CN115980826A - Rock burst intensity prediction method based on weighted meta-heuristic combined model - Google Patents
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Abstract
The invention relates to a rock burst intensity prediction method based on a weighted meta-heuristic combined model, and belongs to the technical field of geotechnical engineering. The method determines the evaluation index of rock burst intensity prediction and the rock burst intensity classification; collecting rock burst cases, establishing a rock burst intensity prediction sample data set, and dividing the rock burst intensity prediction sample data set into a training set and a test set sample; optimizing hyper-parameters in a Random Forest (RF) model by using three meta-heuristic optimization algorithms, and establishing a corresponding rockburst intensity prediction model; respectively inputting the training set samples and the testing set samples into the three rockburst intensity prediction models to obtain predicted rockburst intensity grades, and respectively calculating the prediction accuracy of the three rockburst intensity prediction models; calculating a weight vector of a corresponding rock burst intensity prediction model according to the prediction accuracy; determining a hyper-parameter value according to a weight vector of the rockburst intensity prediction model, and establishing a meta-heuristic combined model based on weighting; and predicting the intensity of the rock burst to be predicted in the engineering case by using a weighted meta-heuristic combined model.
Description
Technical Field
The invention relates to a rock burst intensity prediction method based on a weighted meta-heuristic combined model, and belongs to the technical field of geotechnical engineering.
Background
Rock burst refers to geological disasters of rock block ejection caused by excavation or other load disturbance of surrounding rocks accumulating high elastic strain energy. The occurrence of rock burst is influenced by various factors, has the characteristics of high burstiness, randomness and destructiveness, and can cause potential safety hazards, unnecessary economic loss and delay the progress of engineering on underground construction. At present, with the development of social economy, more and more underground projects (such as hydropower stations, tunnels and mines) enter the deep part, and rock burst disasters are increased day by day. Therefore, how to effectively predict the rockburst intensity is a challenge and a problem in ensuring the safe operation of deep underground engineering. In recent decades, researchers at home and abroad have conducted a great deal of research work on rock burst prediction. At this stage, the rock burst prediction method can be summarized into 4 types. The first category is empirical criteria based on theory, such as Russense criteria, barton criteria, hoek criteria, elastic energy index criteria, and the like; the second type is a method based on-site monitoring, such as tomography, microseismic method, acoustic emission method, and the like; the third category is a mathematical model based on an uncertainty theory, such as a fuzzy comprehensive evaluation method, a grey system theory, a D-S evidence theory, a multi-dimensional cloud model and the like. The fourth method is an intelligent model based on machine learning algorithms, such as support vector machine, decision tree, least squares support vector machine, naive bayes, random forest, gradient elevator, artificial neural network, etc., which achieve better effects to a certain extent.
At present, the research of a machine learning algorithm on rock burst prediction mainly focuses on selection of an algorithm model, selection of rock burst evaluation indexes, optimization of model hyper-parameters and data set preprocessing. Machine learning algorithms can be divided into single models and integrated models based on the number of classifiers. The single model has low generalization capability, can not obtain optimal solutions to all problems, and the prediction performance of the single model changes along with the change of engineering environment or input parameters, so that the rock burst disaster prediction effect in the current underground excavation engineering is poor.
When a machine learning algorithm trains and constructs a model, one or more values of the hyper-parameters need to be determined. The hyper-parameters of a machine learning algorithm may generally be determined by a grid search or meta-heuristic optimization algorithm. At present, in the process of determining the hyper-parameters of the machine learning algorithm, most scholars adopt grid search or determine the hyper-parameters by only one meta-heuristic optimization algorithm, and contrast verification among different methods is lacked.
Disclosure of Invention
The invention provides a rock burst intensity prediction method based on a weighted meta-heuristic combined model aiming at the defects of the traditional machine learning algorithm in rock burst intensity prediction.
A rock burst intensity prediction method based on a weighted meta-heuristic combined model comprises the following specific steps:
(1) Determining evaluation indexes of rockburst intensity prediction and classification of rockburst intensity;
(2) Collecting engineering rockburst accident cases which occur at home and abroad according to the determined evaluation index of rockburst intensity prediction and the rockburst intensity classification, establishing a rockburst intensity prediction sample data set, and randomly dividing the rockburst intensity prediction sample data set into a training set and a testing set according to the proportion of 8:2;
(3) Optimizing the hyperparameter in a Random Forest (RF) model by using three meta-heuristic optimization algorithms, and respectively constructing corresponding rockburst intensity prediction models after acquiring the hyperparameter by taking the average error rate calculated by 5-fold cross validation of the fitness value;
(4) Respectively inputting the training set samples and the test set samples into three rockburst intensity prediction models to obtain predicted rockburst intensity grades, and respectively calculating prediction accuracy rates of the three rockburst intensity prediction models; calculating a weight vector corresponding to the rockburst intensity prediction model according to the prediction accuracy of the three rockburst intensity prediction models;
(5) Determining a hyper-parameter value according to a weight vector of the rockburst intensity prediction model, and establishing a meta-heuristic combined model based on weighting;
(6) And predicting the intensity of the rock burst to be predicted in the engineering case by using a weighted meta-heuristic combined model.
The evaluation index of the rockburst intensity prediction in the step (1) comprises a stress coefficient sigma θ /σ c Brittle coefficient sigma c /σ t And elastic energy index W et 。
The classification of the rockburst intensity in the step (1) comprises non-rockburst, light rockburst, medium rockburst and strong rockburst.
The heuristic optimization algorithm in the step (3) comprises a particle swarm optimization algorithm PSO, a genetic algorithm GA and a wolf optimization algorithm GWO.
The calculation method of the weight vector Q in the step (4) comprises the following steps
In the formula: q is a weight vector, ACC i The accuracy of the optimization algorithm of the ith on the test set is improved.
The invention has the beneficial effects that:
(1) According to the rockburst intensity prediction method based on the weighted meta-heuristic combined model, disclosed by the invention, through establishing a rich rockburst case database, cross validation is adopted and three meta-heuristic optimization algorithms are respectively combined to optimize and train a random forest model, so that the method has the characteristics of rapidness and high efficiency;
(2) According to the method, the results of the three meta-heuristic optimization algorithms are compared, verified and weighted, so that the accuracy of the model can be further improved, and the uncertainty of parameter selection is reduced; on-site constructors only need to input evaluation indexes corresponding to rock burst samples to be predicted in engineering into the established rock burst prediction model, and then rock burst intensity grade pre-judgment values can be obtained.
Drawings
FIG. 1 is a flow chart of rock burst severity prediction;
FIG. 2 is a heat map of the correlation among 3 parameters in the evaluation index of rockburst intensity prediction;
FIG. 3 is an iteration curve of 3 meta-heuristic algorithms in evaluation indexes of rock burst intensity prediction;
FIG. 4 is a confusion matrix of 3 models in the evaluation index of rock burst intensity prediction on a training set.
Detailed Description
The present invention will be described in further detail with reference to specific embodiments, but the scope of the present invention is not limited to the description.
Example 1: a rock burst intensity prediction method based on a weighted meta-heuristic combined model (see figure 1) comprises the following specific steps:
(1) Determining the evaluation index of rock burst intensity prediction and rock burst intensity classification;
the rock burst prediction is a very complex nonlinear process and is influenced by model selection, parameter selection and cognitive uncertainty, so that the rock burst prediction evaluation index is selected reasonably and effectively on the basis of determining the model, and is the key point in rock burst prediction. The occurrence of rock bursts is generally associated with ground stress, rock properties, the presence of groundwater, rock mass characteristics and man-made excavation disturbancesAnd (4) performing dynamic correlation. According to a large number of rock burst accident cases, it is found that rock burst usually occurs in brittle rock mass with high stress concentration degree, and the stress concentration coefficient sigma θ /σ c And brittleness index sigma c /σ t These characteristics can be reflected. In addition, rock burst occurs by requiring the rock mass to store sufficient elastic strain energy, elastic energy index W et Can reflect the energy storage capacity and the energy release performance of the rock mass. Therefore, select σ θ /σ c 、σ c /σ t And W et 3 evaluation indexes are used as input characteristics of the rock burst prediction model; meanwhile, dividing the rockburst intensity into non-rockburst, light rockburst, medium rockburst and strong rockburst according to a conventional mode; wherein, the rock burst prediction experience grading standard corresponding to each evaluation index is shown in table 1;
TABLE 1 empirical grading Standard
(2) Collecting engineering rockburst accident cases which occur at home and abroad according to the determined evaluation index of rockburst intensity prediction and the rockburst intensity classification, establishing a rockburst intensity prediction sample data set, and randomly dividing the rockburst intensity prediction sample data set into a training set and a testing set according to the proportion of 8:2;
(3) Optimizing the hyper-parameters in a Random Forest (RF) model by using three meta-heuristic optimization algorithms, namely a particle swarm optimization algorithm PSO, a genetic algorithm GA and a wolf optimization algorithm GWO, and respectively constructing corresponding rockburst intensity prediction models after obtaining the hyper-parameters by taking the average error rate calculated by 5-fold cross validation;
(4) Respectively inputting the training set samples and the testing set samples into the three rockburst intensity prediction models to obtain predicted rockburst intensity grades, and respectively calculating the prediction accuracy of the three rockburst intensity prediction models; calculating a weight vector corresponding to the rockburst intensity prediction model according to the prediction accuracy of the three rockburst intensity prediction models;
the weight vector Q is calculated by
In the formula: q is a weight vector, ACC i The accuracy of the ith optimization algorithm on the test set is determined;
(5) Determining a hyper-parameter value according to a weight vector of the rockburst intensity prediction model, and establishing a meta-heuristic combined model based on weighting;
(6) And predicting the intensity of the rockburst to be predicted in the engineering case by using a weighted meta-heuristic combined model.
Example 2: a rock burst intensity prediction method based on a weighted meta-heuristic combined model (see figure 2) comprises the following specific steps:
(1) Determining the evaluation index of rock burst intensity prediction and rock burst intensity classification;
rock burst prediction is a very complex nonlinear process and is influenced by model selection, parameter selection and cognitive uncertainty, so that the key point in rock burst prediction is to reasonably and effectively select rock burst prediction evaluation indexes on the basis of determining a model. Rock bursts typically occur in connection with ground stress, rock properties, the presence of ground water, rock mass characteristics and man-made excavation disturbances. According to a large number of rock burst accident cases, it is found that rock burst usually occurs in brittle rock mass with high stress concentration degree, and the stress concentration coefficient sigma θ /σ c And brittleness index sigma c /σ t Can reflect these characteristics. In addition, the occurrence of rock burst requires that the rock mass be able to store sufficient elastic strain energy, elastic energy index W et Can reflect the energy storage capacity and the energy release performance of the rock mass. Therefore, σ is selected θ /σ c 、σ c /σ t And W et 3 evaluation indexes are used as input characteristics of the rock burst prediction model; meanwhile, dividing the rockburst intensity into non-rockburst, light rockburst, medium rockburst and strong rockburst according to a conventional mode; wherein, the rock burst prediction experience grading standard corresponding to each evaluation index is shown in table 1;
(2) Collecting engineering rockburst accident cases which occur at home and abroad according to the determined evaluation index of rockburst intensity prediction and the rockburst intensity classification, establishing a rockburst intensity prediction sample data set, and randomly dividing the rockburst intensity prediction sample data set into a training set and a testing set according to the proportion of 8:2;
after research results in Evaluation of rockburst occurrence and intensity in underlying and structured prediction method and PCA-PNN principle-based rock burst intensity hierarchical prediction method, a data set containing 200 typical rock burst engineering cases at home and abroad is established, the data set contains 34 rock burst-free samples, 60 slight rock burst samples, 78 medium rock burst samples and 28 strong rock burst samples, and partial data are shown in Table 2;
TABLE 2 database of rock burst cases (part)
In order to know the correlation among the three indexes, the Pearson correlation coefficients among the index parameters are calculated by using the formula (1) (see figure 1), and the absolute values of the Pearson correlation coefficients among the evaluation indexes are all below 0.4, so that the correlation is weak; wherein σ c /σ t And σ θ /σ c And W et All have negative correlation coefficients, which indicates that they have negative correlation therebetween
In the formula:
is an index x 1 And x 2 Correlation coefficient between; />
Is an index x 1 Mean of the data; />
Is an index x 2 Mean of the data;
statistical quantity characteristics of index parameters, as shown in Table 3
TABLE 3 statistical characterization of variables
(3) Optimizing the hyperparameter in a Random Forest (RF) model by using three meta-heuristic optimization algorithms, and respectively constructing corresponding rockburst intensity prediction models after acquiring the hyperparameter by taking the average error rate calculated by 5-fold cross validation of the fitness value;
adopting a 5-fold cross validation strategy to further divide the training set into 5 parts, taking 4 parts as the training set in turn, and taking the other parts as the test set; in the process, after the error rates of the 5 models corresponding to the test set are obtained, averaging the error rates, and taking the error rates as fitness values; then, PSO, GA and GWO are used for optimizing the hyper-parameters in the RF model; there are two main hyper-parameters in the random forest algorithm, one for each number of split node sample predictors (m) try ) And the number of classification trees (n) tree ) (ii) a Wherein m is try Has an optimization range of [1,3]，n tree Has an optimization range of [10,600 ]]；
The particle swarm optimization PSO is taken as an example to explain the general calculation process of the meta-heuristic optimization algorithm, and the specific calculation principle and process of the genetic algorithm GA and the gray wolf optimization algorithm GWO are carried out according to the existing documents;
the particle swarm optimization PSO comprises the following specific flows:
(1) setting related parameters and initializing a population;
in the particle swarm optimization algorithm, the parameters to be set in advance mainly include the number of the populations Pop and the learning factor c 1 And c 2 And the number of iterations N, and the optimization range of the parameters (see Table 4); then initializing fitness values of the position, the speed, the individual best position (pbest) and the global best position (gbest) of the particle;
TABLE 4PSO parameter settings
(2) Updating the position of the population;
then, updating the speed and the position of the particles according to the equations (2) and (3), and calculating the fitness value again;
v id (t+1)＝v id (t)+c 1 ·r 1 ·(p id (t)-x id (t))+c 2 ·r 2 ·(p gd (t)-x id (t)) (2)
x id (t+1)＝x id (t)+v id (t+1) (3)
in the formula: c. C 1 ，c 2 Is a learning factor; r is 1 ，r 2 Is a random number; between 0 and 1; p is a radical of gd Is the best position searched by all particles in the past search; p is a radical of id Is the best one of the past positions of the current particle;
(3) updating the optimal particle position through iterative optimization;
the adaptive value of each particle is compared with the individual optimal value pbest in the iteration process, and if the adaptive value is better than the individual optimal value pbest, the individual optimal value pbest is replaced; the adaptive value of each particle is compared with the optimal position gbest of the group history, and if the adaptive value is better than the optimal position gbest of the group history, the gbest is substituted;
(4) and (4) reaching a termination condition:
the processes of (2) to (3) are circulated until the set iteration number is reached;
the parameters and specific values of GA needed to be set in (1) are shown in table 5, GWO has no other parameters needed to be set except for the number of populations and the number of iterations, and the two parameter values are consistent with those set by the first two algorithms;
TABLE 5GA parameter settings
Note: p c Is the cross probability; p is m Is the probability of variation
After parameters in PSO, GA and GWO are set, iterative optimization is carried out on an MATLAB platform; the optimization iteration curves of the three meta-heuristic algorithms on the random forest hyper-parameters are shown in FIG. 2, and it can be found from FIG. 2 that the PSO algorithm reaches convergence at the earliest, but the convergence effect is inferior to that of GA and GWO algorithms; the convergence effect of GWO and the GA algorithm is optimal, but the convergence speed of GWO is superior to that of the GA algorithm, and the difference between the convergence speed and the PSO algorithm is not large;
the determined hyperparameters were iteratively optimized by PSO, GA, and GWO, as shown in table 6;
TABLE 6 meta-heuristic determined hyper-parameters
Three super-parameter combinations are brought into a random forest algorithm, and three combined rockburst intensity prediction models (PSO-RF, GA-RF and GWO-RF) are obtained by training through a training set;
(4) Respectively inputting the training set samples and the test set samples into three rockburst intensity prediction models to obtain predicted rockburst intensity grades, and respectively calculating prediction accuracy rates of the three rockburst intensity prediction models; calculating a weight vector corresponding to the rockburst intensity prediction model according to the prediction accuracy of the three rockburst intensity prediction models;
the prediction results of PSO-RF, GA-RF and GWO-RF on the training set are shown in FIG. 3, and it can be seen from FIG. 3 that all three combined models have excellent performance on the training set, and the accuracy is over 98%; wherein, the GA-RF and GWO-RF models are optimal, and only one sample of strong rockburst with error is predicted;
inputting 20% of the test set into the three constructed combination models to obtain the prediction results of the three combination models on the test set, as shown in fig. 4, the accuracy rates of PSO-RF, GA-RF and GWO-RF on the test set are 82.5%, 85% and 90% respectively as can be seen from fig. 4; method for calculating from weight vector Q
In the formula: q is a weight vector, ACC i The accuracy of the ith optimization algorithm on the test set;
determining a weight vector Q = [ Q ] between combinations of hyper-parameters determined by three optimization algorithms RF ,Q GA ,Q GWO ]＝[0.32,0.33,0.35]；
(5) Determining a value of a hyper-parameter according to the weight vector of the rock burst intensity prediction model, namely the hyper-parameter combination is n tree ＝212，m try =1; establishing a meta-heuristic combined model based on weighting;
(6) Predicting the intensity of the rock burst to be predicted in the engineering case by using a weighted meta-heuristic combined model: combining the hyperparameters determined in the step (4), then, training by using a training set again, applying the obtained weight-based meta-heuristic combined model to 17 engineering cases of Sang Zhu ridge tunnels, and obtaining prediction results shown in a table 7;
TABLE 7 Sang Zhu Ridge tunnel engineering rockburst prediction results
As can be seen from Table 7, the prediction result is excellent, only one case of prediction error exists, and the prediction accuracy reaches 94.12%; according to the prediction results of the model on the test set and the engineering case, the fact that the combination model obtained through training is excellent in generalization capability and has excellent engineering applicability can be found.
While the present invention has been described in detail with reference to the specific embodiments thereof, the present invention is not limited to the embodiments described above, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (5)
1. A rock burst intensity prediction method based on a weighted meta-heuristic combined model is characterized by comprising the following specific steps of:
(1) Determining the evaluation index of rock burst intensity prediction and rock burst intensity classification;
(2) Collecting rockburst cases according to the determined evaluation index of rockburst intensity prediction and the classification of rockburst intensity, establishing a rockburst intensity prediction sample data set, and dividing the rockburst intensity prediction sample data set into a training set and a test set sample;
(3) Optimizing hyper-parameters in a Random Forest (RF) model by using three meta-heuristic optimization algorithms, and establishing a corresponding rockburst intensity prediction model;
(4) Respectively inputting the training set samples and the test set samples into three rockburst intensity prediction models to obtain predicted rockburst intensity grades, and respectively calculating prediction accuracy rates of the three rockburst intensity prediction models; calculating a weight vector corresponding to the rockburst intensity prediction model according to the prediction accuracy of the three rockburst intensity prediction models;
(5) Determining a hyper-parameter value according to a weight vector of the rockburst intensity prediction model, and establishing a meta-heuristic combined model based on weighting;
(6) And predicting the intensity of the rock burst to be predicted in the engineering case by using a weighted meta-heuristic combined model.
2. The rockburst intensity prediction method based on the weighted meta-heuristic combined model according to claim 1, wherein: the evaluation index of the rockburst intensity prediction in the step (1) comprises a stress coefficient sigma θ /σ c Brittle coefficient sigma c /σ t And elastic energy index W et 。
3. The rockburst intensity prediction method based on the weighted meta-heuristic combined model according to claim 1, wherein: and (2) grading the rockburst intensity in the step (1) to include no rockburst, light rockburst, medium rockburst and strong rockburst.
4. The rockburst intensity prediction method based on the weighted meta-heuristic combined model according to claim 1, wherein: the heuristic optimization algorithm in the step (3) comprises a particle swarm optimization algorithm PSO, a genetic algorithm GA and a wolf optimization algorithm GWO.
5. The method for predicting the intensity of the rockburst based on the weighted meta-heuristic combined model according to claim 1, wherein: the calculation method of the weight vector Q in the step (4) is that
In the formula: q is a weight vector, ACC i The accuracy of the optimization algorithm of the ith on the test set is improved.
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| CN117332240A (en) * | 2023-12-01 | 2024-01-02 | 中铁四局集团有限公司 | Rock burst prediction model construction method, storage medium, rock burst prediction method and system |
| CN117669393A (en) * | 2024-02-01 | 2024-03-08 | 昆明理工大学 | Blasting block uncertainty prediction method and system |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117332240A (en) * | 2023-12-01 | 2024-01-02 | 中铁四局集团有限公司 | Rock burst prediction model construction method, storage medium, rock burst prediction method and system |
| CN117332240B (en) * | 2023-12-01 | 2024-04-16 | 中铁四局集团有限公司 | Rock burst prediction model construction method, storage medium, rock burst prediction method and system |
| CN117669393A (en) * | 2024-02-01 | 2024-03-08 | 昆明理工大学 | Blasting block uncertainty prediction method and system |
| CN117669393B (en) * | 2024-02-01 | 2024-04-19 | 昆明理工大学 | Blasting block uncertainty prediction method and system |
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