior knowledge constraints, characterized in that, Includes the following steps: Establish a finite element calculation model for a rockfill dam; Based on the global sensitivity analysis method, material parameters with higher sensitivity are selected as inversion parameters; based on multi-index comprehensive analysis, multiple measuring points on the rockfill dam body are scored, and measuring points with higher scores are selected as calculation measuring points. Based on the inversion parameters, a combination of correlation parameters is generated. The settlement values ​​of the measurement points are extracted through finite element calculation and combined with the obtained calculation measurement points as labels for the sample set, thus generating learning samples. Based on the generated learning samples, the RC-Stacking model is trained and optimized to construct a high-precision multi-output agent model; For each type of measurement point settlement, an objective function is constructed. Considering the uncertainty of the target settlement, an error allowable interval is constructed for the target settlement of each measurement point. The prior relationship between material parameters is used as a constraint condition. The objective is to construct a multi-objective function expression with the goal of minimizing the relative distance between the calculated settlement and the target settlement interval. The search space for material parameters is determined, and the constructed multi-objective function expression is solved using the relaxation-dominated Bayesian multi-objective optimization algorithm to obtain the optimal Pareto solution set for the material parameters. The optimal Pareto solution set is substituted into the finite element calculation model of the rockfill dam to calculate the corresponding settlement value of the measuring point and the corresponding relative error score of the measuring point. According to the engineering requirements, the measuring points at different time and space locations are weighted, and the spatiotemporal weighted TOPSIS method is used to score each Pareto solution. The solution with the highest score is selected as the final parameter inversion result.

2. The efficient inversion method for material parameters of rockfill dams considering target uncertainty and prior knowledge constraints as described in claim 1, characterized in that, The sensitivity analysis process of the material parameters takes into account the synergistic effect of primary and secondary rockfill materials. Both primary and secondary rockfill materials adopt the Duncan-Zhang-EB constitutive model. The global sensitivity analysis method is used to calculate the sensitivity of the primary and secondary rockfill material parameters to the settlement of multiple measuring points of the dam body. The material parameters with higher comprehensive sensitivity are selected as inversion parameters.

3. The efficient inversion method for material parameters of rockfill dams considering target uncertainty and prior knowledge constraints as described in claim 1, characterized in that, When scoring multiple monitoring points on a rockfill dam using a multi-index comprehensive analysis, the parameter sensitivity, settlement magnitude, and monitoring data quality of the monitoring points are comprehensively considered. Parameter sensitivity refers to the sensitivity of the monitoring point's settlement to changes in material parameters. Monitoring data quality comprehensively considers missing values ​​and stability of the monitoring data. After normalization processing, the mean value is obtained and used as the comprehensive evaluation value of the monitoring point. Based on this comprehensive evaluation value, monitoring points are selected.

4. The efficient inversion method for material parameters of rockfill dams considering target uncertainty and prior knowledge constraints as described in claim 1, characterized in that, The RC-Stacking model uses multiple diverse and high-performing machine learning models as base models, logistic regression models as meta-models, integrates models through feature stacking, and optimizes model parameters using a grid search algorithm. The RC-Stacking model uses the regression chain method to consider the correlation between settlements at multiple measurement points. It uses the grey relational analysis method to obtain the correlation matrix between settlements at each measurement point. Based on this correlation matrix, it uses hierarchical clustering to classify the settlements at the measurement points and uses the settlements at measurement points with strong correlations as a set to construct a regression chain.

5. The efficient inversion method for material parameters of rockfill dams considering target uncertainty and prior knowledge constraints as described in claim 1, characterized in that, The multi-objective function expression considering objective uncertainty and prior knowledge constraints is as follows: ， In the formula, p ={ p 1, p 2, ..., p S } represents the material parameter vector to be inverted, and there are a total of S One material parameter; L This is the lower bound of the material parameters. U This is the upper bound of the material parameters; f k Indicates the first k There are n objective functions, totaling n. K One objective function; N k Indicates the first k The number of measurement points considered in each objective function; E and E 'Represents the material strength of the primary and secondary rockfill zones, respectively; R(p) This represents the empirical regression relationship between material parameters; g i (p) This indicates the score for the relative error of the measuring point; relative error score of measuring points g i (p) The expression is as follows: ， in, u i * Indicates the first i Target settlement value at each measuring point; u i Indicates the first i The calculated settlement values ​​of each measuring point are obtained from a high-precision multi-output proxy model calculated by finite element method. L i * Indicates the first i The lower bound of the settlement interval of each measuring point target. U i * Indicates the first i The upper limit of the settlement interval of each measuring point target.

6. The efficient inversion method for material parameters of rockfill dams considering target uncertainty and prior knowledge constraints as described in claim 1, characterized in that, The uncertainty of target settlement is considered from the sources of fluctuation in settlement monitoring data, errors in the high-precision multi-output surrogate model, and allowable errors in the finite element calculation model of the rockfill dam. The uncertainty of target settlement is quantified by adding the fluctuation range of settlement monitoring data, the mean absolute error of the high-precision multi-output surrogate model, and the allowable error of the finite element calculation model of the rockfill dam. An allowable error interval is then constructed for the target settlement at each measuring point. L i * , U i * ].

7. The efficient inversion method for material parameters of rockfill dams considering target uncertainty and prior knowledge constraints as described in claim 1, characterized in that, The relaxed dominance Bayesian multi-objective optimization algorithm improves the dominance relationship of the original Bayesian multi-objective optimization algorithm by relaxing the dominance relationship. The relaxation improvement method is that when the distance between the objective function values ​​corresponding to two solutions is within the range of computational uncertainty, the two solutions can dominate each other on that objective function. The expression for the computational uncertainty of the objective function value is: ， Where, Δ k Indicates the first k The magnitude of the computational uncertainty of each objective function, δ i Indicates the first i The magnitude of fluctuation in settlement monitoring data at each monitoring point MAE i Indicates the first i The mean absolute error of the settlement surrogate model at each measuring point; N k Indicates the first k The number of measurement points whose settlement is considered in each objective function; r c This represents the relaxation coefficient, which reflects the degree of relaxation.

8. The efficient inversion method for material parameters of rockfill dams considering target uncertainty and prior knowledge constraints as described in claim 1, characterized in that, The process of solution set optimization involves directly substituting the optimal Pareto solution set into the finite element calculation model of the rockfill dam to calculate the corresponding settlement values ​​of the measuring points. Higher weights are assigned to the settlement values ​​of the measuring points in the main rockfill area and the water storage period, while lower weights are assigned to the settlement values ​​of the measuring points in the secondary rockfill area and the completion period. The solution with the highest score is obtained through the spatiotemporal weighted TOPSIS method as the final parameter inversion result.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program that, when executed by a processor, implements the efficient inversion method for material parameters of rockfill dams as described in any one of claims 1 to 8, taking into account objective uncertainty and prior knowledge constraints.

10. An electronic device, characterized in that, The electronic device includes at least one processor and at least one memory connected to the processor; wherein the processor is used to call program instructions in the memory to execute the efficient inversion method for rockfill dam material parameters considering target uncertainty and prior knowledge constraints as described in any one of claims 1 to 8.

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