Prediction of the stability of gob‐side entry formation by roof cutting by machine learning‐based models

Gob‐side entry formation by roof cutting is a new technology for no pillar coal mining, which can maximize coal resources and reduce roadway drivage ratio. However, the mechanical behavior of the formed entry is complex while it is crucial to ensure the stability of the entry for mining safety. This paper proposed a machine learning‐based method for predicting the stability of the formed entry, which combined artificial neural network (ANN) with particle swarm optimization (PSO) algorithm or genetic optimization (GO) algorithm. The data set from 75 coal mining faces from 2009 to 2022 was employed to train and test the models. A descriptive variable of dynamic unstable distance was introduced to evaluate the stability state of the formed entry and six other parameters were chosen as influence parameters. The two intelligent models were compared with each other to have a comprehensive assessment. Model assessment indices such as R2, mean absolute error, mean absolute percentage error, and root mean square error were used to evaluate the accuracy of the models. The results of both developed models are promising, and the predictive accuracy of the PSO‐ANN model is higher than that of the GO‐ANN model. Through sensitivity analyses, it has been found that the coal seam thickness and roof rock hardness are the most important parameters for influencing entry stability. The developed method provides a practical tool for the prediction of entry stability and the optimization of entry design.


| INTRODUCTION
Coal is the principal energy source in China, accounting for 56% of the total energy consumption in 2021. 1,2 Moreover, more than 90% of coal mines in China are underground mines. Underground coal pillars that are columns of coal left in place in the mine to support overlying rock not only result in the waste of coal resources but also increase mining cost and accident rate. [3][4][5] Gob-side entry formation (GEF) by roof cutting is an emerging no coal pillar longwall mining technique that can dramatically improve coal recovery ratio. 6 Under the GEF technique, the coal pillar between adjacent mining faces is canceled and one entry of the current mining face is formed and retained for the next mining face. Because the formed entry is reused, and 50% entry excavation is reduced, the GEF technique is of great significance for optimizing the balance relation of mining and entry excavation.
In conventional mining systems with coal pillars, the entries are excavated in the integrated coal seam in advance and the entries collapse after mining. 7,8 However, in the GEF, one entry of the mining face is not excavated, but retained and formed during mining. 9 The formed entry is close to the gob and influenced by caved gangues. Therefore, it is extremely important to evaluate the stable state of the formed entry. Previously, theoretical, numerical, and experimental methods are commonly used to study the stability of the formed entry. He et al. 10,11 and Wang et al. 12,13 established a mechanical model of roof cutting cantilever beam to study the stability of the formed entry. Gao et al. 14 proposed a directional roof split blasting technique to improve the stability of the formed entry. Tao et al. 15 obtained the stress data of the formed entry surroundings by comparing the no pillar mining and pillar mining system using a quasi-distributed Fiber Bragg Grating (FBG) sensing technology. 16 Wang et al. 17,18 established a stability analysis model of the formed entry based on Mohr's circle theory. Yang et al. 19 investigated the breaking states of the main roof using the discrete element method simulation method. Wang et al., 20 Sun et al. 21 showed the caving, compacting, and stabilizing process by physical model test. In recent years, artificial intelligence techniques have been gradually used for prediction in roadway engineering. Mahdevari et al. 22 introduced a multilayer perceptron network to predict the stability of the longwall roadway. Xie et al. 23 introduced various intelligent technologies based on physical optimization algorithms to compare and predict the stability of entry with coal pillars. Li et al. 24 established a support vector machine (SVM) model based on Harris Hawks Optimization Algorithm (HHOA) (i.e., HHOA-SVM) to predict entry deformation. In addition, the hierarchical local model tree (HILOMOT) model 25 and the Adaptive Neuro Fuzzy Inference System (ANFIS) model 26 also show excellent prediction performance in roadway rock migration.
Due to the movement of the overlying strata and dynamic compaction of the gangues, the stabilization of the formed entry is an ongoing process. 27 When the entry section is after a certain distance from the mining coal wall, the entry surroundings will bear each other to be a stable state again. Therefore, the dynamic stable state of the formed entry induced by dynamic mining pressure is important for the support design, and it is related to many factors such as mining depth, coal seam thickness, and roof cutting parameters. [28][29][30] However, previous studies mainly focus on the stabilizing mechanism of the formed entry in a specific condition from local scope. The study on stability prediction of gob-side entry comprehensively considering geological and design factors is lacked. Artificial neural network (ANN) is an abstract mathematical model and a form of artificial intelligence based on neurology which reflects basic characteristics of the human brain. The ANN has a certain learning ability and exhibits good intelligence characteristics in terms of prediction. Particle swarm optimization (PSO) algorithm and genetic optimization (GO) algorithm can improve the efficiency of ANN models. 31,32 Based on 75 sets of data collected from 60 mines in China, new machine learning-based models for predicting the stability of the entry in GEF is introduced based on optimized ANN models by PSO and GO algorithms. The two intelligent methods were compared with each other to have a comprehensive assessment and were evaluated by field monitoring data to verify their accuracy.

| PRINCIPLES OF THE GEF AND MACHINE LEARNING-BASED MODELS
2.1 | GEF by roof cutting GEF by roof cutting is a new technique to achieve no pillar mining. To cancel the coal pillar of the whole mining area, the gob-side entry of the current mining face needs to be retained for the next mining face. To preserve the entry, a series of measures must be taken to prevent the roof from collapsing when the working face is mined.
As shown in Figure 1, the section A-A' is in front of the active mining wall and belongs to the advanced support area. In this area, the NPR cables are installed in the roof to improve the stability of the entry. At the same time, to reduce the influence of the gob roof collapse on the stability of the formed entry, the roof cutting is performed in the middle of the entry roof and the gob roof. The two most critical parameters of roof cutting are the roof cutting height and angle. 33 The roof cutting height will affect the weakening degree of the transmission stress, while the roof cutting angle can affect the load-bearing of the gangue and the entry roof.
The section B-B' is behind the active mining wall and near the hydraulic support. This area is called the temporary support or the dynamic unstable area.
A certain range of the formed entry behind the mining coal wall is the most unstable area. In this area, the overlying strata movement and gangue compaction cause the entry to be subjected to dynamic pressure. Temporary support needs to be installed to further improve entry stability. When entry surroundings stop moving, the collapsed gangue and the entry roof form a stable bearing structure and the entry section is in a stable state. At this time, the temporary support can be removed.
Before mining, the entry roof and gob roof are a whole. When the coal seam is mined, the surrounding rocks of the entry move and form a new equilibrium system. The gob roof caves and a new sidewall is formed by the gangues. The caved gangues exert a friction force on the entry roof. In addition, the overlying strata of the gob moves and deformed. The movement of the overlying strata inevitably influences the stability of the entry. Therefore, for a distance behind the mining wall and hydraulic support, the formed entry is in an unstable condition owing to the caving of the gob roof and movement of the overlying strata. The key to ensuring the success of GEF is to determine the range of the unstable area. The purpose of the study is to investigate an effective method to predict the stability state of the formed entry. Therefore, we introduce a descriptive variable of dynamic unstable distance (DUD) to evaluate the stability state of the formed entry. The value of the DUD can provide a valuable reference for temporary support design. Details on the measurement of DUD will be introduced later.
The section C-C' is located in the stability area of the formed entry. In this area, the gob roof caves and broken, the volume of caved rock increases compared with the original rock. The bulking gangues aslant support the entry roof. Under this condition, when the temporary hydraulic supports are removed, the formed entry can still remain stable.

| ANN
ANN is an effective machine learning method of AI. 34 It is operated and simulated by imitating the function of the human brain, which is very suitable for solving complex nonlinear problems in practical engineering. 35,36 The typical structural model of ANN is shown in Figure 2. The model includes input layer, a hidden layer and an output layer. In the model, ξ k represents the input unit, C j represents the hidden unit and O i represents the output unit. The w jk and W ij are connection weights. w W w = { , } indicates all connection rights.
Output unit subscript i I = 1, 2 …, ; Hidden unit subscript j J = 1, 2 …, ; Input unit subscript k K = 1, 2 …, . In addition, u represents different input modes; P indicates the number of input modes, u P = 1, 2 …, ; g 1 and g 2 correspond to the appropriately selected activation functions of the hidden layer and the output layer, respectively. Under the given input mode u, the input of the hidden unit j is The output is The input of the output unit i is The final output result is In the process of data processing, the signal forward propagation and error back propagation is iterative. 37 In this process, the current weight w is modified to obtain a new weight △w. The error is continuously reduced to meet the set learning objectives through iteration. The flow chart of the learning process of back propagation ANN is shown in Figure 3.

| Optimization algorithms
(1) PSO algorithm PSO algorithm is a population-based random search algorithm inspired by the bird foraging model. PSO algorithm has the characteristics of conciseness and high efficiency, and thus it is widely used in the fields of structural design and engineering optimization. 38 The algorithm can be dynamically adjusted according to the particle individual optimal solution and global optimal solution, so as to improve the candidate solution.
In the PSO algorithm, the solution of the problem F I G U R E 2 Flowchart of artificial neural network for stability prediction of the formed entry. to be optimized is abstracted as particles. The set of n particles in D-dimensional space is X. 39 In each iteration, the update formula is ; t is the number of iterations; v hd is the velocity of the particle and x hd is the position of the particle; c 1 and c 2 are learning factors, c c = = 2 1 2 ; r 1 and r 2 are random numbers uniformly distributed in [0,1].
(2) Genetic Optimization (GO) algorithm GO algorithm is a global optimization search algorithm based on the laws of "survival of the fittest and survival of the fittest" in nature. 39 Unlike the single-point search algorithm, the GO algorithm completes the search process through population and it is highly adaptable. Because the GO algorithm has many searching trajectories, it is easy to be parallelized, which further improves the efficiency of the algorithm. 40 In the iterative process, adaptive crossover probability is adopted. The crossover probability is automatically adjusted with the value of the fitness function during the calculation. The calculation formula is as follows: where Y s is the adaptive crossover probability; f max is the value of the fitness function for which the individual in the population is the largest; f avg is the average value of the fitness function for each generation of the population; f is the value of the fitness function that produces the crossover of two individuals one of which is larger; Q 1 , Q 2 are constants in the interval from 0 to 1.
The adaptive variation probability is calculated as follows: where Y m is the adaptive mutation probability.

| PSO-ANN and GO-ANN
There are two obvious disadvantages in the ANN modeling process. First, the model easily falls into local minimum. Second, the convergence speed of the model is slow. 41 The PSO is capable of searching the entire solution space to find the global optimum according to the particle network with existing information exchange, which can help ANN overcome the shortage of local minimum solution. 38 GO, as an optimal random search algorithm, can also search the entire solution space. 40 Therefore, we try to find an optimal model for the stability prediction of GEF by roof cutting by optimizing the ANN model using PSO and GO algorithms, respectively.
(1) The establishment process of PSO-ANN model is as follows, 42 as shown in Figure 4. ① Determine the neural network structure; ② Initialize the weight and threshold of the ANN; ③ Establish the relationship between PSO and weight and threshold, and initialize the PSO; ④ Calculate the particle fitness value and update the position and speed of each particle; ⑤ Calculate the error of PSO-ANN. If the error meets the requirements, proceed to the next step. If not, repeat step ④; ⑥ Output the optimization results, train the ANN model, and obtain the PSO-ANN structure model.
(2) The establishment process of GO-ANN structure is as follows, 42 as shown in Figure 5. ① Establishment of ANN structure; ② Train the data using ANN and generate the initial population; ③ Initial coding and pre-processing of GO algorithm; ④ Use different initial values for fitness calculation; ⑤ Genetic manipulation processing; ⑥ Obtain the optimal weight and threshold value (or repeat ④ and ⑤, and finally obtain the optimal values); ⑦ Assign values to neural network, find the global optimal solution and establish the GO-ANN structure model.

| Measurement of the DUD
In this study, the DUD data from 75 coal mining faces in 60 underground coal mines were collected from 2009 to 2022 to predict entry stability and train the AI model. The location of the mines is shown in Figure 6. For measuring the value of DUD, the real time on-line monitoring system was used to record the displacement and stress variation in the formed entry, as shown in Figure 7.
Before the entry formation, the displacement monitoring unit was installed on the roof cutting side of the entry, aiming to monitor the roof-to-floor convergence. As the working face advances, the monitoring position gradually moves away from the active working face and enters the dynamic pressure affected area. When the difference between the monitoring values for three consecutive days is less than 1 mm, it is considered that the formed entry has been initially stabilized and the provisional DUD is obtained. To ensure the effectiveness of the monitored DUD, the stress monitoring unit was also installed on the temporary support to monitor the variation of roof load. Only when the displacement and stress are both stable, the distance between the measure point and the active mining face is the finalized DUD value. Figure 7 shows an example of DUD monitoring in the Zhujiamao coal mine in Shaanxi province of China. As the entry is formed and mining face advances, the pressure of the temporary support and deformation of the entry surroundings first increase and then gradually stabilize. The pressure of the temporary support tends to be stable after 172 m behind the working face, and the stable pressure is 31.6 MPa. When the formed entry is 174 m behind the working face, the amount of roof-to-floor convergence no longer changes and the final value is 325 mm. Therefore, to sum up, only when the F I G U R E 4 PSO-ANN system for stability prediction of gob-side entry formation. ANN, artificial neural network; PSO, particle swarm optimization.
F I G U R E 5 GO-ANN system for stability prediction of gob-side entry formation. ANN, artificial neural network; GO, genetic optimization.
| 2207 pressure and deformation of the entry surroundings are both stable can it be regarded that the formed entry is in a stable state. At this time, the maximum distance between the measuring point and the working face is the DUD value. In this case, the DUD value of 1310 working face of Zhujiamao coal mine is 174 m.

| Input and output parameters
Previous studies have found that geological and roof cutting parameters are crucial to the stability of formed entry in GEF. 33 Among the geological factors, the buried depth of the mining face, the thickness of the coal seam, the dip angle of coal seam and the hardness of the roof strata are closely related to the stability of entry formation. The buried depth mainly affects the ground stress of the entry surroundings. With the increase of the buried depth, the ground stress of the entry surroundings increases. The size of the mining room is related to the thickness of the coal seam. The movement of the strata is more vigorous for a thick coal seam. The dip angle of the coal seam and the hardness of the roof strata can influence the caving process of the roof rock. In addition, because the most significant difference between the GER and the conventional entry retaining technology is that the entry in GER is formed using roof cutting method, the roof cutting height and roof cutting angle also have important impacts on the stability of the entry formation. Therefore, they were chosen as the input parameters. To represent the stability of the formed entry, the DUD of the formed entry was used as the output variable.
Box and Whisker plot is a convenient way of visually displaying the data distribution through their quartiles. This type of plot has the advantage of taking up less space, which is useful when comparing distributions between many groups or data sets. The characteristics of the input and output parameters are illustrated in Figure 8. We can see the upper extreme, upper quartile, median, lower quartile and single data point. For example, from the Box and Whisker plot of coal seam thickness data set, we can understand that the minimum and maximum value is 0.78m and 4.9m, respectively. The

| PREPARING DATA
For different types of data, their impacts on the stability of the entry are different and there is an obvious difference between them. Because the input variables have different dimensions, there is no prerequisite for direct comparison, and there may be uncertain correlation. Therefore, before modeling, the Box-Cox transformation technique was used to preprocess the input variable database. 43 Box-Cox transformation is a normalization process for the same class of samples, which enables scattered data to be concentrated in a small area, thereby accelerating the convergence speed of the neural network and greatly improving classification accuracy. Because the transformation is for the same class of samples, the independence of data can be guaranteed. After transformation, the distribution of each type of data is closer to normality, with a relatively small number of cross regions, ultimately leading to clearer categories between data. This process can prevent over or under fitting of the predictive models. After box Cox transformation, normality, symmetry and variance equality of data can be significantly improved. Figure 9 shows the data distribution of the original input variables after normalization and box Cox transformation. Obviously, they have the characteristics of normal distribution.
F I G U R E 9 Distribution of original input and output variables after pre-processing.
To reduce unnecessary interference to the results due to different data magnitudes, the Mapminmax function in the MATLAB was used to normalize the data and Trainlm function was used to train the model.
The training model requires training data sets, verification data sets and testing data sets. 44 The training data sets are used to train the model and determine parameters, the verification data sets are used to determine the network structure and adjust the hyperparameters of the model. The testing data sets tests are mainly used to test the generalization ability of the model. According to the previous research, the ratio of the training data sets, verification data sets and testing data sets is 0.7:0.15:0.15. In our study, 51 observations were used to train the models, 12 observations were used for verification and 12 remaining cases were used for testing. First, the training set data is used to train the model. Based on the error loss of the training results, the parameters of the model are adjusted. After that, the verification set data is used for verification. In this process, a set of hyperparameters was initially set and the corresponding parameters can be obtained by training the training set data. If the effects are not satisfactory, the hyperparameter is adjusted and another corresponding parameter is obtained. This cycle is repeated, resulting in a series of hyperparameters and training parameter pairs. The optimal hyperparameter is then obtained. Finally, test set data are used to verify the generalization effects of the final model parameters. In this stage, model parameters are no longer adjusted.

| PSO-ANN model
Since the algorithm adopted by the back propagation neural network is based on the error function gradient of the network, the algorithm does not have the global searching ability. Therefore, the neural network has shortcomings such as slow convergence, easy to fall into local minimum points, poor robustness and poor network performance in the learning process. To predict the stability of the formed entry, the framework in Figure 4 was used to build an PSO-ANN model. The global search feature of the PSO algorithm is fully utilized to obtain an initial weight matrix and bias vector, and then the back propagation training algorithm is used to obtain the final neural network structure.
According to the characteristics and influence factor of the formed entry, an ANN structure with 6 nodes in the input layer, 20 nodes in the hidden layer and 1 node in the output layer was established. The training times of the network is set to 1000 and the learning efficiency is 0.1. The parameters of the PSO were set up by a trial-anderror procedure. The maximum number of iterations was set to be 100 with a population size of 10. The maximum particle velocity was 10. The individual cognitive and group cognitive were both 1.49. The inertia weight parameter determines how much the particle's previous velocity affects the current velocity, thus balancing the global search and local search capabilities of the algorithm. 45 The adjustment formula of the inertia weight is where w i ( ) is the inertia weight; i is the current iteration number; i max is the maximum number of iteration; w max is the maximum inertia weight, w = 1 max ; w min is the minimum inertia weight, w = 0.2 min . The PSO-ANN was trained and the error curve in the process of particle swarm optimization is shown in Figure 10. It can be seen that the particle swarm optimization algorithm reaches the target error (MSE) after seven iterations. The best validation performance is 0.1077. The results of PSO-ANN prediction are shown in Figure 11. In the trained data, the average absolute value of error between the predicted value of PSO-ANN model and the actual value is less than 5. In the test data, the average absolute value of error between the predicted value of PSO-ANN model and the actual value is 4.6, with a high degree of coincidence, which can accurately predict the DUD value. The error between the predicted value of PSO-ANN model and the actual value is small, basically within 25, with a high degree of coincidence, which can accurately predict the DUD value. By comparing the error bar, the prediction accuracy is obtained.

| GO-ANN model
In the GO algorithm, the selection, crossover and mutation process in the biological genetic process is simulated through the genetic operator to obtain the optimal individual. In view of the characteristics of GO algorithm, a GO-optimized ANN is formed by combining GO algorithm and ANN, and it is applied to the stability prediction of GEF by roof cutting. First, the GO algorithm is used to perform a global search on the weights and thresholds of the neural network. The range of the optimal solution can be located and the weights and threshold populations are gathered in certain places in the parameter space. Then, the local optimization GAO ET AL.
| 2211 ability of the back propagation algorithm is utilized to obtain the optimal solution. In the neural network, the Tansig is chosen as the node transfer function, and the Purelin is chosen as the linear function, and the LM optimization algorithm Trainlm function which has a faster convergence speed is adopted as the training function. In the GO-ANN model, the population size was set to be 60, the crossover probability is 0.4, and the mutation probability is 0.01.
The GO-ANN model was trained and the error curve in the process of genetic optimization is shown in Figure 12. It can be seen that the genetic optimization algorithm reaches the target error (MSE) after 18 iterations. The best validation performance is 0.028. The results of GO-ANN prediction are shown in Figure 13. In 75 cases, GO-ANN model can basically achieve the expected output value. However, there are six cases where the error exceeds 25, including one where the error exceeds 50, which is worse than the PSO-ANN model.

| Evaluating the performance of the models
(1) Performance of the models In this study, the correlation coefficient (R 2 ), mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square error (RMSE) are used F I G U R E 10 Error reduction process of the PSO-ANN model. ANN, artificial neural network; PSO, particle swarm optimization.

F I G U R E 11
Predicting results of the PSO-ANN model during the training and testing process. ANN, artificial neural network; PSO, particle swarm optimization.
to evaluate the reliability and accuracy of the models. The above errors are calculated according to the measured and predicted data, as listed in Table 1. Furthermore, Figure 14 illustrates the performance correlation of the two optimized ANN models based on the testing data set. It can be seen from Table 1 and Figure 14 that the R 2 values of both PSO-ANN model and GO-ANN model are higher than 0.95, indicating that the accuracy of the two optimization models is high. Among them, the prediction accuracy of PSO-ANN model training data set is the highest, which is 0.99083; The prediction accuracy of GO-ANN model testing data set is the highest, 0.98663. Based on this indicator, both models can meet the engineering requirements.
The performance of the PSO-ANN model is the highest (R 2 = 0.99083, MAE = 4.685, MAPE = 3.7%, RMSE = 8.856 on the training data set; R 2 = 0.96035, MAE = 3.615, MAPE = 2.2%, RMSE = 6.463 on the testing data set) to predict the entry stability in the GEF method, whereas the GO-ANN model provided relatively low performance. Specifically, from the perspective of the MAE value, both the training data set and the testing data set, the error of the PSO-ANN model is smaller than that of the GO-ANN model, and the error of the training data set is reduced by 44.7%. According to MAPE, the test data sets of the two models are equally good and bad, while the performance of PSO-ANN model is better in the training data set. In addition, PSO-ANN model also shows superior predictive performance through RMSE value. Therefore, overall, PSO-ANN model has relatively better advantages.
(2) Importance of the input variables The accuracy of the model depends on many factors. Among them, the input variables have prominent influence. From the above research, we can understand that the PSO-ANN model yielded better outstanding performance and six input variables (mining depth, coal seam thickness, coal seam angle, roof cutting height, roof cutting angle and roof rock hardness) influence the results. Therefore, the level of importance of the input variables was evaluated using the Olden method, 46 as shown in Figure 15. The analysis results show that the coal seam thickness and the roof rock hardness have the greatest impact on the stability of the entry, with the importance of 0.4535 and 0.306 respectively. The importance of roof cutting height and mining depth is the third and fourth respectively. The coal seam angle variable has an effect, but not much. The roof cutting angle has little affect the PSO-ANN's performance.

(3) Comparison of previous research
The gob-side entry formed by roof cutting is located near the gob and its stability is related to many factors. To determine the stability condition of the formed entry, many previous studies have been conducted, but all the studies are based on field monitoring. Guo et al. 47 studied the fracturing mechanism and deformation characteristics of the rock surrounding the gate during gob side entry retention through roof pre-fracturing for a medium-thickness coal seam mining, the displacement of the roof and the floor convergence was monitored in the field. The formed entry tends to be stable after 134 m  behind the active mining wall. Using a real-time remote monitoring system, Yang et al. 30 investigated the surrounding rock mass deformation of the formed entry under a thick coal seam condition, the entry roof became stable after the working face passed 140 m. Using similar methods, the stability state of the formed entry under different geological conditions were determined. 17,48 The methods of determining the stability of the formed entry in the above studies are all conducted after implementation of the no pillar mining technology in the field. It is hard to determine the unstable distance before on-site application. However, for the dynamic unstable area of the formed entry, it's very necessary to customize the temporary support equipment and materials before application.
The key parameter of the entry stability is an important reference for determining procurement quantity ahead of schedule. In our study, the measured data in other applied mines were collected and used to build machine learning-based models. Before application of the new technology, considering the influencing factors, the stability of the formed entry can be predicted based on the models, thus providing an important reference for support design and temporary support customization. The stability of the entry is affected by various factors. In addition to the factors mentioned in the text, the faults, collapse columns, etc. are also factors that affect the stability of the formed entry. In this study, special factors were not considered. For predicting the stability conditions of the entry in these special circumstances, the accuracy of the model will be affected, and field monitoring and model prediction should be combined for analysis. On the other hand, the number of applied mines is limited, which also has a certain impact on the accuracy of model training and prediction. However, this study provides a new and economically feasible method for the stability prediction of GEF by roof cutting.

| CONCLUSIONS
GEF by roof cutting is a novel technology for non-pillar mining. Stabilizing of the formed entry is a dynamic process and stability prediction of the formed entry plays an important role in engineering design. According to the characteristics of the entry formation, six parameters were chosen as the input variables and the DUD of the formed entry was used as the output variable to establish a machine learning based model for entry stability prediction based on ANN. To solve the local minimum and convergence speed problems, PSO and GO algorithms were used to optimize the ANN model, respectively.
The input and output variable data from 75 mining faces in 60 coal mines were monitored and trained using the PSO-ANN and GO-ANN models. By comparing the prediction errors, it has been found that both developed models are promising and the PSO-ANN model is more accurate to evaluate the dynamic stability of the formed entry. The performance of the PSO-ANN model is the highest (R 2 = 0.96035, MAE = 3.615, MAPE = 2.2%, RMSE = 6.463), which provides a robust tool for entry formation design. On the basis of the above, the Olden method was used to evaluate the importance of the input variables on the entry stability. The coal seam thickness and roof rock hardness are the most influential factors in the performance of the model. The results have guiding significance to engineering design during entry formation for non-pillar mining.