Accurate measurement of coal gas permeability helps prevent coal gas safety accidents effectively. To predict permeability more accurately, we propose the IDBO-BPNN coal body gas permeability prediction model. This model combines the Improved Dung Beetle algorithm (IDBO) with the BP neural network (BPNN). First, the Sine chaotic mapping, Osprey optimization algorithm, and adaptive T-distribution dynamic selection strategy are integrated to enhance the DBO algorithm and improve its global search capability. Then, IDBO is utilized to optimize the weights and thresholds in BPNN to enhance its prediction accuracy and mitigate the risk of overfitting to some extent. Secondly, based on the influencing factors of gas permeability, effective stress, gas pressure, temperature, and compressive strength, they are chosen as the coupling indicators. The SPSS 27 software is used to analyze the correlation among the indicators using the Pearson correlation coefficient matrix. Additionally, the Kernel Principal Component Analysis (KPCA) is employed to extract the original data. Then, the original data is divided into principal component data for the model input. The prediction results of the IDBO-BPNN model are compared with those of the PSO-BPNN, PSO-LSSVM, PSO-SVM, MPA-BPNN, WOA-SVM, BES-SVM, and DPO-BPNN models. This comparison assesses the capability of KPCA to enhance the accuracy of model predictions and the performance of the IDBO-BPNN model. Finally, the IDBO-BPNN model is tested using data from a coal mine in Shanxi. The results indicate that the predicted outcome closely aligns with the actual value, confirming the reliability and stability of the model. Therefore, the IDBO-BPNN model is better suited for predicting coal gas permeability in academic research writing.
Keywords: coal gas; permeability; improved dung beetle optimizer (IDBO); BP neural network (BPNN); prediction model
Coal mine gas accidents are a significant concern in the global coal mining safety field, posing a serious threat to both coal production and the safety of workers' lives [[
Currently, both domestic and international scholars are primarily focused on studying the factors that influence changes in gas permeability [[
In order to enhance the accuracy of predicting the gas permeability of coal bodies, the author improved the Dung Beetle Optimizer (DBO) algorithm to rectify its shortcomings and prevent the "overfitting" issue of BPNN. The enhanced DBO algorithm, referred to as IDBO, was employed to optimize the weights and thresholds in BPNN, leading to the development of a prediction model for coal gas permeability known as IDBO-BPNN. Subsequently, the performance of this model was compared with that of PSO-BPNN, PSO-SVM, PSO-LSSVM, and SSA-BPNN models to validate its prediction accuracy. Finally, the model was applied to a coal mine in Shanxi Province to investigate its practicality and stability further. These efforts aim to provide theoretical references to ensure safe and efficient production in coal mines and address related issues.
The influencing factors of gas permeability in coal bodies are highly complex, encompassing coal rock properties, stress states, temperature, gas pressure, gas content, and geological structure. An increase in effective stress leads to a reduction in the gap between coal bodies, subsequently decreasing gas permeability. Conversely, an increase in gas pressure leads to higher molecular flow speeds and increased gas permeability. Furthermore, higher temperatures lead to faster movement rates of gas molecules and, consequently, higher permeability [[
BPNN is a widely used artificial neural network algorithm, typically consisting of three layers of neurons: the input layer, hidden layer, and output layer [[
DBO is a novel intelligent optimization algorithm inspired by the rolling, dancing, foraging, stealing, and reproduction behaviors of dung beetles. The algorithm categorizes the dung beetle population into four groups: rolling dung beetle, brooder dung beetle, small dung beetle, and thief dung beetle [[
Overfitting is a common issue encountered by machine learning models. When the model is too complex, interfered with noise, or when there is limited training data, overfitting is more likely to occur. Therefore, Differential Biogeography Optimization (DBO) is used to optimize the hyperparameters of the Back Propagation Neural Network (BPNN). However, DBO has shortcomings, such as an imbalance in global exploration and local development abilities, which can result in local optimal problems and a weak global exploration ability. To enhance the global search capability of DBO and avoid overfitting BPNN, three strategies are employed to improve DBO. Furthermore, the fitness function is not called multiple times in IDBO. The complexity is consistent with the original DBO.
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The introduction of the adaptive T-distribution mutation operator can significantly enhance the optimization performance of the algorithm. However, it is indiscriminately used in all individuals in each iteration, which may lead to an increase in calculation time. Meanwhile, it doesn't take advantage of the benefits of the original algorithm. To address this issue, a dynamic selection probability P is adopted to adjust the use of adaptive T-distribution mutation operators. This ensures that the algorithm demonstrates strong global development ability in the early stage of iteration while maintaining good local exploration ability in the late stage. Additionally, supplementing the algorithm with T-distribution mutation with a small probability further enhances the convergence speed [[
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In order to evaluate the optimization performance of IDBO, the CEC2005 test set is utilized for iterative testing in the Matlab R2023a environment. The algorithm is compared with the Whale Optimization Algorithm (WOA), Subtraction Average Based Optimizer (SABO), Grey Wolf Optimizer (GWO), Northern Goshawk Optimization (NGO), Harris Hawk Optimization (HHO), and the original DBO. Each algorithm's population size and maximum number of iterations are set to 30 and 1000, respectively, with the test being repeated 30 times. The details of the test function information can be found in Table 1.
The seven algorithms are tested for comparison and analysis. The test results are shown in Figure 2. The standard test function generates a two-dimensional convergence curve after each algorithm is executed. In this curve, the x-coordinate represents the number of iterations. During each iteration, the algorithm attempts to optimize the function. Therefore, the x-coordinate records the number of these optimization attempts. The goal of CEC test functions is to find the global minimum of the function, so the ordinate usually represents the function value. If the curve slopes downward, it indicates that the algorithm is approaching the optimal solution. If the curve fluctuates greatly, it may suggest that the algorithm is oscillating near the local optimum. According to Figure 2, the slope of the IDBO curve decline is significantly steeper than that of other algorithms in both single-peak benchmark functions and multi-peak, as well as fixed-dimensional multi-peak benchmark functions, which suggests that IDBO exhibits a faster convergence speed. Other algorithms show a relatively gradual decline, indicating that they may be trapped in local optima or experience slow convergence speeds. At the same time, the optimization accuracy of IDBO in test functions F2, F3, F4, F5, F6, F7, and F8 is the best. The fitness value of IDBO in test function F1 is not the best, but it still ranks ahead of several algorithms. The results show that the local development ability of IDBO is significantly improved, which reveals good local development ability compared with the original DBO. In general, IDBO can not only converge quickly but also have the ability to explore and develop balancedly and escape from local optimal solutions.
The seven algorithms are tested by eight different functions with optimal value, standard deviation, average value, median value, and worst value as evaluation indices, which reflect the convergence accuracy and stability of the algorithms, as shown in Table 2. As can be seen from Table 2, IDBO can accurately find the optimal value 0 in various functions, which can adapt to the transformation in global exploration and local exploration. Therefore, compared with other algorithms, IDBO has improved the accuracy of the solution and is more stable in average optimization performance.
Then, the performance of IDBO is further evaluated by the CEC2017 and CEC2021 test sets, as shown in Table 3. It is evident from Table 3 that IDBO has good performance in both the CEC2017 and CEC2021 test sets, showing strong convergence accuracy and speed. In summary, IDBO excellently performs in different test functions. It not only has absolute advantages in convergence speed but also demonstrates good convergence accuracy. At the same time, IDBO achieves a good balance between development and exploration capabilities, which further indicates that IDBO demonstrates outstanding comprehensive performance in many metaheuristic algorithms.
The metaheuristic optimization algorithm used to optimize machine learning or deep learning models has been demonstrated to significantly improve their prediction accuracy [[
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The correlation analysis chart is a method used to visually represent the distribution of data and the relationship between different factors. In order to accurately capture the impact of different factors, SPSS 27 software was used to perform correlation analysis on the initial data concerning the factors influencing coal gas permeability. This analysis aimed to generate the Pearson correlation coefficient matrix for various indicators, as illustrated in Figure 3. The positive and negative signs in the correlation coefficient indicate the direction of the correlation between variables. A positive correlation coefficient indicates a consistent trend of change between two variables; specifically, when one variable increases, the other variable also increases. A negative correlation coefficient indicates an opposite trend in changes between two variables. This means that when one variable increases, the other variable decreases. According to Figure 4, a negative correlation is observed between effective stress and gas pressure, compressive strength and gas pressure, as well as temperature and compressive strength. Conversely, a positive correlation exists between temperature and effective stress, as well as between temperature and gas pressure. The closer the absolute value of the correlation coefficient is to 1, the stronger the relationship between the variables. A correlation coefficient of 1 indicates a perfect positive correlation, while a correlation coefficient of −1 indicates a perfect negative correlation. A correlation coefficient close to 0 suggests that there is no linear correlation between the two variables. These findings are important for understanding and analyzing relationships between variables in academic research. As shown in Figure 4, the correlation between coal body gas permeability and the influencing factors is not entirely linear; there is a slight correlation between the index factors. For instance, the correlation coefficients between effective stress and gas pressure, temperature, and compressive strength are −0.107, −0.001, and −0.103, respectively. This suggests a limited association among these factors in influencing coal gas permeability. The correlation coefficient between gas pressure and temperature is 0.174. When the correlation value between the two factors is too low (e.g., less than 0.2), it indicates that it may be less helpful for information enrichment. If used directly, it will inevitably affect the result to some extent. Therefore, it is essential to conduct kernel principal component analysis on the original data, which can not only reduce the amount of calculation but also improve the accuracy of model prediction.
Kernel Principal Component Analysis (KPCA) is a nonlinear method for processing data based on a high-dimensional feature space. It involves mapping the data from the original space to a new space and then conducting principal component analysis to successfully achieve dimensionality reduction of linear non-fractional datasets. This technique is widely used in academic research and has proven to be effective in various applications. Due to the nonlinear relationship between the influencing factors of coal gas permeability, Kernel Principal Component Analysis (KPCA) was utilized to reduce the dimensionality of the original data. The selection criteria for this reduction were based on interpreting more than 85% of the cumulative variance. Ultimately, three principal components were extracted and labeled as Y1, Y2, and Y3, respectively. Their respective variance interpretation rates were recorded as 41.74%, 26.83%, and 20.02%. The cumulative interpretive variance is 88.59%, indicating that the three extracted principal components can better reflect the vast majority of information in the original data. Some data after dimensionality reduction are shown in Table 5.
In order to verify the accuracy and reliability of the constructed prediction model, six indicators are used as the basis to test the prediction accuracy, model advantages and disadvantages, and fitting performance of the prediction model [[
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In the process of fitting and mapping multiple indicators, the significant difference in magnitude between the indicators can directly impact the final result. Therefore, the 'mapminmax' function in MATLAB R2023a is used to normalize the original data within a [0, 1] interval. After completing the model simulation and prediction, the mapminmax function is then used to reverse-normalize the data back to its original values. Based on the aforementioned model parameter settings, both the original data and principal component data are used as inputs to obtain permeability prediction results for test samples in each model. The prediction results for the original data are presented in Table 7, while those for the principal component data are shown in Table 8.
By summarizing the aforementioned performance evaluation indicators, the original data evaluation index comparison is shown in Table 9. The comparison of the principal component data evaluation index is shown in Table 10. By comparing the prediction results in Table 7 and Table 8, as well as the performance evaluation indicators in Table 9 and Table 10, principal component extraction of the original data is effectively helpful in concentrating the data, thereby improving the prediction accuracy of the model. Additionally, according to Table 9 and Table 10, the IDBO-BPNN model outperforms other models in various indices. Furthermore, MAE, MAPE, RMSE, R
In machine learning models, model stability refers to the consistency of performance across various datasets, even when the data is slightly altered or affected by noise. Ensuring the stability of a model is crucial to guarantee its reliability and generalization ability in practical applications. A coal mine in Shanxi Province was selected as the research subject to showcase the reliability and stability of the IDBO-BPNN model. The thickness of No. 2 coal seam in the mine is 0.75~1.93 m, the average thickness is 1.07 m, the coal seam inclination is 3~7°, the absolute emission of gas is 22.23 m
In conclusion, the IDBO-BPNN model constructed by the author not only demonstrates high prediction accuracy but also exhibits a certain level of reliability and stability. Furthermore, its prediction results are more aligned with reality and can accurately forecast the gas permeability of coal bodies.
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Graph: Figure 1 Topology structure of BPNN.
Graph: Figure 2 Algorithm convergence curve comparison.
Graph: sensors-24-02873-g002b.tif
Graph: sensors-24-02873-g002c.tif
Graph: Figure 3 IDBO -BPNN model flow.
Graph: Figure 4 Correlation coefficient matrix.
Graph: Figure 5 Comparison of evaluation indexes of different models.
Graph: sensors-24-02873-g005b.tif
Table 1 Test function information.
Reference Functions Dimensionality Radius 30 [−100, 100] 30 [−10, 10] 30 [−100, 100] 30 [−100, 100] 30 [−500, 500] 30 [−32, 32] 4 [0, 10] 30 [−1.28, 1.28]
Table 2 Comparison of test results.
Functions Evaluation Criteria WOA DBO SABO GWO NGO HHO IDBO F1 Optimal value 2.7 × 10−101 2.1 × 10−191 1.6 × 10−241 4.92 × 10−36 1.1 × 10−108 7.6 × 10−132 0 Standard deviation 1.03 × 10−90 1.5 × 10−132 0 1.57 × 10−33 8.7 × 10−106 5.7 × 10−109 0 Mean value 3.09 × 10−91 2.8 × 10−133 2.7 × 10−237 1.18 × 10−33 3.3 × 10−106 1.1 × 10−109 0 mid-value 6.86 × 10−94 1.8 × 10−162 1.5 × 10−238 5.89 × 10−34 1 × 10−106 7.6 × 10−122 0 Worst value 5.47 × 10−90 8.3 × 10−132 2.5 × 10−236 5.73 × 10−33 4.8 × 10−105 3.1 × 10−108 0 F2 Optimal value 5.7 × 10−106 5.2 × 10−206 2.6 × 10−242 1.94 × 10−36 3.9 × 10−109 8.6 × 10−133 0 Standard deviation 9.38 × 10−91 8.5 × 10−137 0 2.09 × 10−34 9.5 × 10−107 6.9 × 10−113 0 Mean value 2.68 × 10−91 1.6 × 10−137 1.3 × 10−236 8.17 × 10−35 4.5 × 10−107 1.3 × 10−113 0 mid-value 5.7 × 10−95 1.7 × 10−160 9 × 10−240 2.76 × 10−35 9.4 × 10−108 1.8 × 10−122 0 Worst value 4.81 × 10−90 4.7 × 10−136 3.4 × 10−235 1.09 × 10−33 4.2 × 10−106 3.8 × 10−112 0 F3 Optimal value 3.31 × 10−68 1.59 × 10−94 4.1 × 10−137 2.58 × 10−21 6.72 × 10−57 2.72 × 10−67 0 Standard deviation 3.19 × 10−61 7.59 × 10−71 5.3 × 10−133 2.75 × 10−20 8.67 × 10−55 4.38 × 10−59 0 Mean value 7.62 × 10−62 1.39 × 10−71 1.9 × 10−133 2.76 × 10−20 5.7 × 10−55 8.82 × 10−60 1.9 × 10−300 mid-value 2.9 × 10−65 5.74 × 10−83 2.1 × 10−134 1.68 × 10−20 2.8 × 10−55 9.15 × 10−64 0 Worst value 1.67 × 10−60 4.16 × 10−70 2.2 × 10−132 1.34 × 10−19 4.54 × 10−54 2.4 × 10−58 5.6 × 10−299 F4 Optimal value 12,353.02 3.6 × 10−157 2.62 × 10−97 1.21 × 10−10 1.03 × 10−34 2.7 × 10−117 0 Standard deviation 12,261.04 2.88 × 10−65 1.15 × 10−51 7.79 × 10−7 2.99 × 10−27 6.18 × 10−72 0 Mean value 40,102.65 5.26 × 10−66 2.13 × 10−52 3.05 × 10−7 9.91 × 10−28 1.13 × 10−72 0 mid-value 38,697.38 7.6 × 10−128 6.67 × 10−72 1.14 × 10−8 4.27 × 10−30 5.5 × 10−102 0 Worst value 64,604.58 1.58 × 10−64 6.31 × 10−51 3.44 × 10−6 1.23 × 10−26 3.38 × 10−71 0 F5 Optimal value 2.7 × 10−164 0 0 9.42 × 10−67 1.2 × 10−210 1.5 × 10−262 0 Standard deviation 5.3 × 10−135 0 0 4.38 × 10−60 0 0 0 Mean value 1.1 × 10−135 6.7 × 10−279 0 9.29 × 10−61 1.7 × 10−204 1.9 × 10−221 0 mid-value 1.7 × 10−145 0 0 4.92 × 10−63 1.5 × 10−207 5.5 × 10−245 0 Worst value 2.9 × 10−134 2 × 10−277 0 2.4 × 10−59 2.6 × 10−203 5.8 × 10−220 0 F6 Optimal value 2.9 × 10−160 5.6 × 10−216 0 6.6 × 10−129 2.4 × 10−224 1.4 × 10−177 0 Standard deviation 3.9 × 10−130 9.2 × 10−137 0 9.4 × 10−111 0 2.7 × 10−147 0 Mean value 8.4 × 10−131 1.7 × 10−137 2.2 × 10−302 1.7 × 10−111 4.9 × 10−217 7.1 × 10−148 0 mid-value 1.1 × 10−138 8.4 × 10−170 3 × 10−308 7.7 × 10−122 2.8 × 10−220 4.9 × 10−157 0 Worst value 2.1 × 10−129 5.1 × 10−136 4.4 × 10−301 5.2 × 10−110 1.2 × 10−215 1.1 × 10−146 0 F7 Optimal value 2.15 × 10−47 3.27 × 10−70 0.099873 0.099873 0.099873 2.98 × 10−66 0 Standard deviation 0.059587 0.042932 1.28 × 10−07 0.055086 1.95 × 10−13 5.98 × 10−58 0 Mean value 0.129878 0.075022 0.099873 0.179873 0.099873 1.86 × 10−58 0 mid-value 0.099873 0.099873 0.099873 0.199873 0.099873 7.44 × 10−62 0 Worst value 0.299873 0.099873 0.099874 0.299873 0.099873 2.73 × 10−57 0 F8 Optimal value 0 0.009716 0.009716 0.009716 0.009716 0 0 Standard deviation 0.018154 2.79 × 10−08 7.25 × 10−08 0.013327 5.29 × 10−14 0 0 Mean value 0.022947 0.009716 0.009716 0.034005 0.009716 0 0 mid-value 0.009716 0.009716 0.009716 0.037224 0.009716 0 0 Worst value 0.078189 0.009716 0.009716 0.078189 0.009716 0 0
Table 3 Optimization curves for different test sets.
Test Set Type Functions Convergence Curves Radius CEC2017 Shifted and Rotated [−100, 100] Shifted and Rotated Rastrigin's Function Shifted and Rotated Levy Function Hybrid Function ( CEC2021 Shifted and Rotated Bent Cigar Function Shifted and Rotated Lunacek bi-Rastrigin Function Hybrid Function ( Composition Function (
Table 4 Coal gas permeability sample data.
No. Effective Stress/MPa Gas Pressure/MPa Temperature/°C Compressive Strength/MPa Permeability/(10−5 m2) 1 2 1.8 40 10.85 0.881 2 1.51 0.5 55 12.85 1.062 3 4.01 0.5 30 14.13 0.559 ... ... ... ... ... ... 24 1.73 1.8 45 14.13 0.805 25 2 1 60 12.62 0.633 26 2.5 1.5 30 12.37 0.677 ... ... ... ... ... ... 48 3.78 1 30 12.85 0.491 49 1.73 0.5 30 14.13 1.189 50 2 1 70 11.5 0.632
Table 5 KPCA dimension reduction data.
No. Y1 Y2 Y3 Permeability/(10−5 m2) 1 0.615 −0.972 1.635 0.881 2 −0.404 −0.453 −0.373 1.062 3 −0.497 2.050 −2.133 0.559 ... ... ... ... ... 24 −0.906 −1.783 −0.342 0.805 25 0.173 −0.330 0.496 0.633 26 −0.190 −0.404 −0.053 0.677 ... ... ... ... 48 0.092 1.489 −0.806 0.491 49 −1.578 −0.560 −2.232 1.189 50 0.967 −0.088 1.646 0.632
Table 6 The parameters of each model are set.
Parameter Name Specific Setting Parameter Name Specific Setting Population size 30 Maximum iterations 100 BPNN training times 1000 BPNN target error 1 × 10−6 BPNN learning rate 0.01 BPNN hidden layer node 12 SVM cross-validate parameters 5 SVM option.gap 0.9 SVM option.cbound [1, 100] SVM option.gbound [1, 100] PSO learning factor 1.5 PSO inertia weight 0.8 PSO maximum speed limit 1 PSO Maximum speed limit PSO minimum speed limit −1 MPA FADs 0.2 Probability of WOA contraction enveloping mechanism [0.1] WOA spiral position update probability [0.1] Variation range of BES spiral trajectory (0.5, 2) BES position change parameters (1.5, 2) BES spiral trajectory parameters (0, 5)
Table 7 Raw data predicted results.
No. True Value Predicted Value PSO-BPNN PSO-LSVM PSO-SVM MPA-BPNN WOA-SVM BES-SVM DBO-BPNN IDBO-BPNN 40 0.891 0.759 0.863 0.804 0.797 0.820 0.801 0.815 0.803 41 0.516 0.548 0.635 0.582 0.584 0.582 0.579 0.588 0.552 42 0.619 0.525 0.582 0.585 0.609 0.600 0.613 0.608 0.611 43 0.632 0.569 0.612 0.613 0.635 0.629 0.641 0.635 0.642 45 0.564 0.602 0.711 0.676 0.680 0.704 0.691 0.683 0.665 46 0.786 0.724 0.867 0.840 0.811 0.870 0.841 0.844 0.865 47 0.683 0.732 0.705 0.784 0.740 0.689 0.670 0.736 0.688 48 0.491 0.412 0.534 0.518 0.544 0.544 0.538 0.518 0.487 49 1.189 1.044 1.171 1.070 1.163 1.146 1.113 1.127 1.151 50 0.632 0.632 0.727 0.704 0.690 0.725 0.695 0.703 0.686
Table 8 Principal component data prediction results.
No. True Value Predicted Value PSO-BPNN PSO-LSSVM PSO-SVM PSO-BPNN WOA-SVM BES-SVM PSO-BPNN IDBO-BPNN 40 0.891 0.746 0.856 0.805 0.850 0.829 0.834 0.830 0.850 41 0.516 0.541 0.472 0.542 0.500 0.505 0.520 0.479 0.518 42 0.619 0.651 0.589 0.607 0.634 0.639 0.558 0.613 0.621 43 0.632 0.685 0.628 0.631 0.637 0.650 0.596 0.620 0.626 45 0.564 0.644 0.498 0.681 0.521 0.514 0.542 0.545 0.558 46 0.786 0.788 0.723 0.864 0.759 0.712 0.750 0.812 0.789 47 0.683 0.759 0.627 0.698 0.676 0.676 0.703 0.653 0.659 48 0.491 0.512 0.553 0.503 0.522 0.518 0.493 0.513 0.511 49 1.189 1.134 1.174 1.165 1.186 1.185 1.153 1.167 1.190 50 0.632 0.655 0.554 0.659 0.587 0.582 0.607 0.622 0.625
Table 9 Comparison of raw data evaluation indicators.
Models Model Performance MAE MAPE/% RMSE MSE FBR/% Train Test Train Test Train Test Train Test Train Test Train Test PSO-BPNN 0.0564 0.0695 7.35 9.65 0.0775 0.0815 0.8568 0.8318 0.0060 0.0066 4.83 5.61 PSO-LSSVM 0.0542 0.0608 8.34 10.00 0.0705 0.0751 0.8817 0.8573 0.0050 0.0056 −5.44 −7.27 PSO-SVM 0.0526 0.0692 7.38 9.95 0.0679 0.0770 0.8903 0.8499 0.0046 0.0059 −2.56 −4.30 MPA-BPNN 0.0457 0.0510 6.65 8.00 0.0569 0.0614 0.9230 0.9046 0.0032 0.0038 −1.49 −5.14 WOA-SVM 0.0462 0.0576 6.75 8.95 0.0582 0.0703 0.9193 0.8748 0.0034 0.0049 −2.64 −5.93 BES-SVM 0.0486 0.0548 7.00 8.19 0.0589 0.0657 0.9173 0.8907 0.0035 0.0043 −1.31 −4.33 DBO-BPNN 0.0447 0.0551 6.54 8.27 0.0570 0.0639 0.9225 0.8966 0.0033 0.0041 −2.60 −5.17 IDBO-BPNN 0.0397 0.0424 5.60 6.11 0.0534 0.0550 0.9319 0.9234 0.0029 0.0030 −0.46 −3.06
Table 10 Comparison of evaluation indexes of principal component data.
Models Model Performance MAE MAPE/% RMSE MSE FBR/% Train Test Train Test Train Test Train Test Train Test Train Test PSO-BPNN 0.0327 0.0511 4.63 7.27 0.0405 0.0644 0.9609 0.8949 0.0016 0.0042 −0.62 −3.10 PSO-LSSVM 0.0167 0.0453 2.56 7.21 0.0422 0.0506 0.9575 0.9352 0.0018 0.0026 1.07 4.67 PSO-SVM 0.0388 0.0398 5.52 5.85 0.0497 0.0544 0.9411 0.9250 0.0025 0.0030 −0.49 −3.08 MPA-BPNN 0.0120 0.0233 1.70 3.67 0.0200 0.0280 0.9905 0.9802 0.0004 0.0008 −0.35 1.77 WOA-SVM 0.0114 0.0322 1.80 4.80 0.0286 0.0398 0.9805 0.9599 0.0008 0.0016 −0.18 2.51 BES-SVM 0.0175 0.0300 2.49 4.16 0.0311 0.0353 0.9770 0.9685 0.0010 0.0012 1.21 3.34 DBO-BPNN 0.0130 0.0246 1.91 3.61 0.0237 0.0288 0.9866 0.9790 0.0006 0.0008 1.02 2.06 IDBO-BPNN 0.0045 0.0112 0.70 1.66 0.0074 0.0168 0.9987 0.9929 0.0001 0.0003 −0.02 0.57
Table 11 Pearson correlation coefficient matrix.
Effective Stress Gas Pressure Compressive Strength Compressive Strength Effective stress 1 −0.062 0.056 −0.122 Gas pressure −0.062 1 0.229 −0.230 Compressive strength 0.056 0.229 1 −0.434 Compressive strength −0.122 −0.230 −0.434 1
Table 12 Each model tested the prediction results of the sample.
No. True Value Predicted Value PSO-BPNN PSO-LSSVM PSO-SVM MPA-BPNN WOA-SVM BES-SVM DBO-BPNN IDBO-BPNN 48 0.516 0.527 0.556 0.516 0.564 0.578 0.567 0.570 0.561 49 0.810 0.834 0.762 0.836 0.840 0.828 0.845 0.827 0.839 50 0.516 0.572 0.568 0.552 0.581 0.566 0.576 0.572 0.567 51 0.514 0.564 0.527 0.554 0.557 0.570 0.551 0.562 0.538 52 0.511 0.557 0.522 0.550 0.516 0.520 0.517 0.518 0.533 53 1.056 1.032 0.832 1.034 0.945 0.929 0.931 0.945 0.935 54 0.489 0.545 0.522 0.537 0.516 0.520 0.519 0.518 0.516 55 0.680 0.649 0.718 0.658 0.742 0.762 0.718 0.752 0.718 56 0.845 0.925 0.844 0.927 0.872 0.869 0.871 0.863 0.853 57 0.645 0.572 0.575 0.560 0.608 0.615 0.616 0.602 0.602 58 0.431 0.667 0.616 0.667 0.598 0.602 0.616 0.590 0.560 59 0.580 0.676 0.649 0.677 0.598 0.602 0.616 0.590 0.595 60 0.768 0.671 0.718 0.677 0.758 0.762 0.777 0.769 0.775 61 0.478 0.547 0.532 0.540 0.549 0.538 0.547 0.535 0.557 62 0.745 0.704 0.691 0.695 0.643 0.645 0.669 0.641 0.673 63 0.850 0.802 0.823 0.808 0.781 0.813 0.793 0.796 0.763 64 0.834 0.862 0.801 0.863 0.817 0.799 0.826 0.802 0.792 65 0.654 0.688 0.629 0.683 0.595 0.578 0.606 0.587 0.608 66 0.567 0.544 0.567 0.537 0.515 0.518 0.518 0.517 0.533 67 0.582 0.561 0.628 0.532 0.589 0.575 0.582 0.580 0.585
Conceptualization: W.W. and X.C.; Data curation: W.W., X.C. and Y.Q.; Funding acquisition: W.W. and Y.Q.; Project administration: K.X. and R.L.; Resources: W.W., X.C. and Y.Q.; Software: W.W., X.C., Y.Q. and K.X.; Supervision: W.W. and Y.Q.; Validation: R.L. and C.B.; Visualization: X.C., K.X. and C.B.; Writing—original draft: W.W. and X.C.; Writing—review & editing: W.W. and Y.Q. All authors have read and agreed to the published version of the manuscript.
Not applicable.
Not applicable.
All data generated or analyzed during this study are included in this published article and its Supplementary Information Files.
The authors declare no conflict of interest.
We thank Xiangyan LI MTI and School of Foreign Languages in GuiZhou University of Finance and Economics for its linguistic assistance during the preparation of this manuscript.
The following supporting information can be downloaded at: https://
By Wei Wang; Xinchao Cui; Yun Qi; Kailong Xue; Ran Liang and Chenhao Bai
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