Prediction of Spontaneous Combustion Three-Zone Distribution in Gobs During the Terminal Mining Phase Based on WOA-BP Model

Abstract

During the terminal mining phase of in gobs, the advancing rate slows gradually, and the distribution of spontaneous combustion three-zone in gobs undergoes significant changes, yet there remains a lack of simple and effective prediction methods. To address this issue, the oxygen concentration distribution and temperature distribution data on both intake-side and return-side at longwall advancing rates of 2 m/d, 1.2 m/d, and 0.6 m/d were obtained through on-site monitoring. A generative adversarial network was employed to learn from measured data, generating additional usable data to build the dataset. Mining status parameters, oxygen concentration distribution, and temperature distribution were extracted as input variables. Whale optimization algorithm-back propagation model was proposed, establishing nonlinear mapping relationships between advancing rate and initiation depth of oxidation zone/asphyxiation zone. The results demonstrate that (i) the WOA-BP model can effectively predict distribution of spontaneous combustion three-zone during terminal mining phase, significantly improving prediction accuracy compared with BP and AdaBoost-BP; (ii) by SHAP feature analysis, contribution of advancing rate is the highest, which can provide reliable predictive performance; (iii) the slower the advancing rate, the closer the oxidation zone and the asphyxiation zone will be to working surface. This provides a foundational direction for preventing spontaneous combustion in gobs.

1. Introduction

Coal spontaneous combustion (CSC), recognized as an intrinsic geochemical phenomenon, has persisted through geological epochs with global evidence of subsurface autoignition events documented across diverse stratigraphic formations [1]. Coal spontaneous combustion severely impacts coal mine safety. The greenhouse gases and hazardous gases released during its combustion pose significant threats to both environmental safety and human health, and may even trigger gas explosions, resulting in substantial losses [2,3,4,5]. The terminal mining phase refers to the phase when the coal mining face advances to the designed stoppage line, where the advancing rate gradually slows down, coal recovery operations are progressively stopped, and preparations are conducted for equipment withdrawal, roof control, and gob closure. This phase is a crucial window period for preventing and controlling coal spontaneous combustion. Determining the distribution of spontaneous combustion three-zone in gobs during the terminal mining phase is the prerequisite for preventing spontaneous ignition in gobs areas, serving as the primary technical basis for measures such as nitrogen injection and air leakage sealing in gobs [6].

Domestic and international researchers have proposed various classification methods for the distribution of spontaneous combustion three-zone in gobs, with two approaches being generally recognized: the field measurement method and the numerical simulation method. Most Chinese academic and industrial researchers define these zones based on oxygen concentration and temperature in gobs, providing a basis for fire prevention in gobs [7,8,9,10]. Chen Weichong et al. [11] investigated the relationship between the three-zone of spontaneous combustion and horizontal pressure in gobs. Chen Long et al. [12] determined the boundaries of the three-zone by analyzing gas composition changes via buried pipe extraction. Yang Yongliang et al. [13] simulated gob roof collapse patterns through similarity experiments and conducted field measurements using bundled tubes. Computer-based simulation for dividing the distribution of spontaneous combustion three-zone in gobs involves establishing mathematical models, setting parameters, and simulating the three-zone under varying conditions [14,15]. Li Zongxiang [16] applied the two-field superposition principle to couple the air leakage seepage equation and oxygen consumption–diffusion equation in heterogeneous gobs, demonstrating that the three-zone are asymmetric. Li Dongfa et al. [17] used Fluent software to simulate the impact of nitrogen injection on the three-zone, building on oxygen concentration and temperature methods. Wen Hu et al. [18] employed Fluent to simulate changes in the three-zone before and after coal seam layering during mining. Pan Rongkun et al. [19] investigated gas concentration distribution in gobs using numerical simulation software and delineated the three-zone based on gas distribution characteristics. Neither method can effectively identify implicit correlations among variables or establish nonlinear mapping relationships, exhibiting poor working condition transferability.

Methods relying solely on buried pipelines for oxygen concentration monitoring or numerical simulation to delineate the distribution of spontaneous combustion three-zone in gobs are insufficient [20]. The introduction of machine learning methods becomes necessary. Kohonen [21] proposed an effective predictive tool—the BP model. Lei [22] and Zhang [23] utilized RF and SVM models to predict spontaneous combustion based on indicator gas concentrations in working faces. Wang Wei et al. [24] developed an SSA-RF model for coal spontaneous combustion in gobs, demonstrating strong stability and generalizability. Jin Yuping et al. [25] established a coal spontaneous combustion prediction model using neural networks. Deng Jun et al. [26,27] applied PCA-PSOSVM and SVM models for coal spontaneous combustion prediction. Wu Jianming et al. [28] and Zhou Fubao et al. [29] created coal spontaneous ignition prediction models via the BP model. Shao Liangshan et al. [30], Gao Yuan et al. [31], Jin Yuping et al. [32], and Meng Qian et al. [33] employed SVM to predict spontaneous ignition in gobs. The WOA-BP effectively addresses the bottlenecks of traditional machine learning models in multi-field coupling modeling of gobs, such as strong sensitivity to initial weights, easy trapping in local optima, and slow convergence speed, by introducing the intelligent search mechanism of whale groups to globally optimize and adaptively adjust network hyperparameters. This enhances the generalization and prediction capabilities of spontaneous combustion three-zone distribution in gobs during the terminal mining phase, providing a new paradigm for intelligent identification of spontaneous combustion hazard zones.

The oxygen concentration distribution and temperature distribution data on both intake-side and return-side at advancing rates of 2 m/d, 1.2 m/d, and 0.6 m/d were obtained through on-site monitoring. Through the GAN to learn the measured data, more usable data were generated to build the dataset, and then the BP, AdaBoost-BP, and WOA-BP models were trained. By inputting parameters such as advancing rate, gob depth, oxygen concentration, and peak temperature on the intake-side and return-side, the model simulates the initiation depth of oxidation zone and asphyxiation zone on both sides. It establishes nonlinear mapping relationships, compares predictive performance across multiple models, analyzes SHAP values of each feature, and identifies the nonlinear mapping relationships between advancing rate and the initiation depth of oxidation zone/asphyxiation zone in gobs during the terminal mining phase.

2. Data Construction

2.1. Field Measurement

Figure 1 shows the gob configuration and instrumentation layout in 8104 working face during the terminal mining phase at Zhuxianzhuang Coal Mine. The schematic adopts conventional ventilation orientation, with the upper section representing the return-side and the lower section the intake-side. The panel configuration features a strike length of 240 m, spanning 120 m along the working face length. Four monitoring points were strategically positioned along the dip direction on the intake-side, complemented by three equivalent monitoring stations on the return-side, maintaining 10 m spacing between adjacent points. Steel conduit protection systems were implemented at all measurement locations. Supplemental steel tubes containing bundled sensing lines were installed along the perimeter of both the intake-side and return-side. Daily monitoring protocols captured oxygen concentration and peak temperature distribution in gobs, with representative data compilation presented in Figure 2.

Figure 2 shows the results of the oxygen concentration and peak temperature distribution on both the intake-side and the return-side as the depth of the gob increases during the terminal mining phase when the advancing rate is reduced from 2 m/d to 1.2 m/d and then to 0.6 m/d. The peak temperature shows a trend of rising first and then falling, while the oxygen concentration gradually decreases. When $v_0$ = 2 m/d, the width of the oxidation zone on the intake-side is from 11m to 28m, and on the return-side, it is from 8 m to 24 m. When $v_0$ = 1.2 m/d, the width of the oxidation zone on the intake-side is from 7 m to 23 m, and on the return-side, it is from 5 m to 20 m. When $v_0$ = 0.6 m/d, the width of the oxidation zone on the intake-side is from 5.1 m to 18.9 m, and on the return-side, it is from 4.1 m to 17.8 m. From this, it can be seen that, in the terminal mining phase of longwall retreating, the distribution of the spontaneous combustion three-zone in gobs undergoes significant changes.

2.2. Generative Adversarial Network (GAN)

The GAN model primarily consists of two adversarial neural networks: the generator network and the discriminator network. The generator network is responsible for producing synthetic data, while the discriminator network evaluates whether the input data are real or generated. The generator continuously optimizes its output to deceive the discriminator, while the discriminator simultaneously refines its ability to distinguish real from synthetic data. This adversarial interplay drives mutual improvement. The model architecture is illustrated in Figure 3.

The loss function of the generator network is as follows:

$$L_{GE}=H(1,D(GE(z)))$$

(1)

In the equation above, $GE$ denotes the generator network, $H$ represents cross entropy, $D$ stands for the discriminator network, and $z$ is the input random data. $D\left(GE\right(z\left)\right)$ indicates the discriminator’s probability judgment for the generated data, where 1 signifies “absolutely real” data and 0 corresponds to “completely synthetic” data. $H(1,D(GE\left(z\right)\left)\right)$ measures the divergence between the discriminator’s output and the ideal value of 1.

The loss function of the discriminator network is as follows:

$$L_D=H\left(1,D\left(x\right)\right)+H\left(0,D\left(GE\left(z\right)\right)\right)$$

(2)

In the equation above, $x$ denotes real data, $H\left(1,D\left(x\right)\right)$ quantifies the divergence between the discriminator’s predictions for real data and the target label 1, and $H(0,D(GE\left(z\right)\left)\right)$ measures the divergence between the discriminator’s predictions for generated data and the target label 0.

During training, the generator network and discriminator network engage in adversarial training. The generator network continuously adjusts its parameters to produce increasingly realistic data that can fool the discriminator network, while the discriminator network iteratively improves its ability to distinguish real from synthetic data. This iterative process continues until an equilibrium point is reached, where the generator network can generate highly realistic data, and the discriminator network is unable to reliably differentiate between generated and real samples.

Figure 4 shows the iteration process of the GAN model. With increasing iteration numbers, the loss values of both the discriminator network and generator network progressively decrease, demonstrating convergence characteristics. When the iteration count reaches the range from 13,500 to 15,000, their numerical values dynamically overlap. This is because in the initial game stage (iterations < 5000), the discriminator network, needing to quickly learn the difference between the real data distribution and the generated samples, has an initial loss value significantly higher than that of the generator network. However, as the gradient descent mechanism in backpropagation is activated, the discriminator network adapts and adjusts the data boundary, causing the loss value to decrease at an exponential rate. In the mid-term equilibrium stage (iterations: 5000–13,500), under the continuous pressure from the discriminator network in the game environment, the generator network gradually optimizes the multi-scale statistical features of the synthetic data, and the slopes of their loss curves converge, narrowing the difference in convergence rates. During the dynamic overlap stage (iterations: 13,500–15,000), the discriminator network and the generator network form a steady-state adversarial relationship, with the fluctuation range of the loss values of both networks dropping to within ±0.3. The dynamic overlap characteristic of their values indicates that the data generated by the model has become indistinguishable from the real measured data of the gob, exhibiting extremely high realism; this phenomenon directly verifies the accuracy of the GAN in this data enhancement task.

Table 1. Dataset.

Input Features	Value Range	Output Features	Total Number of Data
$v_0$ (m/d)	0.3–3	$D_{io}$ (m) $D_{ia}$ (m) $D_{ro}$ (m) $D_{ra}$ (m)	200
$D_i$ (m)	0–30
$C_{O_i}$ (%)	0–21
$T_i$ (℃)	20–40
$D_r$ (m)	0–30
$C_{O_r}$ (%)	0–21
$T_r$ (℃)	20–40

shows the dataset generated by the GAN model, which conforms to the on-site testing rule.

3. Establishing the WOA-BP Model

3.1. Dataset Preprocessing

Based on the established dataset, since the magnitude and variation ranges of individual features differ significantly, data standardization is required. This follows the Min-Max normalization.

$$X_{cd}^{\prime }={\displaystyle \frac{X_{cd}-X_{cmin}}{X_{cmax}-X_{cmin}}}$$

(3)

In this formulation, ${X^{\prime }}_{cd}$ represents the normalized value of the $d$-th data point in the $c$-th feature; $X_{cd}$ denotes the original value of the $d$-th data point in the $c$-th feature; $X_{cmin}$ is the minimum value in the $c$th feature, and $X_{cmax}$ is the maximum value in the $c$-th feature.

The standardized dataset is randomly divided into two subsets: 80% of the samples are used as the training set to train the model, and the remaining 20% are reserved as the test set to evaluate the model’s performance.

3.2. Whale Optimization Algorithm-Back Propagation (WOA-BP)

A backpropagation algorithm employs gradient descent for parameter optimization. However, when the error function contains multiple local minima, the backpropagation algorithm cannot guarantee convergence to the global minimum, meaning parameter optimization may become trapped in local minima. The hidden layer is set to 2, the learning rate is set to 0.01, the optimizer uses Adam, and the activation function uses ReLU. To obtain the best-trained model, the WOA is introduced for global parameter optimization. By optimizing initial weights and biases with WOA, the neural network starts training with near-optimal initial weight and bias values, enabling better convergence toward the global minimum and enhanced generalization capability. The model architecture is illustrated in Figure 5.

The implementation of the algorithm primarily involves four steps:

Step 1: Initialize whale population parameters and positions

$$X_a=(X_{i1},X_{i2},X_{i3},\dots ,X_{i2048})$$

(4)

$X_a$ denotes the position of the $a$-th whale.

Step 2: Calculate individual and group fitness. The feature weight $p\left(i\right)$ for the input features in the dataset during the $i$-th iteration of the model is determined using the following formula:

$$f[X_i(t|G)]={\displaystyle \frac{1}{n}}{\displaystyle {\displaystyle \sum }_{k=1}^n}{(y_k-\widehat{y_k})}^2\dots \dots 1\le t\le G$$

(5)

$$p(i)=arg\underset{X_i(t|G)}{\min }f[X_i(t|G)]$$

(6)

$X_i\left(t|G\right)$ denotes the feature weight updated to the $t$-th iteration during the $i$-th model iteration; $f\left[X_i\left(t|G\right)\right]$ represents the fitness of feature weight ${ X}_i\left(t|G\right)$; $t\in G$, where $G$ is the total update count of input features per model iteration; $t$ and $G$ are positive integers. The parameter $n$ indicates the number of training samples in the dataset, $y_k$ is the output of the $k$-th training sample group in the dataset, and $\widehat{y_k}$ denotes the model’s predicted result derived from the input features of the $k$-th training sample group. All variables satisfy $1\le k\le n$, with $k$ and $n$ being positive integers.

Step 3: Update whale positions. Whales determine the optimal feature weight $X_i^{\ast }\left(t\right)$ of input features during the $t$-th update in the $i$-th model iteration through three mechanisms: encircling prey, spiral attacking prey, and random search.

(1) A random number $p\in \left[0,1\right]$ is selected for feature update. When $p<0.5$ and $A=\left|(2r_1-1)\times (2-2\times {\displaystyle \frac{t}{G}})\right|<1$, the encircling prey mechanism determines the optimal feature weight $X_i^{\ast }\left(t\right)$ of the input features during the $t$-th update in the $i$-th model iteration, formulated as follows:

$$X_i(t+1|G)=X_i^{\ast }(t)-(2r_1-1)\times (2-2\times {\displaystyle \frac{t}{G}})\cdot |2\cdot r_2\cdot X_i^{\ast }(t)-X_i(t|G)|$$

(7)

$$X_i^{\ast }(t)=arg\underset{X_i(m|t)}{\min }f[X_i(m|t)]$$

(8)

$X_i\left(t|G\right)$ denotes the feature weight of the input feature updated to the $t$-th step in the $i$-th iteration; $X_i\left(t+1|G\right)$ represents the feature weight updated to the $t+1$-th step in the $i$-th iteration; $X_i\left(m|t\right)$ indicates the feature weight at the $m$-th step during the $t$-th update process in the $i$-th iteration; $f\left[X_i\left(m|t\right)\right]$ is the fitness value of feature weight $X_i\left(m|t\right)$; $t$ denotes the current update step of the input feature; $G$ represents the total update steps per iteration; $r_1$ and $r_2$ are two random numbers between 0 and 1.

(2) When $p<0.5$ and $A=\left|(2r_1-1)\times (2-2\times {\displaystyle \frac{t}{G}})\right|\ge 1$, the stochastic prey search strategy is adopted to determine the optimal feature weight $i_{\ast }^{ X}\left(t\right)$ during the $t$-th update process in the $i$-th iteration of the predictive model, formulated as follows:

$$X_i(t+1|G)=X_i^{\ast }(t)-(2r_1-1)\times (2-2\times {\displaystyle \frac{t}{G}})\cdot r_1\cdot |2\cdot r_2\cdot X_i^{\ast }(t)-X_i(t|G)|$$

(9)

$$X_i^{\ast }(t)=arg\underset{X_i(m|t)}{\min }f[X_i(m|t)]$$

(10)

(3) When $p\ge 0.5$, the spiral prey attack strategy is adopted to determine the optimal feature weight $X_i^{\ast }\left(t\right)$ during the $t$-th update process in the $i$-th iteration of the model, formulated as follows:

$$X_i(t+1|G)=|X_i^{\ast }(t)-X_i(t|G)|\cdot e^{b\left[\left(-1-{\displaystyle \frac{t}{G}}-1\right)\cdot r_3+1\right]}\cdot cos(2\pi \left[\left(-1-{\displaystyle \frac{t}{G}}-1\right)\cdot r_3+1\right])+X_i^{\ast }(t)$$

(11)

$$X_i^{\ast }(t)=arg\underset{X_i(m|t)}{\min }f[X_i(m|t)]$$

(12)

$b$ is a constant, and $r_3$ is a random number between 0 and 1.

Based on the optimal position of the whale, i.e., the fitness value $f\left[p\left(i\right)\right]$ of the feature weight $p\left(i\right)$, the optimal position $P_g\left(Q\right)$ of the model throughout the entire iteration process is determined. According to the following formula:

$$P_g(pop)=arg\underset{p(i)}{\min }f[p(i)]\cdots \cdots 1\le i\le Q$$

(13)

$$f[p(i)]=minf[X_i(t|G)]\cdots \cdots 1\le t\le G$$

(14)

$p\left(i\right)$ represents the feature weight of input features in the dataset during the $i$-th iteration of the model; $Q$ denotes the total number of iterations of the model, where both $i$ and $pop$ are positive integers; $G$ indicates the total number of updates; $f\left[p\left(i\right)\right]$ corresponds to the fitness of $p\left(i\right)$; $X_i\left(t|G\right)$ represents the feature weight of input features updated to the $t$-th update under $G$; $f\left[X_i\left(t|G\right)\right]$ denotes the fitness corresponding to the feature weight $X_i\left(t|G\right)$.

Step 4: Check whether the stopping criteria are met. If not, repeat steps 2–3; if met, proceed to obtain the optimal solution.

4. Analysis of Results

4.1. Model Evaluation

To evaluate the model’s performance, three metrics were adopted as evaluation criteria: mean absolute error, mean squared error, and coefficient of determination. The corresponding mathematical formulas are listed in

Table 2. Evaluation indicators and its calculation formula.

Evaluation Indicators	Calculation Formula
Mean absolute error	$MAE={\displaystyle \frac{1}{n}}{\displaystyle {\displaystyle \sum }_{i=1}^n}\left|y_i-{\widehat{y}}_i\right|$
Mean squared error	$MSE={\displaystyle \frac{1}{n}}{\displaystyle {\displaystyle \sum }_{i=1}^n}{(y_i-{\widehat{y}}_i)}^2$
Coefficient of determination	$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}}{{\displaystyle \sum _{i=1}^n{(y_i-\overline{y})}^2}}}$

. MAE is a function used to measure the discrepancy between predicted and true values in regression problems. It exhibits insensitivity to outliers, demonstrates a linear relationship between error magnitude and impact, and provides easily interpretable results with unit consistency with the original data, thereby offering superior intuitiveness. MSE calculates the average of squared differences between predicted and true values. The squared term amplifies larger errors, enhancing sensitivity to outliers for capturing their adverse effects. Its gradient decreases proportionally with error reduction, facilitating model convergence while maintaining sensitive identification capability and optimization efficiency. R² metric quantifies the goodness-of-fit and strength of linear relationships in regression models. By directly reflecting the explanatory power of independent variables on dependent variables, it enables effective variable selection and optimal model identification through numerical comparisons.

In the equations, $n$ denotes the sample size, $y_i$ and ${\widehat{y}}_i$ represent the actual value and predicted value, respectively, and $\overline{y}$ indicates the mean of actual values. Smaller MAE and MSE values, along with an R² value closer to 1, indicate superior predictive performance of the model.

4.2. Comparative Analysis

To verify whether the WOA-BP model effectively improves accuracy, this work conducted a comparative analysis to examine the variations in performance evaluation indicators and the predictive accuracy of the BP, AdaBoost-BP, and WOA-BP models.

Table 3. Evaluation indicators results of each model.

Model	MAE	MSE	R2
BP	0.776	1.496	0.948
AdaBoost-BP	0.685	0.689	0.979
WOA-BP	0.378	0.296	0.990

and Figure 6 show that the WOA-BP model achieves the smallest MAE and MSE while attaining the maximum R² value, demonstrating optimal prediction performance with significant improvement in model capability. Compared to the BP model, the WOA-BP model reduces MAE by 51.29% from 0.776 to 0.378, decreases the MSE by 80.21% from 1.496 to 0.296, and improves the R² by 4.43% from 0.948 to 0.990. This is because WOA-BP introduces the global search capability of the whale optimization algorithm, automatically optimizes hyperparameters, avoids the risk of falling into local optima, identifies optimal initial weights and biases, effectively addresses the shortcomings of traditional BP model including susceptibility to local optima, slow convergence, and dependence on manual parameter adjustments, and achieves improvements in accuracy, speed, and robustness. When compared to the AdaBoost-BP model, the WOA-BP model achieves a 44.82% reduction in MAE (from 0.685 to 0.378), a 57.04% reduction in MSE (from 0.689 to 0.296), and a 1.12% increase in R² (from 0.979 to 0.990). This is because the AdaBoost-BP model enhances overall model prediction performance through ensemble learning, where its effectiveness depends on the performance of base learners. However, the training of base learners involves randomness, which cannot guarantee high performance of every base learner. Whereas the WOA-BP model improves model performance through global hyperparameter optimization, thereby avoiding such issues. These results show that the prediction performance of the model is significantly enhanced by the WOA-BP model.

Figure 7 shows the training processes of the BP, AdaBoost-BP, and WOA-BP models—mainly the changes in training loss and determination coefficients. It can be seen that the WOA-BP model converges approximately after 700 iterations, with the fastest convergence, the smallest overall fluctuation, the lowest loss, and the highest determination coefficient. However, BP converges the slowest and has the greatest overall fluctuation. This is because neural networks need to constantly adjust weights and biases and require more iterations and time to converge. The AdaBoost-BP model converges slowly and has a large overall fluctuation. The effect after 10,000 iterations is better than that of the BP model. This might be because multiple base models need to be adjusted, the training time is longer, and the results after combining multiple base models are better than those of a single BP model.

Figure 8 shows the comparison between the predicted values and the actual values of each model, intuitively reflecting the predictive performance of each model. It can be observed that both the BP and AdaBoost-BP models exhibit an overall trend of first rising, then declining, and subsequently rising again in their predictions for both intake-side and return-side, which contradicts the actual situation. Specifically, the BP model shows significant fluctuations and excessive deviations between predicted and actual values in the advancing rate ranges of 1.0–2.5 m/d on the intake-side and 1.2–2.5 m/d on the return-side. Similarly, the AdaBoost-BP model demonstrates substantial prediction volatility with considerable deviations in the advancing rate ranges of 0.7–2.2 m/d on the intake-side and 1.2–2.5 m/d on the return-side. These observations indicate that there exists complex nonlinear mapping relationships between the advancing rate and the initiation depth of oxidation zone/asphyxiation zone in gobs, which the BP and AdaBoost-BP models have only approximately established, resulting in inadequate prediction accuracy. In contrast, the WOA-BP model demonstrates an overall upward trend that precisely matches the actual variation pattern, successfully establishing accurate nonlinear mapping relationships from advancing rate to the initiation depth of oxidation zone/asphyxiation zone in gobs.

In summary, it can be known that the WOA-BP model achieves robustness and accuracy of the model through global search and automatic optimization of hyperparameters. It has better generalization ability and stronger predictive ability and can effectively complete the established goals.

5. Feature Validation and Discussion

The SHAP framework, based on the calculation of Shapley values, is used to measure how features influence the dependent variable [34]. SHAP feature analysis has a strong versatility, which can solve the ‘black box dilemma’ and explain and verify the decision-making of deep learning. Its global interpretation logic is unified, non-contradictory, and can distinguish between ‘positive contribution’ and ‘negative contribution’ of features. The feature importance ranking plot arranges the contribution of each input feature to the output results, quantifying the relative contribution sizes. The SHAP-based feature analysis summary plot aims to show how features in the dataset affect the model output. Such visualization results help to understand how different features contribute to and influence the model’s predictions.

The SHAP value of feature ${\Phi }_j$ is defined as follows:

$${\varphi }_j = {\displaystyle \frac{1}{\left|N\right|!}}{\displaystyle \sum _{S\subseteq Nleftj}\left|S\right|!(\left|N\right|-\left|S\right|}-1)!\left[f\left(S\cup \left\{j\right\}\right)-f\left(S\right)\right]$$

(15)

where $N$ represents the original feature set, $f\left(S\right)$ represents the output of the feature subset $S$ in the model, and $f(S\cup \{j\left\}\right)-f\left(S\right)$ represents the cumulative contribution value of the feature $j$.

Figure 9 shows that the advancing rate plays a dominant role in the initiation depth of the oxidation zone and asphyxiation zone, with the peak temperatures on the corresponding side being secondary. Furthermore, for the initiation depth of intake-side oxidation zone, the intake-side oxygen concentration and the return-side peak temperature have relatively higher importance; for the initiation depth of intake-side asphyxiation zone, the intake-side gob depth and the intake-side oxygen concentration are of greater importance; for the initiation depth of return-side oxidation zone, the return-side oxygen concentration and the intake-side peak temperature are more significant; and for the initiation depth of return-side asphyxiation zone, the return-side oxygen concentration and the return-side gob depth have relatively higher importance. The importance values of other feature parameters are relatively low, but they still make a certain contribution to the prediction results and occupy a certain level of importance in the model. Therefore, in order to achieve the best prediction effect, when predicting the distribution of spontaneous combustion three-zone in gobs during the terminal mining phase, it is obvious that the advancing rate should be given priority, followed by other parameters.

Figure 10 shows that the blue dots for the advancing rate are mostly in the negative region, while the red dots are concentrated in the positive region, indicating that the higher advancing rate results in the greater initiation depth of the oxidation zone and asphyxiation zone. This is because the faster advancing rate leaves insufficient time for coal and oxygen to react fully, thereby increasing the initiation depth of the oxidation zone and asphyxiation zone. For the peak temperature, the blue dots are mostly in the positive region, while the red dots are concentrated in the negative region, suggesting that the higher temperatures correspond to the smaller initiation depth of the oxidation zone and asphyxiation zone. This is due to the heat released from coal-oxygen reactions, which consumes a significant amount of oxygen and reduces the initiation depth of the oxidation zone and asphyxiation zone. Additionally, the blue dots for oxygen concentration and gob depth are mostly in the negative region, while the red dots are concentrated in the positive region. The results show that, among the stated parameters, the advancing rate, oxygen concentration, and gob depth are positively correlated with the initiation depth of the oxidation zone and asphyxiation zone, while the peak temperature is negatively correlated with the initiation depth of the oxidation zone and asphyxiation zone, all of which are consistent with the actual situations.

6. The Relationships Between Advancing Rate and Three-Zone Distribution

Based on the trained WOA-BP model, predictions were made for the initiation depth of oxidation zone and asphyxiation zone on both sides of gobs. These led to the determination of the fitting relationships formula between advancing rate and the initiation depth of oxidation zone and asphyxiation zone in gobs during the terminal mining phase. The results are illustrated in Figure 11.

Figure 11 shows that when the advancing rate of the working face decreases from 3.6 m/d to 0.15 m/d, the initiation depth of intake-side oxidation zone shortens from 16.1 m to 3.97 m, the initiation depth of intake-side asphyxiation zone shortens from 38.1 m to 15.6 m, the initiation depth of return-side oxidation zone shortens from 13.48 m to 2.68 m, and the initiation depth of return-side asphyxiation zone shortens from 35.05 m to 14 m. This phenomenon reveals the dynamic coupling relationships between the advancing rate and the distribution of spontaneous combustion three-zone in gobs: As the advancing rate decreases, the distribution of oxygen will also diffuse near gobs, and the oxidation zone and the asphyxiation zone are getting closer and closer to the working face, and the widths of the oxidation zone and the asphyxiation zone also decrease. This is because the slower the advancing rate, the less the air leakage volume will be. As a result, the oxygen in gobs can fully react in time, leading to an increase in the amount of oxygen consumed. This causes the oxygen distribution to penetrate near gobs, thereby decreasing the width of the oxidation zone and asphyxiation zone. These findings establish a theoretical basis for preventing spontaneous combustion in gobs.

7. Conclusions

This work aims to predict the initiation depth of the oxidation zone and asphyxiation zone in gobs during the terminal mining phase by the WOA-BP model. By monitoring the advancing rate and the oxygen concentration, and the peak temperature distribution on both sides during the terminal mining phase, the nonlinear mapping relationships between the advancing rate and the initiation depth of oxidation zone/asphyxiation zone in gobs were obtained. This points out a new direction for the prevention and control strategy of spontaneous combustion in gobs. The main conclusions of the work are summarized as follows.

The prediction results indicate that the BP model and AdaBoost-BP model fall short in meeting the prediction requirements for this task, but the WOA-BP model ensures prediction errors of less than 5%. The WOA-BP model demonstrates superior generalization capability in prediction and can achieve better outcomes in fewer iterations.

The SHAP feature analysis indicates that the advancing rate contributes the most to the initiation depth of the oxidation zone and asphyxiation zone on both sides. In order to achieve the best prediction effect when predicting the distribution of spontaneous combustion in three-zone gobs during the terminal mining phase, it is obvious that the advancing rate should be given priority.

The prediction results indicate that as the advancing rate decreases, the distribution of oxygen will also diffuse near gobs, and the oxidation zone and the asphyxiation zone are getting closer and closer to the working face, and the widths of the oxidation zone and the asphyxiation zone also decrease.