Rockfill material parameter inversion method based on weight coefficient distribution

Abstract

The invention discloses a rock-fill material parameter inversion method based on weight coefficient distribution. The method is specifically implemented according to the following steps: step 1, collecting rock-fill dam engineering data, establishing a finite element model, screening key material parameters of a Duncan-Zhang E-B model by adopting orthogonal test and range analysis, and establishing a target function; step 2, XGBoost multi-output model training is carried out; step 3, carrying out MOPSO multi-objective optimization and weight distribution; and 4, inputting the inversion parameters into the finite element model, and verifying the consistency of the calculated settlement and the actually measured data. According to the method, the problems of insufficient partition deformation difference description, subjective weight distribution and low calculation efficiency in the prior art are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of water conservancy engineering and geotechnical engineering, and particularly relates to a method for inverting rockfill material parameters based on distribution weight coefficients. Background Art

[0002] Rockfill dam material parameter inversion is a key technology for inferring material constitutive parameters from monitoring data. Traditional methods rely on single-objective optimization and finite element forward modeling, making it difficult to balance multi-zone deformation differences and computational efficiency. With the development of machine learning and multi-objective optimization algorithms, the combination of surrogate models and intelligent algorithms has become an important direction for improving inversion accuracy and efficiency. Existing rockfill material parameter inversion methods use a single objective function and fit global settlement data through a surrogate model, but have the following drawbacks: Unable to reflect the deformation differences of different zones: The material properties of the main rockfill area and the secondary rockfill area are not distinguished, resulting in the inversion parameters being unable to accurately describe the settlement laws of each zone.

[0003] Weight allocation is highly subjective: Traditional weight setting relies on manual experience and lacks a data-driven objective evaluation mechanism.

[0004] Low computational efficiency: Forward calculations based on finite elements are very time-consuming in multi-objective optimization and cannot meet the real-time requirements of engineering. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for inverting rockfill material parameters based on allocated weight coefficients, which solves the problems of insufficient description of zone deformation differences, subjective weight allocation and low calculation efficiency in the prior art.

[0006] The technical solution adopted by the present invention is a method for inverting the parameters of rockfill materials based on the distribution of weight coefficients, which is specifically implemented according to the following steps: Step 1: Collect rockfill dam engineering data, establish a finite element model, use orthogonal testing and range analysis to screen key material parameters of the Duncan-Zhang EB model, and establish an objective function; Step 2: XGBoost multi-output model training; Step 3: MOPSO multi-objective optimization and weight allocation; Step 4: Input the inversion parameters into the finite element model to verify the consistency between the calculated settlement and the measured data.

[0007] The present invention is also characterized in that: Step 1 is implemented as follows: Step 1.1: Obtain the rockfill dam engineering data, including material partitioning, filling process, and settlement monitoring data. Build a 3D finite element model based on ABAQUS, simulate the construction loading process, and arrange finite element nodes at the buried locations of the settlement meters. Step 1.2: Extract the seven parameters of the Duncan-Zhang EB model and set an increment of plus or minus 10% to 30% for each parameter to form a parameter combination set; Step 1.3, use Orthogonal test design, input parameter combinations into the three-dimensional finite element model finite element model, and calculate the settlement response value of each measuring point; Step 1.4: Calculate the parameter range value based on the range method. The larger the range value, the higher the parameter sensitivity. The formula is:

[0008]

[0009] in, is the average value of the test results of the rockfill dam response value j at the i-th level, is the number of tests of the rockfill dam response value j at the i-th level, is the result of the nth test of the rockfill dam response value j at the i-th level, is the average value of all test results of rockfill dam response value j, is the extreme value of the test result of factor j, is the maximum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments, is the minimum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments; Step 1.5, sort by the range value in descending order, extract the first 40% of the parameters as the parameters to be inverted, and select K, K b , m as the key parameters of the main rockfill area and the secondary rockfill area; Step 1.6: Select settlement data from typical measuring points in the upstream and downstream rockfill areas and extract the settlement increment at the completion of the filling. Define the dual objective function as follows:

[0010] in, f 1 represents the objective function of the upstream rockfill area, f 2 represents the objective function of the downstream rockfill area, To predict settlement, is the measured settlement, m i 、n j is the number of partition measurement points and characteristic moments.

[0011] The seven parameters of the Duncan-Zhang EB model extracted in step 1.2 are: tangent modulus coefficient K, modulus index n, failure ratio Rf, initial internal friction angle φ0, bulk modulus index m, change in friction angle Δφ, and bulk modulus parameter Kb.

[0012] Step 2 is implemented as follows: Step 2.1, Latin hypercube sampling LHS generates a sample data set, and the six key parameters K b1 , K 1, m 1, K b2 , K 2, m The value range of 2 is evenly divided into 10 probability intervals, and the cumulative probability of each interval is 10%. K b1 represents the bulk modulus coefficient of the main rockfill area, K 1 represents the initial tangent modulus coefficient of the main rockfill area, m 1 represents the bulk modulus index of the main rockfill area, K b2 represents the bulk modulus coefficient of the secondary rockfill area, K 2 represents the initial tangent modulus coefficient of the secondary rockfill area, m 2 represents the bulk modulus index of the secondary rockfill area. Latin hypercube sampling is used to ensure that exactly one sample point is sampled in each interval and that the samples are evenly distributed in the parameter space. The normalized samples (0–1) obtained by sampling are restored to the actual parameter values. ABAQUS calculations are run on each set of parameter samples, generating a total of 100 sets of samples {( X k , Y k )},in X k is a 6-dimensional parameter vector, Y k It is an 8-dimensional settlement vector in cm. Then the parameters and settlement values ​​are saved in a CSV file. Step 2.2: Use Latin Hypercube Sampling (LHS) to generate 100 sets of parameter combinations. The settlement values ​​of 8 measuring points are obtained by finite element calculation. Random K-fold cross validation is used with K=5 to divide the data into training and test sets, and the input and output parameters are calculated. K b1 , K 1, m 1, K b2 , K 2, m 2. Use normalization; Step 2.3: Train the multi-output XGBoost model. In step 2.4, use Scikit-learn's GridSearchCV to perform 5-fold cross-validation on the multi-output XGBoost model, optimizing to minimize the root mean square error (RMSE). Use an early stopping strategy during training iterations, terminating training when the validation set RMSE does not decrease for 10 consecutive rounds to avoid overfitting.

[0013] Step 2.3 is implemented as follows: Using multi-output regression mode, the settlement prediction of each measuring point is an independent output node, sharing 6-dimensional input features K b1 , K 1, m 1, K b2 , K 2, m 2. Use the multi:linear objective of the multi-output XGBoost model, which supports linear weighted multi-output. The formula is:

[0014] Among them, K is the output dimension, is a set of regression trees.

[0015] Step 3 is implemented as follows: Step 3.1: First, initialize the particle swarm. Step 3.2: In each iteration, the particle predicts the settlement values ​​of the eight measurement points corresponding to the current parameters through the multi-output XGBoost model; Step 3.3: Standardize the objective function value in the Pareto solution set.

[0016] Step 3.1 is implemented as follows: Each particle represents a set of 6-dimensional material parameter vectors The vector X position is randomly generated within the parameter range. The velocity is initialized to ±5% of the parameter range to control the search step size. The population size is set to 50 particles. The maximum capacity of the external archive set is 50 solutions, which is used to store non-dominated solutions found during the iteration. The inertia weight adopts a linear decrease strategy, and the formula is , where t is the current iteration number, This strategy enhances the global search capability in the early stage of iteration and focuses on local fine adjustment in the later stage. The learning factor is set to and , in order to balance the particle's dependence on its own historical optimal solution and the group's global optimal solution.

[0017] Step 3.2 is implemented as follows: Calculate the objective function of the upstream and downstream rockfill areas and sort the particles based on the Pareto dominance principle: if particle A f 1 and f 2 are not inferior to particle B and at least one indicator is strictly better, then A dominates B, and the solutions not dominated by any particle are stored in the external archive set; to maintain the diversity of the archive set, when the archive set is full, if the new solution dominates part of the existing solutions, the dominated solution is replaced, otherwise the grid density method is used to delete the solutions in the high-density area; The selection of the global optimal solution Gbest directly affects the convergence of the algorithm. The specific process is: calculate the Euclidean distance between the particle and all solutions in the archive as the similarity distance SD, such as particle X i With archive solution Y j The SD is , then calculate the average similarity distance ASD, filter out particles with SD smaller than ASD, randomly select one of them as Gbest, and guide the particles to search for the under-explored solution space area to avoid falling into the local optimum; Step 3.3 is implemented as follows: For negative indicators, use the formula ,in: For the i In the group data j The standardized value of each indicator; For the j The maximum value of an indicator; For the j The minimum value of the indicator will f 1 and f 2Normalized to the interval [0,1]; Then calculate the indicator variability and conflict: standard deviation Reflects the ability of indicators to distinguish, correlation coefficient The degree of information overlap between indicators and the amount of information of a single indicator , after normalization, we get the weight Taking the document data as an example, the weights of the main rockfill area and the secondary rockfill area are calculated, indicating that the deformation of the main rockfill area is more important to the parameter inversion. Based on the linear weighted objective function , traverse the Pareto solution set and select the parameter combination that minimizes F as the optimal solution.

[0018] The present invention's beneficial effect is that its weighted coefficient-based inversion method for rockfill material parameters addresses the problems of traditional single-objective inversion methods, such as their inability to reflect deformation differences among rockfill dam subregions, subjective weight assignment, and low computational efficiency. This method achieves optimization through the following steps: First, a dual-objective function is constructed based on settlement monitoring data from upstream and downstream rockfill areas, with the second norm of the monitored and calculated values ​​serving as the optimization objective. Second, Latin hypercube sampling is used to generate parameter-settlement samples, and a multi-output XGBoost surrogate model is trained to replace finite element forward modeling. The model achieves an average goodness-of-fit R² of 0.969, significantly improving computational efficiency. Finally, a multi-objective particle swarm optimization (MOPSO) algorithm is used for global optimization, generating a Pareto front solution set through non-dominated sorting. The CRITIC weighting method is then introduced to dynamically assign objective function weights, identifying the optimal parameter combination that balances deformation coordination among subregions. Finally, finite element calculations are used to verify the engineering reliability of the inversion parameters. By introducing a weighted coefficient allocation strategy and an efficient surrogate model, multi-region deformation coordination and global parameter optimization are achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flow chart of the rockfill material parameter inversion method based on the distribution of weight coefficients provided by the present invention; Figure 2 A schematic diagram of a three-dimensional finite element model of a rockfill dam in the rockfill material parameter inversion method based on distribution weight coefficients provided by the present invention; Figure 3 A schematic diagram of target monitoring positions of a rockfill dam in the rockfill material parameter inversion method based on distribution weight coefficients provided by the present invention; Figure 4 The Pareto solution of the rockfill material parameter inversion method based on the distribution weight coefficient provided by the present invention; Figure 5 A comparison chart of the inversion results of the ES1 survey line in the rockfill material parameter inversion method based on the distribution weight coefficient provided by the present invention; Figure 6 This is a comparison chart of the inversion results of the ES2 survey line in the rockfill material parameter inversion method based on the distribution weight coefficient provided by the present invention. DETAILED DESCRIPTION

[0020] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] The present invention is based on the method for inversion of rockfill material parameters based on the distribution weight coefficient, and the flow chart is as follows: Figure 1 As shown, please follow the steps below: Step 1: Collect rockfill dam engineering data, establish a finite element model, use orthogonal testing and range analysis to screen key material parameters of the Duncan-Zhang EB model, and establish an objective function; Step 1 is implemented as follows: Step 1.1: Obtain the rockfill dam engineering data, including material partitioning, filling process, and settlement monitoring data. Build a 3D finite element model based on ABAQUS, simulate the construction loading process, and arrange finite element nodes at the buried locations of the settlement meters. Step 1.2: Extract the seven parameters of the Duncan-Zhang EB model and set an increment of plus or minus 10% to 30% for each parameter to form a parameter combination set; Step 1.3, use Orthogonal test design, input parameter combinations into the three-dimensional finite element model finite element model, and calculate the settlement response value of each measuring point; Step 1.4: Calculate the parameter range value based on the range method. The larger the range value, the higher the parameter sensitivity. The formula is:

[0022]

[0023] in, is the average value of the test results of the rockfill dam response value j at the i-th level, is the number of tests of the rockfill dam response value j at the i-th level, is the result of the nth test of the rockfill dam response value j at the i-th level, is the average value of all test results of rockfill dam response value j, is the extreme value of the test result of factor j, is the maximum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments, is the minimum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments; Step 1.5, sort by the range value in descending order, extract the first 40% of the parameters as the parameters to be inverted, and select K, K b , m as the key parameters of the main rockfill area and the secondary rockfill area; Step 1.6: Select settlement data from typical measuring points in the upstream and downstream rockfill areas and extract the settlement increment at the completion of the filling. Define the dual objective function as follows:

[0024] in, f 1 represents the objective function of the upstream rockfill area, f 2 represents the objective function of the downstream rockfill area, To predict settlement, is the measured settlement, m i 、n j is the number of partition measurement points and characteristic moments.

[0025] The seven parameters of the Duncan-Zhang EB model extracted in step 1.2 are: tangent modulus coefficient K, modulus index n, failure ratio Rf, initial internal friction angle φ0, bulk modulus index m, change in friction angle Δφ, and bulk modulus parameter Kb.

[0026] Step 2: XGBoost multi-output model training and validation; Step 2 is implemented as follows: Step 2.1, Latin hypercube sampling LHS generates a sample data set, and the six key parameters K b1 , K 1, m 1, K b2 , K 2, m The value range of 2 is evenly divided into 10 probability intervals, and the cumulative probability of each interval is 10%. K b1 represents the bulk modulus coefficient of the main rockfill area, K 1 represents the initial tangent modulus coefficient of the main rockfill area, m 1 represents the bulk modulus index of the main rockfill area, K b2 represents the bulk modulus coefficient of the secondary rockfill area, K 2 represents the initial tangent modulus coefficient of the secondary rockfill area, m 2 represents the bulk modulus index of the secondary rockfill area. Latin hypercube sampling is used to ensure that exactly one sample point is sampled in each interval and that the samples are evenly distributed in the parameter space. The normalized samples (0–1) obtained by sampling are restored to the actual parameter values. ABAQUS calculations are run on each set of parameter samples, generating a total of 100 sets of samples {( X k , Y k )},in X k is a 6-dimensional parameter vector, Y k It is an 8-dimensional settlement vector in cm. Then the parameters and settlement values ​​are saved in a CSV file. Step 2.2: Use Latin Hypercube Sampling (LHS) to generate 100 sets of parameter combinations. Use finite element calculation to obtain the settlement values ​​of 8 measuring points. Use random K-fold cross validation with K=5 to divide the data into training and test sets. The training set is 80 sets (80%) for model training; the test set is 20 sets (20%) for independent verification. K b1 , K 1, m 1, K b2 , K 2, m 2. Use normalization; Step 2.3: Train the multi-output XGBoost model. Steps 2.1 and 2.2 are the preparations for training the multi-output XGBoost model. Only with a dataset can you train the proxy model. Step 2.4: Use Scikit-learn's GridSearchCV to perform 5-fold cross-validation on the multi-output XGBoost model, optimizing for minimizing the root mean square error (RMSE). Use early stopping during training iterations, terminating training when the validation set RMSE does not decrease for 10 consecutive epochs to avoid overfitting. Step 2.5: Model performance was evaluated using four metrics: mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R²). Comparison of the four models, CPO-XGBoost, CPO-MORF, CPO-MSVR, and CPO-HKELM, revealed that XGBoost exhibited significant advantages at most measurement points.

[0027] Step 2.3 is implemented as follows: Using multi-output regression mode, the settlement prediction of each measuring point is an independent output node, sharing 6-dimensional input features K b1 , K 1, m 1, K b2 , K 2, m 2 (Material parameters); Use the multi:linear objective of the multi-output XGBoost model, which supports linearly weighted multi-output. The formula is:

[0028] Among them, K is the output dimension (K=8, the number of measurement points), is a set of regression trees.

[0029] Step 3: MOPSO multi-objective optimization and weight allocation; Step 3 is implemented as follows: Step 3.1: First, initialize the particle swarm. Step 3.1 is implemented as follows: Each particle represents a set of 6-dimensional material parameter vectors The vector X position is randomly generated within the parameter range. The velocity is initialized to ±5% of the parameter range to control the search step size. The population size is set to 50 particles. The maximum capacity of the external archive set is 50 solutions, which is used to store non-dominated solutions found during the iteration. The inertia weight adopts a linear decrease strategy, and the formula is , where t is the current iteration number, This strategy enhances the global search capability in the early stage of iteration and focuses on local fine adjustment in the later stage. The learning factor is set to and , in order to balance the particle's dependence on its own historical optimal solution and the group's global optimal solution.

[0030] Step 3.2: In each iteration, the particle predicts the settlement values ​​of the eight measurement points corresponding to the current parameters through the multi-output XGBoost model; Step 3.2 is implemented as follows: Calculate the objective function of the upstream and downstream rockfill areas and sort the particles based on the Pareto dominance principle: if particle A f 1 and f 2 are not inferior to particle B and at least one indicator is strictly better, then A dominates B, and the solutions not dominated by any particle are stored in the external archive set; to maintain the diversity of the archive set, when the archive set is full, if the new solution dominates part of the existing solutions, the dominated solution is replaced, otherwise the grid density method is used to delete the solutions in the high-density area; The selection of the global optimal solution Gbest directly affects the convergence of the algorithm. The specific process is: calculate the Euclidean distance between the particle and all solutions in the archive as the similarity distance SD, such as particle X i With archive solution Y j The SD is , then calculate the average similarity distance ASD, filter out particles with SD smaller than ASD, randomly select one of them as Gbest, and guide the particles to search for the under-explored solution space area to avoid falling into the local optimum; Step 3.3: Standardize the objective function value in the Pareto solution set.

[0031] Step 3.3 is implemented as follows: For negative indicators (the smaller the value, the better), use the formula ,in: For the i In the group data j The standardized value of each indicator; For the j The maximum value of an indicator; For the j The minimum value of the indicator will f 1 and f 2Normalized to the interval [0,1]; Then calculate the indicator variability and conflict: standard deviation Reflects the ability of indicators to distinguish, correlation coefficient The degree of information overlap between indicators and the amount of information of a single indicator , after normalization, we get the weight Taking the document data as an example, the weights of the main rockfill area and the secondary rockfill area are calculated, indicating that the deformation of the main rockfill area is more important to the parameter inversion. Based on the linear weighted objective function , traverse the Pareto solution set and select the parameter combination that minimizes F as the optimal solution.

[0032] Step 4: Input the inversion parameters into the finite element model to verify the consistency between the calculated settlement and the measured data.

[0033] Example 1 The present invention is based on the method for inversion of rockfill material parameters based on the distribution weight coefficient, and the flow chart is as follows: Figure 1 As shown, please follow the steps below: Step 1: Collect rockfill dam engineering data, establish a finite element model, use orthogonal testing and range analysis to screen key material parameters of the Duncan-Zhang EB model, and establish an objective function; Step 2: XGBoost multi-output model training and validation; Step 3: MOPSO multi-objective optimization and weight allocation; Step 4: Input the inversion parameters into the finite element model to verify the consistency between the calculated settlement and the measured data.

[0034] Example 2 The present invention is based on the method for inversion of rockfill material parameters based on the distribution weight coefficient, and the flow chart is as follows: Figure 1 As shown, please follow the steps below: Step 1: Collect rockfill dam engineering data, establish a finite element model, use orthogonal testing and range analysis to screen key material parameters of the Duncan-Zhang EB model, and establish an objective function; Step 1 is implemented as follows: Step 1.1: Obtain the rockfill dam engineering data, including material partitioning, filling process, and settlement monitoring data. Build a 3D finite element model based on ABAQUS, simulate the construction loading process, and arrange finite element nodes at the buried locations of the settlement meters. Step 1.2: Extract the seven parameters of the Duncan-Zhang EB model and set an increment of plus or minus 10% to 30% for each parameter to form a parameter combination set; Step 1.3, use Orthogonal test design, input parameter combinations into the three-dimensional finite element model finite element model, and calculate the settlement response value of each measuring point; Step 1.4: Calculate the parameter range value based on the range method. The larger the range value, the higher the parameter sensitivity. The formula is:

[0035]

[0036] in, is the average value of the test results of the rockfill dam response value j at the i-th level, is the number of tests of the rockfill dam response value j at the i-th level, is the result of the nth test of the rockfill dam response value j at the i-th level, is the average value of all test results of rockfill dam response value j, is the extreme value of the test result of factor j, is the maximum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments, is the minimum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments; Step 1.5, sort by the range value in descending order, extract the first 40% of the parameters as the parameters to be inverted, and select K, K b , m as the key parameters of the main rockfill area and the secondary rockfill area; Step 1.6: Select settlement data from typical measuring points in the upstream and downstream rockfill areas and extract the settlement increment at the completion of the filling. Define the dual objective function as follows:

[0037] in, f 1 represents the objective function of the upstream rockfill area, f 2 represents the objective function of the downstream rockfill area, To predict settlement, is the measured settlement, m i 、n j is the number of partition measurement points and characteristic moments.

[0038] Step 2: XGBoost multi-output model training and validation; Step 3: MOPSO multi-objective optimization and weight allocation; Step 4: Input the inversion parameters into the finite element model to verify the consistency between the calculated settlement and the measured data.

[0039] Example 3 The present invention is based on the method for inversion of rockfill material parameters based on the distribution weight coefficient, and the flow chart is as follows: Figure 1 As shown, please follow the steps below: Step 1: Collect rockfill dam engineering data, establish a finite element model, use orthogonal testing and range analysis to screen key material parameters of the Duncan-Zhang EB model, and establish an objective function; Step 1 is implemented as follows: Step 1.1: Obtain the rockfill dam engineering data, including material partitioning, filling process, and settlement monitoring data. Build a 3D finite element model based on ABAQUS, simulate the construction loading process, and arrange finite element nodes at the buried locations of the settlement meters. Step 1.2: Extract the seven parameters of the Duncan-Zhang EB model and set an increment of plus or minus 10% to 30% for each parameter to form a parameter combination set; The seven parameters of the Duncan-Zhang EB model extracted in step 1.2 are: tangent modulus coefficient K, modulus index n, failure ratio Rf, initial internal friction angle φ0, bulk modulus index m, change in friction angle Δφ, and bulk modulus parameter Kb.

[0040] Step 1.3, use Orthogonal test design, input parameter combinations into the three-dimensional finite element model finite element model, and calculate the settlement response value of each measuring point; Step 1.4: Calculate the parameter range value based on the range method. The larger the range value, the higher the parameter sensitivity. The formula is:

[0041]

[0042] in, is the average value of the test results of the rockfill dam response value j at the i-th level, is the number of tests of the rockfill dam response value j at the i-th level, is the result of the nth test of the rockfill dam response value j at the i-th level, is the average value of all test results of rockfill dam response value j, is the extreme value of the test result of factor j, is the maximum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments, is the minimum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments; Step 1.5, sort by the range value in descending order, extract the first 40% of the parameters as the parameters to be inverted, and select K, K b , m as the key parameters of the main rockfill area and the secondary rockfill area; Step 1.6: Select settlement data from typical measuring points in the upstream and downstream rockfill areas and extract the settlement increment at the completion of the filling. Define the dual objective function as follows:

[0043] in, f 1 represents the objective function of the upstream rockfill area, f 2 represents the objective function of the downstream rockfill area, To predict settlement, is the measured settlement, m i 、n j is the number of partition measurement points and characteristic moments.

[0044] Step 2: XGBoost multi-output model training and validation; Step 3: MOPSO multi-objective optimization and weight allocation; Step 3 is implemented as follows: Step 3.1: First, initialize the particle swarm. Step 3.2: In each iteration, the particle predicts the settlement values ​​of the eight measurement points corresponding to the current parameters through the multi-output XGBoost model; Step 3.3: Standardize the objective function value in the Pareto solution set.

[0045] Step 4: Input the inversion parameters into the finite element model to verify the consistency between the calculated settlement and the measured data.

[0046] Example 4 The present invention is based on the method for inversion of rockfill material parameters based on the distribution weight coefficient, and the flow chart is as follows: Figure 1 As shown, please follow the steps below: Step 1: Collect rockfill dam engineering data, establish a finite element model, use orthogonal testing and range analysis to screen key material parameters of the Duncan-Zhang EB model, and establish an objective function; Step 1 is implemented as follows: Step 1.1: Obtain the rockfill dam engineering data, including material partitioning, filling process, and settlement monitoring data. Build a 3D finite element model based on ABAQUS, simulate the construction loading process, and arrange finite element nodes at the buried locations of the settlement meters. Step 1.2: Extract the seven parameters of the Duncan-Zhang EB model and set an increment of plus or minus 10% to 30% for each parameter to form a parameter combination set; Step 1.3, use Orthogonal test design, input parameter combinations into the three-dimensional finite element model finite element model, and calculate the settlement response value of each measuring point; Step 1.4: Calculate the parameter range value based on the range method. The larger the range value, the higher the parameter sensitivity. The formula is:

[0047]

[0048] in, is the average value of the test results of the rockfill dam response value j at the i-th level, is the number of tests of the rockfill dam response value j at the i-th level, is the result of the nth test of the rockfill dam response value j at the i-th level, is the average value of all test results of rockfill dam response value j, is the extreme value of the test result of factor j, is the maximum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments, is the minimum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments; Step 1.5, sort by the range value in descending order, extract the first 40% of the parameters as the parameters to be inverted, and select K, K b , m as the key parameters of the main rockfill area and the secondary rockfill area; Step 1.6: Select settlement data from typical measuring points in the upstream and downstream rockfill areas and extract the settlement increment at the completion of the filling. Define the dual objective function as follows:

[0049] in, f 1 represents the objective function of the upstream rockfill area, f 2 represents the objective function of the downstream rockfill area, To predict settlement, is the measured settlement, m i 、n j is the number of partition measurement points and characteristic moments.

[0050] The seven parameters of the Duncan-Zhang EB model extracted in step 1.2 are: tangent modulus coefficient K, modulus index n, failure ratio Rf, initial internal friction angle φ0, bulk modulus index m, change in friction angle Δφ, and bulk modulus parameter Kb.

[0051] Step 2: XGBoost multi-output model training and validation; Step 2 is implemented as follows: Step 2.1, Latin hypercube sampling LHS generates a sample data set, and the six key parameters K b1 , K 1, m 1, K b2 , K 2, m The value range of 2 is evenly divided into 10 probability intervals, and the cumulative probability of each interval is 10%. K b1 represents the bulk modulus coefficient of the main rockfill area, K 1 represents the initial tangent modulus coefficient of the main rockfill area, m 1 represents the bulk modulus index of the main rockfill area, K b2 represents the bulk modulus coefficient of the secondary rockfill area, K 2 represents the initial tangent modulus coefficient of the secondary rockfill area, m 2 represents the bulk modulus index of the secondary rockfill area. Latin hypercube sampling is used to ensure that exactly one sample point is sampled in each interval and that the samples are evenly distributed in the parameter space. The normalized samples (0–1) obtained by sampling are restored to the actual parameter values. ABAQUS calculations are run on each set of parameter samples, generating a total of 100 sets of samples {( X k , Y k )},in X k is a 6-dimensional parameter vector, Y k It is an 8-dimensional settlement vector in cm. Then the parameters and settlement values ​​are saved in a CSV file. Step 2.2: Use Latin Hypercube Sampling (LHS) to generate 100 sets of parameter combinations. Use finite element calculation to obtain the settlement values ​​of 8 measuring points. Use random K-fold cross validation with K=5 to divide the data into training and test sets. The training set is 80 sets (80%) for model training; the test set is 20 sets (20%) for independent verification. K b1 , K 1, m 1, K b2 , K 2, m 2. Use normalization; Step 2.3: Train the multi-output XGBoost model. Steps 2.1 and 2.2 are the preparations for training the multi-output XGBoost model. Only with a dataset can you train the proxy model. Step 2.4: Use Scikit-learn's GridSearchCV to perform 5-fold cross-validation on the multi-output XGBoost model, optimizing for minimizing the root mean square error (RMSE). Use early stopping during training iterations, terminating training when the validation set RMSE does not decrease for 10 consecutive epochs to avoid overfitting. Step 2.5: Model performance was evaluated using four metrics: mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R²). Comparison of the four models, CPO-XGBoost, CPO-MORF, CPO-MSVR, and CPO-HKELM, revealed that XGBoost exhibited significant advantages at most measurement points.

[0052] Step 3: MOPSO multi-objective optimization and weight allocation; Step 4: Input the inversion parameters into the finite element model to verify the consistency between the calculated settlement and the measured data.

[0053] Example 5 The present invention is based on the method for inversion of rockfill material parameters based on the distribution weight coefficient, and the flow chart is as follows: Figure 1 As shown, please follow the steps below: Step 1: Collect rockfill dam engineering data, establish a finite element model, use orthogonal testing and range analysis to screen key material parameters of the Duncan-Zhang EB model, and establish an objective function; Step 1 is implemented as follows: Step 1.1: Obtain the rockfill dam engineering data, including material partitioning, filling process, and settlement monitoring data. Build a 3D finite element model based on ABAQUS, simulate the construction loading process, and arrange finite element nodes at the buried locations of the settlement meters. Step 1.2: Extract the seven parameters of the Duncan-Zhang EB model and set an increment of plus or minus 10% to 30% for each parameter to form a parameter combination set; Step 1.3, use Orthogonal test design, input parameter combinations into the three-dimensional finite element model finite element model, and calculate the settlement response value of each measuring point; Step 1.4: Calculate the parameter range value based on the range method. The larger the range value, the higher the parameter sensitivity. The formula is:

[0054]

[0055] in, is the average value of the test results of the rockfill dam response value j at the i-th level, is the number of tests of the rockfill dam response value j at the i-th level, is the result of the nth test of the rockfill dam response value j at the i-th level, is the average value of all test results of rockfill dam response value j, is the extreme value of the test result of factor j, is the maximum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments, is the minimum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments; Step 1.5, sort by the range value in descending order, extract the first 40% of the parameters as the parameters to be inverted, and select K, K b , m as the key parameters of the main rockfill area and the secondary rockfill area; Step 1.6: Select settlement data from typical measuring points in the upstream and downstream rockfill areas and extract the settlement increment at the completion of the filling. Define the dual objective function as follows:

[0056] in, f 1 represents the objective function of the upstream rockfill area, f 2 represents the objective function of the downstream rockfill area, To predict settlement, is the measured settlement, m i 、n j is the number of partition measurement points and characteristic moments.

[0057] The seven parameters of the Duncan-Zhang EB model extracted in step 1.2 are: tangent modulus coefficient K, modulus index n, failure ratio Rf, initial internal friction angle φ0, bulk modulus index m, change in friction angle Δφ, and bulk modulus parameter Kb.

[0058] Step 2: XGBoost multi-output model training and validation; Step 2 is implemented as follows: Step 2.1, Latin hypercube sampling LHS generates a sample data set, and the six key parameters K b1 , K 1, m 1, K b2 , K 2, mThe value range of 2 is evenly divided into 10 probability intervals, and the cumulative probability of each interval is 10%. K b1 represents the bulk modulus coefficient of the main rockfill area, K 1 represents the initial tangent modulus coefficient of the main rockfill area, m 1 represents the bulk modulus index of the main rockfill area, K b2 represents the bulk modulus coefficient of the secondary rockfill area, K 2 represents the initial tangent modulus coefficient of the secondary rockfill area, m 2 represents the bulk modulus index of the secondary rockfill area. Latin hypercube sampling is used to ensure that exactly one sample point is sampled in each interval and that the samples are evenly distributed in the parameter space. The normalized samples (0–1) obtained by sampling are restored to the actual parameter values. ABAQUS calculations are run on each set of parameter samples, generating a total of 100 sets of samples {( X k , Y k )},in X k is a 6-dimensional parameter vector, Y k It is an 8-dimensional settlement vector in cm. Then the parameters and settlement values ​​are saved in a CSV file. Step 2.2: Use Latin Hypercube Sampling (LHS) to generate 100 sets of parameter combinations. Use finite element calculation to obtain the settlement values ​​of 8 measuring points. Use random K-fold cross validation with K=5 to divide the data into training and test sets. The training set is 80 sets (80%) for model training; the test set is 20 sets (20%) for independent verification. K b1 , K 1, m 1, K b2 , K 2, m 2. Use normalization; Step 2.3: Train the multi-output XGBoost model. Steps 2.1 and 2.2 are the preparations for training the multi-output XGBoost model. Only with a dataset can you train the proxy model. Step 2.4: Use Scikit-learn's GridSearchCV to perform 5-fold cross-validation on the multi-output XGBoost model, optimizing for minimizing the root mean square error (RMSE). Use early stopping during training iterations, terminating training when the validation set RMSE does not decrease for 10 consecutive epochs to avoid overfitting. Step 2.5: Model performance was evaluated using four metrics: mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R²). Comparison of the four models, CPO-XGBoost, CPO-MORF, CPO-MSVR, and CPO-HKELM, revealed that XGBoost exhibited significant advantages at most measurement points.

[0059] Step 2.3 is implemented as follows: Using multi-output regression mode, the settlement prediction of each measuring point is an independent output node, sharing 6-dimensional input features K b1 , K 1, m 1, K b2 , K 2, m 2 (Material parameters); Use the multi:linear objective of the multi-output XGBoost model, which supports linearly weighted multi-output. The formula is:

[0060] Among them, K is the output dimension (K=8, the number of measurement points), is a set of regression trees.

[0061] Step 3: MOPSO multi-objective optimization and weight allocation; Step 3 is implemented as follows: Step 3.1: First, initialize the particle swarm. Step 3.1 is implemented as follows: Each particle represents a set of 6-dimensional material parameter vectors The vector X position is randomly generated within the parameter range. The velocity is initialized to ±5% of the parameter range to control the search step size. The population size is set to 50 particles. The maximum capacity of the external archive set is 50 solutions, which is used to store non-dominated solutions found during the iteration. The inertia weight adopts a linear decrease strategy, and the formula is , where t is the current iteration number, This strategy enhances the global search capability in the early stage of iteration and focuses on local fine adjustment in the later stage. The learning factor is set to and , in order to balance the particle's dependence on its own historical optimal solution and the group's global optimal solution.

[0062] Step 3.2: In each iteration, the particle predicts the settlement values ​​of the eight measurement points corresponding to the current parameters through the multi-output XGBoost model; Step 3.3: Standardize the objective function value in the Pareto solution set.

[0063] Step 4: Input the inversion parameters into the finite element model to verify the consistency between the calculated settlement and the measured data.

[0064] Example 6 The present invention is based on the method for inversion of rockfill material parameters based on the distribution weight coefficient, and the flow chart is as follows: Figure 1 As shown, please follow the steps below: Step 1: Collect rockfill dam engineering data, establish a finite element model, use orthogonal testing and range analysis to screen key material parameters of the Duncan-Zhang EB model, and establish an objective function; Step 1 is implemented as follows: Step 1.1: Obtain the rockfill dam engineering data, including material partitioning, filling process, and settlement monitoring data. Build a 3D finite element model based on ABAQUS, simulate the construction loading process, and arrange finite element nodes at the buried locations of the settlement meters. Step 1.2: Extract the seven parameters of the Duncan-Zhang EB model and set an increment of plus or minus 10% to 30% for each parameter to form a parameter combination set; Step 1.3, use Orthogonal test design, input parameter combinations into the three-dimensional finite element model finite element model, and calculate the settlement response value of each measuring point; Step 1.4: Calculate the parameter range value based on the range method. The larger the range value, the higher the parameter sensitivity. The formula is:

[0065]

[0066] in, is the average value of the test results of the rockfill dam response value j at the i-th level, is the number of tests of the rockfill dam response value j at the i-th level, is the result of the nth test of the rockfill dam response value j at the i-th level, is the average value of all test results of rockfill dam response value j, is the extreme value of the test result of factor j, is the maximum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments, is the minimum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments; Step 1.5, sort by the range value in descending order, extract the first 40% of the parameters as the parameters to be inverted, and select K, K b , m as the key parameters of the main rockfill area and the secondary rockfill area; Step 1.6: Select settlement data from typical measuring points in the upstream and downstream rockfill areas and extract the settlement increment at the completion of the filling. Define the dual objective function as follows:

[0067] in, f 1 represents the objective function of the upstream rockfill area, f 2 represents the objective function of the downstream rockfill area, To predict settlement, is the measured settlement, m i 、n j is the number of partition measurement points and characteristic moments.

[0068] Step 2: XGBoost multi-output model training and validation; Combine Figures 2 to 6 , step 2 is implemented according to the following steps: Step 2.1, Latin hypercube sampling LHS generates a sample data set, and the six key parameters K b1 , K 1, m 1, K b2 , K 2, m The value range of 2 is evenly divided into 10 probability intervals, and the cumulative probability of each interval is 10%. K b1 represents the bulk modulus coefficient of the main rockfill area, K 1 represents the initial tangent modulus coefficient of the main rockfill area, m 1 represents the bulk modulus index of the main rockfill area, K b2 represents the bulk modulus coefficient of the secondary rockfill area, K 2 represents the initial tangent modulus coefficient of the secondary rockfill area, m 2 represents the bulk modulus index of the secondary rockfill area. Latin hypercube sampling is used to ensure that exactly one sample point is sampled in each interval and that the samples are evenly distributed in the parameter space. The normalized samples (0–1) obtained by sampling are restored to the actual parameter values. ABAQUS calculations are run on each set of parameter samples, generating a total of 100 sets of samples {( X k , Y k )},in X k is a 6-dimensional parameter vector, Y k It is an 8-dimensional settlement vector in cm. Then the parameters and settlement values ​​are saved in a CSV file. Step 2.2: Use Latin Hypercube Sampling (LHS) to generate 100 sets of parameter combinations. Use finite element calculation to obtain the settlement values ​​of 8 measuring points. Use random K-fold cross validation with K=5 to divide the data into training and test sets. The training set is 80 sets (80%) for model training; the test set is 20 sets (20%) for independent verification. K b1 , K 1, m 1, K b2 , K 2, m 2. Use normalization; Step 2.3: Train the multi-output XGBoost model. Steps 2.1 and 2.2 are the preparations for training the multi-output XGBoost model. Only with a dataset can you train the proxy model. Step 2.4: Use Scikit-learn's GridSearchCV to perform 5-fold cross-validation on the multi-output XGBoost model, optimizing for minimizing the root mean square error (RMSE). Use early stopping during training iterations, terminating training when the validation set RMSE does not decrease for 10 consecutive epochs to avoid overfitting. Step 2.5: Model performance was evaluated using four metrics: mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R²). Comparison of the four models, CPO-XGBoost, CPO-MORF, CPO-MSVR, and CPO-HKELM, revealed that XGBoost exhibited significant advantages at most measurement points.

[0069] Step 2.3 is implemented as follows: Using multi-output regression mode, the settlement prediction of each measuring point is an independent output node, sharing 6-dimensional input features K b1 , K 1, m 1, K b2 , K 2, m 2 (Material parameters); Use the multi:linear objective of the multi-output XGBoost model, which supports linearly weighted multi-output. The formula is:

[0070] Among them, K is the output dimension (K=8, the number of measurement points), is a set of regression trees.

[0071] Step 3: MOPSO multi-objective optimization and weight allocation; Step 3 is implemented as follows: Step 3.1: First, initialize the particle swarm. Step 3.1 is implemented as follows: Each particle represents a set of 6-dimensional material parameter vectors The vector X position is randomly generated within the parameter range. The velocity is initialized to ±5% of the parameter range to control the search step size. The population size is set to 50 particles. The maximum capacity of the external archive set is 50 solutions, which is used to store non-dominated solutions found during the iteration. The inertia weight adopts a linear decrease strategy, and the formula is , where t is the current iteration number, This strategy enhances the global search capability in the early stage of iteration and focuses on local fine adjustment in the later stage. The learning factor is set to and , in order to balance the particle's dependence on its own historical optimal solution and the group's global optimal solution.

[0072] Step 3.2: In each iteration, the particle predicts the settlement values ​​of the eight measurement points corresponding to the current parameters through the multi-output XGBoost model; Step 3.2 is implemented as follows: Calculate the objective function of the upstream and downstream rockfill areas and sort the particles based on the Pareto dominance principle: if particle A f 1 and f 2 are not inferior to particle B and at least one indicator is strictly better, then A dominates B, and the solutions not dominated by any particle are stored in the external archive set; to maintain the diversity of the archive set, when the archive set is full, if the new solution dominates part of the existing solutions, the dominated solution is replaced, otherwise the grid density method is used to delete the solutions in the high-density area; The selection of the global optimal solution Gbest directly affects the convergence of the algorithm. The specific process is: calculate the Euclidean distance between the particle and all solutions in the archive as the similarity distance SD, such as particle X i With archive solution Y j The SD is , then calculate the average similarity distance ASD, filter out particles with SD smaller than ASD, randomly select one of them as Gbest, and guide the particles to search for the under-explored solution space area to avoid falling into the local optimum; Step 3.3: Standardize the objective function value in the Pareto solution set.

[0073] Step 3.3 is implemented as follows: For negative indicators (the smaller the value, the better), use the formula ,in: For the i In the group data j The standardized value of each indicator; For the j The maximum value of an indicator; For the j The minimum value of the indicator will f 1 and f 2Normalized to the interval [0,1]; Then calculate the indicator variability and conflict: standard deviation Reflects the ability of indicators to distinguish, correlation coefficient The degree of information overlap between indicators and the amount of information of a single indicator , after normalization, we get the weight Taking the document data as an example, the weights of the main rockfill area and the secondary rockfill area are calculated, indicating that the deformation of the main rockfill area is more important to the parameter inversion. Based on the linear weighted objective function , traverse the Pareto solution set and select the parameter combination that minimizes F as the optimal solution.

[0074] Step 4: Input the inversion parameters into the finite element model to verify the consistency between the calculated settlement and the measured data.

Claims

1. A method for inverting rockfill material parameters based on the distribution of weight coefficients, characterized in that: Please follow the steps below to implement: Step 1: Collect rockfill dam project data, establish a finite element model, use orthogonal testing and range analysis to screen key material parameters of the Duncan-Zhang EB model, and establish an objective function; Step 2: XGBoost multi-output model training; Step 3: MOPSO multi-objective optimization and weight allocation; Step 4: Input the inversion parameters into the finite element model to verify the consistency between the calculated settlement and the measured data.

2. The method for inversion of rockfill material parameters based on distribution weight coefficients according to claim 1, characterized in that: The step 1 is specifically implemented according to the following steps: Step 1.1: Obtain the rockfill dam engineering data, including material partitioning, filling process, and settlement monitoring data. Build a 3D finite element model based on ABAQUS, simulate the construction loading process, and arrange finite element nodes at the buried locations of the settlement meters. Step 1.2: Extract the seven parameters of the Duncan-Zhang EB model and set an increment of plus or minus 10% to 30% for each parameter to form a parameter combination set; Step 1.3, use Orthogonal test design, input parameter combinations into the three-dimensional finite element model finite element model, and calculate the settlement response value of each measuring point; Step 1.4: Calculate the parameter range value based on the range method. The larger the range value, the higher the parameter sensitivity. The formula is: in, is the average value of the test results of the rockfill dam response value j at the i-th level, is the number of tests of the rockfill dam response value j at the i-th level, is the result of the nth test of the rockfill dam response value j at the i-th level, is the average value of all test results of rockfill dam response value j, is the extreme value of the test result of factor j, is the maximum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments, is the minimum value of the rockfill dam response value j corresponding to the same parameter obtained through multiple experiments; Step 1.5, sort by the range value in descending order, extract the first 40% of the parameters as the parameters to be inverted, and select K, K b , m as the key parameters of the main rockfill area and the secondary rockfill area; Step 1.6: Select settlement data from typical measuring points in the upstream and downstream rockfill areas and extract the settlement increment at the completion of the filling. Define the dual objective function as follows: in, f 1 represents the objective function of the upstream rockfill area, f 2 represents the objective function of the downstream rockfill area, To predict settlement, is the measured settlement, m i 、n j is the number of partition measurement points and characteristic moments.

3. The method for inversion of rockfill material parameters based on distribution weight coefficients according to claim 2, characterized in that: The seven parameters of the Duncan-Zhang EB model extracted in step 1.2 are: tangent modulus coefficient K, modulus index n, failure ratio Rf, initial internal friction angle φ0, bulk modulus index m, change in friction angle Δφ and bulk modulus parameter Kb.

4. The method for inversion of rockfill material parameters based on distribution weight coefficients according to claim 2, characterized in that: The step 2 is specifically implemented according to the following steps: Step 2.1, Latin hypercube sampling LHS generates a sample data set, and the six key parameters K b1 , K 1, m 1, K b2 , K 2, m The value range of 2 is evenly divided into 10 probability intervals, and the cumulative probability of each interval is 10%. K b1 represents the bulk modulus coefficient of the main rockfill area, K 1 represents the initial tangent modulus coefficient of the main rockfill area, m 1 represents the bulk modulus index of the main rockfill area, K b2 represents the bulk modulus coefficient of the secondary rockfill area, K 2 represents the initial tangent modulus coefficient of the secondary rockfill area, m 2 represents the bulk modulus index of the secondary rockfill area. Latin hypercube sampling is used to ensure that exactly one sample point is sampled in each interval and that the samples are evenly distributed in the parameter space. The normalized samples (0–1) obtained by sampling are restored to the actual parameter values. ABAQUS calculations are run on each set of parameter samples, generating a total of 100 sets of samples {( X k , Y k )},in X k is a 6-dimensional parameter vector, Y k It is an 8-dimensional settlement vector in cm. Then the parameters and settlement values ​​are saved in a CSV file. Step 2.2: Use Latin hypercube sampling (LHS) to generate 100 sets of parameter combinations, obtain the settlement values ​​of 8 measuring points through finite element calculation, use random K-fold cross validation, K=5, divide the data into training and test sets, and perform the input and output parameters. K b1 , K 1, m 1, K b2 , K 2, m 2. Use normalization; Step 2.3: Train the multi-output XGBoost model. Step 2.4: Use Scikit-learn's GridSearchCV to perform 5-fold cross-validation on the multi-output XGBoost model, optimizing to minimize the root mean square error (RMSE). An early stopping strategy is used in the training iterations. When the RMSE of the validation set does not decrease for 10 consecutive rounds, the training is terminated to avoid overfitting.

5. The method for inversion of rockfill material parameters based on distribution weight coefficients according to claim 4, characterized in that: The step 2.3 is specifically implemented according to the following steps: Using multi-output regression mode, the settlement prediction of each measuring point is an independent output node, sharing 6-dimensional input features K b1 , K 1, m 1, K b2 , K 2, m 2. Use the multi:linear objective of the multi-output XGBoost model, which supports linear weighted multi-output. The formula is: Among them, K is the output dimension, is a set of regression trees.

6. The method for inversion of rockfill material parameters based on distribution weight coefficients according to claim 5, characterized in that: The step 3 is specifically implemented according to the following steps: Step 3.1: First, initialize the particle swarm. Step 3.2: In each iteration, the particle predicts the settlement values ​​of the eight measurement points corresponding to the current parameters through the multi-output XGBoost model; Step 3.3: Standardize the objective function value in the Pareto solution set.

7. The method for inversion of rockfill material parameters based on distribution weight coefficients according to claim 6, characterized in that: The step 3.1 is specifically implemented according to the following steps: Each particle represents a set of 6-dimensional material parameter vectors The vector X position is randomly generated within the parameter range. The velocity is initialized to ±5% of the parameter range to control the search step size. The population size is set to 50 particles. The maximum capacity of the external archive set is 50 solutions, which is used to store non-dominated solutions found during the iteration. The inertia weight adopts a linear decrease strategy, and the formula is , where t is the current iteration number, This strategy enhances the global search capability in the early stage of iteration and focuses on local fine adjustment in the later stage. The learning factor is set to and , in order to balance the particle's dependence on its own historical optimal solution and the group's global optimal solution.

8. The method for inversion of rockfill material parameters based on distribution weight coefficients according to claim 7, characterized in that: The step 3.2 is specifically implemented according to the following steps: Calculate the objective function of the upstream and downstream rockfill areas, and perform non-dominated sorting of particles based on the Pareto dominance principle: if particle A f 1 and f 2 are not inferior to particle B and at least one indicator is strictly better, then A dominates B, and the solutions not dominated by any particle are stored in the external archive set; to maintain the diversity of the archive set, when the archive set is full, if the new solution dominates part of the existing solutions, the dominated solution is replaced, otherwise the grid density method is used to delete the solutions in the high-density area; The selection of the global optimal solution Gbest directly affects the convergence of the algorithm. The specific process is: calculate the Euclidean distance between the particle and all solutions in the archive as the similarity distance SD, such as particle X i With archive solution Y j The SD is , then calculate the average similarity distance ASD, screen out particles with SD smaller than ASD, randomly select one of them as Gbest, and guide the particles to search for the under-explored solution space area to avoid falling into the local optimum.

9. The method for inversion of rockfill material parameters based on distribution weight coefficients according to claim 8, characterized in that: The step 3.3 is specifically implemented according to the following steps: For negative indicators, use the formula , ,in: For the i In the group data j The standardized value of each indicator; For the j The maximum value of an indicator; For the j The minimum value of the indicator will f 1 and f 2Normalized to the interval [0,1]; Then calculate the indicator variability and conflict: standard deviation Reflects the ability of indicators to distinguish, correlation coefficient The degree of information overlap between indicators and the amount of information of a single indicator , after normalization, we get the weight Taking the document data as an example, the weights of the main rockfill area and the secondary rockfill area are calculated, which shows that the deformation of the main rockfill area is more important for the parameter inversion. Based on the linear weighted objective function , traverse the Pareto solution set and select the parameter combination that minimizes F as the optimal solution.

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