Joint Prediction of Goaf Temperature and CO Concentration Using Multi-Source Monitoring Feature Fusion and CA-WOA-Optimized Models

Abstract

Variations in goaf temperature and CO concentration during low-temperature oxidation are jointly affected by residual-coal oxidation, air-leakage oxygen supply, gas generation, migration, dilution, and ventilation disturbance, resulting in nonlinear multi-source responses. This study investigated a joint prediction framework based on multi-source monitoring feature fusion and covariance-adaptive whale optimization algorithm (CA-WOA)-optimized models. Daily monitoring data from goaf pipes, the working face, the upper corner, and the return-air side were integrated. Pearson correlation analysis and random forest feature-importance ranking were used to construct top-$k$ feature subsets. CA-WOA incorporates rank-weighted elite-center reconstruction, covariance-adaptive direction learning, WOA random-search injection, and geometric step-size decay, and was used to optimize RF, XGBoost, LightGBM, CatBoost, LSSVM, and TABM under a unified dual-output fitness function. CA-WOA improved all six models, with a maximum mean $R^2$ increase of 0.076 and a maximum fitness reduction of 22.8%. CA-WOA–TABM achieved the best fivefold performance, with a mean $R^2$ of 0.924 and $F=0.273$, while its out-of-fold $R^2$ values for temperature and CO concentration were 0.928 and 0.931, respectively. On the additional 1202 working-face dataset, TABM achieved a later-period test $R_{\mathrm{C}\mathrm{O}}^2$ of 0.766 under chronological splitting, and CA-WOA–TABM obtained a fivefold mean $R_{\mathrm{C}\mathrm{O}}^2$ of 0.948. SHAP and PDP analyses identified GoafPipe_CH4, GoafPipe_CO2, GoafPipe_C2H6, and GoafPipe_O2 as the main predictive variables.

1. Introduction

Coal remains a fundamental energy source in the global energy supply system and plays a crucial role in China’s energy security. Despite the rapid development of renewable energy, coal is still indispensable for electricity generation, industrial production, and basic energy supply [1]. Mine fires are a major threat to coal mine safety, and spontaneous coal combustion is one of their principal causes. Some statistics indicate that spontaneous coal combustion accounts for approximately 90% of mine fire events, leading to resource losses, production interruption, and secondary hazards such as gas explosions [2]. As mining depth increases, the occurrence of residual coal, air-leakage oxygen supply, and heat accumulation in goafs becomes more complex, thereby increasing the uncertainty of internal temperature evolution and gas migration processes [3]. In an actual working-face goaf, monitoring points such as goaf pipes, upper corners, return-air sides, and working-face sides reflect different aspects of the system. Therefore, a single monitoring point or gas indicator is insufficient to fully characterize the low-temperature oxidation state, and multi-source monitoring information is required to jointly describe oxidation-related gas generation and thermal evolution in the goaf [4].

The low-temperature oxidation mechanism of spontaneous coal combustion provides the basis for selecting monitoring indicators and evaluating coal temperature. Anghelescu et al. [2] and Liu et al. [5] reported that exothermic low-temperature oxidation caused by coal–oxygen interaction is the core process underlying the incubation of spontaneous coal combustion. A rise in temperature further accelerates oxidation reactions and promotes heat accumulation. Ma et al. [6] combined programmed heating with Fourier-transform infrared spectroscopy (FTIR) to analyze gas-release differences at different oxidation stages and suggested that CO, C₂H₄, and the Graham coefficient can serve as important discriminant indicators. Liu et al. [7] used wavelet analysis to reveal the multi-scale evolution of CO and O₂ volume fractions in different areas of a working face. These studies show that O₂, CO, CO₂, and hydrocarbon gases can reflect the degree of coal oxidation; however, their responses are jointly affected by coal quality, oxygen supply, temperature stage, and sampling location [8].

Spontaneous goaf coal combustion differs from the oxidation of a single coal sample. Its occurrence and development are controlled by residual-coal distribution, air-leakage oxygen supply, overburden fractures, heat accumulation, and ventilation boundaries [3]. Zhang et al. [9] pointed out that multifactor coupled hazards become more prominent under deep mining conditions, and monitoring-based identification should develop toward spatiotemporal, multi-scale, and multiparameter approaches. Jin et al. [10] summarized the insufficient field observability and spatial inversion difficulties associated with hidden fire-source localization. Zhai et al. [11] revised the relationship between CO and coal temperature under air-leakage conditions and established a corresponding discrimination method. These findings indicate that the low-temperature oxidation state of a goaf is not directly determined by a single gas indicator. Instead, it is jointly shaped by oxygen supply, oxidation heat release, gas generation, air-leakage dilution, and migration lag. Consequently, variations in temperature and CO concentration depend more strongly on the joint characterization of multi-source information [5].

Traditional discrimination methods for spontaneous coal combustion mainly rely on indicator gases, composite gas ratios, critical temperatures, and empirical thresholds. A previous study [12], Hao et al. [13], and Zhang et al. [14] developed discrimination criteria based on composite gas characteristics, the Graham coefficient, and multi-indicator collaborative analysis. Wang et al. [15] and Zhongyu et al. [16] further improved traditional methods by analyzing CO source identification and gas–temperature statistical relationships. These methods have clear physical meanings and are convenient for engineering deployment. However, under air-leakage dilution, gas-response lag, multipoint differences, and spatial coupling, fixed thresholds are difficult to use for a stable description of the continuous evolution process during the low-temperature oxidation stage [11].

With the accumulation of mine monitoring data, machine-learning methods have increasingly been applied to coal temperature prediction and spontaneous coal combustion state identification. Wang et al. [16] developed a BPNN model based on gas composition, spatial distance, and coal temperature data for spatiotemporal temperature prediction. Lei et al. [8] established an RF model using programmed-heating data from coal samples collected from 12 coal mines and compared it with GBM, BPNN, and KNN, confirming the effectiveness of multi-indicator gases for coal temperature prediction. Zhuo et al. [17] and Zou et al. [18] applied PSO-XGBoost to coal temperature or spontaneous combustion tendency prediction, indicating that swarm-intelligence optimization can improve parameter selection and model accuracy. Guo et al. [19] combined PSO with GRU for coal temperature inversion in concealed spaces, enhancing the nonlinear mapping from gas indicators to coal temperature. For state identification, Zhang et al. [20] used t-SNE and k-means for spontaneous coal combustion state classification. Li et al. [21] constructed an NSGA-II-RF prediction model. Long et al. [22] applied BO-LightGBM for coal temperature prediction and state discrimination. Pan et al. [23] represented gas associations through GCN, while Zhao et al. [24] and Liu et al. [25] improved model generalization and joint identification from the perspectives of ensemble modeling and multitask learning, respectively. Overall, existing studies have promoted the transition of spontaneous coal combustion monitoring from empirical thresholds to data-driven methods. Nevertheless, many studies are still oriented toward coal-sample experiments or general goaf scenarios. The fusion of multi-source information, including goaf-pipe gas, working-face gas, upper-corner gas, return-air-side gas, and ventilation disturbance, remains insufficient. In addition, most studies focus on single coal temperature prediction or state classification, while less attention has been paid to the continuous joint prediction of temperature and CO concentration during the low-temperature oxidation stage.

To address these issues, this study focused on the low-temperature oxidation stage of a working-face goaf and investigated a joint prediction method for temperature and CO concentration based on multi-source monitoring feature fusion and CA-WOA–TABM. First, multi-source monitoring variables, including goaf-pipe gas, working-face-side gas, upper-corner gas, and return-air-side gas, were integrated to construct a daily-scale sample system. Correlation analysis and tree-model feature importance were then combined to select dominant features. Second, a covariance-adaptive whale optimization algorithm (CA-WOA) was developed from the original WOA. Through rank-weighted elite-center reconstruction, covariance-adaptive direction learning, WOA random-search injection, and geometric step-size decay, the search stability in complex hyperparameter spaces was improved. The composite normalized error of temperature and CO concentration was used as the optimization objective to adaptively optimize six candidate regression models. Finally, SHAP and PDP methods were used to interpret the contribution magnitude, effect direction, and response ranges of key gas indicators for the dual-output prediction results, providing data-driven support for continuous characterization of the low-temperature oxidation state of the goaf.

2. Models and Methods

2.1. Overall Framework

This study constructed a joint prediction framework based on multi-source monitoring feature fusion and CA-WOA–TABM for the continuous prediction of goaf temperature and CO concentration during the low-temperature oxidation stage. As shown in Figure 1, the overall workflow consists of five components: data preprocessing, key feature screening, CA-WOA-based hyperparameter optimization, dual-output prediction using candidate regression models, and SHAP/PDP interpretation. The framework takes multi-source monitoring data as input and uses goaf temperature and CO concentration as dual-output targets, thereby characterizing the low-temperature oxidation process from the perspectives of thermal-state evolution and gas-generation response.

In the data preprocessing stage, variables related to goaf-pipe gas, upper-corner gas, return-air-side gas, working-face-side gas, and ventilation disturbance are organized in a unified manner. Outlier identification, incomplete-record screening, temporal alignment, daily-scale aggregation, and robust standardization are then performed sequentially to form a daily-scale multi-source monitoring dataset. The model outputs are defined as goaf temperature and CO concentration. Temperature is used to characterize the evolution of the goaf thermal state, whereas CO concentration reflects the gas-generation response during low-temperature oxidation [26]. Because the monitoring period mainly corresponded to the low-temperature oxidation stage, this study did not construct a multilevel early-warning classification model, but focused on continuous prediction.

In the feature-screening stage, correlation analysis and tree-model importance evaluation are combined to identify key variables. Correlation analysis is used to describe statistical associations between monitoring variables and prediction targets, whereas random forest-based feature importance is used to evaluate the nonlinear contribution of variables to the dual-output task. Based on the integrated importance ranking, different top-k feature subsets are constructed and separately input into six candidate regression models, namely RF, XGBoost, LightGBM, CatBoost, LSSVM, and TABM. This procedure aims to determine a compact feature combination that balances prediction accuracy, model complexity, and interpretability.

In the model optimization stage, CA-WOA is introduced to optimize the key hyperparameters of the six candidate regression models. The composite normalized error of temperature and CO concentration is used as a unified fitness function, enabling the parameter search to account for both output targets simultaneously and reducing the risk of optimizing the model toward only one variable. After optimization, all models are evaluated using the same feature subset and evaluation criteria under fivefold cross-validation, and out-of-fold predictions are used to assess internal validation stability.

In the interpretation stage, SHAP and PDP methods are applied to the better-performing models. SHAP quantifies the global contribution and local effects of key monitoring variables on temperature and CO predictions, whereas PDP analyzes the marginal response trends of model outputs as important variables and their combinations vary. Through this workflow, the study establishes a complete modeling chain from multi-source monitoring data fusion, key feature screening, and adaptive hyperparameter optimization to model interpretation, providing a data-driven method for the continuous characterization of the low-temperature oxidation state of the goaf.

2.2. Integrated Feature Ranking and Candidate-Subset Construction

Multi-source monitoring variables are collected from different spatial locations, including goaf pipes, upper corners, return-air sides, and working-face sides, and can reflect changes in the low-temperature oxidation state at different spatial scales. However, strong correlations and information redundancy may exist among these variables. If all variables are directly used as input features, model complexity may increase and internal validation stability may be weakened. Therefore, before model training, a tree-model-based dominant feature selection method is introduced to rank the importance of multi-source variables in a unified manner. This procedure constructs a compact and effective input-feature subset and provides a basis for subsequent CA-WOA optimization and model comparison.

The basic idea of tree-model-based feature selection is that if a variable participates in node splitting and substantially reduces sample uncertainty, it contributes more to the prediction task [27]. For a regression problem, node impurity is usually measured by the mean squared error. When feature $x_j$ divides a sample set $S$ into the left and right subsets $S_L$ and $S_R$, the impurity reduction can be defined as:

$$\Delta I_j=I(S)-{\displaystyle \frac{\mid S_L\mid }{\mid S\mid }}I(S_L)-{\displaystyle \frac{\mid S_R\mid }{\mid S\mid }}I(S_R)$$

(1)

Random forests integrate multiple regression trees and can effectively reduce the randomness associated with a single tree. The impurity reduction contributed by feature $x_j$ is accumulated over all trees and all relevant splitting nodes and then normalized to obtain its feature-importance index $F{I}_j$. A larger $F{I}_j$ indicates a greater contribution of the corresponding variable to target prediction.

Because this study addressed a dual-output prediction task involving goaf temperature and CO concentration, the importance ranking derived from a single target cannot fully reflect the role of each variable. Therefore, two random forest regression models are trained separately using temperature and CO concentration as output targets, yielding the corresponding importance values $F{I}_j^T$ and $F{I}_j^{CO}$. The two sets of importance values are then normalized and fused as:

$$F{I}_j^{\ast }={\displaystyle \frac{1}{2}}{\widetilde{FI}}_j^T+{\displaystyle \frac{1}{2}}{\widetilde{FI}}_j^{CO}$$

(2)

where ${\widetilde{FI}}_j^T$ and ${\widetilde{FI}}_j^{CO}$ denote the normalized single-target importance values for temperature and CO concentration, respectively, and $F{I}_j^{\ast }$ represents the integrated feature contribution for the dual-output prediction task.

All variables are ranked in descending order according to $F{I}_j^{\ast }$, and top-$k$ feature subsets are constructed as:

$$F_k=\{x_{\left(1\right)},x_{\left(2\right)},\dots ,x_{\left(k\right)}\},k=1,2,\dots ,p$$

(3)

where $p$ is the total number of candidate features and $x_{\left(k\right)}$ denotes the feature ranked $k$-th by integrated importance. The different top-$k$ subsets are then input into six candidate regression models, namely RF, XGBoost, LightGBM, CatBoost, LSSVM, and TABM, under a unified evaluation framework. The final feature subset is selected by jointly considering prediction accuracy, model complexity, and interpretability, and is subsequently used for CA-WOA hyperparameter optimization and model performance analysis.

The feature-screening procedure consists of two stages: integrated feature-importance ranking and validation of top-$k$ candidate subsets. The integrated importance scores are used to establish the relative contribution order of the candidate variables, whereas the final input dimensionality is determined by evaluating the predictive performance of feature subsets of different sizes. This procedure combines contribution assessment with subset-level performance validation, rather than determining a fixed number of input variables solely from a single importance ranking.

2.3. TABM Regression Model

TABM is a parameter-efficient deep model designed for tabular data. Its core idea is to construct multiple implicit submodels within a shared MLP framework and to generate prediction diversity through lightweight parameter modulation [28]. Unlike conventional ensemble models that require multiple independently trained networks, TABM shares backbone-network parameters and uses only a small number of submodel-specific adaptation vectors. This design provides ensemble-like stability with relatively low computational cost.

Let the input sample be $x\in {\mathbb{R}}^p$, where $p$ is the input-feature dimension. The $l$-th layer of a standard MLP can be written as:

$$h^{\left(0\right)}=x,h^{\left(l\right)}=\varphi \left(W^{\left(l\right)}{h}^{\left(l−1\right)}+b^{\left(l\right)}\right),l=1,\dots ,L$$

(4)

where $h^{\left(l\right)}$ is the hidden representation at layer $l$, $W^{\left(l\right)}$ and $b^{\left(l\right)}$ are the weight matrix and bias term, respectively, and $\varphi (\cdot )$ denotes the nonlinear activation function.

TABM introduces $K$ implicit submodels on this shared MLP backbone. For the $k$-th submodel, the $l$-th layer representation is defined as:

$$h_k^{\left(l\right)}=\varphi [s_k^{\left(l\right)}\odot W^{\left(l\right)}(r_k^{\left(l\right)}\odot h_k^{(l-1)})+b_k^{\left(l\right)}]$$

(5)

where $W^{\left(l\right)}$ is the shared main weight matrix, $r_k^{\left(l\right)}$ and $s_k^{\left(l\right)}$ are the input and output adaptation vectors of the $k$-th submodel, respectively, $b_k^{\left(l\right)}$ is the submodel-specific bias term, and $\odot$ denotes element-wise multiplication. This structure is equivalent to a low-rank modulation of the shared weight matrix:

$$W_k^{\left(l\right)}=W^{\left(l\right)}\odot [s_k^{\left(l\right)}{(r_k^{\left(l\right)})}^T]$$

(6)

Thus, TABM does not duplicate a complete network for each submodel. Instead, it generates diverse mappings through a shared backbone and lightweight adaptation vectors. This structure reduces the parameter scale while enhancing the ability to represent nonlinear relationships, making it suitable for small-sample, multi-source tabular-data modeling.

The prediction targets in this study are goaf temperature and CO concentration. The output of the $k$-th implicit submodel is defined as:

$${\widehat{y}}_k=g\left(h_k^{\left(L\right)}\right)=\left[{\widehat{T}}_k,{\widehat{CO}}_k\right]$$

(7)

where ${\widehat{T}}_k$ and ${\widehat{CO}}_k$ denote the predicted goaf temperature and CO concentration, respectively, and $g(\cdot )$ is the dual-output regression head. The final prediction is obtained by averaging the outputs of all implicit submodels:

$$\widehat{y}={\displaystyle \frac{1}{K}}{\displaystyle \sum _{k=1}^K}{\widehat{y}}_k=[\widehat{T},\widehat{CO}]$$

(8)

The training objective is defined as:

$${\mathcal{L}}_{TABM}={\lambda }_T{\mathcal{L}}_T(T,\widehat{T})+{\lambda }_{CO}{\mathcal{L}}_{CO}(CO,\widehat{CO})+\Omega (\Theta )$$

(9)

where ${\mathcal{L}}_T$ and ${\mathcal{L}}_{CO}$ denote the regression losses for temperature and CO concentration, respectively, ${\lambda }_T$ and ${\lambda }_{CO}$ are the corresponding weighting coefficients, and $\Omega (\Theta )$ is the regularization term for the model parameters. In this study, TABM was used as a parameter-efficient tabular regressor rather than an unrestricted high-capacity deep network. Its shared backbone, low-rank submodel-specific modulation, and output averaging reduce the number of independent trainable parameters and improve prediction stability. In addition, $\Omega (\Theta )$, dropout, weight decay, and early stopping are used to constrain model complexity. Combined with the compact top-6 input feature subset used in the final modeling stage, this design helps reduce overfitting risk under the available daily-scale field samples while retaining the ability to represent nonlinear relationships among multi-source gas variables and dual-output targets.

2.4. CA-WOA Optimization Algorithm

2.4.1. Limitations of WOA and Improvement Strategy

The whale optimization algorithm (WOA) achieves global optimization by simulating the encircling-prey, spiral-updating, and random-search behaviors of humpback whales. It has a simple structure, few control parameters, and convenient implementation. In the standard WOA, the current best individual is regarded as the prey position and is used to guide population updating, which enables rapid convergence in low-dimensional or weakly coupled optimization problems [29,30].

However, this mechanism has clear limitations in complex continuous optimization and machine-learning hyperparameter optimization. First, the search center depends on a single best individual and is easily affected by local optima, which may lead to premature convergence [31]. Second, the position update is mainly based on dimension-wise random perturbation and therefore cannot effectively capture coupling relationships among parameters, resulting in reduced search efficiency in high-dimensional spaces with rotation, scaling, or mixed structures. Third, the standard WOA lacks a cumulative memory mechanism for historical successful directions, which may cause oscillation or convergence stagnation in complex multimodal spaces.

To address these limitations, this paper proposes a covariance-adaptive whale optimization algorithm (CA-WOA). The proposed algorithm improves the original WOA from three linked aspects: search target, search direction, and search scale. First, the single best-individual attraction in WOA is replaced by a rank-weighted elite center such that the population is guided by the distribution of several high-quality solutions rather than by one accidental best solution. Second, covariance-adaptive sampling is introduced to learn the coupled search directions among hyperparameters, reducing the limitation of dimension-wise perturbation. Third, the WOA random-search branch is retained and combined with geometric step-size contraction, so that the algorithm can preserve global exploratory jumps while gradually refining the search near promising regions. In this way, CA-WOA keeps the basic exploration structure of WOA, but improves its stability and direction adaptability for complex hyperparameter optimization tasks.

2.4.2. Improvement Strategies of CA-WOA

The improvement strategy of CA-WOA is not an isolated covariance update added after WOA, but a coordinated redesign of the WOA search process. Specifically, rank-weighted elite-center reconstruction determines where the population should contract, covariance-adaptive direction learning determines how candidate solutions should be generated, and random-search injection with step-size contraction determines how the algorithm balances exploration and exploitation [32]. These components are connected sequentially in each iteration: the elite group first defines a stable search center, the covariance matrix then learns the dominant search directions around this center, and the WOA random-search branch provides additional long-distance exploration when needed. Therefore, CA-WOA forms an integrated search mechanism for coupled and mixed hyperparameter spaces.

(1)

Rank-weighted elite-center reconstruction

In the original WOA, the current best individual is used as the main attraction target, which may amplify the accidental advantage of a single individual. To improve the stability of the search center, CA-WOA no longer directly depends on a single best solution. Instead, it selects the top-$\mu$ elite individuals with better fitness in the current population and assigns different weights according to their ranks, thereby reconstructing the search center as a weighted mean.

For the population at generation $t$ with size $\lambda$, after sorting the fitness values in ascending order, the $i$-th elite individual is denoted $x_{\left(i:\lambda \right)}^t$, where $i=1,2,\dots ,\mu$ and $\mu =\lfloor \lambda /2\rfloor$. The rank weight of each elite individual is defined as:

$${\omega }_i={\displaystyle \frac{\mathrm{l}\mathrm{n}(\lambda /2+0.5)-\ln i}{{\displaystyle {\sum }_{j=1}^{\mu }}\left[\ln \right(\lambda /2+0.5)-\ln j]}},i=1,2,\dots ,\mu$$

(10)

where the weights satisfy ${\sum }_{i=1}^{\mu }{\omega }_i=1$. Based on these weights, the search center for generation $t+1$ is updated as:

$$m^{t+1}={\displaystyle \sum _{i=1}^{\mu }}{\omega }_i{x}_{\left(i:\lambda \right)}^t$$

(11)

where $m^{t+1}\in {\mathbb{R}}^n$ is the updated search center and $n$ is the dimension of the optimization problem. This mechanism transforms the search target from a single best point into an elite-group center, reducing the interference of accidental individuals on the search direction and making population contraction smoother and more robust.

(2)

Covariance-adaptive direction learning

In machine-learning hyperparameter spaces, different parameters are often not independent. For example, tree depth, learning rate, sampling ratio, and regularization strength may jointly affect model complexity and internal validation performance. If dimension-wise random perturbation is still used, the algorithm may fail to search along potentially high-quality directions. Therefore, CA-WOA expresses candidate-solution generation as covariance-controlled distribution sampling:

$$x_k^t=m^t+{\sigma }^t{U}^t({\Lambda }^t{)}^{1/2}{z}_k^t,z_k^t\sim N(0,I)$$

(12)

where $x_k^t$ is the $k$-th candidate solution, ${\sigma }^t$ is the global search step size, and $z_k^t$ is a standard normal random vector. Matrices $U^t$ and ${\Lambda }^t$ are obtained from the eigendecomposition of the covariance matrix ${\Sigma }^t$:

$${\Sigma }^t=U^t{\Lambda }^t(U^t{)}^T$$

(13)

By modeling the covariance matrix, candidate solutions can be sampled along the principal directions of high-quality regions rather than being perturbed independently in each dimension. This improves the adaptability of the algorithm to variable coupling, scale differences, and rotational structures.

To dynamically update the covariance matrix during the search process, the effective selection mass is first defined as:

$${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}={\displaystyle \frac{1}{{\displaystyle {\sum }_{i=1}^{\mu }}{\omega }_i^2}}$$

(14)

The normalized displacement vector of each elite individual relative to the current search center and its weighted mean are then defined as:

$$y_i^t={\displaystyle \frac{x_{\left(i:\lambda \right)}^t-m^t}{{\sigma }^t}},{\overline{y}}^t={\displaystyle \sum _{i=1}^{\mu }}{\omega }_i{y}_i^t$$

(15)

Based on ${\overline{y}}^t$, the evolution path is updated as:

$$p_c^{t+1}=(1-c_c)p_c^t+\sqrt{c_c(2-c_c){\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}}{\overline{y}}^t$$

(16)

where $p_c^t$ is the evolution path at generation $t$ and $c_c$ is the path-accumulation coefficient. The evolution path accumulates successful search directions over consecutive iterations, so covariance updating depends not only on the current population but also on historical directional information. Furthermore, the covariance matrix is updated using a rank-one term and a rank-$\mu$ term:

$${\Sigma }^{t+1}=(1-c_1-c_{\mu }){\Sigma }^t+c_1{p}_c^{t+1}(p_c^{t+1}{)}^T+c_{\mu }{\displaystyle \sum _{i=1}^{\mu }}{\omega }_i{y}_i^t(y_i^t{)}^T$$

(17)

where the rank-one term retains directional memory in the evolution path and the rank-$\mu$ term learns the spatial shape of high-quality regions from multiple elite individuals. Their combination allows the algorithm to adaptively adjust subsequent sampling directions according to historical search results.

(3)

Random-search injection and step-size contraction

Covariance-adaptive sampling helps improve local search efficiency. However, if the search distribution contracts too quickly, the algorithm may still become trapped in a local optimum. To maintain the global exploration ability of WOA, CA-WOA retains the random-search branch. When the global exploration condition is satisfied, a population individual $x_r^t$ is randomly selected as the reference position, and a candidate solution is generated as:

$$v_k^t=x_r^t-A^t\mid C^t\odot x_r^t-x_k^t\mid$$

(18)

where $v_k^t$ is the candidate solution generated by random search, $A^t=2a^t{r}_1-a^t$, $C^t=2r_2$, $r_1,r_2\in [0,1]$, and $\odot$ denotes element-wise multiplication. This mechanism injects long-distance jumping ability into covariance sampling and reduces the probability that the algorithm becomes trapped in a local region.

Meanwhile, to guide the search process from global exploration toward local exploitation, CA-WOA adopts geometric step-size decay:

$${\sigma }^t={\sigma }_0\cdot {\sigma }_{\mathrm{e}\mathrm{n}\mathrm{d}}^{t/(T-1)}$$

(19)

where ${\sigma }_0$ is the initial step size, ${\sigma }_{\mathrm{e}\mathrm{n}\mathrm{d}}$ is the terminal step-size ratio, and $T$ is the maximum number of iterations. A larger early step is beneficial for expanding the search range, whereas gradual step-size contraction in later iterations helps refine the search near promising regions. In this way, CA-WOA forms a dynamic balance between exploration and exploitation.

2.4.3. CA-WOA Algorithm Procedure

As shown in Figure 2, the overall CA-WOA procedure includes initialization, candidate-solution generation, fitness evaluation, elite updating, covariance updating, step-size decay, and termination output. First, the population, search center $m^0$, covariance matrix ${\Sigma }^0=I$, evolution path $p_c^0=0$, and initial step size ${\sigma }_0$ are initialized within the variable bounds. During each generation, candidate solutions are generated according to the current covariance matrix, and WOA random-search candidates are introduced when the global exploration condition is satisfied. All candidate solutions are repaired according to the boundary constraints, their fitness values are calculated, and the current global best solution is recorded [33,34].

After fitness evaluation, the population is sorted by fitness. The top-$\mu$ elite individuals are selected to update the search center through the rank-weighted elite-center mechanism. The elite displacement is then used to update the evolution path, and the covariance matrix is updated by combining the rank-one and rank-$\mu$ terms, allowing subsequent sampling to proceed along more promising directions. The step size is then updated according to the geometric decay rule, and the current best fitness is stored in the convergence curve. If the maximum number of iterations is reached, the best fitness, best solution position, and convergence curve are output. Otherwise, the algorithm proceeds to the next generation.

The integrated feature ranking was established during the feature-screening stage. Starting from the highest-ranked variable, the next highest-ranked remaining variable was added sequentially to construct nested top-$k$ candidate subsets. The recommended top-6 subset was then fixed according to the cross-model comparison described in Section 4.2.3. During fivefold model evaluation, robust-scaling parameters, model fitting, and CA-WOA-based hyperparameter evaluation were performed using only the training fold, whereas the held-out fold was used only for calculating prediction metrics. No missing-value imputation was performed after the final daily-scale sample set had been established.

2.5. SHAP/PDP Interpretation Methods

Machine-learning models can capture nonlinear mapping relationships between multi-source monitoring variables and goaf temperature and CO concentration, but their prediction processes are partly opaque. To improve the interpretability of the prediction results, this study introduced Shapley additive explanations (SHAP) and partial dependence plot (PDP) methods to explain the model from two perspectives: feature contribution and response trend. SHAP is used to quantify the contribution direction and magnitude of different monitoring variables to the prediction results, whereas PDP is used to analyze the average response of model outputs when key variables vary.

The SHAP method is based on the Shapley value in cooperative game theory and decomposes a model prediction into a baseline value and the additive contributions of individual input features. For a sample $x$, the model output can be expressed as:

$$f(x)={\varphi }_0+{\displaystyle \sum _{j=1}^p}{\varphi }_j$$

(20)

where ${\varphi }_0$ is the baseline value of the model output, ${\varphi }_j$ is the contribution of the $j$-th feature to the current prediction, and $p$ is the number of input features. When ${\varphi }_j>0$, the feature increases the predicted value; when ${\varphi }_j<0$, the feature decreases the predicted value. In this study, SHAP values were calculated separately for goaf temperature and CO concentration. Global importance rankings, bee-swarm plots, and representative-sample explanations were then used to compare the contribution differences of monitoring variables in the dual-output prediction task.

The PDP method is used to analyze the average effect of a feature of interest on the model output. For a feature $x_s$, its partial dependence function can be written as:

$${\widehat{f}}_s(x_s)={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}f(x_s,x_{i,c})$$

(21)

where $x_{i,c}$ denotes the remaining features except $x_s$ in the $i$-th sample, and $N$ is the number of samples. By changing the value of $x_s$ within its observed range while averaging over the remaining features, PDP reflects the marginal response trend of the model output as the feature varies. In this study, two-factor PDP analysis was further used to examine the interaction responses of important variable combinations for goaf temperature and CO concentration prediction.

It should be noted that SHAP and PDP reflect the feature contributions and response relationships learned by the model from the available data. They are not equivalent to strict physical causal relationships. Therefore, the interpretation results should be analyzed together with the low-temperature oxidation, gas generation, air-leakage dilution, and ventilation-driven migration processes of the goaf.

2.6. Evaluation Metrics and Fitness Function

To quantitatively evaluate the prediction performance of different models for goaf temperature and CO concentration, this study selected MAE, RMSE, MAPE, and $R^2$ as basic evaluation metrics. MAE reflects the mean absolute deviation, RMSE is more sensitive to large errors, MAPE characterizes the relative error level, and $R^2$ measures the ability of the model to explain variations in the target variable. Let $N$ be the number of samples, and let $y_i$ and ${\widehat{y}}_i$ denote the measured and predicted values of the $i$-th sample, respectively. These metrics are defined as:

$$MAE={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}\mid y_i-{\widehat{y}}_i\mid$$

(22)

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}(y_i-{\widehat{y}}_i{)}^2}$$

(23)

$$MAPE={\displaystyle \frac{100\mathrm{\%}}{N}}{\displaystyle \sum _{i=1}^N}\mid {\displaystyle \frac{y_i-{\widehat{y}}_i}{y_i+\epsilon }}\mid$$

(24)

$$R^2=1-{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N}(y_i-{\widehat{y}}_i{)}^2}{{\displaystyle {\sum }_{i=1}^N}(y_i-\overline{y}{)}^2}}$$

(25)

where $\overline{y}$ is the mean of the measured values and $\epsilon$ is a small constant used to avoid denominator anomalies when the CO concentration is close to zero. Smaller MAE, RMSE, and MAPE values indicate lower prediction errors, whereas an $R^2$ value closer to 1 indicates stronger explanatory ability.

Because goaf temperature and CO concentration have different dimensions, direct comparison using raw RMSE may be affected by scale differences. Therefore, the normalized root mean square error (NRMSE) is introduced as:

$$NRMSE={\displaystyle \frac{RMSE}{{\sigma }_y}}$$

(26)

where ${\sigma }_y$ is the standard deviation of the measured values for the corresponding target variable. NRMSE reduces the influence of dimensional differences and is more suitable for evaluating dual-output prediction models.

During CA-WOA hyperparameter optimization, the composite normalized error of goaf temperature and CO concentration is used as the fitness function:

$$\min F={\displaystyle \frac{1}{2}}(NRMS{E}_T+NRMS{E}_{CO})$$

(27)

where $NRMS{E}_T$ and $NRMS{E}_{CO}$ denote the normalized prediction errors of goaf temperature and CO concentration, respectively. This fitness function constrains both output targets simultaneously, preventing the hyperparameter search from favoring a single prediction task. It is therefore suitable for the joint prediction of goaf temperature and CO concentration.

For cross-validation-based model evaluation, the selected top-6 feature subset was kept fixed. In each fold, robust-scaling parameters, model fitting, and hyperparameter evaluation were completed using only the training partition and were then applied to the held-out validation partition. The fold-level MAE, RMSE, MAPE, $R^2$, NRMSE, and $F$ values were averaged to obtain the reported fivefold results.

3. Data Sources and Preprocessing

This study used the 1806 working-face goaf of a mine in Gansu Province as the research object. The data were obtained from field multi-source monitoring records collected from 1 January to 31 May 2026. To characterize the thermal state and gas-generation response during the low-temperature oxidation stage, the daily mean goaf-pipe temperature and daily mean CO concentration were selected as dual-output targets and denoted $Y_T$ and $Y_{CO}$, respectively. After date alignment, incomplete-record screening, and target-availability checking, 151 valid daily-scale samples were obtained. Although this sample size is limited for large-scale deep learning, it represents continuous daily field observations during a low-temperature oxidation monitoring period. Therefore, this study treated the task as a small-sample tabular regression problem and used compact feature selection and internal validation to evaluate model robustness. $Y_{CO}$ was used only as a prediction target and was not included as an input variable, thereby preventing target-source information from entering the feature set.

The original input variables included 17 monitoring variables: goaf-pipe O₂, CO₂, CH₄, and C₂H₆; face-frame CH₄; upper-corner O₂, CO, CO₂, and CH₄; return-air-side O₂, CO, CO₂, and CH₄; intake-air-side O₂, CO₂, and CH₄; and wind-air-volume information. These variables reflect internal oxygen consumption and oxidation-related gas generation, working-face boundary response, return-air-side migration and dilution, and ventilation disturbance. Before modeling, CO records from different sources were converted to a consistent volume-fraction scale. In the figures and tables, CO concentration is displayed in units of $\times {10}^{-3}$ to avoid the influence of mixed units on model training and error evaluation.

Before correlation and feature-importance analyses, the candidate variables were further screened according to daily-record completeness, effective temporal variability, and information redundancy. IntakeAir_O2, IntakeAir_CO2, IntakeAir_CH4, ReturnAir_O2, and the wind-air-volume variable were excluded because they exhibited incomplete date matching, limited variation, or strong redundancy with the retained monitoring variables. The remaining 12 variables were used for the subsequent correlation analysis, integrated importance ranking, and top-$k$ subset construction.

Data preprocessing included outlier identification, temporal alignment, daily-scale aggregation, target-availability screening, and robust standardization. Outliers were checked according to field-record ranges and the physical meaning of each variable, and obvious entry errors or unreasonable abrupt changes were corrected or removed. Records with unavailable target values or incomplete key monitoring variables were excluded before modeling, and no missing-value imputation was performed after the final sample set was determined. To reduce the influence of dimensional differences and extreme values, the input variables were processed using robust standardization. To avoid data-distribution leakage, standardization parameters were estimated only from the training set and then applied to validation or test samples.

Figure 3 presents the distribution characteristics of the input variables and prediction targets. Figure 3a shows that the dispersion of the robust-standardized multi-source variables differs substantially, and several gas indicators exhibit long-tailed distributions and outlying fluctuations. Figure 3b shows that the goaf temperature is mainly concentrated between 30 and 33 °C, indicating that the monitoring period generally corresponds to the low-temperature oxidation stage. Figure 3c shows that the CO concentration is right-skewed, with most samples located in the low-concentration range. Figure 3d further indicates that temperature varies relatively smoothly, whereas CO concentration exhibits staged fluctuations and local abrupt increases, suggesting that CO is more sensitive to local oxidation-related gas generation and gas migration. Therefore, this study focused on the continuous joint prediction of goaf temperature and CO concentration and did not construct a multilevel early-warning classification model.

4. Experimental Results and Analysis

4.1. Benchmark Test of CA-WOA

To evaluate the global optimization ability of CA-WOA and its improvement over the original WOA, nine representative functions from the CEC2022 test suite were selected for benchmark testing, namely F1, F2, F3, F4, F5, F6, F8, F9, and F10. The competing algorithms included WOA, HHO, FLA, PSO, DBO, GWO, and IDBO. All algorithms were executed on the same platform using a population size of 60, a maximum of 300 iterations, a search dimension of 10, and 50 independent runs for each function. The benchmark and ablation algorithms were implemented in MATLAB R2025a (The MathWorks, Inc., Natick, MA, USA), while the machine-learning experiments were conducted in Python 3.11.7 within an Anaconda environment using scikit-learn 1.7.2, XGBoost 3.1.1, LightGBM 4.6.0, CatBoost 1.2.8, PyTorch 2.9.1+cpu, TabM 0.0.3, SHAP 0.48.0, Boruta 0.4.3, and Optuna 4.6.0. The PyTorch-based models were trained on the CPU. Detailed parameter configurations, MATLAB source codes, and repeated-run data are provided in the Supplementary Materials. Algorithm performance was evaluated in terms of average fitness convergence, final fitness distribution, overall ranking, and summary statistics.

Figure 4 presents the average fitness convergence curves of the eight algorithms on the nine benchmark functions. Overall, CA-WOA exhibits faster convergence and lower final fitness values on most functions. On F1, F3, F5, and F9, CA-WOA rapidly approaches high-quality regions in the early iterations and maintains stable convergence in the later stage. On F4, F6, and F8, its convergence curves also show a clear and continuous downward trend, generally outperforming the original WOA and most competing algorithms. By contrast, the original WOA converges more slowly on several complex functions and tends to stagnate in later iterations, indicating that single-best-individual attraction and dimension-wise random perturbation are insufficient for complex search spaces. Through rank-weighted elite-center reconstruction and covariance-adaptive direction learning, CA-WOA can more stably estimate promising search regions and adjust the search direction, thereby improving convergence efficiency. It should also be noted that FLA achieves a slightly better average result on F2 and DBO obtains a lower final value on F10. Therefore, CA-WOA is not absolutely superior on every function, but its overall convergence performance remains competitive.

Figure 5 shows the final fitness distributions of the algorithms after 50 independent runs. CA-WOA exhibits more concentrated distributions and lower dispersion on F1, F3, F5, and F9, indicating good stability across repeated runs. For complex functions with larger fluctuations, such as F6, the final fitness distributions of WOA, HHO, DBO, GWO, and IDBO expand substantially, and several algorithms produce poor extreme values. In contrast, CA-WOA maintains a relatively concentrated distribution, suggesting stronger robustness in complex search spaces. On F8 and F10, the differences among algorithms are relatively small, but CA-WOA still shows a stable distribution pattern. Taken together, Figure 4 and Figure 5 indicate that CA-WOA improves average convergence performance while reducing uncertainty across repeated runs.

Table 1. Overall ranking and win/tie/loss statistics of CA-WOA and competing algorithms on nine CEC2022 functions.

Algorithm	Friedman Mean Rank	Overall Rank	Top-3 Count	W/T/L vs. CA-WOA
CA-WOA	1.39	1	9	—
FLA	3.06	2	5	1/1/7
IDBO	3.5	3	6	0/1/8
PSO	3.94	4	3	0/1/8
GWO	4.56	5	3	0/0/9
DBO	6.22	6	1	1/0/8
WOA	6.61	7	1	0/0/9
HHO	6.72	8	0	0/0/9

reports the Friedman mean rank, overall rank, top-three count, and win/tie/loss statistics relative to CA-WOA for the nine test functions. CA-WOA obtains a Friedman mean rank of 1.39, ranks first overall, and enters the top three on all nine functions, indicating stable overall performance. Compared with the original WOA, CA-WOA achieves 9 wins, 0 ties, and 0 losses, showing that the covariance-adaptive improvement enhances the optimization ability of the original WOA. FLA and IDBO rank second and third, respectively, but their win/tie/loss statistics relative to CA-WOA are 1/1/7 and 0/1/8, respectively. PSO ranks fourth with 0/1/8. These results further indicate that CA-WOA maintains an advantage on most benchmark functions.

To further examine the roles of the individual CA-WOA components, one-factor ablation variants were constructed by removing covariance adaptation, rank-weighted elite-center reconstruction, WOA random-search injection, and geometric step-size decay. The complete CA-WOA outperformed the original WOA on all nine benchmark functions. Removing covariance adaptation or elite-center reconstruction reduced performance on most functions, supporting their respective roles in coupled-direction learning and population guidance. The effect of geometric step-size decay was more function-dependent, although the complete algorithm achieved more wins than losses. The random-search injection produced results similar to those of the complete CA-WOA on most functions. Its removal improved performance on a limited number of functions, and the cross-function difference was not statistically significant. This indicates that the mechanism primarily serves to preserve global exploration rather than to uniformly reduce final fitness on every benchmark problem. Overall, the components play different roles in direction learning, population guidance, global exploration, and local refinement, while the complete CA-WOA provides a significant overall improvement over the original WOA. Detailed ablation results are provided in the Supplementary Materials.

Table 2. Summary statistics of eight algorithms on nine representative CEC2022 functions.

Function	CA-WOA	WOA	HHO	FLA	PSO	DBO	GWO	IDBO
F1	3.00 × 102 ±1.99 × 10−14	2.60 × 104 ±1.50 × 104	9.15 × 102 ±3.47 × 102	3.00 × 102 ±1.17 × 10−2	3.00 × 102 ±8.02 × 10−9	5.53 × 103 ±1.85 × 103	1.73 × 103 ±1.67 × 103	3.00 × 102 ±2.55 × 10−9
F2	4.07 × 102 ±2.32 × 100	4.74 × 102 ±8.64 × 101	4.52 × 102 ±4.68 × 101	4.06 × 102 ±3.00 × 100	4.12 × 102 ±1.69 × 101	5.75 × 102 ±1.04 × 102	4.26 × 102 ±2.30 × 101	4.13 × 102 ±1.87 × 101
F3	6.00 × 102 ±2.10 × 10−6	6.37 × 102 ±1.12 × 101	6.38 × 102 ±1.11 × 101	6.02 × 102 ±3.04 × 100	6.03 × 102 ±4.12 × 100	6.25 × 102 ±5.89 × 100	6.01 × 102 ±1.14 × 100	6.02 × 102 ±2.59 × 100
F4	8.03 × 102 ±1.55 × 100	8.41 × 102 ±1.47 × 101	8.25 × 102 ±6.35 × 100	8.19 × 102 ±7.01 × 100	8.18 × 102 ±8.82 × 100	8.35 × 102 ±7.46 × 100	8.15 × 102 ±8.11 × 100	8.16 × 102 ±9.67 × 100
F5	9.00 × 102 ±0.00 × 100	1.59 × 103 ±5.10 × 102	1.34 × 103 ±1.75 × 102	9.03 × 102 ±7.46 × 100	9.09 × 102 ±3.57 × 101	1.09 × 103 ±7.16 × 101	9.07 × 102 ±1.54 × 101	9.06 × 102 ±2.62 × 101
F6	1.81 × 103 ±9.30 × 100	5.58 × 103 ±5.66 × 103	5.84 × 103 ±4.20 × 103	4.83 × 103 ±2.17 × 103	3.66 × 103 ±2.23 × 103	1.93 × 106 ±4.77 × 106	6.53 × 103 ±2.19 × 103	4.50 × 103 ±2.37 × 103
F8	2.22 × 103 ±7.61 × 100	2.24 × 103 ±1.12 × 101	2.24 × 103 ±1.90 × 101	2.22 × 103 ±4.62 × 100	2.23 × 103 ±2.85 × 101	2.23 × 103 ±6.85 × 100	2.23 × 103 ±1.81 × 101	2.24 × 103 ±4.16 × 101
F9	2.53 × 103 ±5.86 × 10−11	2.60 × 103 ±5.01 × 101	2.60 × 103 ±4.35 × 101	2.53 × 103 ±2.08 × 101	2.54 × 103 ±2.24 × 101	2.63 × 103 ±5.21 × 101	2.56 × 103 ±2.66 × 101	2.53 × 103 ±2.09 × 101
F10	2.54 × 103 ±5.13 × 101	2.55 × 103 ±7.16 × 101	2.58 × 103 ±6.84 × 101	2.57 × 103 ±1.21 × 102	2.57 × 103 ±7.77 × 101	2.51 × 103 ±2.57 × 101	2.57 × 103 ±1.24 × 102	2.55 × 103 ±8.05 × 101

further reports the summary statistics of the eight algorithms on the nine functions, expressed as mean ± standard deviation. CA-WOA achieves the best or near-best mean values on F1, F3, F4, F5, F6, F8, and F9. The standard deviations on F1, F5, and F9 are very small, indicating stable convergence to high-quality regions. Compared with the original WOA, CA-WOA obtains lower average fitness values on all nine displayed functions, especially on F1, F5, and F6, where the improvement is more pronounced. This suggests that covariance-adaptive sampling can alleviate premature convergence and later-stage stagnation of the original WOA on complex functions. Although CA-WOA does not achieve the absolute best results on F2 and F10, its overall ranking, top-three count, and stability remain better than those of most competing algorithms.

To assess whether the observed differences among the optimization algorithms could be attributed to random variation across independent runs, nonparametric statistical tests were conducted using the final-fitness results from 50 runs on the nine benchmark functions. The Friedman test yielded a statistic of 39.1481 and a $p$-value of $1.8313\times {10}^{-6}$, indicating a significant overall difference among the eight algorithms. Function-wise Wilcoxon rank-sum tests were further performed between CA-WOA and the competing algorithms. The raw repeated-run data and complete statistical results are provided in the Supplementary Materials.

Overall, the benchmark results show that CA-WOA improves convergence speed, optimization accuracy, and running stability compared with the original WOA. This improvement is mainly reflected in three aspects. First, the rank-weighted elite center reduces the instability caused by attraction to a single best individual. Second, covariance-adaptive direction learning enables the algorithm to search along the dominant directions of high-quality solution regions rather than relying only on dimension-wise random perturbation. Third, the retained WOA random-search branch and step-size contraction help maintain exploration in the early stage and improve local refinement in the later stage. The results in Figure 4 and Figure 5 and Table 1 and Table 2 therefore support the effectiveness of the proposed WOA-based improvement strategy. Although CA-WOA does not achieve the best value on every test function, it shows better overall ranking and stability than the original WOA and most competing metaheuristic algorithms, which supports its use as the hyperparameter optimizer in the subsequent regression modeling.

4.2. Correlation and Feature Selection

4.2.1. Feature Correlation Analysis

To preliminarily identify the statistical associations between multi-source monitoring variables and goaf temperature and CO concentration, Pearson correlation analysis was conducted on 12 main input features and two prediction targets in the training set. The results are shown in Figure 6. The correlation heatmap describes the linear covariation among variables and provides a reference for subsequent random forest-based importance ranking and top-$k$ feature-subset construction. It should be noted that $Y_T$ and $Y_{CO}$ are included only as prediction targets in the correlation display and are not used as input variables for model training.

Figure 6 shows that goaf-pipe gas variables have relatively clear statistical associations with the prediction targets. GoafPipe_CH4 is strongly and positively correlated with goaf temperature, while GoafPipe_CO2, FaceFrame_CH4, UpperCorner_CH4, and ReturnAir_CH4 also show positive correlations with temperature to varying degrees. GoafPipe_O2 is negatively correlated with GoafPipe_CO2 and GoafPipe_CH4, suggesting that oxygen consumption and gas-product accumulation may vary synchronously during low-temperature oxidation. For CO concentration, GoafPipe_C2H6, GoafPipe_CO2, and UpperCorner_CH4 show relatively high correlations, indicating that the CO response is related not only to internal gas generation in the goaf but also to boundary gas migration.

Some input variables also exhibit strong mutual correlations. For example, relatively high correlation coefficients are observed among goaf-pipe gas components, between upper-corner CO₂ and CH₄, and between return-air-side CO₂ and CH₄. This indicates that multi-source monitoring variables contain overlapping information. Directly inputting all variables into the model may therefore increase redundancy and model complexity. It is necessary to further screen suitable feature combinations for the dual-output prediction task by combining tree-model importance with top-$k$ subset performance.

4.2.2. Feature-Importance Ranking

To further evaluate the contribution differences of different monitoring variables to the joint prediction of goaf temperature and CO concentration, a random forest regression model was used to calculate comprehensive feature importance on the training set. Repeated training was performed to obtain the mean importance and standard deviation, as shown in Figure 7. The horizontal bars represent the mean importance estimates, whereas the error bars indicate the fluctuation range across repeated training runs and reflect the stability of feature contributions.

Figure 7 shows that goaf-pipe gas variables provide the highest overall contribution. GoafPipe_CH4 has the largest importance value, reaching 0.182. GoafPipe_CO2, GoafPipe_O2, and GoafPipe_C2H6 have importance values of 0.153, 0.106, and 0.090, respectively, and all rank near the top. This indicates that goaf-pipe monitoring points more directly capture internal oxygen consumption, oxidation-related gas generation, and gas-enrichment information in the goaf, making them the main information source for temperature and CO concentration prediction. In addition to goaf-pipe variables, UpperCorner_CH4, ReturnAir_CO2, ReturnAir_CO, and ReturnAir_CH4 show moderate importance, suggesting that upper-corner and return-air-side variables can supplement the boundary response after gas migrates from the goaf toward the working face and return-air system. FaceFrame_CH4 has a relatively lower contribution and mainly reflects an auxiliary response in the local working-face-side space.

During the integrated importance-ranking stage, random forest regression models were used to calculate the importance of each monitoring variable separately for temperature and CO concentration prediction. The two sets of importance scores were normalized and then combined using equal weights. Because random sampling and variations in tree structure may introduce fluctuations in random forest importance estimates, multiple independent training runs were conducted on the training set. The mean and standard deviation of the integrated importance were then calculated for each variable, as shown in Figure 7. The horizontal bars represent the mean importance values, whereas the error bars indicate the variation across repeated training runs. These results characterize both the relative contribution of each variable to the dual-output prediction task and the stability of the resulting candidate-feature ranking.

4.2.3. Cross-Model Validation of Top-$k$ Feature Subsets

Based on the integrated feature-importance ranking, top-$k$ candidate subsets were sequentially constructed in descending order of importance, with $k=1,2,\dots ,12$. To compare model performance under different input dimensions, RF, XGBoost, LightGBM, CatBoost, LSSVM, and TABM were configured using the unified baseline hyperparameters listed in

Table 3. Baseline hyperparameter settings of candidate regression models.

Model	Hyperparameter	Baseline Value	Model	Hyperparameter	Baseline Value
RF	n_estimators	220	RF	max_depth	4
RF	min_samples_leaf	5	RF	max_features	0.7
RF	n_jobs	1
XGBoost	n_estimators	80	XGBoost	max_depth	2
XGBoost	learning_rate	0.04	XGBoost	subsample	0.8
XGBoost	colsample_bytree	0.8	XGBoost	min_child_weight	4
XGBoost	reg_lambda	8	XGBoost	n_jobs	1
LightGBM	n_estimators	90	LightGBM	max_depth	2
LightGBM	learning_rate	0.04	LightGBM	subsample	0.8
LightGBM	colsample_bytree	0.8	LightGBM	min_child_samples	12
LightGBM	reg_lambda	8	LightGBM	n_jobs	1
CatBoost	iterations	90	CatBoost	depth	2
CatBoost	learning_rate	0.04	CatBoost	l2_leaf_reg	20
CatBoost	random_strength	2	CatBoost	thread_count	1
LSSVM	alpha	10−3	LSSVM	gamma	0.005
TABM	max_epochs	300	TABM	patience	30
TABM	lr	1 × 10−3	TABM	weight_decay	3 × 10−4
TABM	batch_size	512	TABM	d_block	128
TABM	n_blocks	3	TABM	k	16
TABM	dropout	0.1	TABM	val_fraction	0.15

. Each top-$k$ subset was then evaluated using the six candidate regression models, and $R^2$ and RMSE were employed to quantify the effect of input dimensionality on temperature and CO concentration prediction. The parameters in Table 3 were used only for the feature-subset comparison, whereas the subsequent model-performance analysis was conducted using CA-WOA-optimized hyperparameters.

For the temperature prediction task, Figure 8 shows that the overall predictive ability of the models was relatively limited when only a small number of features were included. This result indicates that a single gas variable or a small group of monitoring variables cannot adequately characterize variations in the thermal state of the goaf. As additional high-contribution features were introduced, most models exhibited higher $R^2$ values and lower RMSE values, demonstrating the benefit of integrating multi-source monitoring information. Most models entered a favorable performance range when $k=5$–8, with particularly strong overall performance observed around $k=6$. When further variables were added, several models exhibited different degrees of performance fluctuation, suggesting that low-contribution or highly correlated features may increase input redundancy and reduce model stability.

For the CO concentration prediction task, Figure 9 indicates that model performance was more sensitive to changes in the number of input features. When $k$ was small, the addition of dominant gas-generation and migration-response variables resulted in a rapid increase in $R^2$ and a clear reduction in RMSE. Most models reached a favorable performance range when $k=4$–6, while XGBoost, CatBoost, and TABM exhibited relatively stable prediction results. Further increasing the number of input variables did not produce continuous improvement and even reduced the performance of some models. This result suggests that CO concentration prediction depends primarily on a limited number of key gas variables, whereas additional low-contribution or strongly correlated variables may introduce redundant information.

Taken together, Figure 8 and Figure 9 show that the prediction performance for neither temperature nor CO concentration improved monotonically with the number of input features. When too few variables were included, the available multi-source information was insufficient to describe the coupled variation between the thermal state and gas response in the goaf. By contrast, the continued inclusion of low-contribution or highly correlated variables caused increased errors or performance fluctuations in several models. The integrated importance ranking was therefore used to generate candidate subsets of different sizes rather than to directly determine the final input dimensionality.

In the integrated importance calculation, the feature-importance vectors corresponding to temperature and CO concentration were normalized separately and then combined using equal weights. Because temperature and CO concentration were treated as co-primary outputs of the joint-prediction task and no engineering priority was assigned to either output in advance, equal weighting was used to construct a task-balanced candidate-feature ranking. More importantly, the final feature number was not determined solely by the equal-weight coefficients: it was further selected through top-$k$ performance validation using six models for both prediction targets.

The detailed results show that temperature prediction achieved favorable overall performance around $k=6$, whereas CO concentration prediction attained relatively high $R^2$ values and low RMSE values within the range $k=4$–6. Although some models achieved their best individual metric at $k=4$ or $k=5$, CO prediction remained within a favorable performance range at $k=6$, while temperature prediction showed more consistently strong overall performance. Therefore, considering the performance trends of six models for both prediction targets, together with input complexity and model stability, $k=6$ was selected as the recommended feature number for subsequent CA-WOA optimization and model comparison.

The resulting top-six feature subset consisted of GoafPipe_CH4, GoafPipe_CO2, GoafPipe_O2, GoafPipe_C2H6, UpperCorner_CH4, and ReturnAir_CO2. To examine whether this subset depended on a single ranking strategy, Boruta, recursive feature elimination (RFE), mutual information (MI), and SHAP-based selection were additionally applied to the same 12 candidate variables. All five methods selected GoafPipe_CH4, GoafPipe_CO2, GoafPipe_O2, and UpperCorner_CH4. The proposed and SHAP-based methods yielded identical top-six sets, while Boruta and RFE shared five of the six variables with the proposed subset. This agreement supports the robustness of the selected compact feature set. Detailed rankings and process figures are provided in the Supplementary Materials.

4.3. CA-WOA-Based Model Optimization Analysis

4.3.1. Optimization Settings and Search Space

After the recommended top-six feature subset had been determined, CA-WOA was used to optimize the hyperparameters of the six candidate regression models: RF, XGBoost, LightGBM, CatBoost, LSSVM, and TABM. To avoid information leakage during feature selection and parameter optimization, dominant-feature ranking, top-$k$ subset determination, and CA-WOA-based hyperparameter search were all conducted within the training workflow. Test samples were not involved in feature selection or parameter search and were used only for subsequent performance evaluation. Compared with fixed empirical parameters, CA-WOA can simultaneously adjust model structure, learning rate, sampling ratio, regularization strength, and training-control parameters within a predefined search space, thereby reducing the dependence of model performance on manual parameter tuning.

Each candidate hyperparameter set was evaluated using the composite normalized error defined in Section 2.6 as the fitness function. This function simultaneously accounts for the NRMSE values of goaf temperature and CO concentration, preventing the search process from being biased toward a single output target. The population size of CA-WOA was set to 20 and the maximum number of iterations was set to 30; therefore, all models were optimized under the same search budget. For tree-based models, the optimized parameters mainly included the number of trees, tree depth, learning rate, sampling ratio, and regularization parameters. For LSSVM, the kernel parameter and regularization coefficient were optimized. For TABM, the optimized structural and training parameters included network width, number of blocks, learning rate, weight decay, batch size, and dropout. The search spaces and selected optimal values of the six models are listed in

Table 4. Hyperparameter search spaces and selected optimal values.

Model	Hyperparameter	Search Range	Value	Model	Hyperparameter	Search Range	Value
RF	n_estimators	50–500	239	RF	max_depth	2–20	17
RF	min_samples_leaf	1–8	1	RF	max_features	0.5–1.0	0.797948795
XGBoost	n_estimators	50–500	166	XGBoost	max_depth	2–10	6
XGBoost	learning_rate	0.01–0.30	0.3	XGBoost	subsample	0.6–1.0	0.6
XGBoost	colsample_bytree	0.6–1.0	1	XGBoost	min_child_weight	1–10	1
XGBoost	reg_lambda	10−6–50	50
LightGBM	n_estimators	50–500	113	LightGBM	max_depth	2–12	6
LightGBM	learning_rate	0.01–0.30	0.26171755	LightGBM	subsample	0.6–1.0	0.755818689
LightGBM	colsample_bytree	0.6–1.0	0.827405489	LightGBM	min_child_samples	5–30	5
LightGBM	reg_lambda	10−6–50	42.39844725	LightGBM
CatBoost	iterations	50–500	335	CatBoost	depth	2–10	8
CatBoost	learning_rate	0.01–0.30	0.297133605	CatBoost	l2_leaf_reg	0.001–50	27.4900443
CatBoost	random_strength	0–2	0.746715595	CatBoost
LSSVM	alpha	10−4–100	0.077669431	LSSVM	gamma	10−4–100	0.06395764
TABM	max_epochs	180–420	315	TABM
TABM	lr (learning_rate)	3 × 10−4–0.005	0.001376567	TABM	weight_decay	10−5–0.002	2.7 × 10−5
TABM	batch_size	64–512	489	TABM	d_block	64–256	96
TABM	n_blocks	2–4	4	TABM	k	8–24	16
TABM	dropout	0–0.25	0.25	TABM

.

Table 4 shows clear differences among the selected optimal parameters of different models. Some learning-rate and regularization parameters of XGBoost, LightGBM, and CatBoost are close to the search boundaries, indicating that under the current sample size and feature structure, relatively rapid iterative updating should be combined with appropriate complexity constraints. RF has a relatively large optimal tree depth and feature-sampling ratio, suggesting that sufficient tree-structure representation is needed to capture nonlinear relationships. The optimal parameters of LSSVM fall within low-to-medium ranges, reflecting the need for kernel methods to balance smoothness and fitting ability. TABM has a relatively high selected dropout value, indicating that deep tabular models rely more on regularization to suppress overfitting under small-sample and multi-source feature conditions. It should be noted that these selected parameters represent favorable combinations only under the search ranges and data conditions of this study and should not be interpreted as generally optimal model parameters.

4.3.2. Fitness Convergence Analysis

To analyze the optimization process of CA-WOA for the six candidate regression models, the composite fitness values over 30 iterations were recorded, as shown in Figure 10. A lower fitness value indicates a smaller overall prediction error for the dual-output task of goaf temperature and CO concentration. Overall, all six models show different degrees of fitness reduction during optimization, indicating that the defined hyperparameter spaces have practical effects on model performance.

From the convergence process, the fitness values of most models decrease rapidly during the first 5–15 iterations and then gradually stabilize, suggesting that CA-WOA can complete the main search process within a limited iteration budget. RF shows a relatively small decrease, which may be related to the inherent robustness of its multi-tree averaging structure to hyperparameter variations. XGBoost, LightGBM, and CatBoost exhibit clear early-stage decreases, indicating that learning rate, tree depth, sampling ratio, and regularization parameters directly affect the performance of gradient-boosting models. LSSVM decreases rapidly at the beginning but shows more pronounced fluctuations in later iterations, suggesting that its kernel parameter and regularization coefficient are sensitive to data partitioning. TABM starts with a relatively low fitness value and obtains further modest improvement in the middle and later stages, finally achieving the lowest composite error, which reflects its strong ability to represent nonlinear mappings among multi-source features.

Table 5. Fivefold average performance of the six CA-WOA-optimized base models.

Model	R2_T	R2_CO	Mean R2	NRMSE_T	NRMSE_CO	F
CA-WOA-RF	0.861 ± 0.023	0.876 ± 0.038	0.868 ± 0.015	0.372 ± 0.031	0.349 ± 0.056	0.360 ± 0.022
CA-WOA–XGBoost	0.904 ± 0.037	0.907 ± 0.052	0.905 ± 0.021	0.305 ± 0.064	0.296 ± 0.083	0.300 ± 0.033
CA-WOA-LightGBM	0.872 ± 0.025	0.903 ± 0.024	0.887 ± 0.012	0.356 ± 0.034	0.310 ± 0.039	0.333 ± 0.018
CA-WOA-CatBoost	0.895 ± 0.023	0.876 ± 0.039	0.885 ± 0.023	0.323 ± 0.036	0.349 ± 0.057	0.336 ± 0.034
CA-WOA-LSSVM	0.839 ± 0.056	0.855 ± 0.069	0.847 ± 0.054	0.396 ± 0.074	0.372 ± 0.090	0.384 ± 0.071
CA-WOA–TABM	0.921 ± 0.028	0.927 ± 0.017	0.924 ± 0.020	0.278 ± 0.050	0.268 ± 0.033	0.273 ± 0.036

reports the internal fivefold average performance of the six models after CA-WOA optimization. CA-WOA–TABM obtains the lowest composite fitness, with $F=0.273$, and achieves a mean $R^2$ of 0.924, ranking first among the six models. CA-WOA–XGBoost ranks second, with a composite fitness of 0.300 and a mean $R^2$ of 0.905. LightGBM and CatBoost show relatively similar overall performance, whereas RF and LSSVM have higher composite errors. These results indicate that CA-WOA can distinguish the suitability of different model structures under a unified fitness criterion, and that TABM and XGBoost are more suitable for the current dual-output prediction task.

Compared with the unoptimized baseline models, CA-WOA produces positive improvements for all six models, as shown in

Table 6. Comparison of comprehensive model performance before and after CA-WOA optimization.

Model	Before Mean R2	After Mean R2	Improvement	Before F	After F	Reduction
RF	0.83	0.868	0.039	0.401	0.36	10.10%
XGBoost	0.882	0.905	0.023	0.336	0.3	10.50%
LightGBM	0.811	0.887	0.076	0.423	0.333	21.30%
CatBoost	0.844	0.885	0.041	0.391	0.336	14.10%
LSSVM	0.811	0.847	0.036	0.43	0.384	10.80%
TABM	0.868	0.924	0.056	0.354	0.273	22.80%

. TABM and LightGBM show the largest reductions in fitness, reaching 22.8% and 21.3%, respectively. This indicates that deep tabular models and gradient-boosting tree models are sensitive to hyperparameter configuration and that suitable parameter combinations can improve their utilization of multi-source gas features. CatBoost shows a fitness reduction of 14.1%, while the reductions for XGBoost, LSSVM, and RF are 10.5%, 10.8%, and 10.1%, respectively. RF shows a relatively limited improvement, which may be related to the inherent stability of its ensemble structure. Although LSSVM shows a reduction in prediction error after optimization, its fivefold fluctuation remains relatively large, indicating insufficient stability of the kernel method under limited sample size and uneven feature distributions.

The fold-wise results in Table 6 also provide evidence of internal validation stability under the current sample size. Model performance is jointly affected by hyperparameter sensitivity and the compatibility between model architecture and data characteristics. Before optimization, XGBoost achieved the highest mean $R^2$ of 0.882, with a composite fitness $F$ of 0.336. After CA-WOA optimization, its mean $R^2$ increased to 0.905 and $F$ decreased to 0.300. By progressively fitting residuals through tree-based splitting, XGBoost can effectively represent nonlinear relationships among continuous monitoring variables. It therefore already provided strong baseline performance, leaving relatively limited room for further improvement.

In comparison, the mean $R^2$ of TABM increased from 0.868 to 0.924, while its composite fitness decreased from 0.354 to 0.273, corresponding to a reduction of 22.8%. The optimized TABM achieved the best overall performance among the six models. The present dataset is characterized by a limited sample size, low input dimensionality, relatively strong feature correlations, and nonlinear relationships between the monitoring variables and the temperature and CO targets. TABM learns common representations through a shared backbone and forms an implicit ensemble through lightweight submodel-specific modulation and output averaging. This structure improves the representation of complex feature interactions while reducing the sensitivity of an individual network to limited samples and local fluctuations. Together with dropout, weight decay, and early stopping, TABM is well matched to the present small-sample, continuous multi-source, dual-output prediction task.

LightGBM exhibited the largest increase in mean $R^2$ and a 21.3% reduction in composite fitness, indicating strong sensitivity to learning rate, tree structure, and regularization settings. However, its final performance remained below those of TABM and XGBoost. CatBoost achieved a moderate improvement, while some of its advantages in handling categorical variables were not fully utilized because the current inputs were continuous monitoring variables. RF showed a relatively limited improvement because its multi-tree averaging structure was already comparatively stable. Although optimization reduced the error of LSSVM, the model retained relatively large fold-to-fold variability, reflecting its sensitivity to kernel and regularization parameters.

Overall, the advantage of TABM does not arise solely from increased model complexity, but from the compatibility between its parameter-efficient implicit ensemble structure and the characteristics of the current dataset. XGBoost, in contrast, maintained strong baseline performance through its robust boosting-tree architecture. The remaining models further demonstrate that a larger optimization gain does not necessarily lead to the best final predictive performance.

4.3.3. Out-of-Fold Prediction and Model Comparison

To further examine the stability of the CA-WOA-optimized models under different internal data partitions, out-of-fold prediction results were constructed based on fivefold cross-validation. In each fold, the validation samples were predicted by a model that had not been trained on that fold, and the predictions were then concatenated according to the original sample order to form complete out-of-fold prediction sequences. It should be noted that out-of-fold prediction reflects internal validation stability under the current data conditions and is not equivalent to external generalization across mines or operating conditions. Figure 11 compares the observed and predicted values of the six CA-WOA-optimized models for goaf temperature and CO concentration.

For goaf temperature prediction, all six models can track the overall fluctuation trend of the temperature sequence, but differences remain in peak response and local trough representation. CA-WOA–TABM achieves the best out-of-fold prediction performance, with an $R^2$ of 0.928 and an RMSE of 0.487 °C. Its prediction curve remains highly consistent with the observed curve at most peaks and troughs. CA-WOA–XGBoost and CA-WOA-CatBoost also show strong nonlinear fitting ability, with temperature-prediction $R^2$ values of 0.913 and 0.902, respectively. By contrast, RF, LightGBM, and LSSVM show smoothing effects in some peak intervals and LSSVM has a larger error, indicating relatively limited ability to represent local fluctuations.

For CO concentration prediction, all models generally reflect the main variation trend, but their ability to track spike samples and local abrupt fluctuations differs more clearly. CA-WOA–TABM again performs best, with an $R^2$ of 0.931 and an RMSE of $4.72\times {10}^{-4}$, indicating a strong ability to represent complex coupling relationships among multi-source gas variables. CA-WOA–XGBoost achieves a CO-prediction $R^2$ of 0.916 and an RMSE of $5.21\times {10}^{-4}$, showing stable trend tracking and spike-response performance. LightGBM and CatBoost can characterize changes in the low- to medium-concentration range, but amplitude deviations remain in some high-value fluctuation intervals. RF and LSSVM perform relatively weakly, especially LSSVM, which shows insufficient fitting ability for local spikes.

Table 7. Out-of-fold prediction performance under fivefold cross-validation.

Model	R2_T	RMSE_T	R2_CO	RMSE_CO
CA-WOA-RF	0.868	0.659	0.886	6.07 × 10−4
CA-WOA–XGBoost	0.913	0.535	0.916	5.21 × 10−4
CA-WOA-LightGBM	0.878	0.633	0.903	5.60 × 10−4
CA-WOA-CatBoost	0.902	0.568	0.891	5.93 × 10−4
CA-WOA-LSSVM	0.855	0.691	0.846	7.05 × 10−4
CA-WOA–TABM	0.928	0.487	0.931	4.72 × 10−4

summarizes the out-of-fold prediction performance of the six models. Overall, CA-WOA–TABM obtains the highest $R^2$ and the lowest RMSE for both goaf temperature and CO concentration, indicating the best comprehensive prediction ability under the current low-temperature oxidation monitoring data. CA-WOA–XGBoost ranks second and shows balanced performance for both outputs. CatBoost and LightGBM provide useful supplementary performance, whereas RF and LSSVM show relatively higher overall errors.

The radar charts in Figure 12 further show that the overall performance of each model improves after CA-WOA optimization compared with the corresponding baseline models. In the radar charts, larger $R_T^2$, $R_{CO}^2$, and mean $R^2$ values indicate better fitting performance. The NRMSE metrics are inversely normalized, so points farther outward correspond to lower prediction errors. Compared with the baseline models, the CA-WOA-optimized models expand outward overall in the $R^2$ and NRMSE dimensions, indicating that hyperparameter optimization does not improve only a single output target but enhances the overall performance of both temperature and CO prediction tasks. Among the optimized models, CA-WOA–TABM is optimal or near optimal in multiple dimensions and shows the strongest comprehensive prediction ability. CA-WOA–XGBoost ranks second and exhibits good error control and stability.

Overall, the out-of-fold predictions and radar charts reveal the performance differences among the models from the perspectives of sequence tracking and multi-metric evaluation. CA-WOA–TABM achieved the best overall predictive performance, while CA-WOA–XGBoost also exhibited favorable accuracy and stability. The contribution directions and response relationships of the main monitoring variables for temperature and CO concentration prediction are further examined using SHAP and PDP in Section 4.4.

4.3.4. Hyperparameter Response and Sensitivity Analysis

To examine the sensitivity of prediction performance to model-training hyperparameters, two representative parameters with relatively clear fitness responses were selected for each model and two-dimensional fitness-response maps were constructed, as shown in Figure 13. These maps describe how the composite fitness changes within the investigated parameter ranges and identify relatively stable and parameter-sensitive regions. They are intended as a local response and sensitivity analysis within the predefined search space rather than as a global variance-based sensitivity analysis.

It should be noted that Figure 13 is a two-dimensional projection of a high-dimensional hyperparameter space onto two selected parameter dimensions. It is mainly used to observe parameter-sensitive intervals and search convergence directions and does not represent the complete global response surface of the full hyperparameter space. Therefore, the low-error regions and selected points in the figure should be interpreted as parameter-response characteristics under the current search records rather than as strict proof of global optimality.

Figure 13 shows that the six models exhibit different parameter-sensitivity patterns. RF has lower fitness when the number of estimators and feature-sampling ratio are in medium-to-high ranges, but further increasing the number of trees brings limited improvement. The low-error region of XGBoost corresponds to stronger sample perturbation and sufficient feature use, indicating that it needs to balance randomness and feature-information retention. LightGBM and CatBoost are sensitive to learning rate and regularization or random-perturbation parameters, so higher learning rates need to be combined with suitable complexity constraints to avoid local overfitting. The low-error region of LSSVM is relatively narrow, indicating that its performance strongly depends on the kernel parameter and regularization coefficient. The response map of TABM shows that learning rate and weight decay jointly affect model stability, and a moderate learning rate combined with appropriate regularization is more favorable for maintaining nonlinear representation ability and training stability.

The widths and shapes of the low-fitness regions differed among the six models, indicating different degrees of hyperparameter sensitivity. RF exhibited a relatively broad favorable region, whereas LSSVM showed a narrower low-error region. TABM displayed a coupled response to learning rate and weight decay, but retained a continuous favorable region around the selected parameter combination. These results indicate that the reported model performance was not confined to a single isolated parameter point.

4.4. SHAP/PDP Interpretation Analysis

To further analyze the basis of the model predictions, SHAP and PDP methods were combined to interpret the predicted goaf temperature and CO concentration. Considering that CA-WOA–XGBoost showed balanced out-of-fold prediction performance and that tree-based models allow stable calculation of SHAP contribution values, CA-WOA–XGBoost was selected as the representative interpretation model. In the following analysis, GP, UC, and RA denote goaf-pipe, upper-corner, and return-air-side monitoring variables, respectively. SHAP was used to quantify the contribution magnitude and direction of monitoring variables to model outputs, whereas PDP was used to characterize the average response trends of model outputs when key variables or variable combinations changed.

4.4.1. Interpretation of Temperature Prediction

As shown in Figure 14a, GP_CH4 has the highest mean absolute SHAP value in the temperature prediction task, indicating that it is the most important variable for the model when estimating goaf temperature variation. RA_CO2, GP_C2H6, GP_O2, UC_CH4, and GP_CO2 also show relatively high contributions, suggesting that temperature prediction is not determined by a single gas indicator. Instead, it is jointly represented by internal gas generation in the goaf, return-air-side migration response, and boundary gas changes.

Figure 14b,e,f further show that GP_CH4, RA_CO2, and GP_C2H6 provide positive SHAP contributions in some samples, thereby increasing the predicted temperature. In contrast, the contribution directions of GP_O2 and UC_CH4 vary across samples, indicating that their effects on the model output depend on the combined conditions of oxygen supply, air-leakage dilution, and gas enrichment. Figure 14c,d, and the two-factor PDP results show clear response relationships between GP_CH4 and variables such as GP_CO2, GP_O2, and RA_CO2. When GP_CH4 and GP_CO2 are both at relatively high levels, the predicted temperature increases. The combination of RA_CO2 and GP_CH4 also corresponds to a high-temperature response region. Overall, the temperature prediction mainly depends on the coordinated variation of CH₄-, CO₂-, C₂H₆-, and O₂-related variables, reflecting the model-learned response pattern associated with gas generation and thermal-state evolution in the goaf.

4.4.2. Interpretation of CO Prediction

For CO concentration prediction, Figure 15a shows that GP_CO2, GP_CH4, GP_C2H6, and GP_O2 are the main contributing variables, among which GP_CO2 has the largest contribution. This indicates that goaf-pipe CO₂ provides a strong indicator for CO prediction. Compared with temperature prediction, CO prediction relies more strongly on internal goaf-pipe gas variables, whereas the global contribution of return-air-side variables such as RA_CO2 is relatively low.

Figure 15b,e,f show that GP_CO2, GP_CH4, GP_C2H6, and GP_O2 mostly provide positive SHAP contributions in high-contribution samples. This suggests that the model does not rely on a single gas-generation indicator when identifying elevated CO responses, but instead uses the synchronous variation of multiple gas variables. Figure 15c,d and the two-factor PDP results show that GP_CO2 and GP_CH4 are located at the core of the interaction response and form clear high-CO response regions with GP_O2 and GP_C2H6.

Considering the two output targets together, GP_CH4, GP_CO2, GP_C2H6, and GP_O2 are common key variables for temperature and CO prediction, but their contribution emphases differ. GP_CH4 is more prominent in temperature prediction, GP_CO2 is more prominent in CO prediction, and GP_C2H6 and GP_O2 provide important auxiliary contributions in both tasks. Because multi-source gas variables are correlated, these results should be interpreted as model-learned response characteristics rather than strict physical causality. They should therefore be analyzed together with the processes of low-temperature oxidation, gas generation, oxygen supply, and ventilation-driven migration in the goaf.

When considered together with the model-comparison results in Section 4.3, the SHAP/PDP analysis shows that the predictions primarily depend on the oxygen-consumption, gas-generation, and migration responses represented by key variables such as goaf-pipe CH₄, CO₂, C₂H₆, and O₂. CA-WOA–TABM achieved high dual-output prediction accuracy, whereas CA-WOA–XGBoost was used to analyze the contribution directions and response ranges of the main variables. The model-performance and interpretability results therefore support the effectiveness of multi-source monitoring information fusion from the perspectives of predictive capability and variable-response relationships, respectively.

4.5. Engineering Validation on the 1202 Working Face

Monitoring data from the 1202 return-air roadway sealing area were used to examine the performance of the proposed modeling framework under an additional working-face condition. The dataset covered the period from 2 January to 28 May 2026 and contained 147 valid records. Four goaf-pipe gas variables, namely CH₄, CO₂, O₂, and C₂H₆ concentrations, were selected as model inputs and goaf CO concentration was used as the prediction target.

Two experiments were conducted from complementary perspectives. First, the samples were divided chronologically to evaluate model performance as the monitoring period progressed. Second, fivefold cross-validation was performed to compare different regression models and hyperparameter optimization strategies. Statistical analysis and computational-time comparison were subsequently conducted using the corresponding cross-validation results.

4.5.1. Temporal Generalization Under Chronological Splitting

The monitoring records were arranged by date and divided sequentially into training, validation, and test periods without random shuffling. The training set was used for model fitting and preprocessing-parameter estimation, the validation set was used for model selection and training control, and the test set represented the subsequent monitoring period. The preprocessing parameters obtained from the training data were applied directly to the validation and test sets.

XGBoost, LSTM, and TABM were developed using the same monitoring variables and temporal partitions. XGBoost characterized nonlinear relationships through a tree-ensemble structure, LSTM represented sequential variations through recurrent hidden states, and TABM constructed multiple implicit submodels on a shared network backbone. Figure 16 presents the observed and predicted CO concentrations over the three periods together with the validation- and test-error distributions. The corresponding metrics are given in

Table 8. CO concentration prediction results of XGBoost, LSTM, and TABM over different temporal periods.

Dataset	Model	${\mathit{R}}_{\mathit{C}\mathit{O}}^2$	${\mathbf{R}\mathbf{M}\mathbf{S}\mathbf{E}}_{\mathit{C}\mathit{O}}$ (×10−5)	${\mathbf{M}\mathbf{A}\mathbf{E}}_{\mathit{C}\mathit{O}}$ (×10−5)	${\mathbf{M}\mathbf{A}\mathbf{P}\mathbf{E}}_{\mathit{C}\mathit{O}}$ (%)	${\mathbf{N}\mathbf{R}\mathbf{M}\mathbf{S}\mathbf{E}}_{\mathit{C}\mathit{O}}$
Training set	XGBoost	0.9988	0.4400	0.3481	1.4624	0.0351
Training set	LSTM	0.9981	0.5343	0.4329	1.7733	0.0434
Training set	TABM	0.9242	3.3889	2.8376	10.7704	0.2754
Validation set	XGBoost	0.8054	3.0032	2.5337	12.0452	0.4412
Validation set	LSTM	0.8029	3.0221	2.6272	11.2584	0.4439
Validation set	TABM	0.7937	3.0924	2.3866	10.0391	0.4542
Test set	XGBoost	0.5633	4.1041	3.2274	12.8483	0.6608
Test set	LSTM	0.6778	3.5253	2.8518	10.3755	0.5676
Test set	TABM	0.7661	3.0037	2.5523	9.7089	0.4836

.

As shown in Figure 16a, all three models captured the principal variation in CO concentration over the monitoring period. XGBoost and LSTM closely fitted the training observations, with $R_{\mathrm{C}\mathrm{O}}^2$ values of 0.9988 and 0.9981, respectively. Their training RMSE values were $0.4400\times {10}^{-5}$ and $0.5343\times {10}^{-5}$. TABM produced a more moderate training fit, with an $R_{\mathrm{C}\mathrm{O}}^2$ of 0.9242 and an RMSE of $3.3889\times {10}^{-5}$.

The performances of the three models were similar during the validation period. Their $R_{\mathrm{C}\mathrm{O}}^2$ values ranged from 0.7937 to 0.8054. XGBoost obtained the lowest RMSE and NRMSE, whereas TABM achieved the lowest MAE and MAPE. Thus, the models exhibited comparable overall explanatory capability, but differed in their sensitivity to local deviations and average prediction errors.

The differences became clearer on the later-period test set. XGBoost achieved an $R_{\mathrm{C}\mathrm{O}}^2$ of 0.5633, with an RMSE of $4.1041\times {10}^{-5}$ and a MAPE of 12.8483%. LSTM improved the test performance to an $R_{\mathrm{C}\mathrm{O}}^2$ of 0.6778 and an RMSE of $3.5253\times {10}^{-5}$. TABM obtained the best results for all five test metrics, with an $R_{\mathrm{C}\mathrm{O}}^2$ of 0.7661, an RMSE of $3.0037\times {10}^{-5}$, an MAE of $2.5523\times {10}^{-5}$, a MAPE of 9.7089%, and an NRMSE of 0.4836.

Compared with XGBoost, TABM increased the test-set $R_{\mathrm{C}\mathrm{O}}^2$ by 0.2028 and reduced RMSE and MAE by approximately 26.8% and 20.9%, respectively. Compared with LSTM, TABM increased $R_{\mathrm{C}\mathrm{O}}^2$ by 0.0883 and reduced RMSE by approximately 14.8%. These differences indicate that TABM maintained better error control as the monitoring period shifted from the training stage to the subsequent test stage.

The training–testing performance gaps also differed among the models. XGBoost and LSTM achieved nearly complete fitting of the training data, but their $R_{\mathrm{C}\mathrm{O}}^2$ values decreased markedly during testing. TABM showed a lower training fit, but a smaller deterioration in the later period. The results suggest that the ability to fit the early-period samples was not directly equivalent to predictive stability under subsequent data conditions.

Figure 16b shows that the validation errors of the three models were generally distributed around zero. On the test set, XGBoost exhibited a wider error range and a more distinct positive tail, whereas the TABM errors remained more concentrated. This pattern is consistent with the lower test-set MAE, MAPE, and NRMSE obtained by TABM.

Overall, the chronological experiment reveals clear differences between early-period fitting and later-period prediction. XGBoost and LSTM provided high training accuracy, whereas TABM maintained more stable performance across the successive monitoring periods and achieved the best comprehensive results on the test set.

4.5.2. Model and Optimizer Comparison on the 1202 Working Face

A fivefold cross-validation experiment was conducted using the same four input variables to examine the influence of model structure and hyperparameter search strategy. The comparison included XGBoost, TABM, RS–TABM, WOA–TABM, GPBO–TABM, TPE–TABM, CMAES–TABM, CA-WOA–XGBoost, and CA-WOA–TABM.

All optimization methods used consistent data partitions, evaluation metrics, parameter ranges, and a budget of 60 objective-function evaluations. Model performance was assessed using $R_{\mathrm{C}\mathrm{O}}^2$, RMSE, MAE, MAPE, and NRMSE. The fivefold results are summarized in

Table 9. Fivefold cross-validation results for CO concentration prediction using data from the 1202 working face.

Model	${\mathit{R}}_{\mathit{C}\mathit{O}}^2$	${\mathbf{R}\mathbf{M}\mathbf{S}\mathbf{E}}_{\mathit{C}\mathit{O}}$ (×10−5)	${\mathbf{M}\mathbf{A}\mathbf{E}}_{\mathit{C}\mathit{O}}$ (×10−5)	${\mathbf{M}\mathbf{A}\mathbf{P}\mathbf{E}}_{\mathit{C}\mathit{O}}$ (%)	${\mathbf{N}\mathbf{R}\mathbf{M}\mathbf{S}\mathbf{E}}_{\mathit{C}\mathit{O}}$
XGBoost	0.7741 ± 0.1196	3.253 ± 0.889	2.539 ± 0.787	9.34 ± 3.45	0.4599 ± 0.1340
TABM	0.9093 ± 0.0304	2.121 ± 0.391	1.619 ± 0.249	6.08 ± 1.12	0.2976 ± 0.0511
RS–TABM	0.9052 ± 0.0873	2.092 ± 1.056	1.446 ± 0.637	5.47 ± 2.65	0.2880 ± 0.1220
WOA–TABM	0.9323 ± 0.0366	1.826 ± 0.611	1.339 ± 0.413	4.93 ± 1.83	0.2532 ± 0.0671
GPBO–TABM	0.9351 ± 0.0431	1.768 ± 0.697	1.219 ± 0.382	4.63 ± 1.78	0.2448 ± 0.0791
TPE–TABM	0.9468 ± 0.0256	1.616 ± 0.454	1.152 ± 0.252	4.36 ± 1.24	0.2254 ± 0.0544
CMAES–TABM	0.9456 ± 0.0202	1.654 ± 0.403	1.210 ± 0.296	4.57 ± 1.25	0.2304 ± 0.0398
CA-WOA–XGBoost	0.9055 ± 0.1146	1.936 ± 1.153	1.509 ± 0.935	5.49 ± 3.72	0.2712 ± 0.1619
CA-WOA–TABM	0.9481 ± 0.0401	1.565 ± 0.706	1.175 ± 0.546	4.27 ± 2.03	0.2159 ± 0.0816

.

TABM increased the mean $R_{\mathrm{C}\mathrm{O}}^2$ from 0.7741 for XGBoost to 0.9093 and reduced RMSE from $3.253\times {10}^{-5}$ to $2.121\times {10}^{-5}$. The corresponding MAPE decreased from 9.34% to 6.08%. This comparison indicates that the shared backbone and implicit-submodel ensemble of TABM were effective for representing the multivariable gas–CO relationship.

The performance of RS–TABM remained close to that of the baseline TABM, whereas WOA–TABM increased the mean $R_{\mathrm{C}\mathrm{O}}^2$ to 0.9323. GPBO–TABM, TPE–TABM, and CMAES–TABM all achieved mean $R_{\mathrm{C}\mathrm{O}}^2$ values above 0.935, demonstrating that the parameter space contained multiple favorable regions that could be reached through different search mechanisms.

CA-WOA–TABM achieved the highest mean $R_{\mathrm{C}\mathrm{O}}^2$ of $0.9481\pm 0.0401$, together with the lowest mean RMSE, MAPE, and NRMSE. TPE–TABM obtained the lowest MAE, while CMAES–TABM showed the smallest fold-to-fold variation in $R_{\mathrm{C}\mathrm{O}}^2$. Consequently, the three methods provided closely competitive results, but exhibited different strengths in average error, relative error, and fold stability.

CA-WOA and CMA-ES both use covariance information to describe the distribution of favorable candidate solutions, but their search processes differ. CMA-ES jointly updates the distribution center, covariance matrix, and global step size. CA-WOA constructs a rank-weighted elite center within the WOA population framework and combines covariance-direction learning with an accumulated evolution path and rank-one and rank-$\mu$ updates. The WOA random-search branch remains active during global exploration, while geometric step-size decay gradually increases the resolution of the local search. The resulting mechanism integrates elite-group guidance, interparameter directional information, and population-level exploration.

A paired bootstrap analysis was subsequently performed using the complete out-of-fold predictions. The analysis used 20,000 stratified resamples and compared TABM with XGBoost under both baseline and CA-WOA-optimized configurations. The results are listed in

Table 10. Paired OOF bootstrap comparison of TABM and XGBoost (differences reported as point estimates [95% CI]).

Model Comparison	$\mathbf{∆}{\mathit{R}}_{\mathit{C}\mathit{O}}^2$	$\mathbf{∆}\mathbf{R}\mathbf{M}\mathbf{S}\mathbf{E}$ (×10−5)	$\mathbf{∆}\mathbf{M}\mathbf{A}\mathbf{E}$ (×10−5)	$\mathbf{∆}\mathbf{M}\mathbf{A}\mathbf{P}\mathbf{E}$ (pp)	$\mathbf{∆}\mathbf{N}\mathbf{R}\mathbf{M}\mathbf{S}\mathbf{E}$
TABM vs. XGBoost	0.1262 [0.0847, 0.1716]	1.196 [0.796, 1.610]	0.921 [0.594, 1.258]	3.270 [2.040, 4.506]	0.1656 [0.1128, 0.2202]
CA-WOA–TABM vs. CA-WOA–XGBoost	0.0382 [0.0076, 0.0717]	0.511 [0.104, 0.923]	0.339 [0.083, 0.597]	1.235 [0.353, 2.152]	0.0707 [0.0146, 0.1270]

Note: Confidence intervals were obtained from 20,000 stratified paired OOF bootstrap resamples. For $R^2$, $\Delta R^2=R_{\mathrm{f}\mathrm{i}\mathrm{r}\mathrm{s}\mathrm{t}}^2-R_{\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}^2$; for error metrics, $\Delta E=E_{\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}-E_{\mathrm{f}\mathrm{i}\mathrm{r}\mathrm{s}\mathrm{t}}$. Therefore, positive values favor the first model. pp, percentage points.

.

The pooled OOF $R_{\mathrm{C}\mathrm{O}}^2$ values of TABM and XGBoost were 0.9111 and 0.7849, respectively. The $R_{\mathrm{C}\mathrm{O}}^2$ difference was 0.1262, with a 95% confidence interval of 0.0847–0.1716. TABM also reduced RMSE, MAE, MAPE, and NRMSE, and the confidence intervals for all five differences remained above zero.

Under CA-WOA optimization, the pooled OOF $R_{\mathrm{C}\mathrm{O}}^2$ values of TABM and XGBoost were 0.9448 and 0.9066, respectively. The corresponding $R_{\mathrm{C}\mathrm{O}}^2$ difference was 0.0382. Reductions were also obtained in RMSE, MAE, MAPE, and NRMSE, with all confidence intervals remaining above zero. The OOF results therefore show that the performance differences between the two model structures persisted across paired sample resampling.

The computational times of the baseline and optimized models are provided in

Table 11. Computational-time comparison of the main models and optimization methods.

Model	Objective Evaluations	Optimization Time (s)	Final Fitting Time (s)	Total Pipeline Time (s)	Inference Latency (ms/Sample)
XGBoost	—	—	0.08	0.083	0.098
TABM	—	—	0.489	0.496	0.188
RS–TABM	60	6.996	0.219	7.213	0.166
WOA–TABM	60	5.853	0.174	6.081	0.166
GPBO–TABM	60	7.073	0.253	7.275	0.157
TPE–TABM	60	7.108	0.247	7.388	0.161
CMAES–TABM	60	6.938	0.22	7.317	0.192
CA-WOA–XGBoost	60	4.604	0.079	4.68	0.098
CA-WOA–TABM	60	6.267	0.239	6.493	0.163

Notes: RS, random search; GPBO, Gaussian-process Bayesian optimization; TPE, tree-structured Parzen estimator; CMA-ES, covariance matrix adaptation evolution strategy. Baseline models did not include a hyperparameter-optimization stage, and “—” indicates not applicable. Optimization time, final fitting time, and total pipeline time are reported as median values from repeated experiments.

. To ensure a consistent comparison, the reported values were calculated from the same ten matched runs in the optimizer-comparison experiment. Optimization time, final fitting time, and total pipeline time are reported as median values from repeated experiments.

XGBoost required less time for final fitting than TABM, with median fitting times of 0.080 and 0.489 s, respectively. Under the common budget of 60 objective-function evaluations, the optimization times of the TABM-based variants ranged from 5.853 to 7.108 s. WOA–TABM required the shortest optimization time, whereas the times of RS–TABM, GPBO–TABM, TPE–TABM, and CMAES–TABM were concentrated between 6.938 and 7.108 s.

CA-WOA–TABM required 6.267 s for hyperparameter optimization and 6.493 s for the complete pipeline. Its computational time was slightly higher than that of WOA–TABM, but lower than those of RS–TABM, GPBO–TABM, TPE–TABM, and CMAES–TABM. By comparison, the total pipeline time of CA-WOA–XGBoost was 4.680 s. Thus, CA-WOA–TABM required approximately 1.39 times the total computational time of CA-WOA–XGBoost under the current data scale and evaluation budget.

The single-sample inference latencies of all evaluated models were below 0.20 ms. CA-WOA–TABM required 0.163 ms per sample, compared with 0.098 ms for CA-WOA–XGBoost. These results indicate that the principal computational differences occurred during offline model fitting and hyperparameter search, whereas all models retained rapid prediction capability.

5. Discussion

This study developed a joint prediction framework for goaf temperature and CO concentration during low-temperature oxidation by integrating multi-source monitoring fusion, CA-WOA-based hyperparameter optimization, and TABM regression. Compared with single-gas thresholds, the framework combines goaf-pipe, upper-corner, return-air-side, and working-face-side variables to characterize both internal oxidation and boundary migration responses. The feature-screening results show that goaf-pipe variables provide the dominant information, whereas upper-corner and return-air-side variables supply complementary evidence on gas transport and dilution. This combination supports a more complete description of the monitored oxidation process.

The model comparison indicates that prediction performance depends on both hyperparameter configuration and the match between model architecture and data characteristics. XGBoost retained strong baseline performance because residual boosting and tree-based splitting effectively capture nonlinear interactions in continuous tabular data. TABM achieved the best overall performance after CA-WOA optimization. Its shared backbone, lightweight submodel modulation, and output averaging form a parameter-efficient implicit ensemble that represents correlated variables and nonlinear dual-output relationships while reducing sensitivity to limited samples and local fluctuations. Together with regularized training and the compact top-six feature subset, this structure is well suited to the present small-sample, multi-source dataset. Its advantage should therefore be interpreted as task-specific architectural compatibility rather than universal superiority over conventional models.

The SHAP and PDP analyses identified GP_CH4, GP_CO2, GP_C2H6, and GP_O2 as common key variables for both outputs, although their roles differed. GP_CH4 contributed more strongly to temperature prediction, whereas GP_CO2 was more influential for CO prediction. These response patterns are consistent with the coupled effects of oxygen consumption, gas generation, enrichment, and ventilation-driven migration during low-temperature oxidation. However, they represent statistical relationships learned from the available data and should not be interpreted as direct physical causality.

The additional evaluation on the 1202 working face extended the analysis beyond the original 1806 dataset. Under chronological splitting, TABM maintained better later-period prediction accuracy than XGBoost and LSTM, while the fivefold comparison also confirmed favorable CO prediction under another working-face condition. These results reduce the possibility that the reported performance arises from a single random partition, although they do not establish cross-mine generalization.

Several limitations remain. The primary dual-output dataset was obtained from one working face, and the additional dataset supported only CO prediction. The sample size is still limited, and the monitoring period does not cover rapid heating or open-flame development. The method is therefore more appropriate for continuous prediction under low-temperature conditions than for high-temperature diagnosis or multilevel risk classification. Future work should incorporate longer monitoring periods, additional mines, programmed-heating experiments, time-lag features, online updating, and uncertainty quantification to evaluate broader applicability and the transition from low-temperature oxidation to accelerated heating.

6. Conclusions

This study investigated a joint prediction method for goaf temperature and CO concentration based on multi-source monitoring feature fusion and CA-WOA–TABM. The main conclusions are as follows.

(1)

A daily-scale multi-source monitoring sample system was constructed for the low-temperature oxidation stage of a goaf. Correlation analysis and random forest-based importance ranking indicate that GoafPipe_CH4, GoafPipe_CO2, GoafPipe_O2, and GoafPipe_C2H6 are the main features and provide key inputs for the continuous prediction of goaf temperature and CO concentration.

(2)

CA-WOA was developed by integrating rank-weighted elite-center reconstruction, covariance-adaptive direction learning, random-search injection, and geometric step-size decay. The Friedman test confirmed significant overall differences among the compared algorithms. The ablation results showed that covariance adaptation and elite-center reconstruction contributed positively on most benchmark functions, while the effects of step-size decay and random-search injection were more problem-dependent.

(3)

CA-WOA improved the dual-output prediction performance of all six candidate models. CA-WOA–TABM achieved the best performance, with a fivefold average mean $R^2$ of 0.924 and a composite fitness of 0.273. In out-of-fold prediction, the $R^2$ values for goaf temperature and CO concentration were 0.928 and 0.931, respectively, indicating stable internal validation performance under the current data conditions. Additional evaluation using data from the 1202 working face showed that TABM achieved a later-period test $R_{\mathrm{C}\mathrm{O}}^2$ of 0.766 under chronological splitting, while CA-WOA–TABM achieved a fivefold mean $R_{\mathrm{C}\mathrm{O}}^2$ of 0.948.

(4)

SHAP/PDP analysis indicates that the model captures nonlinear response relationships between key gas variables and the dual-output targets. Temperature prediction is mainly affected by GP_CH4, RA_CO2, GP_C2H6, and GP_O2, whereas CO prediction is mainly affected by GP_CO2, GP_CH4, GP_C2H6, and GP_O2. The proposed method provides data-driven support for continuous prediction of goaf temperature and CO concentration during the low-temperature oxidation stage, but further validation using more field samples and cross-mine data is still required.