Coal mining subsidence prediction method based on gene expression programming and artificial bee colony

Abstract

The invention relates to the technical field of coal mine safety monitoring, in particular to a coal mining subsidence prediction method based on gene expression programming and artificial bee colony, which uses a gene expression programming (GEP) algorithm to establish a basic prediction model to simulate a subsidence event, and uses an artificial bee colony (ABC) algorithm to optimize the basic prediction model to simulate the subsidence event. GEP parameters are obtained from a GEP algorithm, the GEP parameters are optimized through an artificial bee colony (ABC) algorithm, a subsidence prediction model is established, and the subsidence prediction accuracy is improved; the optimal model is selected through the square correlation coefficient, the root-mean-square error, the square absolute error and the Nash efficiency, the indexes quantify the prediction accuracy of each model, and the selection process is guided. The model is subjected to thorough cross validation so as to evaluate the universality and the robustness of the model; the influence of each parameter on land subsidence is clarified through multi-parameter sensitivity analysis, and valuable insights are provided for mining engineers and stakeholders.

Description

Technical Field

[0001] The present invention relates to the technical field of coal mine safety monitoring, and particularly to a coal mining subsidence prediction method based on gene expression programming and artificial bee colony. Background Art

[0002] Main ground subsidence of limestone is an environmental disaster characterized by surface subsidence or vertical displacement. Its occurrence will cause significant economic and social consequences. Although subsidence can be caused by natural processes such as rock dissolution, earthquakes, and volcanic activities, human activities, especially underground mining, often exacerbate this problem. Mining valuable minerals and resources from below the surface will damage the geological structure of a region, leading to gravitational instability and subsequent ground subsidence, which in turn will damage the ecosystem by changing vegetation growth, habitats, rivers, streams, ecological integrity, biodiversity, and species distribution. Therefore, subsidence will cause structural damage, land deformation, and environmental interference.

[0003] The longwall mining method is widely used in underground coal mines to mine shallow horizontal coal seams, which usually causes subsidence of the mined surface; another important factor leading to ground subsidence in underground mines is the gradual weakening of the support system over time. The support system is installed to stabilize the goaf during mining operations and prevent the collapse of the stope roof. In addition, the dynamic loads and vibrations generated by heavy machinery, explosives, and drilling equipment used in mining operations may damage the stability of the stope and cause subsidence. Therefore, ground subsidence caused by underground mining is a complex problem with various potential causes. Currently, most models for predicting ground subsidence are based on the training method of traditional machine learning, but the models established by this method have low accuracy and cannot accurately predict ground subsidence. Summary of the Invention

[0004] The purpose of the present invention is to provide a coal mining subsidence prediction method based on gene expression programming and artificial bee colony, which can combine the gene expression programming algorithm with the artificial bee colony algorithm, aiming to improve the accuracy and robustness of ground subsidence prediction, thereby improving safety standards and operation stability in the challenging longwall coal mining environment.

[0005] To achieve the above purpose, the present invention provides the following technical solution: A coal mining subsidence prediction method based on gene expression programming and artificial bee colony, characterized in that: the method includes the following steps:

[0006] Step S1: Obtain historical parameter data required for the study of coal mining subsidence safety and construct a sample set;

[0007] Step S2: Split the sample set into a first training set, a first test set, and a first validation set;

[0008] Step S3: Conduct data correlation analysis on the relationship between the parameter data and ground settlement;

[0009] Step S4: Construct a basic prediction model through the Gene Expression Programming (GEP) algorithm; and input the first training set into the basic prediction model;

[0010] Step S5: Train the basic prediction model with the first training set until convergence, calculate and verify the error through the first test set and the first validation set, and output the GEP parameter set;

[0011] Step S6: Split the GEP parameter set into a second training set, a second test set, and a second validation set;

[0012] Step S7: Optimize the GEP parameter set through the Artificial Bee Colony (ABC) algorithm, construct an optimized prediction model, and input the second training set into the optimized prediction model;

[0013] Step S8: Train the optimized prediction model with the second training set until convergence, calculate and verify the error through the second test set and the second validation set, obtain the optimized parameters, and output the subsidence prediction model;

[0014] Step S9: Conduct multi-parameter sensitivity analysis on the optimized parameters of the subsidence prediction model to identify the importance or influence degree of the parameter data on coal mining subsidence.

[0015] Preferably, in step S1, the parameter data includes the coal mining thickness, mining depth, and parameter data related to overlying rock such as density, cohesion, internal friction angle, elastic modulus, bulk modulus, shear modulus, Poisson's ratio, uniaxial compressive strength, and tensile strength.

[0016] Preferably, in step S3, the analysis of the data correlation is used to obtain a mathematical expression that encapsulates the relationship between the parameter data and ground settlement.

[0017] Preferably, in step S4, the steps of constructing a basic prediction model through the Gene Expression Programming (GEP) algorithm include the following steps:

[0018] Step S41: Initialize the chromosome population: Each chromosome population represents a potential solution to the optimization problem, and these chromosomes are composed of genes encoding mathematical expressions.

[0019] Step S42: Fitness evaluation: The fitness of each chromosome is measured by a fitness function to evaluate its performance in solving the optimization problem;

[0020] Step S43: Crossover and mutation: Generate new offspring from the parental chromosomes through crossover and mutation operators;

[0021] Step S44: Selection: The selection process determines which individuals in the parent and offspring populations will enter the next generation based on their fitness values;

[0022] Step S45: Termination condition judgment: The optimization process iterates continuously until a termination condition is met, such as reaching the maximum number of generations or obtaining a satisfactory solution.

[0023] Step S46: Return the optimal solution: Return the one with the highest fitness as the optimal solution.

[0024] Preferably, in the said step S5, the error calculation methods include root mean square error, mean absolute error, square correlation coefficient, and Nash efficiency coefficient.

[0025] Preferably, in the said step S7, the steps of constructing an optimized prediction model by the artificial bee colony (ABC) algorithm include:

[0026] Step S71: Optimize the GEP parameters using the artificial bee colony (ABC) algorithm;

[0027] Step S72: Search space exploration: During the optimization process, the ABC algorithm guides the search for the optimal parameter values of the GEP algorithm; ensuring that the GEP algorithm effectively converges to a promising region;

[0028] Step S73: Recombination and mutation: Based on the optimized parameters obtained by the ABC algorithm, recombine and mutate the individuals in the GEP population;

[0029] Step S74: Replacement: Replace some individuals in the current GEP population with the offspring generated by recombination and mutation, ensuring that the population maintains diversity and adapts to changes in the search environment;

[0030] Step S75: Iterative optimization: Iterate the optimization process through the processes of fitness evaluation, optimized parameters, genetic operations, and population replacement;

[0031] Step S76: Iterate until a termination criterion is met, such as the maximum number of iterations or obtaining a satisfactory solution.

[0032] Preferably, the gene expression programming (GEP) algorithm is implemented by GeneXproTools V.5 software.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] 1. By combining GEP and ABC, the present invention enhances the algorithm's ability to comprehensively search the solution space, thereby finding high-quality solutions for complex optimization problems.

[0035] 2. The present invention calculates the error vector by adopting strict performance indicators, including root mean square error, mean absolute error, squared correlation coefficient, and Nash efficiency coefficient, so as to obtain the optimal model, and these indicators quantify the prediction accuracy of each model.

[0036] 3. The present invention improves the interpretability of the selected model by performing sensitivity analysis on parameters, clarifies the influence of each parameter on ground subsidence, and provides valuable insights for mining engineers and stakeholders.

[0037] 4. The present invention constructs a subsidence prediction model by combining GEP and ABC algorithms. The optimization process of this model is iterative, and each cycle aims to improve the accuracy and prediction ability of the model, thereby improving the accuracy of subsidence prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of the overall process in the present invention;

[0039] Figure 2 It is a schematic diagram of the process of optimizing the gene expression programming algorithm by the artificial bee colony in the present invention;

[0040] Figure 3 It is a schematic diagram of the framework of the artificial bee colony and the gene expression programming algorithm in the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0041] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0042] The present invention uses the gene expression programming (GEP) algorithm to establish a basic prediction model to simulate subsidence events. The gene expression programming algorithm uses GeneXproTools V.5 software. The ABC algorithm is used to optimize the basic prediction model. The GEP parameters are obtained from the GEP algorithm, and the artificial bee colony (ABC) algorithm is used to optimize the GEP parameters to establish a ground subsidence prediction model. The optimization process of the present invention is iterative, and each cycle aims to improve the accuracy and prediction ability of the model.

[0043] The present invention selects the optimal model through the squared correlation coefficient, root mean square error, squared absolute error, and Nash efficiency. These indicators quantify the prediction accuracy of each model and guide the selection process. The model undergoes thorough cross-validation to evaluate its generality and robustness.

[0044] To improve the interpretability of the land subsidence model, a sensitivity analysis was conducted. This analysis clarified the impact of each parameter on land subsidence, providing valuable insights for mining engineers and stakeholders.

[0045] Please refer to Figures 1 - 3 , a coal mining subsidence prediction method based on gene expression programming and artificial bee colony, characterized in that: the method comprises the following steps:

[0046] Step S101: Obtain parameter data to construct a sample set;

[0047] Obtain historical parameter data required for the study of coal mining subsidence safety to construct a sample set. In the embodiments of the present invention, the data is extracted from previous underground coal mine working parameter data. The parameter data includes 2 variables related to thickness and mining depth, and 9 variables related to overlying rock, namely density, cohesion, internal friction angle, elastic modulus, bulk modulus, shear modulus, Poisson's ratio, uniaxial compressive strength, and tensile strength. The embodiments of the present invention contain 1740 data points, and the data points include parameter data and settlement data. The collected parameter data and its minimum and maximum values are shown in Table 1.

[0048] Table 1 Parameter data and land subsidence data

[0049]

[0050] Step S102: Split the sample set into a first training set, a first test set, and a first validation set;

[0051] Step S103: Parameter data correlation analysis;

[0052] Conduct data correlation analysis on the relationship between the parameter data and land subsidence; through data correlation analysis, relevant features in the sample set can be identified, and irrelevant features can be filtered out, thereby simplifying the data structure and obtaining a mathematical expression of the parameter data and land subsidence. The mathematical expression encapsulates the correlation between the parameter data and land subsidence, as shown in Table 2, which is the correlation between the parameter data and land subsidence.

[0053] Table 2 Data correlation between parameter data and land subsidence

[0054] Uniaxial compressive strength -0.21 Mining depth -0.06 -0.01 Tensile strength 0.12 -0.21 0.06 Poisson's ratio 0 0.28 -0.01 -0.07 Elastic modulus 0.01 0.63 0.01 -0.15 0.23 Cohesion 0.12 -0.17 0 0.79 -0.06 -0.12 Internal friction angle -0.12 -0.04 0.01 0.21 0.05 -0.17 0.24 Shear modulus 0.13 -0.03 -0.12 -0.05 -0.05 -0.01 -0.03 0.01 Bulk modulus 0.17 -0.01 -0.16 -0.05 -0.02 -0.01 -0.06 0.05 0.95 Density -0.13 0.22 -0.06 -0.04 0.08 0.17 0.08 0.07 0.25 0.25 Coal seam thickness -0.01 -0.06 0.07 -0.02 0 -0.08 0.05 -0.06 0.01 0.02 -0.06 Subsidence Uniaxial compressive strength Mining depth Tensile strength Poisson's ratio Elastic modulus Cohesion Internal friction angle Shear modulus Bulk modulus Density Coal seam thickness

[0055] From Table 2, the strength of the correlation between the parameter data and land subsidence can be identified. The closer the absolute value of the value is to 1, the stronger the correlation; the closer the absolute value is to 0, the weaker the correlation. For example, the correlation between the bulk modulus and the shear modulus is strong, with a correlation of 0.95. There is no correlation between the Poisson's ratio and the subsidence degree, with a correlation of 0, and there is no correlation between the Poisson's ratio and the coal seam thickness, with a correlation of 0. Through correlation analysis, the mathematical expressions between the parameter data and land subsidence are obtained.

[0056] Step S104: Construct a basic prediction model using the GEP algorithm;

[0057] The Gene Expression Programming (GEP) algorithm uses the GeneXproTools V.5 software. The steps for constructing a basic prediction model using the Gene Expression Programming (GEP) algorithm are as follows:

[0058] Step S401: Initialize the chromosome population: Each chromosome population represents a potential solution to the optimization problem. These chromosomes are composed of genes encoding mathematical expressions.

[0059] Step S402: Fitness evaluation: The fitness of each chromosome is measured by a fitness function to evaluate its performance in solving the optimization problem. This fitness function guides the evolutionary process by selecting individuals for reproduction based on their fitness scores.

[0060] Step S403: Crossover and mutation: Generate new offspring from the parental chromosomes through crossover and mutation operators. Crossover refers to exchanging genetic material between parental chromosomes to produce diverse offspring, while mutation refers to promoting exploration of the search space through random changes.

[0061] Step S404: Selection: The selection process determines which individuals in the parental and offspring populations will enter the next generation based on their fitness values. This selection mechanism ensures that more suitable individuals have a higher probability of being selected for reproduction.

[0062] Step S405: Judgment of termination conditions: The optimization process iteratively continues until the termination conditions are met, such as reaching the maximum number of generations or obtaining a satisfactory solution.

[0063] Step S406: Return the optimal solution: Return the one with the highest fitness as the optimal solution.

[0064] Input the first training set into the basic prediction model for model training.

[0065] Step S105: Calculate the error and output the GEP parameter set;

[0066] Train the first training set on the basic prediction model until convergence, calculate and verify the error through the first test set and the first validation set, and output the GEP parameter set; the error calculation methods include root mean square error, mean absolute error, squared correlation coefficient, and Nash efficiency coefficient; the calculation formulas are as follows:

[0067] Root mean square error (RMSE):

[0068] where, O i represents the data value (observed value) of the first validation set, P i represents the output (predicted value) of the first test set of the basic prediction model, and N represents the number of data points; through the root mean square error, the predicted value and the observed value of the basic prediction model can be statistically measured.

[0069] Mean absolute error (MAE):

[0070] where, O i represents the data value of the first validation set, P i represents the output of the first test set of the basic prediction model, and N represents the number of data points; the squared absolute error represents a measure of the error between paired observed values of the same phenomenon.

[0071] Squared correlation coefficient:

[0072] where, R 2 represents the squared correlation coefficient, which reflects the proportion of the observed dispersion accounted for by the prediction, O i represents the observed value, P i represents the predicted value output by the basic prediction model, represents the average value of the observed values, represents the average value of the predicted values output by the basic prediction model; N represents the number of data points. The R 2 value ranges from 0 to 1, where 0 indicates no correlation between the observed value and the predicted value, and 1 indicates that the observed value is equal to the observed value. The closer to 1, the better the fitting effect of the basic prediction model and the higher the prediction accuracy.

[0073] Nash efficiency coefficient (NSE):

[0074]

[0075] where, O i represents the observed value, P i represents the predicted value output by the basic prediction model, represents the average value of the observed values, N represents the number of data points, the NSE standard quantifies the normalized sum of the squared differences between the observed values and the predicted values, with a variance of -1, and the range of NSE is from 1 to negative infinity.

[0076] Through error calculation, it can be used to evaluate the fitting effect of the basic prediction model, thereby providing accurate ground settlement prediction.

[0077] Step S106: Split the GEP parameter set into a second training set, a second test set, and a second validation set;

[0078] Step S107: Optimize the GEP parameters through the ABC algorithm;

[0079] Optimize the GEP parameter set through the Artificial Bee Colony (ABC) algorithm, construct an optimized prediction model, and input the second training set into the optimized prediction model; please refer to Figure 3 , which is a schematic flowchart of optimizing the GEP algorithm by the ABC algorithm. The steps of constructing an optimized prediction model through the Artificial Bee Colony (ABC) algorithm include:

[0080] Step S701: Optimize the GEP parameters using the ABC algorithm;

[0081] The Artificial Bee Colony (ABC) algorithm uses three types of bees: employed bees, which utilize known food sources (solutions); observing bees, which select promising food sources based on pheromone trails; and scout bees, which explore new search spaces. The ABC algorithm is used to update the parameters of the GEP algorithm, such as the mutation rate, recombination probability, and population size.

[0082] Step S702: Search space exploration: During the optimization process, the ABC algorithm guides the search for the optimal parameter values of the GEP algorithm; ensuring that the GEP algorithm effectively converges to a promising region;

[0083] Step S703: Recombination and mutation: Based on the optimized parameters obtained by the ABC algorithm, perform recombination and mutation on the individuals in the GEP population; these operations generate new offspring with different genetic characteristics, promoting the exploration of the solution space.

[0084] Step S704: Replacement: The offspring generated through recombination and mutation replace some individuals in the current GEP population, ensuring that the population maintains diversity and adapts to changes in the search environment;

[0085] Step S705: Iterative optimization: Optimize the process iteratively through the processes of fitness evaluation, optimized parameters, genetic operations, and population replacement;

[0086] Step S706: Termination condition judgment: Iterate until the termination criterion is met, such as the maximum number of iterations or obtaining a satisfactory solution.

[0087] Step S108: Error calculation, and output of the subsidence prediction model;

[0088] Train the optimization prediction model with the second training set until convergence, perform error calculation and verification through the second test set and the second validation set to obtain optimization parameters, and output the subsidence prediction model; the error calculation formula is the same as that in Step S105, which will not be elaborated here.

[0089] Step S109: Multi-parameter sensitivity analysis;

[0090] Perform multi-parameter sensitivity analysis on the optimization parameters of the subsidence prediction model to identify the importance or influence degree of the parameter data on coal mining subsidence. Through multi-parameter sensitivity analysis, the influence of all parameters changing simultaneously on ground settlement can be investigated, which can comprehensively reflect the possible factors affecting ground settlement and provide valuable insights for mining engineers and stakeholders.

[0091] Please refer to Figure 3 , through the local exploitation of employed bees and the global exploration of scout bees, the ABC algorithm promotes diverse search strategies, enabling the discovery of the optimal solution in the solution space. The integration of the GEP algorithm and the ABC algorithm enhances the algorithm's ability to comprehensively search the solution space, thus finding high-quality solutions for complex optimization problems. The balance between exploration (scouting) and exploitation (utilizing known solutions) of the ABC algorithm synergizes with the evolutionary mechanism of GEP, resulting in efficient optimization performance.

[0092] The integration of the Gene Expression Programming (GEP) algorithm and the Artificial Bee Colony (ABC) algorithm provides a robust and general optimization framework capable of solving complex optimization challenges. By leveraging the complementary advantages of evolutionary programming and swarm intelligence, this hybrid approach offers effective solutions for a wide range of optimization problems.

[0093] It should be noted that in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising one..." does not exclude the existence of additional identical elements in the process, method, article or device comprising the element.

[0094] Although embodiments of the present invention have been shown and described, those of ordinary skill in the art will appreciate that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for predicting coal mining subsidence based on gene expression programming and artificial bee colonies, characterized in that: The method comprises the following steps: Step S1: Acquire historical parameter data required for the study of coal mining subsidence safety to construct a sample set; Step S2: Split the sample set into a training set, a test set and a validation set; Step S3: performing data correlation analysis on the relationship between the parameter data and ground subsidence; Step S4: constructing a basic prediction model by using a gene expression programming (GEP) algorithm; and inputting the first training set into the basic prediction model; Step S5: training the basic prediction model with the first training set until convergence, performing error calculation and verification with the first test set and the first validation set, and outputting a GEP parameter set; Step S6: Split the GEP parameter set into a second training set, a second test set and a second validation set; Step S7: Optimizing the GEP parameter set by using an artificial bee colony (ABC) algorithm, constructing an optimized prediction model, and inputting the second training set into the optimized prediction model; Step S8: training the optimization prediction model with the second training set until convergence, and performing error calculation and verification with the second test set and the second validation set to obtain optimization parameters and output a subsidence prediction model; Step S9: performing a multi-parameter sensitivity analysis on the optimized parameters of the subsidence prediction model to identify the importance or influence of the parameter data on coal mining subsidence.

2. The method for predicting coal mining subsidence based on genetic expression programming and artificial bee colonies according to claim 1 is characterized in that: In step S1, the parameter data include coal mining thickness, mining depth, and parameter data of density, cohesion, internal friction angle, elastic modulus, bulk modulus, shear modulus, Poisson's ratio, uniaxial compressive strength and tensile strength related to overloaded rock.

3. The method for predicting coal mining subsidence based on genetic expression programming and artificial bee colony according to claim 1, characterized in that: In step S3, the analysis of the data correlation is used to obtain a mathematical expression, which encapsulates the relationship between the parameter data and the ground subsidence.

4. The method for predicting coal mining subsidence based on genetic expression programming and artificial bee colony according to claim 1, characterized in that: In step S4, the step of constructing a basic prediction model by a gene expression programming (GEP) algorithm comprises the following steps: Step S41: Initialize chromosome groups: Each chromosome group represents a potential solution to the optimization problem, and the chromosomes are composed of genes that encode mathematical expressions. Step S42: Fitness evaluation: The fitness of each chromosome is measured using a fitness function to measure its performance in solving the optimization problem; Step S43: crossover mutation: generate new offspring from the parent chromosome through crossover and mutation operators; Step S44: Selection: The selection process determines which individuals in the parent and offspring population will enter the next generation based on their fitness values; Step S45: Termination condition judgment: The optimization process continues iteratively until the termination condition is met, such as reaching the maximum number of generations or obtaining a satisfactory solution. Step S46: Return the optimal solution: return the one with the highest fitness as the optimal solution.

5. The method for predicting coal mining subsidence based on genetic expression programming and artificial bee colony according to claim 1, characterized in that: In step S5, the error calculation method includes root mean square error, mean absolute error, square correlation coefficient and Nash efficiency coefficient.

6. The method for predicting coal mining subsidence based on genetic expression programming and artificial bee colony according to claim 1, characterized in that: In step S7, the step of constructing an optimization prediction model by using an artificial bee colony (ABC) algorithm includes: Step S71: Optimizing GEP parameters using artificial bee colony (ABC) algorithm; Step S72: Search space exploration: During the optimization process, the ABC algorithm guides the search for the optimal parameter values ​​of the GEP algorithm; ensuring that the GEP algorithm effectively converges to a promising area; Step S73: recombination and mutation: based on the optimization parameters obtained by the ABC algorithm, the individuals in the GEP population are recombined and mutated; Step S74: Replacement: The offspring generated through recombination and mutation replace some individuals in the current GEP population to ensure that the population maintains diversity and adapts to changes in the search environment; Step S75: Iterative optimization: iterating the optimization process through the processes of fitness evaluation, optimization parameters, genetic operations and population replacement; Step S76: Iterate until a termination criterion is met, such as a maximum number of iterations or a satisfactory solution is obtained.

7. The method for predicting coal mining subsidence based on genetic expression programming and artificial bee colony according to claim 1, characterized in that: The gene expression programming (GEP) algorithm was implemented by GeneXproTools V.5 software.

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