A SMOGN-based MPSO-BP model to predict the height of a hydraulically conductive fracture zone

Objective The height of a hydraulically conductive fracture zone, a significant factor influencing roof water inrushes and groundwater resource loss, is identified as a research focus of the prevention and control of mine water disasters. Method To accurately predict the heights of hydraulically conductive fracture zones in coal seam roofs, five parameters were selected as the primary factors influencing hydraulically conductive fracture zones the mining depth: mining height, coal seam inclination, the length of the mining face along its dip direction, proportional coefficient of hard rocks (i.e., the ratio of the cumulative thickness of hard rocks within the statistical height above the coal seam roof to the statistical height), and mining method. A total of 200 measured samples concerning the heights of hydraulically conductive fracture zones were collected as the model dataset. First, over-sampling of the original dataset was conducted using the synthetic minority over-sampling technique for regression (SmoteR) combined with the introduction of Gaussian Noise (SMOGN). In conjunction with 8-fold cross-validation, the optimal back propagation (BP) neural network structure was determined by using the mean absolute error (MAE, denoted by E_MA), root mean square error (RMSE, denoted by E_RMS), and coefficient of determination (denoted by R²) as the assessment indices of the regression model. Then, the initial weights and thresholds of the BP neural network were optimized using the mutation particle swarm optimization (MPSO) algorithm. Finally, the optimized prediction model, i.e., the MPSO-BP model, was applied to the engineering field. Results and Conclusion The results indicate that based on the original dataset, the BP neural network, using the Huber loss and Adam first-order optimization algorithm, enhanced the training speed and stability. Consequently, the optimal activation function was determined at Tanh and the optimal hidden layer node number at 12. The MPSO-BP model yielded the optimal performance where the MPSO population number was 50. After SMOGN-based over-sampling and MPSO-based hyperparameter optimization, the training set yielded an E_MA value of 0.163, an E_RMS value of 0.216, and an R² value of 0.948, and these values were 0.260, 0.341, and 0.901, respectively, for the validation set. The field application indicated that the MPSO-BP model yielded relative errors of below 9% in the prediction. Therefore, the innovative combination of SMOGN-based over-sampling and MPSO-based hyperparameter optimization can significantly enhance the stability and generalization capability of the prediction model, the sample distribution characteristics, the sample utilization efficiency, and the predicted effects of the model. This study can serve as a reference for the training and prediction of models for the heights of hydraulically conductive fracture zones.