A rock burst intensity prediction method based on a weighted meta-heuristic combination model

Abstract

The present application relates to a kind of rock burst intensity prediction method based on weighted meta-heuristic combination model, belong to geotechnical engineering technical field.The present application determines the evaluation index of rock burst intensity prediction and rock burst intensity classification;Rock burst case is collected, rock burst intensity prediction sample data set is established, and is divided into training set and test set sample;Three meta-heuristic optimization algorithms are used to optimize hyperparameters in random forest (RF) model, and corresponding rock burst intensity prediction model is established;Training set and test set sample are respectively input into three rock burst intensity prediction models to obtain the predicted rock burst intensity classification, and the prediction accuracy of three rock burst intensity prediction models is calculated respectively;According to the prediction accuracy, the weight vector of corresponding rock burst intensity prediction model is calculated;According to the weight vector of rock burst intensity prediction model, the value of hyperparameter is determined, and the meta-heuristic combination model based on weighting is established;The rock burst intensity to be predicted in engineering case is predicted using the meta-heuristic combination model based on weighting.

Description

Technical Field

[0001] This invention relates to a method for predicting rockburst intensity based on a weighted metaheuristic combined model, belonging to the field of geotechnical engineering technology. Background Technology

[0002] Rockburst refers to a geological hazard caused by the ejection of rock fragments from surrounding rock that has accumulated high elastic strain energy due to excavation or other load disturbances. Rockbursts are influenced by multiple factors and are characterized by their suddenness, randomness, and high destructiveness, posing safety hazards, unnecessary economic losses, and delays to underground construction. Currently, with socio-economic development, more and more underground engineering projects (such as hydropower stations, tunnels, and mines) are venturing deeper, leading to an increasing number of rockburst hazards. Therefore, effectively predicting rockburst intensity is a challenge and problem in ensuring safe operations in deep underground engineering. In recent decades, scholars both domestically and internationally have conducted extensive research on rockburst prediction. Currently, rockburst prediction methods can be summarized into four categories. The first category comprises theoretically based empirical criteria, such as the Russense criterion, Barton criterion, Hoek criterion, and elastic energy index criterion. The second category includes methods based on in-situ monitoring, such as tomography, microseismic methods, and acoustic emission methods. The third category consists of mathematical models based on uncertainty theory, such as fuzzy comprehensive evaluation, grey system theory, DS evidence theory, and multidimensional cloud models. The fourth category comprises intelligent models based on machine learning algorithms, such as support vector machines, decision trees, least squares support vector machines, Naive Bayes, random forests, gradient boosting machines, and artificial neural networks. These machine learning algorithms have achieved good results to a certain extent.

[0003] Currently, research on machine learning algorithms for rockburst prediction mainly focuses on the selection of algorithm models, the selection of rockburst evaluation indicators, the optimization of model hyperparameters, and dataset preprocessing. Machine learning algorithms can be divided into single models and ensemble models based on the number of classifiers. Single models have low generalization ability and cannot obtain optimal solutions for all problems. Their predictive performance varies with changes in the engineering environment or input parameters, resulting in poor rockburst disaster prediction effects in current underground excavation projects.

[0004] When training and building models, machine learning algorithms require determining the values ​​of one or more hyperparameters. Hyperparameters are typically determined using grid search or metaheuristic optimization algorithms. Currently, most researchers use grid search or only one metaheuristic optimization algorithm to determine hyperparameters, lacking comparative verification between different methods. Summary of the Invention

[0005] This invention addresses the shortcomings of current machine learning algorithms in predicting rockburst intensity by proposing a rockburst intensity prediction method based on a weighted metaheuristic combined model. This invention, based on a weighted metaheuristic combined model, further improves the accuracy of the model and reduces the uncertainty of parameter selection by comparing and verifying the results of three metaheuristic optimization algorithms and performing weighted calculations.

[0006] A method for predicting rockburst intensity based on a weighted metaheuristic combined model, the specific steps of which are as follows:

[0007] (1) Determine the evaluation indicators for rockburst intensity prediction and the rockburst intensity classification;

[0008] (2) Based on the evaluation index and rockburst intensity classification of the determined rockburst intensity prediction, collect domestic and foreign engineering rockburst accident cases, establish a rockburst intensity prediction sample dataset, and randomly divide it into training set and test set samples in a ratio of 8:2.

[0009] (3) Three metaheuristic optimization algorithms were used to optimize the hyperparameters in the random forest (RF) model. The fitness value was taken as the average error rate calculated by 5-fold cross-validation. After obtaining the hyperparameters, the corresponding rockburst intensity prediction models were constructed respectively.

[0010] (4) Input the training set and test set samples into the three rockburst intensity prediction models respectively to obtain the predicted rockburst intensity level, and calculate the prediction accuracy of the three rockburst intensity prediction models respectively; calculate the weight vector of the corresponding rockburst intensity prediction model based on the prediction accuracy of the three rockburst intensity prediction models.

[0011] (5) Determine the hyperparameter values ​​based on the weight vector of the rockburst intensity prediction model and establish a weighted metaheuristic combination model.

[0012] (6) Use a weighted metaheuristic combination model to predict the rockburst intensity in engineering cases.

[0013] The evaluation index for rockburst intensity prediction in step (1) includes the stress coefficient σ. θ / σ c Brittleness coefficient σ c / σ t and elastic energy index W et .

[0014] The rockburst intensity classification in step (1) includes no rockburst, slight rockburst, moderate rockburst and severe rockburst.

[0015] The heuristic optimization algorithms in step (3) include Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Grey Wolf Optimization (GWO).

[0016] The method for calculating the weight vector Q in step (4) is as follows:

[0017]

[0018] In the formula: Q is the weight vector, ACC i Let be the accuracy of the i-th optimization algorithm on the test set.

[0019] The beneficial effects of this invention are:

[0020] (1) The rockburst intensity prediction method based on the weighted metaheuristic combination model of this invention establishes a rich rockburst case database, adopts cross-validation and combines three metaheuristic optimization algorithms to optimize and train the random forest model, which has the characteristics of being fast and efficient.

[0021] (2) By comparing and verifying the results of three metaheuristic optimization algorithms and performing weighted calculations, this invention can further improve the accuracy of the model and reduce the uncertainty of parameter selection. On-site construction personnel only need to input the evaluation index corresponding to the rockburst sample to be predicted in the project into the established rockburst prediction model to obtain the predicted value of rockburst intensity level, which has the advantages of strong practicality and high efficiency. Attached Figure Description

[0022] Figure 1 Flowchart for predicting rockburst intensity;

[0023] Figure 2 A heatmap showing the correlation between three parameters in the evaluation index for predicting rockburst intensity;

[0024] Figure 3 Iteration curves of three metaheuristic algorithms in the evaluation index of rockburst intensity prediction;

[0025] Figure 4 This is the confusion matrix of the three models on the training set in the evaluation index for rockburst intensity prediction. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to specific embodiments, but the scope of protection of the present invention is not limited to the content described.

[0027] Example 1: A method for predicting rockburst intensity based on a weighted metaheuristic combined model (see Example 2) Figure 1 The specific steps are as follows:

[0028] (1) Determine the evaluation indicators for rockburst intensity prediction and the rockburst intensity classification;

[0029] Rockburst prediction is a highly complex nonlinear process, influenced by model selection, parameter selection, and cognitive uncertainties. Therefore, after determining the model, rationally and effectively selecting rockburst prediction evaluation indicators is crucial. Rockbursts are typically related to in-situ stress, rock properties, groundwater occurrence, rock mass characteristics, and human-induced excavation disturbance. Based on numerous rockburst accident cases, it has been found that rockbursts usually occur in brittle rock masses with high stress concentration, where the stress concentration factor σ... θ / σ c and brittleness index σ c / σ t This can reflect these characteristics. In addition, rock bursts require the rock mass to store sufficient elastic strain energy, as indicated by the elastic energy index W. et It can reflect the energy storage capacity and energy release performance of the rock mass. Therefore, σ is selected. θ / σ c σ c / σ t and W et Three evaluation indicators are used as input features for the rockburst prediction model. At the same time, the rockburst intensity is divided into no rockburst, slight rockburst, moderate rockburst and severe rockburst in a conventional way. The empirical grading standard for rockburst prediction corresponding to each evaluation indicator is shown in Table 1.

[0030] Table 1 Experience Grading Standards

[0031]

[0032] (2) Based on the evaluation index and rockburst intensity classification of the determined rockburst intensity prediction, collect domestic and foreign engineering rockburst accident cases, establish a rockburst intensity prediction sample dataset, and randomly divide it into training set and test set samples in a ratio of 8:2.

[0033] (3) Three metaheuristic optimization algorithms, namely particle swarm optimization algorithm (PSO), genetic algorithm (GA) and gray wolf optimization algorithm (GWO), are used to optimize the hyperparameters in the random forest (RF) model. The fitness value is taken as the average error rate calculated by 5-fold cross-validation. After obtaining the hyperparameters, the corresponding rockburst intensity prediction models are constructed respectively.

[0034] (4) Input the training set and test set samples into the three rockburst intensity prediction models respectively to obtain the predicted rockburst intensity level, and calculate the prediction accuracy of the three rockburst intensity prediction models respectively; calculate the weight vector of the corresponding rockburst intensity prediction model based on the prediction accuracy of the three rockburst intensity prediction models.

[0035] The method for calculating the weight vector Q is as follows:

[0036]

[0037] In the formula: Q is the weight vector, ACCi Let be the accuracy of the i-th optimization algorithm on the test set;

[0038] (5) Determine the hyperparameter values ​​based on the weight vector of the rockburst intensity prediction model and establish a weighted metaheuristic combination model.

[0039] (6) Use a weighted metaheuristic combination model to predict the rockburst intensity in engineering cases.

[0040] Example 2: A method for predicting rockburst intensity based on a weighted metaheuristic combined model (see Example 2) Figure 2 The specific steps are as follows:

[0041] (1) Determine the evaluation indicators for rockburst intensity prediction and the rockburst intensity classification;

[0042] Rockburst prediction is a highly complex nonlinear process, influenced by model selection, parameter selection, and cognitive uncertainties. Therefore, after determining the model, rationally and effectively selecting rockburst prediction evaluation indicators is crucial. Rockbursts are typically related to in-situ stress, rock properties, groundwater occurrence, rock mass characteristics, and human-induced excavation disturbance. Based on numerous rockburst accident cases, it has been found that rockbursts usually occur in brittle rock masses with high stress concentration, where the stress concentration factor σ... θ / σ c and brittleness index σ c / σ t This can reflect these characteristics. In addition, rock bursts require the rock mass to store sufficient elastic strain energy, as indicated by the elastic energy index W. et It can reflect the energy storage capacity and energy release performance of the rock mass. Therefore, σ is selected. θ / σ c σ c / σ t and W et Three evaluation indicators are used as input features for the rockburst prediction model. At the same time, the rockburst intensity is divided into no rockburst, slight rockburst, moderate rockburst and severe rockburst in a conventional way. The empirical grading standard for rockburst prediction corresponding to each evaluation indicator is shown in Table 1.

[0043] (2) Based on the evaluation index and rockburst intensity classification of the determined rockburst intensity prediction, collect domestic and foreign engineering rockburst accident cases, establish a rockburst intensity prediction sample dataset, and randomly divide it into training set and test set samples in a ratio of 8:2.

[0044] Based on the research results in the references "Evaluation of rockburst occurrence and intensity in underground structures using decision tree approach" and "A rockburst intensity classification prediction method based on PCA-PNN principle", a dataset containing 200 typical rockburst engineering cases from home and abroad was established. This dataset includes 34 samples without rockburst, 60 samples with slight rockburst, 78 samples with moderate rockburst, and 28 samples with severe rockburst. Some data are shown in Table 2.

[0045] Table 2. Rockburst Case Database (Partial)

[0046]

[0047] To understand the correlation among the three indicators, the Pearson correlation coefficient between the indicator parameters was calculated using equation (1) (see Figure 1 As shown in the figure, the absolute values ​​of the Pearson correlation coefficients among the evaluation indicators are all below 0.4, indicating a weak correlation; among them, σ c / σ t With σ θ / σ c and W et The correlation coefficients of all three are negative, indicating a negative correlation between them.

[0048]

[0049] In the formula: The correlation coefficient between indicators x1 and x2; The mean of the data for indicator x1; The mean of the x2 data for the indicator;

[0050] The statistical characteristics of the indicator parameters are shown in Table 3.

[0051] Table 3 describes the statistical characteristics of the variables.

[0052]

[0053] (3) Three metaheuristic optimization algorithms were used to optimize the hyperparameters in the random forest (RF) model. The fitness value was taken as the average error rate calculated by 5-fold cross-validation. After obtaining the hyperparameters, the corresponding rockburst intensity prediction models were constructed respectively.

[0054] A 5-fold cross-validation strategy was adopted to further divide the training set into 5 parts, with 4 parts used as the training set and the remaining part as the test set in turn. During this process, the error rates of the 5 models on the corresponding test set were averaged and used as the fitness value. Then, PSO, GA, and GWO were used to optimize the hyperparameters of the RF model. The random forest algorithm has two main hyperparameters: the number of sample predictors per split node (m...). try ) and the number of classification trees (n tree ); where m try The search range is [1,3], n tree The optimization range is [10, 600];

[0055] Taking the Particle Swarm Optimization (PSO) algorithm as an example, the general computational process of metaheuristic optimization algorithms is explained. The specific computational principles and processes of the Genetic Algorithm (GA) and the Grey Wolf Optimization (GWO) algorithm are based on existing literature.

[0056] The specific process of the Particle Swarm Optimization (PSO) algorithm is as follows:

[0057] ① Set relevant parameters and initialize the population;

[0058] In the particle swarm optimization algorithm, the parameters that need to be set in advance are mainly the population size Pop, learning factors c1 and c2, the number of iterations N, and the optimization range of the parameters (see Table 4); then initialize the position, velocity, individual best position (pbest) and global best position (gbest) of the particles.

[0059] Table 4 PSO Parameter Settings

[0060]

[0061] ② Update population location;

[0062] Then, the velocity and position of the particles are updated according to equations (2) and (3), and the fitness value is calculated again;

[0063] v id (t+1)=v id (t)+c1·r1·(p id (t)-x id (t))+c2·r2·(p gd (t)-x id (t)) (2)

[0064] x id (t+1)=x id (t)+v id (t+1) (3)

[0065] In the formula: c1 and c2 are learning factors; r1 and r2 are random numbers; ranging from 0 to 1; p gd It is the best position found by all particles in the past search; p id It is the best position of the current particle in the past.

[0066] ③ Iteratively optimize and update the optimal particle position;

[0067] During the iteration process, the fitness value of each particle is compared with its individual best value pbest. If it is better than pbest, it is replaced. The fitness value of each particle is also compared with the group's historical best position gbest. If it is better than the group's historical best position, it is replaced.

[0068] ④ The termination condition is met:

[0069] Repeat steps ② to ③ until the set number of iterations is reached;

[0070] Among them, the parameters that need to be set for GA in ① and their specific values ​​are shown in Table 5, while GWO has no other parameters that need to be set except for the population size and the number of iterations, and the values ​​of these two parameters are consistent with those of the first two algorithms.

[0071] Table 5 GA Parameter Settings

[0072]

[0073] Note: P c P represents the crossover probability. m Probability of mutation

[0074] After setting the parameters in PSO, GA, and GWO, iterative optimization is performed on the MATLAB platform; the iterative curves for optimizing the hyperparameters of the random forest using the three metaheuristic algorithms are shown below. Figure 2 ,from Figure 2 It can be observed that the PSO algorithm reaches convergence earliest, but its convergence performance is not as good as that of the GA and GWO algorithms. Among them, the GWO and GA algorithms have the best convergence performance, but the convergence speed of GWO is worse than that of the GA algorithm and not much different from that of the PSO algorithm.

[0075] The hyperparameters determined by PSO, GA and GWO iterative optimization are shown in Table 6.

[0076] Table 6. Hyperparameters determined by the three metaheuristic algorithms

[0077]

[0078] Three hyperparameter combinations were incorporated into the random forest algorithm and trained using the training set to obtain three combined rockburst intensity prediction models (PSO-RF, GA-RF, and GWO-RF).

[0079] (4) Input the training set and test set samples into the three rockburst intensity prediction models respectively to obtain the predicted rockburst intensity level, and calculate the prediction accuracy of the three rockburst intensity prediction models respectively; calculate the weight vector of the corresponding rockburst intensity prediction model based on the prediction accuracy of the three rockburst intensity prediction models.

[0080] The prediction results of PSO-RF, GA-RF, and GWO-RF on the training set are shown below. Figure 3 ,from Figure 3 It can be seen that all three combined models have excellent performance on the training set, with an accuracy of over 98%; among them, the GA-RF and GWO-RF models are the best, each only mispredicting one strong rockburst sample.

[0081] Inputting 20% ​​of the test set into the three combined models yields their predictions on the test set, such as... Figure 4 As shown, from Figure 4 As can be seen, the accuracy rates of PSO-RF, GA-RF, and GWO-RF on the test set are 82.5%, 85%, and 90%, respectively; based on the calculation method of the weight vector Q...

[0082]

[0083] In the formula: Q is the weight vector, ACC i Let be the accuracy of the i-th optimization algorithm on the test set;

[0084] The weight vector Q = [Q] is determined among the combinations of hyperparameters determined by the three optimization algorithms. RF Q GA Q GWO = [0.32, 0.33, 0.35];

[0085] (5) Determine the hyperparameter values ​​based on the weight vector of the rockburst intensity prediction model, i.e., the hyperparameter combination is n. tree =212,m try =1; Establish a weighted metaheuristic combinatorial model;

[0086] (6) Using a weighted metaheuristic combination model to predict the rockburst intensity in engineering cases: After retraining the training set based on the hyperparameter combination determined in step (4), the obtained weighted metaheuristic combination model was applied to 17 engineering cases of Sangzhuling Tunnel. The prediction results are shown in Table 7.

[0087] Table 7. Rockburst Prediction Results for Sangzhuling Tunnel Project

[0088]

[0089] As shown in Table 7, the prediction results are excellent, with only one prediction error and a prediction accuracy of 94.12%. Based on the prediction results of the model on the test set and engineering cases, it can be found that the trained combined model has excellent generalization ability and good engineering applicability.

[0090] The specific embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for predicting rockburst intensity based on a weighted metaheuristic combined model, characterized in that, The specific steps are as follows: (1) Determine the evaluation indicators for rockburst intensity prediction and the rockburst intensity classification; (2) Based on the determined evaluation index and rockburst intensity classification for rockburst intensity prediction, collect rockburst cases, establish a rockburst intensity prediction sample dataset, and divide it into training set and test set samples. (3) Three metaheuristic optimization algorithms were used to optimize the hyperparameters in the random forest (RF) model and establish a corresponding rockburst intensity prediction model. (4) Input the training set and test set samples into the three rockburst intensity prediction models respectively to obtain the predicted rockburst intensity level, and calculate the prediction accuracy of the three rockburst intensity prediction models respectively; calculate the weight vector of the corresponding rockburst intensity prediction model based on the prediction accuracy of the three rockburst intensity prediction models. (5) Determine the hyperparameter values ​​based on the weight vector of the rockburst intensity prediction model and establish a weighted metaheuristic combination model. (6) Use a weighted metaheuristic combination model to predict the rockburst intensity in engineering cases.

2. The rockburst intensity prediction method based on a weighted metaheuristic combined model according to claim 1, characterized in that: Step (1) The evaluation index for rockburst intensity prediction includes the stress coefficient σ θ / σ c Brittleness coefficient σ c / σ t and elastic energy index W et .

3. The rockburst intensity prediction method based on a weighted metaheuristic combined model according to claim 1, characterized in that: Step (1) Rockburst intensity classification includes no rockburst, slight rockburst, moderate rockburst and severe rockburst.

4. The rockburst intensity prediction method based on a weighted metaheuristic combined model according to claim 1, characterized in that: Step (3) Heuristic optimization algorithms include Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Grey Wolf Optimization (GWO).

5. The rockburst intensity prediction method based on a weighted metaheuristic combined model according to claim 1, characterized in that: The method for calculating the weight vector Q in step (4) is as follows: In the formula: Q is the weight vector, ACC i Let be the accuracy of the i-th optimization algorithm on the test set.

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