Grouting amount integrated agent prediction model and prediction method based on stacking

Abstract

The application discloses a grouting amount integrated agent prediction model based on stacking, which comprises an integrated agent model, the integrated agent model is provided with two layers, the first layer comprises three base learners which are trained and verified by using a five-fold cross-validation method, and the second layer comprises one meta learner; the three base learners are respectively an SVR neural network, a BPNN neural network and an RF model; the meta learner is an ANFIS neural network; and training data in a training set of the meta learner comprises prediction result data of the three base learners. The application further discloses a prediction method of the grouting amount integrated agent prediction model based on stacking. The application can increase model diversity, reduce overfitting and prediction uncertainty, and generate more accurate and more robust prediction results.

Description

Technical Field

[0001] This invention relates to the field of bedrock grouting construction in water conservancy and hydropower engineering, and particularly to an integrated proxy prediction model and method for grouting volume based on Stacking. Background Technology

[0002] Currently, grouting is a primary method for dam foundation seepage prevention, ground improvement, and repair, and is crucial for ensuring the stable operation of hydraulic structures. Grouting volume is an important parameter characterizing the quality of grouting construction and is closely related to its cost-effectiveness. Predicting grouting volume allows for the improvement of grouting design schemes, savings in grouting materials and equipment investment, and guidance for subsequent grouting construction control and project optimization.

[0003] However, due to the concealed and complex nature of grouting projects, the grouting volume estimated by traditional methods such as construction personnel experience and simplified physical model tests often deviates significantly from the actual situation. With the rapid development of computational fluid dynamics and discrete fracture network modeling methods, numerical simulation technology has become a powerful tool for calculating dam foundation grouting volume. However, numerical simulation suffers from problems such as complex modeling processes, large computational loads, and long processing times, resulting in low efficiency in grouting volume calculation and failing to meet the needs of guiding grouting project construction. Surrogate models based on machine learning algorithms can replace the complex and time-consuming numerical simulation process, balancing computational efficiency and prediction accuracy. Therefore, surrogate model technology based on machine learning algorithms has become an effective approach to solving the problem of predicting grouting volume in complex engineering projects.

[0004] However, single-machine learning surrogate models exhibit poor predictive stability, potentially leading to poor generalization performance due to randomness. Furthermore, using only one machine learning model can easily underestimate predictive uncertainty, resulting in poor accuracy. Therefore, some studies have employed combined surrogate models to improve overall prediction accuracy. However, combined surrogate models suffer from subjectivity and uncertainty in determining the weights of each algorithm, and cannot train a superior model. Ensemble learning methods, by fusing information from multiple individual models through ensemble strategies, can increase model diversity, reduce overfitting and predictive uncertainty, and produce more accurate and robust predictions. Ensemble learning typically includes three strategies: Bagging, Boosting, and Stacking. Among these, Stacking algorithms are widely used in various fields to address prediction problems because they can flexibly combine different types of base learners to construct suitable ensemble learning models based on the specific problem, achieving better predictive performance and model generalization ability.

[0005] Furthermore, considering the significant impact of model parameter selection on the final prediction performance, determining the optimal model parameters is a core issue in model building. Swarm intelligence algorithms, due to their simplicity and strong problem-solving capabilities, excel in parameter optimization and are widely used in parameter optimization for machine learning algorithms. Sparrow Search Algorithm (SSA), a novel swarm intelligence optimization algorithm proposed by Xue et al. in 2020, has proven to outperform current mainstream algorithms such as Gray Wolf Optimization (GWO), Particle Swarm Optimization (PSO), Gravity Search Algorithm (GSA), and Antlion Optimization (ALO) in terms of search accuracy, convergence speed, and stability. However, SSA suffers from a gradual decrease in population diversity in the later stages of the search, leading to an inability to escape local optima. Therefore, there is an urgent need for an optimization algorithm that can balance global search capability, local search capability, and computational efficiency.

[0006] In summary, existing research on dam foundation grouting volume prediction models suffers from problems such as complex modeling processes, large computational loads, and long time consumption in numerical simulation. Using only one machine learning model can easily underestimate the uncertainty of prediction, resulting in poor accuracy. Furthermore, combined surrogate models have subjectivity and uncertainty in determining the weight values ​​of each algorithm, making it impossible to train a better model. Summary of the Invention

[0007] This invention provides a stacking-based integrated proxy prediction model and method for grouting volume to address the technical problems existing in the prior art.

[0008] The technical solution adopted by this invention to solve the technical problems existing in the prior art is: a stacking-based integrated proxy prediction model for grouting volume, comprising an integrated proxy model with two layers. The first layer includes three base learners trained and validated using a five-fold cross-validation method, and the second layer includes a meta-learner. The three base learners are an SVR neural network, a BPNN neural network, and an RF model, respectively. The meta-learner is an ANFIS neural network. The training data in the training set of the meta-learner includes the prediction results data of the three base learners.

[0009] Furthermore, it also includes a grouting numerical simulation model based on three-dimensional fine fracture modeling. The grouting numerical simulation model takes geological parameters, construction parameters and grout characteristic parameters as inputs and outputs simulated values ​​of grouting volume. The training data in the training set of the meta-learner also includes simulated values ​​of grouting volume.

[0010] This invention also provides a prediction method for an integrated proxy prediction model of grouting volume based on Stacking. The integrated proxy prediction model is constructed with two layers: the first layer has three base learners, and the second layer has one meta-learner. The three base learners are an SVR neural network, a BPNN neural network, and an RF model, respectively; the meta-learner is an ANFIS neural network. Historical data including geological parameters, construction parameters, and grout characteristic parameters are collected as training samples to construct training and validation sets. Five-fold cross-validation is used to train the three base learners. A training set including the prediction results obtained from the three base learners is constructed to train the meta-learner. Input parameters including geological parameters, construction parameters, and grout characteristic parameters are simultaneously input to the three base learners, and then the prediction results obtained from the three base learners are input to the meta-learner, which outputs the predicted grouting volume value.

[0011] Furthermore, a grouting numerical simulation model based on three-dimensional fine fracture modeling is set up, which takes geological parameters, construction parameters and grout characteristic parameters as input and outputs simulated grouting volume values. The prediction results obtained by the three base learners are combined with the corresponding simulated grouting volume values ​​to construct a new training set to train the meta learner.

[0012] Furthermore, the method for constructing the training set and validation set includes: extracting multiple sets of geological parameters using the Latin hypercube sampling method, combining them with different construction parameters and grout characteristic parameters to construct a parameter sample set representing various fracture geological conditions and construction conditions; inputting the data in the parameter sample set into the grouting numerical simulation model to obtain the simulated grouting volume; using the geological parameters, construction parameters, grout characteristic parameters, and the corresponding generated simulated grouting volume values ​​as sample data to construct a sample set, and dividing the sample set into a training set and a test set according to the proportion.

[0013] Furthermore, the method of collecting historical data, including geological parameters, construction parameters, and grout characteristic parameters, as training samples includes: obtaining the following geological parameters based on a three-dimensional fine fracture network model: number of fractures, average fracture dip, average dip angle, and average fracture width; obtaining the following construction condition parameters based on the actual construction plan and the technical specifications for cement grouting construction of hydraulic structures: sequence of grouting holes, hole order, hole depth, and grouting pressure; and obtaining the following grout parameters based on the actual construction plan: grout water-cement ratio.

[0014] Furthermore, the sparrow search algorithm is improved based on chaos theory and Lévy flight strategy, and the improved sparrow search algorithm is used to simultaneously optimize the model parameters of the base learner and the meta learner.

[0015] Furthermore, methods for improving the sparrow search algorithm based on chaos theory and Lévy flight strategy include:

[0016] Sparrow population initialization based on chaos theory, using Tent chaotic mapping to generate chaotic sequences to initialize sparrow positions (xp) i,j , where i = 1, 2, 3…n, n represents the number of sparrows in the population, j = 1, 2, 3…d, d represents the dimension of the variable to be optimized;

[0017] Randomly generate an initial value x between [0, 1]. pi，0 At this point, j = 0;

[0018] Generating chaotic sequences using the Tent chaotic map:

[0019]

[0020] Mapping the chaotic sequence to the search space of solutions yields the chaotic initialization population:

[0021]

[0022] The Lévy flight strategy is used to improve the position update formulas for explorers, followers, and scouts, expanding the search range and enhancing global search capabilities. The improved explorer position update formula is as follows:

[0023]

[0024]

[0025] The improved explorer location update formula is as follows:

[0026]

[0027] The improved explorer location update formula is as follows:

[0028]

[0029] In the above formulas:

[0030] Y = {y i , i = 1, 2, 3, ..., n} represents the response grouting volume value;

[0031] F={f i , i = 1, 2, 3, ..., k} represents the predicted final grouting volume;

[0032] xp represents the population vector set of the parameters to be optimized;

[0033] i represents an individual in the sparrow population;

[0034] j represents the variable to be optimized;

[0035] Initialize the chaotic population using the Tent chaotic map;

[0036] xp min，j The minimum value of the j-th dimension population vector;

[0037] xp max，j The maximum value of the j-th dimension population vector;

[0038] Let be the j-th dimension of the population vector value of the i-th sparrow individual at the t-th iteration;

[0039] It is represented as the j-th dimension of the population vector of the i-th sparrow individual at the (t+1)-th iteration;

[0040] t represents the current iteration number;

[0041] iter max Indicates the maximum number of iterations;

[0042] α∈(0,1) represents random coefficients;

[0043] R2∈[0,1] represents the warning value;

[0044] ST∈[0.5,1] represents a safe value;

[0045] It is an intermediate variable in the iterative calculation;

[0046] This indicates the current globally optimal position;

[0047] ⊕ represents dot product;

[0048] Lévy(λ) represents the Lévy random search path;

[0049] This indicates the optimal position currently occupied by the explorer.

[0050] It is currently the worst position in the entire system.

[0051] n is the total number of individuals in the sparrow population.

[0052] Let A represent a 1×d matrix, where each element takes the value 1 or -1, and A + =A T (AA T ) -1 ;

[0053] f bThis represents the current global best fitness value;

[0054] f w This represents the current worst-case fitness value globally.

[0055] f i This represents the fitness value of the individual sparrow to be updated.

[0056] ε is a small constant to prevent the denominator from being zero.

[0057] Furthermore, the method for simultaneously optimizing the model parameters of the base learner and the meta-learner using the improved sparrow search algorithm includes the following steps:

[0058] Step 1: Determine the population size, maximum number of iterations, fitness value range, solution interval range, explorer ratio, and scout ratio;

[0059] Step 2: Initialize the population using Tent chaotic mapping;

[0060] Step 3: Increment the iteration count by 1; calculate the sparrow population fitness value;

[0061] Step 4: Select some sparrows with better fitness values ​​as explorers and update their positions;

[0062] Step 5: The remaining sparrows, acting as followers, update their positions.

[0063] Step 6: Select a portion of the sparrow population as scouts and update their locations;

[0064] Step 7: Calculate the fitness value of the sparrow population;

[0065] Step 8: Determine if the fitness value meets the condition. If not, proceed to step 9; if it does, proceed to step 10.

[0066] Step 9: Determine if the number of iterations is less than the maximum number of iterations. If it is less than the maximum number of iterations, proceed to step 3; otherwise, proceed to step 10.

[0067] Step 10: End the optimization and obtain the optimal model parameters.

[0068] Furthermore, the model parameters optimized using the sparrow search algorithm include: the penalty factor and kernel parameters of the SVR neural network, the initial threshold and weights of the BPNN neural network, the number of decision trees n and the maximum depth h of the RF model, and the antecedent parameters of the ANFIS neural network.

[0069] The advantages and positive effects of this invention are as follows: This invention employs a Stacking-based ensemble prediction model to build an ensemble prediction model for grouting volume, which increases model diversity, reduces overfitting and prediction uncertainty, and produces more accurate and robust prediction results. This invention uses an improved sparrow search algorithm to optimize model parameters, ensuring the uniformity and diversity of the initial model parameter population distribution, and overcoming the potential for decreased population diversity during the search process, thus avoiding getting trapped in local optima. This invention solves the following technical problems of existing machine learning grouting volume prediction models: lack of consideration for geological parameters, complex and time-consuming numerical simulation of grouting, low accuracy of single surrogate models, and high subjectivity in weighting of combined surrogate models. Compared to single surrogate models, this invention improves prediction performance, enabling rapid and accurate prediction of grouting volume, thereby obtaining more accurate and reliable prediction results, providing guidance for decision-making, and ensuring the safety and quality of grouting. In actual grouting projects, it can provide reliable methodological support for estimating the grouting volume of the area to be grouted, and has significant engineering application value. At the same time, the model proposed in this invention also provides new ideas for predicting other engineering parameters, and has good prospects for engineering application. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of a stacking-based integrated agent prediction model for grouting volume according to the present invention.

[0071] Figure 2 This is a schematic diagram of the training process of a stacking-based integrated agent prediction model for grouting volume according to the present invention.

[0072] Figure 3 This is a flowchart illustrating a prediction method based on a Stacking-based integrated agent prediction model for grouting volume according to the present invention.

[0073] In the picture:

[0074] SVR: Support Vector Regression.

[0075] BPNN: Backpropagation neural network model.

[0076] RF: Random Forest model.

[0077] ANFIS: Adaptive Neural Fuzzy Reasoning System.

[0078] X: The set of decision variables.

[0079] Y: Set of response quantities.

[0080] X tr : Decision variables in the training samples.

[0081] Y tr: The response quantity in the training samples.

[0082] X te : Decision variables in the test sample.

[0083] Y te : The response quantity in the test sample.

[0084] P tr-SVR : Response prediction values ​​obtained from training samples using a support vector machine model.

[0085] P tr-BPNN : Response prediction values ​​obtained from training samples using a BP neural network model.

[0086] P tr-RF : Response prediction values ​​obtained from training samples using a random forest model.

[0087] P tr-1～5 The predicted response values ​​are obtained by training the base learner five times based on the training samples.

[0088] P tr A new training sample is formed by combining the outputs of the three base learners on the training samples.

[0089] P te-SVR : Response prediction values ​​obtained based on test samples using a support vector machine model.

[0090] P te-BPNN The predicted response value is obtained based on the test sample using a BP neural network model.

[0091] P te-RF The predicted response values ​​are obtained based on the test samples using a random forest model.

[0092] P te A new test sample is formed by combining the outputs of the three base learners on the test sample.

[0093] F te : Final prediction result. Detailed Implementation

[0094] To further understand the invention's content, features, and effects, the following embodiments are provided, along with detailed descriptions in conjunction with the accompanying drawings:

[0095] The Chinese definitions of the following foreign words and abbreviations in this application are as follows:

[0096] Stacking: An ensemble learning strategy that trains a meta-learner to learn the relationship between the model outputs and actual outputs of each base learner, thereby combining different types of base learners to build an ensemble model.

[0097] Bagging: A type of ensemble learning strategy that generates multiple base learners of the same type in parallel through sample training and then linearly combines their results.

[0098] Boosting: A type of ensemble learning strategy that generates multiple base learners of the same type in a sequential manner through sample training and then linearly combines their results.

[0099] SSA: Sparrow Search Algorithm, a novel swarm intelligence optimization algorithm.

[0100] ISSA-Stacking: An ensemble learning algorithm based on an improved sparrow search algorithm.

[0101] SVR: Support Vector Regression, a prediction model based on a hyperplane, has unique advantages in solving nonlinear regression prediction problems with small samples and high dimensions.

[0102] BPNN: Backpropagation neural network model, a classic neural network model with good numerical processing and approximation capabilities.

[0103] RF: Random Forest model, a representative of Bagging ensemble algorithms, has advantages such as low generalization error, good stability, and low risk of overfitting.

[0104] ANFIS: Adaptive Neural Fuzzy Reasoning System.

[0105] LHS: Latin hypercube sampling method.

[0106] Lévy: The Lévy flight strategy is a class of non-Gaussian stochastic processes.

[0107] Tent: Tent chaotic mapping, refers to a piecewise linear mapping.

[0108] Please see Figures 1 to 3 A stacking-based integrated agent prediction model for grouting volume includes an integrated agent model with two layers. The first layer includes three base learners trained and validated using a five-fold cross-validation method. The second layer includes a meta-learner. The three base learners are an SVR neural network, a BPNN neural network, and an RF model, respectively. The meta-learner is an ANFIS neural network. The training data in the training set of the meta-learner includes the prediction results data of the three base learners.

[0109] Preferably, it may also include a grouting numerical simulation model based on three-dimensional fine fracture modeling. The grouting numerical simulation model can take geological parameters, construction parameters and grout characteristic parameters as inputs and output simulated values ​​of grouting volume. The training data in the training set of the meta-learner may also include simulated values ​​of grouting volume.

[0110] This invention also provides a prediction method for an integrated proxy prediction model of grouting volume based on Stacking. The integrated proxy prediction model is constructed with two layers: the first layer has three base learners, and the second layer has one meta-learner. The three base learners are an SVR neural network, a BPNN neural network, and an RF model, respectively; the meta-learner is an ANFIS neural network. Historical data including geological parameters, construction parameters, and grout characteristic parameters are collected as training samples to construct training and validation sets. Five-fold cross-validation is used to train the three base learners. A training set including the prediction results obtained from the three base learners is constructed to train the meta-learner. Input parameters including geological parameters, construction parameters, and grout characteristic parameters are simultaneously input to the three base learners, and then the prediction results obtained from the three base learners are input to the meta-learner, which outputs the predicted grouting volume value.

[0111] Preferably, a grouting numerical simulation model based on three-dimensional fine fracture modeling can also be set up, which can input geological parameters, construction parameters and grout characteristic parameters, and output simulated grouting volume values; the prediction results obtained by the three base learners can be combined with the corresponding simulated grouting volume values ​​to construct a new training set to train the meta learner.

[0112] Preferably, the method for constructing the training set and validation set may include: using the Latin hypercube sampling method to extract multiple sets of geological parameters, combining them with different construction parameters and grout characteristic parameters to construct a parameter sample set representing various fracture geological conditions and construction conditions; inputting the data in the parameter sample set into the grouting numerical simulation model to obtain the simulated grouting volume value; using the geological parameters, construction parameters, grout characteristic parameters, and the corresponding generated simulated grouting volume value as sample data to construct a sample set, which may be divided into a training set and a test set according to the proportion.

[0113] Preferably, the method for collecting historical data including geological parameters, construction parameters, and grout characteristic parameters as training samples may include: obtaining the following geological parameters based on a three-dimensional fine fracture network model: number of fractures, average fracture dip, average dip angle, and average fracture width; obtaining the following construction condition parameters based on the actual construction plan of the project and the technical specifications for cement grouting construction of hydraulic structures: sequence of grouting holes, hole order, hole depth, and grouting pressure; and obtaining the following grout parameters based on the actual construction plan of the project: grout water-cement ratio.

[0114] Preferably, the sparrow search algorithm can be improved based on chaos theory and Lévy flight strategy, and the improved sparrow search algorithm can be used to simultaneously optimize the model parameters of the base learner and the meta learner.

[0115] Preferably, the method for improving the sparrow search algorithm based on chaos theory and Lévy flight strategy may include:

[0116] Sparrow population initialization can be performed based on chaos theory. The Tent chaotic mapping can be used to generate chaotic sequences to initialize sparrow positions. i,j , where i = 1, 2, 3…n, n represents the number of sparrows in the population, j = 1, 2, 3…d, d represents the dimension of the variable to be optimized.

[0117] An initial value x between [0, 1] can be randomly generated. pi，0 At this point, j = 0.

[0118] Chaotic sequences can be generated using the Tent chaotic map:

[0119]

[0120] The chaotic sequence can be mapped to the search space of solutions to obtain the chaotic initialization population:

[0121]

[0122] The Lévy flight strategy can be used to improve the position update formulas for explorers, followers, and scouts, expanding the search range and enhancing global search capabilities. The improved explorer position update formula can be as follows:

[0123]

[0124]

[0125] The improved explorer location update formula can be as follows:

[0126]

[0127] The improved explorer location update formula can be as follows:

[0128]

[0129] In the above formulas:

[0130] Y = {y i , i = 1, 2, 3, ..., n} represents the response grouting volume value.

[0131] F={f i , i = 1, 2, 3, ..., k} represents the predicted final grouting volume.

[0132] xp represents the population vector set of parameters to be optimized.

[0133] i represents an individual in the sparrow population.

[0134] j represents the variable to be optimized.

[0135] Initialize the chaotic population obtained using the Tent chaotic map.

[0136] xp min，j It is the minimum value of the population vector in the j-th dimension.

[0137] xp max，j It represents the maximum value of the j-th dimension population vector.

[0138] Let be the j-th dimension of the population vector of the i-th sparrow individual at the t-th iteration.

[0139] It is represented as the j-th dimension of the population vector of the i-th sparrow individual at the (t+1)-th iteration.

[0140] t represents the current iteration number.

[0141] iter max This indicates the maximum number of iterations.

[0142] α∈(0,1) represents random coefficients.

[0143] R2∈[0,1] represents the warning value.

[0144] ST∈[0.5,1] represents a safe value.

[0145] It is an intermediate variable in the iterative calculation.

[0146] This indicates the current globally optimal position.

[0147] ⊕ represents dot product.

[0148] Lévy(λ) represents the Lévy random search path.

[0149] This indicates the optimal position currently occupied by the explorer.

[0150] It is currently the worst position in the entire system.

[0151] n is the total number of individuals in the sparrow population.

[0152] Let A represent a 1×d matrix, where each element takes the value 1 or -1, and A + =A T (AA T ) -1 .

[0153] fb This represents the current global best fitness value.

[0154] f w This represents the current worst fitness value globally.

[0155] f i This indicates the fitness value of the individual sparrow to be updated.

[0156] ε is a small constant to prevent the denominator from being zero.

[0157] Preferably, the method for simultaneously optimizing the model parameters of the base learner and the meta learner using an improved sparrow search algorithm may include the following steps:

[0158] Step 1 determines the population size, maximum number of iterations, fitness value range, solution interval range, explorer ratio, and scout ratio.

[0159] Step 2: Initialize the population using Tent chaotic mapping.

[0160] Step 3: Increment the iteration count by 1. Calculate the sparrow population fitness value.

[0161] Step 4: Select some sparrows with better fitness values ​​as explorers and update their positions.

[0162] Step 5: The remaining sparrows can act as followers and update their positions.

[0163] Step 6: Select a portion of the sparrow population as scouts to update their locations.

[0164] Step 7: Calculate the fitness value of the sparrow population.

[0165] Step 8: Determine if the fitness value meets the condition. If not, proceed to step 9; if it does, proceed to step 10.

[0166] Step 9: Determine if the number of iterations is less than the maximum number of iterations. If it is less than the maximum number of iterations, proceed to step 3; otherwise, proceed to step 10.

[0167] Step 10: End the optimization and obtain the optimal model parameters.

[0168] Preferably, the model parameters optimized using the sparrow search algorithm may include: the penalty factor and kernel parameters of the SVR neural network, the initial threshold and weights of the BPNN neural network, the number of decision trees n and the maximum depth h of the RF model, and the antecedent parameters of the ANFIS neural network.

[0169] The workflow and working principle of the present invention will be further described below with reference to a preferred embodiment:

[0170] This invention employs a Stacking ensemble learning strategy that increases model diversity, reduces overfitting and prediction uncertainty, and produces more accurate and robust prediction results. It also utilizes an improved sparrow search algorithm that ensures the uniformity and diversity of the initial population distribution and overcomes the potential for decreased population diversity during the search process, while avoiding getting trapped in local optima. This invention addresses the problems of existing machine learning grouting volume prediction models, such as the lack of consideration for geological parameters, the complexity and time-consuming nature of grouting numerical simulation, the low accuracy of single surrogate models, and the high subjectivity of weighting in combined surrogate models. Compared to single surrogate models, this invention significantly improves prediction performance, enabling fast and accurate grouting volume prediction, thus obtaining more accurate and reliable prediction results, providing guidance for decision-making, and ensuring the safety and quality of grouting. In practical grouting projects, it provides reliable methodological support for estimating grouting volume in the area to be grouted, demonstrating significant engineering application value. Furthermore, the model proposed in this paper also provides new ideas for predicting other engineering parameters, showing promising prospects for engineering applications.

[0171] In practical engineering, accurate and reliable grouting volume prediction is of great significance for the control of the grouting construction process. Addressing the shortcomings of existing grouting volume prediction research, such as the complexity and time-consuming nature of numerical simulation methods and the low accuracy of surrogate models based on single machine learning methods, this paper adopts an integrated surrogate model for dam foundation grouting volume prediction based on ISSA-Stacking. This model rapidly and accurately predicts grouting volumes under various geological conditions and grouting scenarios, thus providing effective and reliable theoretical guidance for subsequent grouting construction control and engineering quantity optimization. The integrated surrogate model for dam foundation grouting volume prediction based on ISSA-Stacking specifically includes the following steps:

[0172] A. Obtain input parameters including three factors: geological properties, construction conditions, and slurry properties.

[0173] B. Generate dataset.

[0174] C. Construct an integrated agent model based on Stacking.

[0175] D. Optimize the parameters of the Stacking-based integrated agent model using the improved SSA, and establish a Stacking-based integrated agent model.

[0176] To make the objectives, technical solutions, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0177] 1. Obtain input parameters including three factors: geological properties, construction conditions, and grout properties.

[0178] Based on the three-dimensional fine fracture network model, the fracture parameters such as the number of fractures, average fracture dip, average dip angle, and average fracture width are obtained; based on the actual construction measures of the project and the "Technical Specification for Cement Grouting Construction of Hydraulic Structures" (DL / T5148-2012), the sequence, order, depth, and grouting pressure of the grouting holes are determined; based on the actual construction measures of the project, the water-cement ratio of the grout is determined.

[0179] 2. Generate dataset

[0180] Based on the parameter sample space of fractured rock mass, multiple sets of geological parameters are extracted using the Latin hypercube (LHS) sampling method. These parameters are then combined with different construction parameters and grout characteristic parameters to construct parameter sample points representing various fractured geological conditions and construction scenarios. These parameter sample points are then input into a grouting numerical simulation model based on three-dimensional fine fracture modeling to calculate simulated grouting volumes. This generates a dataset consisting of parameter sample points and corresponding simulated grouting volumes, which is further divided proportionally into training and test sets.

[0181] 3. Construct an integrated proxy model based on Stacking

[0182] The obtained training set was used to train the three base learners, SVR, BPNN, and RF, using five-fold cross-validation to improve the overall generalization and diversity of the model. The obtained prediction results and simulated response values ​​were then combined to form a new training set to train the ANFIS meta-learner. This process, considering the uncertainty in the prediction process, achieves the inductive fusion of the base learner results. The method flow is as follows: Figure 1 As shown. The specific steps are as follows:

[0183] 3-1, the sample dataset (X, Y) consisting of input data and simulated grouting volume values ​​is proportionally divided into a training set (Xi, Yj). tr Y tr ) and test set (X) te Y te );

[0184] 3-2, Five-fold cross-validation is used to train the SVR, BPNN, and RF base learners, and a prediction result p is obtained. tr-j This process is repeated five times to obtain the prediction results P of each base learner for the entire original training set. tr-SVR ={p tr-j ,j=1,2,3,4,5}、P tr-BPNN ={p tr-j ,j=1,2,3,4,5} and P tr-RF ={p tr-j The values ​​j = 1, 2, 3, 4, 5 are used to construct a new training set (P) by combining the response values ​​from the original training set with the response values ​​from the original training set. tr Y tr) is used to train the meta-learner ANFIS, where P tr ={P tr-SVR P tr-BPNN P tr-RF};

[0185] 3-3, During the testing process, each pre-trained base learner obtains the corresponding prediction results of the original test set, and constructs a new test set (P) by combining these predictions with the response values ​​in the original test set. te Y te ) is used to test the pre-trained meta-learner ANFIS, where P te ={P te -SVR, P te -BPANN, P te -RF}. This yields the final prediction result F. te ={f i , i = 1, 2, 3, ..., k}.

[0186] 3-4. Optimize the parameters of the Stacking-based integrated agent model using the improved SSA, and establish a Stacking-based integrated agent prediction model for grouting volume.

[0187] An improved sparrow search algorithm based on chaos theory and Lévy flight strategy is used to simultaneously optimize the model parameters of the base learner and meta-learner, thereby establishing a stacking-based ensemble prediction model for grouting volume, achieving high-precision prediction of grouting volume. The specific steps are as follows:

[0188] 3-4-1. The sparrow population is initialized using chaos theory. The Tent chaotic map is used to generate a chaotic sequence to initialize the sparrow positions x. pi,j , where i = 1, 2, 3…n, n represents the number of sparrows in the population, j = 1, 2, 3…d, d represents the dimension of the variable to be optimized.

[0189] a. Randomly generate an initial value x between [0, 1]. pi，0 At this point, j = 0.

[0190] b. Generate chaotic sequences using the Tent chaotic map:

[0191]

[0192] c. Map the chaotic sequence to the search space of solutions to obtain the chaotic initialization population:

[0193]

[0194] In the formula, xp min，j XP max，j These are the minimum and maximum values ​​of the j-th dimension, respectively.

[0195] 3-4-2, using the Lévy flight strategy, improves the position update formulas for explorers, followers, and scouts, expanding the search range and enhancing global search capabilities. The improved explorer position update formula is as follows:

[0196]

[0197] In the formula, t represents the current iteration number, iter max The maximum number of iterations is represented by α∈(0,1), which is a random number. R2∈[0,1] represents the warning value, and ST∈[0.5,1] represents the safety value. λ is the current globally optimal position, ⊕ is the dot product, and Lévy(λ) is the Lévy random search path.

[0198] The improved explorer location update formula is as follows:

[0199]

[0200] In the formula This indicates the optimal position currently occupied by the explorer. It is the worst position in the current global array. A represents a 1×d matrix where each element takes the value 1 or -1, and A + =A T (AA T ) -1 .

[0201] The improved explorer location update formula is as follows:

[0202]

[0203] In the formula, f b and f w These are the current best and worst fitness values ​​globally, respectively. i Let ε represent the fitness value of the sparrow individual to be updated; ε is a small constant used to prevent the denominator from being zero.

[0204] 3-4-2, The ISSA proposed above, which has superior global search capabilities and convergence performance, is used to synchronously optimize the parameters of each machine learning algorithm in the Stacking-based ensemble agent model.

[0205] The predictive performance of stacking-based ensemble agent models is influenced by the following parameters: primarily the penalty factor C and kernel parameter g of SVR, the initial threshold b and weights w of BPNN, the number of decision trees n and maximum depth h of RF, and the antecedent parameters ai, bi, and ci of ANFIS. The parameter search process based on ISSA can be transformed into the following optimization problem:

[0206]

[0207] In the formula, Y = {yi, i = 1, 2, 3, ..., n} and F = {fi, i = 1, 2, 3, ..., n} represent the response grouting volume and the predicted final grouting volume, respectively, and xp represents the population vector set of the parameters to be optimized. lb and XP ub These represent the lower and upper limits of the parameter to be optimized, respectively. This leads to the construction of an integrated agent model based on ISSA-Stacking.

[0208] The embodiments described above are only used to illustrate the technical ideas and features of the present invention. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The patent scope of the present invention should not be limited by these embodiments. That is, all equivalent changes or modifications made in accordance with the spirit disclosed in the present invention still fall within the patent scope of the present invention.

Claims

1. A prediction method based on a stacking-based integrated proxy prediction model for grouting volume, characterized in that, A stacking-based integrated proxy prediction model for grouting volume was constructed. This model consists of two layers: the first layer uses three base learners, and the second layer uses one meta-learner. The three base learners are an SVR neural network, a BPNN neural network, and an RF model, respectively; the meta-learner is an ANFIS neural network. Historical data including geological parameters, construction parameters, and grout characteristic parameters were collected as training samples to construct training and validation sets. Five-fold cross-validation was used to train the three base learners. A training set containing the prediction results from the three base learners was constructed to train the meta-learner. Input parameters including geological parameters, construction parameters, and grout characteristic parameters were simultaneously input into the three base learners. The prediction results from the three base learners were then input into the meta-learner, which outputs the predicted grouting volume.

2. The prediction method of the stacking-based integrated proxy prediction model for grouting volume according to claim 1, characterized in that, A grouting numerical simulation model based on three-dimensional fine fracture modeling is also set up. The grouting numerical simulation model takes geological parameters, construction parameters and grout characteristic parameters as input and outputs the simulated value of grouting volume. The prediction results obtained by the three base learners are combined with the corresponding simulated value of grouting volume to construct a new training set to train the meta learner.

3. The prediction method of the stacking-based integrated proxy prediction model for grouting volume according to claim 2, characterized in that, The method for constructing the training and validation sets includes: extracting multiple sets of geological parameters using the Latin hypercube sampling method, combining them with different construction parameters and grout characteristic parameters to construct a parameter sample set representing various fracture geological conditions and construction conditions; inputting the data from the parameter sample set into the grouting numerical simulation model to obtain the simulated grouting volume; using the geological parameters, construction parameters, grout characteristic parameters, and the corresponding generated simulated grouting volume values ​​as sample data to construct a sample set, and dividing the sample set into a training set and a test set proportionally.

4. The prediction method of the stacking-based integrated proxy prediction model for grouting volume according to claim 2, characterized in that, The method for collecting historical data, including geological parameters, construction parameters, and grout characteristic parameters, as training samples includes: obtaining the following geological parameters based on a three-dimensional fine fracture network model: number of fractures, average fracture dip, average dip angle, and average fracture width; obtaining the following construction condition parameters based on the actual construction plan and the technical specifications for cement grouting construction of hydraulic structures: sequence of grouting holes, hole order, hole depth, and grouting pressure; and obtaining the following grout parameters based on the actual construction plan: grout water-cement ratio.

5. The prediction method of the stacking-based integrated proxy prediction model for grouting volume according to claim 2, characterized in that, An improved sparrow search algorithm is proposed based on chaos theory and Lévy flight strategy. The improved sparrow search algorithm is used to simultaneously optimize the model parameters of the base learner and meta learner.

6. The prediction method of the stacking-based integrated proxy prediction model for grouting volume according to claim 5, characterized in that, Methods for improving the sparrow search algorithm based on chaos theory and Lévy flight strategy include: Sparrow population initialization based on chaos theory, using Tent chaotic mapping to generate chaotic sequences to initialize sparrow positions (xp) i,j , where i=1,2,3…n, n represents the number of sparrows in the population, j=1,2,3…d, d represents the dimension of the variable to be optimized; Randomly generate initial values ​​between [0, 1] x pi，0 ,at this time j =0; Generating chaotic sequences using the Tent chaotic map: ； Mapping the chaotic sequence to the search space of solutions yields the chaotic initialization population: ； The Lévy flight strategy is used to improve the position update formulas for explorers, followers, and scouts, expanding the search range and enhancing global search capabilities. The improved explorer position update formula is as follows: ； ； The improved explorer location update formula is as follows: ； The improved explorer location update formula is as follows: ； In the above formulas: xp represents the population vector set of the parameters to be optimized; This refers to an individual within a sparrow population. j Indicates the variable to be optimized; Initialize the chaotic population using the Tent chaotic map; xp min，j For the first j The minimum value of the population vector; xp max，j For the first j The maximum value of the population vector; Let be the j-th dimension of the population vector value of the i-th sparrow individual at the t-th iteration; It is represented as the j-th dimension of the population vector of the i-th sparrow individual at the (t+1)-th iteration; t Indicates the current iteration number; iter max Indicates the maximum number of iterations; α ∈(0,1) represents a random coefficient; R 2 ∈[0,1] represents the warning value; ST ∈[0.5,1] represents a safe value; , is an intermediate variable in the iterative calculation; This indicates the current globally optimal position; ⊕ represents dot product; This indicates Lévy's random search path; This indicates the optimal position currently occupied by the explorer. It is currently the worst position in the entire system. n is the total number of individuals in the sparrow population. A Represents a 1× d A matrix, where each element takes the value 1 or -1, and A + =A T (AA T ) -1 ; f b This represents the current global best fitness value; f w This represents the current worst-case fitness value globally. This represents the fitness value of the individual sparrow to be updated. ε It is a relatively small constant to prevent the denominator from being zero.

7. The prediction method of the stacking-based integrated proxy prediction model for grouting volume according to claim 6, characterized in that, The method for simultaneously optimizing the model parameters of the base learner and the meta learner using an improved sparrow search algorithm includes the following steps: Step 1: Determine the population size, maximum number of iterations, fitness value range, solution interval range, explorer ratio, and scout ratio; Step 2: Initialize the population using Tent chaotic mapping; Step 3, increment the iteration count by 1; Calculate the fitness value of the sparrow population; Step 4: Select some sparrows with better fitness values ​​as explorers and update their positions; Step 5: The remaining sparrows, acting as followers, update their positions. Step 6: Select a portion of the sparrow population as scouts and update their locations; Step 7: Calculate the fitness value of the sparrow population; Step 8: Determine if the fitness value meets the condition. If not, proceed to step 9; if it does, proceed to step 10. Step 9: Determine if the number of iterations is less than the maximum number of iterations. If it is less than the maximum number of iterations, proceed to step 3; otherwise, proceed to step 10. Step 10: End the optimization and obtain the optimal model parameters.

8. The prediction method of the stacking-based integrated proxy prediction model for grouting volume according to claim 5, characterized in that, The model parameters optimized using the sparrow search algorithm include: the penalty factor and kernel parameters of the SVR neural network, the initial threshold and weights of the BPNN neural network, the number of decision trees n and the maximum depth h of the RF model, and the antecedent parameters of the ANFIS neural network.

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