The Prediction of Aquifer Water Abundance in Coal Mines Using a Convolutional Neural Network–Bidirectional Long Short-Term Memory Model: A Case Study of the 1301E Working Face in the Yili No. 1 Coal Mine

Abstract

To address the challenges in predicting roof water hazards in weakly cemented strata of Northwest China, this study pioneers an integrated CNN-BiLSTM model for aquifer water abundance prediction. Focusing on the 1301E working face in the Yili No. 1 Coal Mine, we employed kriging interpolation to process sparse hydrological datasets (mean relative error: 8.7%), identifying five dominant controlling factors—aquifer burial depth, hydraulic conductivity, core recovery rate, sandstone–mudstone interbedded layer count, and sandstone equivalent thickness. The proposed bidirectional architecture synergizes CNN-based spatial feature extraction with BiLSTM-driven nonlinear temporal modeling, optimized via Bayesian algorithms to determine hyperparameters (32-channel convolutional kernels and 64-unit BiLSTM hidden layers). This framework achieves the comprehensive characterization of multifactorial synergistic effects. The experimental results demonstrate: (1) that the test set root mean square error (1.57 × 10⁻³) shows 65.3% and 85.9% reductions compared to the GA-BP and standalone CNN models, respectively; (2) that the coefficient of determination (R² = 0.9966) significantly outperforms the conventional fuzzy analytic hierarchy process (FAHP, error: 0.071 L/(s·m)) and BP-based neural networks; (3) that water abundance zoning reveals predominantly weak water-rich zones (q = 0.05–0.1 L/(s·m)), with 93.3% spatial consistency between predictions and pumping test data.

1. Introduction

With over twenty years of implementation of China’s strategic westward shift in coal resource development, the northwestern region has become a major coal-producing area. However, coal mining under weakly cemented strata in the northwest exhibits distinct differences from mining in the eastern regions. The northwestern mining areas underwent later diagenesis, with the widespread distribution of weakly and extremely weakly cemented mudstones. The weakly cemented mudstones were characterized through a series of tests including in situ borehole exploration, pumping tests, laboratory X-ray diffraction (XRD) analysis, and scanning electron microscopy (SEM) analysis. These characteristics manifest as low strength, minimal cementing components, extreme susceptibility to weathering and disintegration, rapid argillization upon water exposure, heightened sensitivity to mining-induced disturbances, and the increased complexity of roof water hazards during coal seam extraction [1,2]. Therefore, evaluating water abundance in coal seam roof aquifers under the unique geological conditions of the western regions holds significant importance for the safe and efficient production of coal mines.

Many scholars have conducted extensive research on aquifer water abundance, primarily involving field pumping tests, geophysical exploration methods, and multi-factor comprehensive analysis [3,4,5,6,7,8,9,10,11]. Geophysical exploration is constrained by physical principles, demanding stringent requirements on surrounding environments and geological conditions. Secondly, the nonuniqueness problem is prevalent, where similar petrophysical properties across distinct geological formations and oversimplified inverse models frequently lead to nonunique interpretation results. Simultaneously, data interpretation remains heavily dependent on empirical experience and prior geological knowledge, with different algorithms or parameter settings potentially yielding divergent conclusions. Although pumping tests can directly acquire critical parameters such as aquifer permeability and water storage capacity, they only reflect local aquifer characteristics near boreholes, struggling to characterize complex aquifer structures, where single-point data risk underestimating or overestimating overall water abundance. Additionally, the high operational and temporal costs require prolonged stable observations, while borehole construction, equipment maintenance, and data processing demand substantial resources. Furthermore, significant anthropogenic and engineering interferences—such as improper screen positioning, well completion defects, or inadequate pumping rate control—may induce wellbore damage, clogging, or mixed flows, ultimately compromising test results. The multi-factor comprehensive analysis method predicts aquifer water abundance scientifically by extracting key influencing factors, integrating hydrogeological data from field tests, and applying statistical analysis techniques. Due to its scientifically sound analytical results, this method has garnered widespread attention and in-depth research from scholars both domestically and internationally [12,13].

Some scholars have established comprehensive evaluation frameworks for aquifer water abundance by integrating the analytic hierarchy process (AHP) with the entropy weight method, variable weight theory, and GIS-based spatial analysis, combining expert knowledge with field measurements to determine indicator weights [14,15,16,17,18]. Others introduced fuzzy AHP (FAHP), using fuzzy numbers to represent expert judgments, thereby reducing bias from single-value decisions and improving prediction accuracy [19,20,21]. However, traditional linear methods like AHP and FAHP face limitations due to incomplete site-specific data and strong subjectivity in weight assignment, often failing to reflect true aquifer water abundance.

In contrast, artificial neural networks (ANNs) overcome these shortcomings through adaptive learning and fault tolerance. Researchers have developed water abundance prediction models using BP neural networks coupled with multi-factor analyses, where specific yield serves as the target variable [22,23]. Yet, BP networks exhibit low accuracy, slow convergence, and high computational costs, leading to prediction errors.

Recent efforts explore alternative neural networks, such as convolutional neural networks (CNNs), which excel in deep feature extraction and computational depth. For instance, Chen et al. [24] achieved precise coal seam floor water inrush predictions using a CNN model incorporating 15 key controlling factors. Nevertheless, CNNs struggle with nonlinear relationships, require large training datasets, and are sensitive to hyperparameter choices, limiting their prediction accuracy for water abundance.

To further enhance the accuracy of water abundance prediction, a CNN-BiLSTM prediction model was constructed by integrating a bidirectional long short-term memory (BiLSTM) network with a convolutional neural network (CNN). While BiLSTM excels in temporal modeling, it demonstrates unique advantages in processing multivariate features. The bidirectional architecture (forward LSTM + backward LSTM) enables the modeling of both forward and inverse correlations among features, uncovering implicit sequential or hierarchical relationships within multivariate data. Simultaneously, its gate mechanisms (input gate, forget gate, and output gate) dynamically modulate feature contributions, thereby flexibly capturing nonlinear interactions between variables, perceiving global feature distributions, and mitigating information loss inherent in local perspectives. The CNN-BiLSTM model synergizes the strengths of convolutional neural networks (CNNs) in spatial feature extraction with the robust capabilities of BiLSTM in processing multivariate features. CNN excels at efficiently extracting local features and spatial patterns from data, while BiLSTM captures nonlinear interactions among variables, thereby addressing CNN’s susceptibility to local optima traps. By feeding the locally extracted spatial features from CNN into BiLSTM for global feature modeling, the CNN-BiLSTM model integrates both local and global characteristics, significantly enhancing prediction accuracy.

Based on borehole data from the 1301E working face of the Yili No. 1 Coal Mine, this study employs correlation analysis to screen evaluation indices for aquifer water abundance, pioneering the application of the CNN-BiLSTM model in hydrogeology and mine safety. The model integrates sparse borehole sampling with low-cost packer tests (minimal operational/time expenditures) to derive hydrogeological parameters, enabling water abundance prediction across the entire working face. This approach effectively overcomes limitations of traditional methods—notably large errors caused by restricted site data and human interference—significantly enhancing prediction accuracy and reliability. Unlike prior BP neural network studies that relied on the simplified linear weighting of independent factors, the proposed model implements multivariate co-modeling. Its bidirectional gated architecture synchronously captures nonlinear synergies among geological variables while fusing localized spatial features with global patterns, thereby improving both accuracy and stability. These advancements provide robust technical support for coal mine safety management.

2. Study Area

Xinwen Mining Group (Yili) Energy Development Co., Ltd., Xinjiang, China Mine No. 1 (hereinafter referred to as the “Yili Mine No. 1”) is located in the southwestern part of the Yili Kazakh Autonomous Prefecture, Xinjiang (Figure 1a). The mine field is situated on the southern margin of the Ili Basin, encompassing the Chabuchaer piedmont slope and alluvial plain. The terrain is higher in the south and lower in the north, with the southern part being a hilly area characterized by intense topographic dissection, while the northern alluvial plain is relatively flat. The surface of the mine field is covered by Quaternary strata.

According to the actual borehole data, the strata developed in the area, from oldest to youngest, are the Middle-Upper Triassic Xiaoquangou Group (T_2–3xq), the Middle Jurassic Xishanyao Formation (J₂x) and Toutunhe Formation (J₂t), the Cretaceous Donggou Formation (K₂d), the Neogene (N), and the Quaternary (Q). Among these, the coal-bearing strata belong to the Middle Jurassic Xishanyao Formation (J₂x). A comparative analysis of the coal seams reveals that the No. 3 and No. 5 coal seams are stably distributed throughout the area and are the main minable coal seams (Figure 2).

The main study area of this paper is the 1301E working face (Figure 1b), the first mining face of the No. 3 coal seam in the eastern wing of the mine. The groundwater aquifer groups in this area primarily include the Quaternary loose gravel layer, the Neogene sandstone aquifer, and the Jurassic fractured porous confined aquifer. The aquitards are mainly composed of Neogene and Jurassic mudstone, siltstone, and coal, and are divided into four aquitard layers from the top to the floor of the No. 5 coal seam, interbedded with the aquifers (Figure 3). The distribution of the aquitards is generally extensive, with good water-resisting properties. The water-filling sources in the 1301E working face primarily include atmospheric precipitation (annual average 440.6 mm, with mountain infiltration recharge), abandoned mine water (from decommissioned workings of the Zhongyangchang and Qiongbologongshe coal mines located 530–1000 m eastward, exhibiting limited water volume), groundwater (from Quaternary sand and gravel layers and Jurassic No. 3 coal seam roof sandstone aquifers), and localized surface water (Taskemorgou Gully and irrigation channels, with implemented protective measures). The dominant water-conducting pathways consist of mining-induced fracture zones and floor failure zones, which may connect with aquifers, while faults and poorly sealed boreholes (not intersecting the working area) pose minimal impact. Vertical hydraulic connectivity between aquifers remains weak, but mining activities could compromise aquitards and enhance hydraulic connectivity. The working face exhibits simple geological structures without fault-induced water inrush. However, the soft roof/floor lithology with water-softening characteristics necessitates strict prevention of water and sand inrush risks during extraction. Among these, the aquifer in the roof of the No. 3 coal seam, located within the Jurassic fractured porous confined aquifer, serves as the direct water-filling aquifer for the roof of the 1301E working face. Research on this aquifer is essential to ensuring safe production. Therefore, this paper focuses on the analysis of the water abundance of the No. 3 coal seam roof aquifer.

3. Aquifer Water Abundance: Dominant Controlling Factors

3.1. Analysis of Dominant Controlling Factors of Water Abundance

The water abundance characteristics of weakly cemented formation aquifers are influenced by multiple interrelated factors. To accurately evaluate aquifer water abundance, based on previous scholarly research, six key aspects were thoroughly investigated—the aquifer burial depth, sand–mud ratio, hydraulic conductivity, core recovery rate, number of interbedded sand–mudstone layers, and equivalent sandstone thickness [14,15].

Data collection for these controlling factors is complex, involving specialized operations such as drilling and pumping tests, resulting in data that are difficult to obtain, limited in quantity, and sparsely distributed. To maximize the acquisition of continuous and reliable data from limited datasets, the study employs the kriging interpolation method to process data interpolation for 15 boreholes, whose accuracy critically depends on sampling density and spatial distribution patterns. To assess the uncertainty of the interpolation results, this study implemented cross-validation to derive predictive standard deviations. Based on these deviations, 95% confidence interval limits were calculated for each grid node. Fifteen measured data points were selected as validation points to evaluate stability by determining the target coverage rate—defined as the proportion of actual values falling within the predicted intervals. As shown in

Table 1. Confidence interval coverage rate.

Dominant Controlling Factors	Aquifer Depth	Sand–Mud Ratio	Hydraulic Conductivity	Core Recovery	Sand–Mudstone Interlayer Number	Equivalent Sandstone Thickness
95% confidence interval coverage rate	93.3%	100%	93.3%	93.3%	100%	93.3%

, all key controlling factors achieved coverage rates ≥ 92%, confirming data reliability.

Concurrently, the mean relative error (MRE) of the dataset was calculated as 8.7% via leave-one-out cross-validation (LOO-CV) in kriging interpolation, meeting the engineering accuracy requirement (error < 10%). Therefore, contour maps of controlling factors were generated via kriging interpolation.

• Aquifer depth:

Underground rock formations develop fractures under geostress, which nonlinearly intensifies with increasing burial depth. Deeper aquifers experience greater geostress, promoting further fracture propagation and connectivity. Enhanced fracture networks amplify water storage capacity, thereby improving aquifer productivity (Figure 4a).

2.

Sand–mud ratio:

For the sandstone–mudstone interbedded multilayer structures commonly found in coal seam roof strata, the sand–mud ratio quantifies the thickness ratio between sandstone (or conglomerate) and mudstone (or siltstone) within the aquifer. Analysis of hydrogeological borehole data reveals a positive correlation between the sand–mud ratio and aquifer water abundance. Under conditions of relatively stable and intact aquifer thickness, a higher sand–mud ratio typically corresponds to enhanced water abundance (Figure 4b).

3.

Hydraulic conductivity:

Hydraulic conductivity, a key indicator of an aquifer’s water transmission capacity, reflects groundwater recharge, flow, and discharge efficiency. Simply put, higher hydraulic conductivity denotes greater permeability. This parameter is primarily controlled by fissure development in the rock mass—denser, better-connected fractures with minimal infilling enhance permeability, yielding higher conductivity values. Pump tests from hydrogeological boreholes at the Yili Mine 1 reveal a hydraulic conductivity range of 0.006–0.655 m/d for the No. 3 coal seam roof aquifer, classifying it as slightly to moderately permeable (Figure 4c).

4.

Core recovery:

The core recovery rate, defined as the ratio of the retrieved core length to the total drilling footage, inversely correlates with fracture development in rock strata. Lower core recovery rates indicate more fractured and permeable aquifers, as enhanced fracturing expands water storage capacity per unit volume, thereby increasing water abundance. In the study area, core recovery rates range from 0.51 to 0.98 (Figure 4d).

5.

Sand–mudstone interlayer number:

The alternating sand–mudstone interbedding pattern reveals complex aquifer–aquitard configurations, indirectly reflecting groundwater system connectivity. Under constant total aquifer thickness, an increased sand–mudstone interlayer number implies denser aquitard distribution, thereby reducing aquifer storage capacity (Figure 4e).

6.

Equivalent Sandstone Thickness:

Sandstone, with its relatively small clastic particles and filling materials conducive to water storage, represents one of the fundamental indicator factors. The thickness of the aquifer above coal seams is generally derived from the total accumulated thickness of fine, medium, and coarse sandstone layers. However, sandstones of different grain sizes exhibit varying water-bearing capacities, with larger sandstone particles corresponding to higher water abundance. Therefore, to differentiate the impact of sandstone layers of varying grain sizes on aquifer water abundance, the thicknesses of these three types of sandstone are converted into an equivalent sandstone thickness, which serves as the effective aquifer thickness (Figure 4f). Compared to conventional aquifer thickness metrics, this approach refines water abundance quantification by incorporating a granulometric weighting coefficient to convert physical thickness into equivalent water-conductive thickness, thereby differentially weighting sandstone grain-size contributions. This eliminates biases from homogenization assumptions in traditional methods, which overestimate low-efficiency layers or underestimate high-efficiency layers. The specific calculation method is as follows [25]:

$$L=(a+0.8b+0.6c)$$

(1)

where L represents the equivalent thickness of sandstone (m), a represents the thickness of coarse sandstone (m), b represents the thickness of medium sandstone (m), and c represents the thickness of fine sandstone (m).

3.2. Correlation Analysis of Water Abundance Control Factors

In the natural sciences, the Pearson correlation coefficient is widely employed to quantify linear relationships between two variables. Its broad applicability and reliability are particularly evident when analyzing complex datasets with multifactorial interactions. The strength and direction of the association are measured by the correlation coefficient (r), which ranges from −1 to 1: negative values indicate inverse correlations, positive values denote direct correlations, and larger absolute values signify stronger associations [26,27].

The formula for evaluating the pairwise correlation degree between water abundance control factors using the Pearson correlation coefficient is:

$$r={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n\left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)}}{\sqrt{{{\displaystyle {\sum }_{i=1}^n\left(X_i-\overline{X}\right)}}^2}\sqrt{{\displaystyle {\sum }_{i=1}^n{\left(X_i-\overline{Y}\right)}^2}}}}$$

(2)

where n is the number of samples, $X_i$ and $Y_i$ refer to the i-th sample value of $X$ and $Y$, and $\overline{X}$ and $\overline{Y}$ are the mean values of the samples. When $\left|r\right|$ ≤ 0.2, the two control factors are either extremely weakly correlated or uncorrelated. When 0.2 < $\left|r\right|$ ≤ 0.4, the two control factors are weakly correlated. When 0.4 < $\left|r\right|$ ≤ 0.6, the two control factors are moderately correlated. When 0.6 < $\left|r\right|$ ≤ 0.8, the two control factors are highly correlated. When 0.8 < $\left|r\right|$ ≤ 1, the two control factors are extremely highly correlated.

In this study, a threshold of 0.7 was set. When the correlation coefficient between two controlling factors exceeded 0.7, one factor was excluded, and the other was retained for subsequent analysis. Specifically, the correlation coefficient between the hydraulic conductivity and the sand–mud ratio was found to exceed 0.7 (Figure 5), necessitating the exclusion of one of these factors. Through analysis, it was determined that the other four controlling factors exhibited lower correlations with the hydraulic conductivity compared to the sand–mud ratio. Consequently, the sand–mud ratio factor was excluded from further analysis.

4. Model Development and Application

4.1. CNN Convolutional Neural Network

A CNN is essentially a network model that automatically extracts multi-level features from input data by simulating the operational mechanism of biological visual systems. Its core mechanism lies in utilizing convolution operations to capture local spatial characteristics in data, while effectively reducing data dimensionality and complexity through weight sharing, local connectivity, and pooling operations, thereby enhancing model generalization performance and computational speed [28]. The CNN consists of multiple layers of grid structures, primarily comprising three types—convolutional layers, pooling layers, and fully connected layers (Figure 6). Convolutional layers are responsible for capturing feature information from input data, while pooling layers filter and refine these features. Through alternating applications of convolutional and pooling layers, the model can progressively extract more abstract features that better reflect the essential characteristics of the subject, thereby improving prediction accuracy. The function of fully connected layers is to integrate the feature information processed by pooling layers and map them to final classification results.

4.2. BiLSTM (Bidirectional Long Short-Term Memory) Network

Long short-term memory (LSTM) effectively addresses the vanishing gradient problem in traditional recurrent neural networks for long-sequence data processing through its gating mechanisms (input gate, forget gate, and output gate). However, its unidirectional structure restricts the comprehensive exploration of complex multifactorial interactions, as it only captures sequential dependencies from past to future. To overcome this limitation, bidirectional LSTM (BiLSTM) integrates forward and backward LSTM layers, enabling holistic analysis of multivariate data. Specifically, BiLSTM’s dual-directional information flow design (Figure 7) allows for the simultaneous integration of contextual relationships among variables from both temporal orientations, making it particularly suited for scenarios requiring multifactorial synergy. $x_1,x_2,\dots ,x_t$ denote the structural response input data at different time steps; $A_1,A_2,\dots ,A_t$ represent the forward LSTM hidden states, capturing cumulative effects of the current time step on subsequent factors; while $B_1,B_2,\dots ,B_t$ indicate the backward hidden states, tracing historical influences on the current state; $Y_1,Y_2,\dots ,Y_t$ correspond to the output data; $w_1,w_2,\dots ,w_6$ signify hierarchical weights. Leveraging gating mechanisms, BiLSTM dynamically assigns factor-specific weights, suppresses noise interference, amplifies critical feature contributions, and precisely models nonlinear coupling relationships among multivariables.

In the BiLSTM network, the output states of hidden layers at different levels and the final output of the network are expressed by Equation (3) [29]:

$$\left\{\begin{array}{l}{A}_i=f_1({\omega }_1{x}_i+{\omega }_2{A}_{i-1})\\ B_i=f_2({\omega }_4{x}_i+{\omega }_3{A}_{i+1})\\ Y_i=f_3({\omega }_5{A}_i+{\omega }_6{B}_i)\end{array}\right.$$

(3)

where $f_1,f_2,f_3$ represent the activation functions applied at distinct hierarchical levels.

4.3. CNN-BiLSTM Model

The prediction process of the combined CNN and BiLSTM model [30,31] proceeds as follows: The CNN component initially explores and extracts core data features. In this stage, convolutional layers efficiently capture local spatial patterns through multiple kernels, while pooling layers compress and integrate features, achieving dimensionality reduction while preserving critical information for optimized feature processing. Subsequently, the processed multi-dimensional features are transmitted to the BiLSTM module. Leveraging its bidirectional architecture (forward and backward LSTMs operating synergistically), BiLSTM comprehensively parses complex inter-factor relationships, concurrently integrating contextual information across feature orientations to effectively capture nonlinear interactions among multivariables. The gating mechanisms (input gate, forget gate, and output gate) dynamically adjust feature importance weights, preventing single-factor dominance in model decisions and thereby enhancing the robustness of multifactorial synergy analysis. Finally, the fully connected layer outputs prediction results. This layer employs a linear activation function for continuous prediction generation, while integrating a ReLU activation layer to strengthen the nonlinear representation capabilities of both the convolutional and BiLSTM layers. Combined with the Adam optimizer for efficient network parameter updates, this configuration ensures predictions align with actual data distributions and accelerates model convergence.

This study systematically optimizes hyperparameter combinations for the CNN-BiLSTM model through a Bayesian optimization framework. Initial search spaces are defined based on architectural constraints and computational efficiency—convolutional kernels (16–128), BiLSTM hidden units (16–128), batch size (16–64), training epochs (50–200), and initial learning rate (10⁻⁴–10⁻²)—balancing model capacity with training stability. The objective function prioritizes validation set root mean square error (RMSE) minimization. A hybrid architecture integrating convolutional layers, pooling layers, bidirectional LSTM, and regression head is dynamically configured, with an Adam optimizer deployed for training while simultaneously monitoring validation performance. The Bayesian optimization engine employs a Gaussian process surrogate model. During iterative phases, the expected improvement (EI) acquisition function actively selects hyperparameter combinations, updating the surrogate model through an exploration-exploitation trade-off strategy until meeting termination criteria: maximum evaluation iterations (30) or RMSE fluctuation threshold (consecutive 5 iterations < 1%). The optimal parameter set minimizing RMSE is ultimately extracted (Figure 8).

4.4. Case Analysis

For predicting coal seam roof water hazards, based on the previous analysis, a CNN-BiLSTM water abundance prediction model was constructed using five primary control factors (aquifer burial depth, hydraulic conductivity, core recovery rate, number of interbedded sandstone–mudstone layers, and equivalent sandstone thickness). The model’s input layer has a dimensionality of 5 (representing the main controlling factors), and the output layer predicts the specific yield. The hidden layer structure dynamically adjusts feature weights through a global feature fusion mechanism. A total of 150 samples (including field-measured borehole data) extracted from the contour maps were divided into training, validation, and test sets at an 8:1:1 ratio (the test set being an independent field-measured dataset). Training and validation data were utilized within the Bayesian optimization framework to derive optimal hyperparameters. Based on optimization results, The CNN layer employs 2 × 1 convolution kernels with 32 output channels per kernel, followed by maximum pooling layers with size 2 to compress spatial dimensions. The BiLSTM layer is configured with 64 hidden units to capture temporal dynamic features. During model optimization, mean square error serves as the loss function, with Adam algorithm selected as the optimizer, initial learning rate set at 0.001, maximum training epochs at 100, and batch size at 6.

Compared to neural network training in other domains, this model operates with relatively limited sample data. Therefore, the model employs Z-score normalization to eliminate dimensional discrepancies among input features, accelerating convergence and enhancing robustness against distributional shifts. Batch normalization layers are integrated to reduce internal covariate shift, mitigate gradient vanishing, and improve training stability; the Adam optimizer with mini-batch processing and shuffle-enabled training is employed to prevent overfitting to data sequence patterns; and it utilizes validation set monitoring for overfitting detection to enable timely hyperparameter adjustments. Training results demonstrate that the CNN-BiLSTM model achieved a root mean square error (RMSE) of 1.23 × 10⁻³ and a coefficient of determination (R²) of 0.9924 for the training set; an RMSE of 1.88 × 10⁻³ and an R² of 0.9550 for the validation set; and an RMSE of 1.57 × 10⁻³ and an R² of 0.9966 for the test set.

5. Discussion

To validate the superiority of the CNN-BiLSTM water abundance prediction model, this study conducts comparative analysis against conventional FAHP and other neural models. Prediction performance is quantitatively evaluated utilizing AE (absolute error), RMSE (root mean square error), and R² (coefficient of determination), with results demonstrating that CNN-BiLSTM significantly outperforms baseline methods in both prediction accuracy and fitting capability.

5.1. FAHP

To address the limitations of the traditional analytic hierarchy process (AHP) in handling subjective judgment ambiguities, which often lead to challenges in meeting judgment matrix consistency requirements, logical conflicts in expert scoring, and consequently increased complexity in consistency verification and the reduced credibility of the evaluation results, this study employs the fuzzy analytic hierarchy process (FAHP) as the predictive methodology [32]. By introducing a 0.1–0.9 fuzzy scaling system, we systematically compare the pairwise importance of five principal controlling factors: aquifer burial depth, hydraulic conductivity, core recovery rate, sand-mudstone interbedded layer count, and sandstone equivalent thickness. This approach constructs a fuzzy complementary judgment matrix A. To ensure standardized prediction targets and comparative consistency, the test dataset from the aforementioned CNN-BiLSTM model was adopted as the research subject for predictive analysis.

$$A=a_{ij}=\left[\begin{array}{ccccc}0.50& 0.30& 0.50& 0.40& 0.40\\ 0.70& 0.50& 0.70& 0.60& 0.60\\ 0.50& 0.30& 0.50& 0.40& 0.40\\ 0.60& 0.40& 0.60& 0.50& 0.40\\ 0.60& 0.40& 0.60& 0.60& 0.50\end{array}\right]$$

(4)

$$w_i={\displaystyle \frac{1}{n\left(n-1\right)}}\left({\displaystyle \sum _{j=1}^n{a}_{ij}+\frac{n}{2}}-1\right),(i=1,2,\dots ,n)$$

(5)

$$W^{\ast }={\left(w_{ij}^{\ast }\right)}_{n\times n}$$

(6)

$$w_{ij}^{\ast }={\displaystyle \frac{w_i}{w_i+w_j}}(i=1,2,\dots ,n;j=1,2,\dots ,n)$$

(7)

Based on matrix A and Equation (5), the weights of evaluation indices were calculated through row sum normalization, yielding the weight vector W, $W={(0.18,0.23,0.18,0.2,0.21)}^T$. To validate the rationality of judgment matrix A and weight values W, a consistency check was implemented. According to Equations (6) and (7), the characteristic matrix W* of the fuzzy complementary judgment matrix A can be expressed as:

$$W^{\ast }={\left(w_{ij}^{\ast }\right)}_{n\times n}=\left[\begin{array}{ccccc}0.50& 0.44& 0.50& 0.47& 0.46\\ 0.56& 0.50& 0.56& 0.53& 0.52\\ 0.50& 0.44& 0.50& 0.47& 0.46\\ 0.53& 0.47& 0.53& 0.50& 0.49\\ 0.54& 0.48& 0.54& 0.51& 0.50\end{array}\right]$$

(8)

The compatibility index I was calculated as 0.06 based on Equation (9), confirming that the fuzzy complementary judgment matrix A satisfies the consistency requirement.

$$I\left(A,W^{\ast }\right)={\displaystyle \frac{1}{n^2}}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n\left|a_{ij}+w_{ij}^{\ast }-1\right|}}$$

(9)

$$V=w_i{y}_i$$

(10)

where $y_i$ represents the dimensionless processed value of the i-th indicator.

The dimensionless processed evaluation indicators were integrated with their calculated weights to predict specific water yield values through Equation (10) (

Table 2. Water abundance evaluation and prediction results based on the FAHP.

Sample Number	Actual Value L/(s·m)	Water Abundance Class	Predicted Value L/(s·m)	Water Abundance Class	Error
1	0.012	Weak	0.058	Weak	0.046
2	0.018	Weak	0.042	Weak	0.024
3	0.021	Weak	0.047	Weak	0.026
4	0.013	Weak	0.056	Weak	0.043
5	0.014	Weak	0.056	Weak	0.042
6	0.003	Weak	0.024	Weak	0.021
7	0.077	Weak	0.064	Weak	−0.013
8	0.001	Weak	0.072	Weak	0.071
9	0.017	Weak	0.064	Weak	0.047
10	0.047	Weak	0.117	Medium	0.070
11	0.067	Weak	0.063	Weak	−0.004
12	0.080	Weak	0.122	Medium	0.042
13	0.071	Weak	0.065	Weak	−0.006
14	0.037	Weak	0.083	Weak	0.046
15	0.020	Weak	0.066	Weak	0.046

). Comparative analysis with actual measurements revealed water abundance classification discrepancies in Samples 10 and 12 based on specific water yield criteria. Although the remaining samples shared identical water abundance grades, significant prediction errors in specific water yield magnitudes were observed. Only Samples 7, 11, and 13 demonstrated predictions within acceptable error margins.

5.2. Other Neural Network Prediction Models

Previously, most scholars predominantly selected backpropagation (BP) neural networks as predictive models in their studies. However, to comparatively analyze the prediction accuracy between the convolutional neural network–bidirectional long short-term memory (CNN-BiLSTM) model and other architectures, this study adopted an identical sample dataset and partitioning protocol—150 datasets were divided into training, validation, and test sets at an 8:1:1 ratio—to construct and train a genetic algorithm-optimized BP (GA-BP) neural network and standalone CNN model. This experimental design ensures comprehensive evaluation of inter-model performance differences under consistent data foundation and experimental conditions, thereby guaranteeing the scientific validity and comparability of results.

During the construction of the GA-BP neural network model, the number of hidden layer nodes was first optimized through empirical formula-based training. Iterative experimental validation revealed that when the hidden layer nodes were set to 7, the model achieved a minimum root mean square error (RMSE) of 4.93 × 10⁻³, indicating optimal performance. Based on this result, the BP neural network architecture was finalized with 5, 7, and 1 neurons in the input, hidden, and output layers, respectively. The encoding length for the genetic algorithm was subsequently calculated according to the neuron counts across layers. With a total of 42 weights and 8 thresholds in the neural network, the genetic algorithm encoding length was determined as 50. After optimizing the number of hidden layer nodes, the BP neural network was constructed using the determined optimal node count. The network was configured with a maximum of 1000 training epochs, a learning rate of 0.01, and a target minimum error of 1 × 10⁻⁵. To further enhance model performance, the genetic algorithm was employed to optimize the weights and thresholds of the BP neural network. During genetic algorithm parameter initialization, key settings included a population size of 30, maximum iterations of 50, crossover probability of 0.8, and mutation probability of 0.1.

During the training of the convolutional neural network (CNN), two convolutional layers were employed, each containing 16 filters. To ensure comprehensive learning of data features, the maximum number of iterations was set to 600 with an initial learning rate of 0.001. The Adam optimizer—which integrates the advantages of AdaGrad and RMSProp—was selected for optimization due to its strong adaptability, high computational efficiency, insensitivity to gradient scaling, and dynamic learning rate adjustment, thereby enhancing training efficiency and stability. The mean squared error (MSE) was selected as the loss function.

According to the training and testing results, The GA-BP neural network achieved an RMSE of 4.53 × 10⁻³ and a test set R² of 0.9010, while the standalone CNN model attained an RMSE of 1.11 × 10⁻² and R² of 0.8297. Comparative analysis with the CNN-BiLSTM model reveals that the standalone CNN exhibited a 7-fold higher MSE than CNN-BiLSTM, likely due to the absence of BiLSTM modules or inadequate feature extraction, resulting in weaker fitting capability for complex data patterns. Although GA-BP outperformed the standalone CNN, it still showed significant gaps compared to CNN-BiLSTM. The genetic algorithm optimization likely enhanced parameter search efficiency, yet traditional neural architectures inherently struggle to capture complex nonlinear relationships. Figure 9 presents a comparative analysis of measured values, predicted values from various methods, and their absolute errors in the testing set samples.

In comparison with prediction outcomes, the CNN-BiLSTM neural network model demonstrates significant performance advantages, with its predictions exhibiting high consistency with the measured sample data. The maximum error is 2.70 × 10⁻³ and the minimum error is merely 1.98 × 10⁻⁵. The error curve displays a stable distribution with minimal fluctuations, indicating superior prediction accuracy and the stability of the model. In comparative analysis, although the GA-BP neural network maintains errors within a relatively small range, a persistent performance gap remains relative to the CNN-BiLSTM neural network; meanwhile, the standalone CNN model exhibits the poorest predictive performance, with a maximum error of 2.67 × 10⁻² and a minimum error of 2.50 × 10⁻⁴. The broad error distribution range, particularly the significant deviation in predictions for individual boreholes from measured values, reveals lower prediction consistency.

Table 3. The results of neural network prediction Unit: L/(s·m).

Sample Number	Actual Value	GA-BP	GA-BP Absolute Errors	CNN	CNN Absolute Errors	CNN-BiLSTM	CNN-BiLSTM Absolute Errors
1	0.012	0.016	0.0041	0.016	0.0038	0.014	0.046
2	0.018	0.014	0.0041	0.009	0.0095	0.016	0.024
3	0.021	0.016	0.0046	0.026	0.0053	0.023	0.026
4	0.013	0.011	0.0024	0.017	0.0040	0.014	0.043
5	0.014	0.012	0.0020	0.019	0.0047	0.015	0.042
6	0.003	0.002	0.0009	0.003	0.0002	0.004	0.021
7	0.077	0.076	0.0013	0.058	0.0191	0.077	−0.013
8	0.001	0.004	0.0029	0.003	0.0018	0.000	0.071
9	0.017	0.013	0.0036	0.016	0.0012	0.019	0.047
10	0.047	0.042	0.0045	0.047	0.0003	0.047	0.070
11	0.067	0.070	0.0025	0.046	0.0205	0.064	−0.004
12	0.080	0.075	0.0046	0.107	0.0267	0.078	0.042
13	0.071	0.066	0.0048	0.069	0.0024	0.070	−0.006
14	0.037	0.040	0.0032	0.050	0.0129	0.038	0.046
15	0.020	0.024	0.0043	0.019	0.0014	0.020	0.046

provides a detailed comparison of prediction results and absolute errors for both models on the testing set.

5.3. Productivity Zonation of Water Abundance

Based on the aforementioned findings, the prediction results from the CNN-BiLSTM neural network model were adopted to evaluate the water abundance characteristics of the weakly cemented sandstone aquifer in the No. 3 coal seam roof across the study area. Classification was performed according to the specific water yield (q), dividing the region into three zones—extremely weak water abundance (q < 0.01 L/(s·m)), weaker water abundance (0.01 ≤ q < 0.05 L/(s·m)), and weak water abundance (0.05 ≤ q < 0.1 L/(s·m)) [33]. To validate the model’s reliability, the same borehole samples from the testing set were utilized, with identical classification thresholds applied to both measured and predicted q values. Comparative analysis of the water abundance zonation maps derived from measured and predicted data revealed that the measured extremely low productivity zone was marginally larger than the predicted zone, with a similar minor discrepancy observed in the low productivity zone. However, the overall spatial distribution patterns exhibited strong agreement, confirming the model’s accuracy in water abundance prediction. The slight zonation differences may stem from localized hydrogeological complexities, but the model effectively captures the regional water abundance distribution, providing a robust theoretical foundation for subsequent hydrogeological assessments and engineering decisions.

As illustrated in Figure 10, the weakly cemented sandstone aquifer predominantly exhibits low productivity, with only a small area near the western flank of the 1301E working face showing slightly higher water abundance. For practical applications, integrated validation using borehole exploration and geophysical prospecting techniques is recommended. Strict adherence to coal mine safety protocols and operational standards is imperative to ensure mining safety.

6. Conclusions

This study addresses the prediction challenges of roof water hazards in weakly cemented mining areas of Northwest China by developing a CNN-BiLSTM hybrid neural network model, revealing the dynamic response mechanisms of aquifer water abundance under multifactorial synergies. Engineering validation at the 1301E working face of the Yili No. 1 Mine demonstrates three key findings:

(1)

The five-category controlling factor system (including aquifer burial depth and hydraulic conductivity), screened via the kriging interpolation and Pearson correlation coefficients, effectively quantifies the regulatory effects of fracture development and lithologic combinations in weakly cemented strata on water abundance;

(2)

The CNN-BiLSTM model achieves collaborative modeling of localized spatial features and global nonlinear relationships through deep integration of convolutional kernels (32 channels) and BiLSTM hidden layers (64 units), attaining test set prediction accuracy (RMSE = 1.57 × 10⁻³, R² = 0.9966) that improves by 85.2% over traditional FAHP methods, with 65.3% and 85.9% error reductions compared to the GA-BP and standalone CNN models, respectively;

(3)

The established three-tier water abundance zoning system (extremely weak/relatively weak/weak) achieves a 93.3% spatial consistency with field pumping test data, confirming the model’s engineering applicability under complex geological conditions.

The innovations of this study are twofold: (1) overcoming the limitations of traditional linear weighting methods to achieve dynamic characterization of multifactorial nonlinear synergies in water abundance prediction for weakly cemented strata; (2) establishing an engineering validation-oriented water abundance evaluation paradigm, providing a replicable technical framework for intelligent mine water hazard prevention. Future research will focus on multisource data integration, 3D geological model coupling, and real-time underground monitoring system development to further enhance the model’s engineering applicability and decision-support capabilities.