###### Abstract  
Given that the conventional back propagation neural network (BPNN) easily falls into the local optimal solutions, resulting in poor prediction accuracy, an improved BPNN based on the differential evolution and grey wolf optimizer (DEGWO) is proposed, the so-called DEGWO-BPNN. The prediction of the water-conducting fracture zone (WCFZ) height is significant for mine safety operations. A total of 104 sample data are trained and 25 sample data are tested to identify the optimal prediction model. Five evaluation indexes are selected to assess the prediction performance of the models quantitatively. Finally, the DEGWO-BPNN model is applied to a specific engineering case. The main conclusions are as follows: (1) Mining height, mining depth, coal seam dip, panel width, and ratio of hard rock as the main factors affecting the WCFZ height are selected. The topology structure of the model is defined as '5-12-1'; (2) the bias between the predicted value and the actual value of the training samples is smaller with an average error of 2.39. Test samples further validate the prediction precision through evaluation indexes. The values of MAE, RMSE, MAPE, and R\({}^{2}\) are 2.3952, 3.4674, 5.3148%, and 0.99077, respectively. The prediction accuracy is 94.6852%; (3) Mining Code', MLR, BPNN, and GWO-BPNN models are treated as the comparison groups. The comparative analysis shows that the prediction performance of 'Mining Code' is the worst, while that of DEGWO-BPNN is the best, and it outperforms other algorithms and statistical approaches; (4) the prediction of WCFZ height in the 11601 panel is in line with the actual value. The prediction error of the DEGWO-BPNN model is lower than that of the comparison models. As such, the DEGWO-BPNN model can be well applied to the prediction of WCFZ height and is suitable for coal mines with different regional geological conditions. It can provide a valuable reference for mine safety operations. differential evolution; grey wolf optimizer; DEGWO-BPNN; water-conducting fracture zone; prediction performance; evaluation indexes +
Footnote †: journal: Medical  
zone (WCFZ) height is summarized [7]. Nevertheless, with the change in geological conditions, the empirical formula may not accurately predict the WCFZ height, and the applicability is relatively poor. As such, scholars have conducted in-depth research on the WCFZ development [7; 8; 9]. Limited by the surroundings, the microtremor survey and the opposing coil transient electromagnetic methods were applied to investigate the distribution of the water-conducting fracture passageways and further validated by the drilling [10]. Geophysical explorations and borehole investigation were adopted in the spatial distribution characteristics of WCFZ [11; 12; 13; 14]. An approach based on the Brillouin optical time-domain reflectometry was proposed [15; 16]. In addition, tracer tests were used to identify the water-conducting channels [17; 18; 19]. However, these methods not only consume time and economic cost but are also influenced by the operating circumstances. Considering that the WCFZ is affected by many factors, the weight of factors is identified by grey correlation, principal component analysis, and so on, and a multivariate regression model was established to predict its height [16; 20; 21; 22; 23]. Moreover, numerical simulation and physical material simulation were conducted to survey the fissure development law and its height [12; 24; 25; 26]. The theoretical calculation of WCFZ was proposed by analyzing the ultimate deflection and free space height of overburden and tensile strain [27]. With the continuous promotion of artificial intelligence, machine learning has been gradually applied to various fields. [PERSON] and [PERSON] et al. [11; 28] used different optimization algorithms to optimize the prediction ability of extreme learning machine models for predicting the WCFZ height. The genetic algorithm (GA) was employed to search for the optimal support vector regression model to improve the prediction accuracy [29].