Predicting roof displacement of roadways in underground coal mines using adaptive neuro-fuzzy inference system optimized by various physics-based optimization algorithms

Chngyu Xi, Hong Nguyn, Xun-Nm Bui, Vn-Thiu Nguyn, Jin Zhou

a School of Environment and Resources, Xiangtan University, Xiangtan, 411105, China

b Mining Faculty, Hanoi University of Mining and Geology, Hanoi,100000, Viet Nam

c Innovations for Sustainable and Responsible Mining (ISRM) Group, Hanoi University of Mining and Geology, Hanoi,100000, Viet Nam

d Artificial Intelligence Independent Research Group, Hanoi,100000, Viet Nam

e School of Resources and Safety Engineering, Central South University, Changsha, 410083, China

Keywords:Roof displacement Longwall mining Underground mine Physics-based optimization Risk assessment Mining hazards

ABSTRACT Due to the rapid industrialization and the development of the economy in each country,the demand for energy is increasing rapidly.The coal mines have to pace up the mining operations with large production to meet the energy demand. This requirement has led underground coal mines to go deeper with more difficult conditions,especially the mining hazards,such as large deformations,rockburst,coal burst,roof collapse, to name a few. Therefore, this study aims at investigating and predicting the stability of the roadways in underground coal mines exploited by longwall mining method, using various novel intelligent techniques based on physics-based optimization algorithms (i.e. multi-verse optimizer (MVO),equilibrium optimizer(EO),simulated annealing(SA),and Henry gas solubility optimization(HGSO))and adaptive neuro-fuzzy inference system (ANFIS), named as MVO-ANFIS, EO-ANFIS, SA-ANFIS and HGSOANFIS models. Accordingly,162 roof displacement events were investigated based on the characteristics of surrounding rocks, such as cohesion, Young’s modulus, density, shear strength, angle of internal friction, uniaxial compressive strength, quench durability index, rock mass rating, and tensile strength.The MVO-ANFIS, EO-ANFIS, SA-ANFIS and HGSO-ANFIS models were then developed and evaluated based on this dataset for predicting roof displacements in roadways of underground mines. The results indicated that the proposed intelligent techniques could accurately predict the roof displacements in roadways of underground mines with an accuracy in the range of 83%-92%. Remarkably, the SA-ANFIS model yielded the most dominant accuracy (i.e. 92%). Based on the accurate predictions from the proposed techniques, the reinforced solutions can be timely suggested to ensure the stability of roadways during exploiting coal, especially in the underground coal mines exploited by the longwall mining.

1. Introduction

Nowadays, most underground coal mines worldwide entered the stage of deep mining, and longwall mining has been widely applied with many technological advances (Sinha and Walton,2019; Darvishi et al., 2020). In advanced longwall mining, roadways play an essential role in terms of safety and coal production efficiency (Jiao et al., 2013). However, longwall mining allows the roof to collapse once the coal has been mined out in some cases.With the large width of longwall face and complex geological conditions, the ground stress in the surrounding rock can be redistributed in the longwall face of roadways, and large deformations are promising candidates in such cases(Luo et al.,2021)(Fig.1).Therefore,monitoring,predicting and controlling the large deformations,especially roof displacement,are necessary to ensure roadways’ stability and maintain safety during the service periods of underground coal mines.

Fig.1. Large deformation and roof collapse in underground mines (Qian et al., 2017; Yang et al., 2018).

Monitoring roof displacement helps to detect the deformations,and timely solutions can be adopted to reinforce the roadways,aiming to ensure safety during coal mining. So far, the main methods and devices used to monitor roof displacement events are based on microseismic systems(Fig.2).In addition,many solutions have been proposed to reinforce and control the stability of roadway in longwall mining, such as the use of steel fiberreinforced shotcrete (Zhang et al., 2019), yielding bolt combined with W steel strip and shotcrete (Mu et al., 2020), bolt combined with metal mesh, U-steel arch, shotcrete, grouting and cable (Yu et al., 2015), bolt-grouting (Wang et al., 2019), whole section anchor-grouting reinforcement(Wang et al.,2016), to name a few.However,an accurate forecast of roof displacement is considered a more comprehensive solution to be able to reinforce roadways earlier, ensuring long-term safety during longwall mining of underground coal mines.

In this regard, Mahdevari et al. (2017) developed an artificial neural network(ANN)to predict and assess the stability of the gate roadways through the roof displacements with a long roadway of 1.2 km. An ANN composed of two hidden layers was designed for this aim, and they found that it provided high conformity with a coefficient of determination(R2) of 0.911. Zhang et al. (2020a)also developed an ANN-based particle swarm optimization (PSO) algorithm for the same purpose.In addition,some benchmark models,such as hybrid system of neural fuzzy inference (HYFIS), support vector machine (SVM), conditional inference tree (CIT), classification and regression tree (CART), and multiple linear regression(MLR), were also investigated to compare and evaluate the ANNbased PSO model in estimating roadway stability. Their results reported that the ANN-based PSO model is the most superior one with an accuracy of 97%.An improved version of the SVM model for regression problem (abbreviated as ISVR) was successfully developed by Mahdevari (2021) to predict tailgate stability in longwall mines,and it yielded an accuracy of 91%instead of the accuracy of 81% and 87% for the ANN and MLR models, respectively.

After understanding the risks of roof displacements in roadways of underground mines exploited by longwall mining and its hazardous, many researchers claimed that accurate predictive techniques are potential solutions for avoiding and mitigating the accidents and risks induced by roof displacements in roadways.Nevertheless, as is known, predictive techniques, especially artificial intelligence (AI) techniques, are still sketchy in this field, as referred to above. Meanwhile, AI techniques have been widely applied in various areas in engineering(Zhang and Goh,2013,2016;Armaghani et al., 2016a, b; Hasanipanah et al., 2018a, b;Hasanipanah and Amnieh,2020;Zhang,2020;Zhang et al.,2020b,c; Zhou et al., 2020). Optimization algorithms and their efficiency were also interpreted in many previous publications(Nguyen et al.,2019,2020;Zhang et al.,2020d;Fang et al.,2021).Accordingly,the performance of AI models tends to improve with the support of optimization algorithms.However,they have not been investigated in predicting roof displacements in roadways of underground mines exploited by longwall mining except for the PSO algorithm.Therefore,this study developed four novel AI models for predicting roof displacements in roadways of underground mines exploited by longwall mining based on the adaptive neuro-fuzzy inference system (ANFIS) and physics-based optimization algorithms,including multi-verse optimizer (MVO), equilibrium optimizer(EO), simulated annealing (SA), and Henry gas solubility optimization (HGSO), named as MVO-ANFIS, EO-ANFIS, SA-ANFIS, and HGSO-ANFIS.It is worth noting that these models have not yet been developed for predicting roof displacements in roadways of underground mines exploited by longwall mining and similar problem in underground mines. In addition, the standalone ANFIS model was also applied to comprehensive assessment of these methods in predicting roof displacements in roadways of underground mines exploited by longwall mining and similar problem in underground mines.

2. Data preparation and statistical analysis

As is known,data preparation is a crucial step in data mining.It is composed of a set of procedures with the aim of providing the dataset more suitable for predictive models. In this study, a set of data with 162 roof displacement (RD) values in roadways was collected with the properties of surrounding rocks related to cohesion (c), Young’s modulus (E), density (ρ), shear strength (τ),angle of internal friction (φ), uniaxial compressive strength of(UCS), quench durability index (Id2), rock mass rating (RMR) and tensile strength (σt). Based on the roof displacement values, the roadway stability in underground mines exploited by longwall mining can be evaluated. Therefore, the predictive models, i.e.ANFIS, MVO-ANFIS, EO-ANFIS, SA-ANFIS and HGSO-ANFIS, were developed to predict the roof displacement based on the properties of the surrounding rocks, as described above.

For data collection,the roof displacement values were recorded by dual height telltale devices at different locations(Fig.3).Besides,the input variables (i.e. properties of surrounding rocks) were determined in the laboratory based on the rock samples. The measurements show that the roof displacements are in the range of 0.615-324.427 mm in different roadways of underground mines exploited by longwall mining.The statistical analysis of the dataset is referred to in Table 1,and their visualizations are shown in Fig.4.

Fig.2. Monitoring and illustrating roof displacement events in roadways:(a)Microseismic system(Xiao et al.,2016),and(b)Microseismic events and roof displacement examples(Zhang et al., 2020e).

3. Methodology

3.1. ANFIS

ANFIS is a form of ANN with the support of the fuzzy inference system (FIS). ANFIS is also referred to as a hybrid neural network with outstanding systematic and less dependent on expert knowledge(Ahsan et al.,2018).It was recommended for complex nonlinearity problems (Cuevas et al., 2018, 2020; Jing et al., 2020).Theoretically,ANFIS is designed based on a set of if-then rules along with membership functions.The membership functions of ANFIS are taken into account as the fuzzy logic function in the network. The network topology of ANFIS includes five layers:membership,fuzzification,normalization,defuzzification and combination(Fig.5).

3.2. MVO

MVO is a nature-based optimization algorithm that was proposed by Mirjalili et al. (2016). It was designed inspired by the multi-verse theory in physics. It consists of three phases: exploration,exploitation and local search based on the main concepts and mathematical of a black hole, white hole and wormhole (Ali et al.,2020).A white hole is referred to as the main part of a universe with a hypothetical region that emits matter,as opposed to a black hole that attracts all matter.A wormhole is where objects can act as their space/time travel. In a wormhole, the objects can move in a universe or between multiple universes. For these holes, the MVO optimization adopts two concepts:

Fig. 3. Dual height telltale devices for monitoring roof displacements (Bigby et al.,2010).

(1) Exploration of a particular search space by the black hole and white hole, and

(2) Exploitation of the particular search space and boosting it by the wormhole.

In the MVO algorithm, universes are taken into account as solutions, and they are denoted by the population size. In each universe, each object is given as a variable in the search space of the universe. The inflation rate is used to evaluate each universe’s fitness during the movement of the objects in the search space.Theoretically, the MVO algorithm employs the following rules for its optimization process:

(1) The inflation rate and the prospect of owning a white hole are in direct proportion.

(2) The inflation rate and the prospect of owning a black hole are in inverse proportions.

(3) Solutions (i.e. universes) with a greater inflation rate can transfer objects through white holes.

(4) Solutions (i.e. universes) with a lower rate of inflation can win more objects through black holes.

(5) A random motion may be met with the objects (in all universe)across the best universe through wormholes with any inflation rate.

The illustration of the parts of a universe and the concept of the MVO optimization algorithm are shown in Fig.6.The procedure of the MVO algorithm is depicted in Fig. A1 in Appendix A.

3.3. EO

EO is a metaheuristic algorithm that was inspired by the dynamic mass balance in physics (Faramarzi et al., 2020). As in most metaheuristic algorithm,the first step of the EO in the optimization process is the random initialization of the population of candidate solutions as follows:

where Ciis the initial population of the ith candidate solution(i=1,2, …, n); Cmaxand Cminstand for the maximum and minimum of the optimization variables,respectively;and v→is a random vector in the range of [0,1].

In the second step, the positions of the candidate solutions are updated:

Table 1 Statistical analysis of the roof displacement dataset in roadways.

Fig. 4. Understanding the dataset through visualizations.

Fig. 5. General architecture of ANFIS model.

Fig.6. (a)Illustration of the black hole,white hole and wormhole in a universe and(b)the concept of the MVO optimization algorithm(after Mirjalili et al.,2016).n is the number of solutions.

where GP is the generation probability.

The local search is employed and repeated until the best solution is found with the best fitness of the position defined. Further details of the EO algorithm are presented in Faramarzi et al.(2020),Gupta et al. (2020), Rabehi et al. (2020), Micev et al. (2021), and Shaheen et al. (2021).

3.4. SA

Like the MVO and EO algorithms, SA is a physics-based optimization algorithm proposed by Van Laarhoven and Aarts (1987).In theory, a random solution is selected for the SA starting. Subsequently, a neighboring solution is generated by the use of a perturbation method to slightly modify the current solution (Lee and Perkins, 2021). If the energy of the newly generated solution is lower than the current solution,SA will accept the new solution.It is worth mentioning that the cost function is used for this evaluation. Otherwise, a probability eΔE/Twill be accepted for a solution, in which ΔE stands for the difference of energy between solutions, and T is the temperature of solutions. Herein, temperature acts as a control parameter of the algorithm(Rutenbar,1989).

The SA implementation is often considering two categories,including problem-specific and generic choices (Henderson et al.,2003). Whereas the problem-specific choices mention various SA functions (e.g. the cost function, solution structure, perturbation method and the interest problem), the common options are not performed in the SA algorithm since it is not related to the SA’s specific problem.The procedure of the SA algorithm is presented in Fig. A2 in Appendix A. Further details of the SA can be found in Pinheiro et al. (2017), Haznedar and Kalinli (2018), Ming et al.(2019), and Tóth et al. (2020).

3.5. HGSO

As stated in the Introduction, HGSO is the last physics-based optimization algorithm that was used to predict roof displacement of roadways in underground coal mines exploited by longwall mining in this study.It was proposed by Hashim et al.(2019)based on the Henry’s law of physics. This law aims at defining the relationship between gas solubility, temperature and pressure(Agarwal et al.,2021).The implementation of the HGSO is described through seven steps:

Fig. 7. Flowchart of physics-based optimization-ANFIS models for predicting roof displacement in roadways of underground mines. MHA represents the metaheuristic algorithms.

Table 2 Parameters of the physics-based algorithm for optimization processes.

Fig. 8. Performance of the optimal physics-based-ANFIS models for predicting roof displacement in roadways of underground mines: (a) SA-ANFIS,(b)EO-ANFIS, (c) MVO-ANFIS,and (d) HGSO-ANFIS.

Table 3 Performance metrics of the proposed physics-based-ANFIS optimization models.

(1) Step 1: Generation of the initial number of populations (gas size). In this step, the position of each population (gas) is considered as one solution.Subsequently,their positions are randomly defined using the following equation:

where xlowand xhighstand for the boundaries of the search space; and t is the current position of gas.

(2) Step 2: Grouping of solutions into clusters. In this step, the gases are grouped into clusters,and they are then assigned to the Henry constants(Hj).

(3) Step 3: Evaluation of fitness. In this step, each group is evaluated, and the best gas is the highest stability state gas.For each cluster, the best gas is taken into consideration.Then, the optimal gas is selected from the gas size.

(4) Step 4: Update the Henry’s constant Hj. In this task, the Hjvalues are updated for each iteration using the following equation:

where Miteris the number of iterations.

Fig.9. Measured versus predicted roof displacements through various physics-based-ANFIS optimization models:(a)SA-ANFIS,(b)EO-ANFIS,(c)MVO-ANFIS,and(d)HGSO-ANFIS.

Fig. 10. Comparison of roof displacements by the monitored values and various physics-based-ANFIS optimization models.

(5) Step 5: Update the position of gases using the following equation:

(6) Step 6:Selection and update of the positions of worst gases.In this step, the worst number of gases (Ngas_worst) are optimized and ranked based on their fitness values using Eq.(12).Finally,the position of the worst gases is updated using Eq. (13).

Fig. 11. Reliability evaluation of the proposed physics-based-ANFIS optimization models for predicting roof displacement in roadways through the Taylor diagram.

The procedure of the HGSO algorithm is presented in Fig.A3 in Appendix, and further details of this algorithm can be found in Hashim et al. (2019), Mirza et al. (2020), Neggaz et al. (2020),Saranya and Saravanan (2020), Abdel-Mawgoud et al. (2021),Agarwal et al. (2021), and Ekinci et al. (2021).

3.6. Hybridization of MVO, EO, SA, HGSO and ANFIS

In this section, the detail of the mechanism of the MVO-ANFIS,EO-ANFIS, SA-ANFIS and HGSO-ANFIS is presented, as the main parts of this work for predicting roof displacement in roadways of underground coal mines exploited by longwall mining. To do this,the roof displacements with characteristics of surrounding rocks were collected and prepared as a sufficient dataset. This dataset is then normalized by the MinMax scaling method with the interval[-1,1] to avoid overfitting of the models. Subsequently, it is split into two sections with a 70/30 ratio for developing and testing the models,respectively.In the first phase,70%of the whole dataset is selected randomly to develop the initial ANFIS model.As is known,weights are considered as controllable parameters of the network in ANFIS,and they are often adjusted to control the accuracy of the ANFIS model. To this end, the physics-based optimization algorithms (i.e. MVO, EO, SA and HGSO) are used to optimize the weights of the ANFIS model as the second phase. The optimized ANFIS models with the optimized weights are also referred to as the hybrid models (e.g. MVO-ANFIS, EO-ANFIS, SA-ANFIS and HGSOANFIS). Prior to optimizing the ANFIS model, the optimization algorithms’ parameters need to be set up. Then, root mean squared error (RMSE) is applied as an objective function during the optimization processes as a stopping condition. The lowest RMSE values are corresponding to the best MVO-ANFIS, EO-ANFIS, SAANFIS and HGSO-ANFIS models.

Once the optimal MVO-ANFIS, EO-ANFIS, SA-ANFIS and HGSOANFIS models are well-developed, they are compared and comprehensively assessed through the testing dataset (30%), and statistical metrics in the third phase to define the best model should be used in this study. Finally, the best physics-based optimization-ANFIS model with the highest accuracy is selected for the purpose of roof displacement prediction.The flowchart of physicsbased optimization-ANFIS models for predicting roof displacement in roadways of underground mines is proposed in Fig. 7.

4. Results

In this study, the physics-based optimization algorithm, i.e. SA,EO,MVO and HGSO,were taken into consideration to combine with the ANFIS model for predicting roof displacement of roadways in underground mines.The mission of these algorithms is to improve the accuracy of the ANFIS inherently. As is known, optimization algorithms require the establishment of the parameters before implementation as mandatory. Thus, prior to the development of the hybrid models (i.e. SA-ANFIS, EO-ANFIS, MVO-ANFIS and HGSO-ANFIS), the parameters of the selected physics-based optimization algorithms were set up,as listed in Table 2.The flowchart in Fig.7 was then applied to developing the hybrid models for the goal of this work.

Prior to implementation of the optimization process, an ANFIS model was developed first as the initial predictor.In this sense,70%of the dataset was selected to develop the ANFIS model. Since the number of input variables used is equal to 9 in this study,hence,36 rules were established for the network topology of the ANFIS model. The physics-based optimization algorithms were then embedded to optimize the weights of the ANFIS model, as described in Fig. 7. It is worth mentioning that the physics-based optimization algorithms were applied to overcoming the drawbacks of the conventional ANFIS model. To evaluate the fitness of the model in each iteration,RMSE was used as the objective function.The optimization processes of the ANFIS model were looped in 1000 epochs, and the lowest RMSE was selected as the optimal model. Fig. 8 shows the training error of the hybrid models with different population sizes.

As seen from Fig.8,the proposed hybrid intelligent models with the optimization processes are well worked. All the models with different populations are convergent within 1000 iterations.In this sense,the best fit of the SA-ANFIS model was convergent with the population size of 500 and 999 iterations; the best fit of the EOANFIS model was achieved with the population size of 500 and 997 iterations;the best fit of the MVO-ANFIS model was found with the population size of 450 iterations;and the best fit of the HGSOANFIS model was defined with the population size of 250 and 245 iterations. However, to avoid the models’ overfitting, the testing dataset was validated with different population sizes and iterations.Finally,the best fit of the models for both training and testing phases were selected as follows:

(1) The best SA-ANFIS model:The population size of 50 and 999 iterations;

(2) The best EO-ANFIS model: The population size of 350 and 997 iterations;

(3) The best MVO-ANFIS model:The population size of 400 and 997 iterations; and

(4) The best HGSO-ANFIS model:The population size of 450 and 699 iterations.

For evaluating the performance of the selected optimization models,criteria such as mean absolute error(MAE),RMSE,R2,mean absolute percentage error (MAPE) and Nash-Sutcliffe error (NSE)were used as the performance metrics for both datasets of training and testing. They are calculated using Eqs. 15-19, respectively.Finally, the best results of the selected optimization models are computed and listed in Table 3. It is worth noting that these performance indices were computed based on the ground-truth values and predicted values of the proposed hybrid models.

5. Discussion

As seen from Table 3, the SA-ANFIS model provided the lowest MAE and RMSE (i.e. 7.368 and 11.788, respectively), in accordance with the highest R2(i.e. 0.964) and NSE (i.e. 0.964), in the training phase.Whereas the MAPE value is acceptable with 0.544%of error,although it is not the lowest MAPE value.Similar findings were also found in the testing phase,with the SA-ANFIS model which was the most dominant model for predicting roof displacement of roadways in underground coal mines exploited by longwall mining.Followed by the MVO-ANFIS and EO-ANFIS models, the HGSOANFIS model provided the poorest performance, with the lowest performance metrics.Remarkably,the overfitting phenomenon did not occur for the developed models with the training and testing performance’ consistency. Aiming at the assessment of the developed physics-based-ANFIS models for predicting roof displacement in this study, the measured roof displacements and predicted roof displacements by various physics-based-ANFIS optimization models were visualized through the correlation plots,as shown in Fig. 9.

From Fig. 9, good fitting results were observed for the hybrid models,especially the SA-ANFIS model with the highest correlation(i.e.R2=0.9642 in the training phase,and R2=0.9213 in the testing phase). In contrast, the HGSO-ANFIS model provided the poorest correlation(i.e.R2=0.7422 in the training phase,and R2=0.8341 in the testing phase).Taking a closer look at Fig. 9b-d, we can see an outlier prediction with an absolute error of approximately 200 mm(in the training phase)for predicting roof displacement of roadways. Remarkably, the predicted value of this point is too smaller than the measured one,and it may lead to a high risk in the roadways. Furthermore, this predicted data point contributed significantly to the violin of the EO-ANFIS,MVO-ANFIS and HGSOANFIS models. Meanwhile, this data point was precisely predicted by the SA-ANFIS model.Considering the testing phase in Fig.9,the correlation between measured and predicted roof displacements in practice is highly appropriated,especially the SA-ANFIS model with the best fit of the correlation. To evaluate the absolute accuracy of the developed intelligent models in practice, a comparison between measured and predicted roof displacements by the individual models was conducted in Fig.10.Moreover,the reliability of the developed models is compared and evaluated through the Taylor diagram and the actual model in Fig.11.

Fig. 12. Sensitivity of the input variables for predicting roof displacement: (a) Feature value of the input variables, and (b) Statistics of sensitivity analysis. Sen represents the sensitivity, and std is the standard deviation.

As can be seen in Fig.10,the difference between measured and predicted roof displacements by the developed models is incredibly low. In other words, the accuracy of the developed models in practice for predicting roof displacement of roadways is high, as described in Table 3, the error of the models is in the range of 0.186%-0.239%.As illustrated in Fig.11,it can be observed that the SA-ANFIS model is closest to the actual model,and therefore,it was evaluated as the best model for predicting roof displacement of roadways in underground coal mines exploited by longwall mining in this study.

6. Sensitivity analysis

In order to diagnose the influence of the input variables on the roof displacement predictions,a sensitivity analysis is necessary in this study. For this aim, a sensitivity analysis (Kirsch et al., 2005;Bogomolni et al., 2006) were conducted to quantify inputs importance, as shown in Fig.12. The results show that the RMR and UCS variables provided the highest sensitivity to the roof displacement predictions. In Fig. 12a, the different values of the independent variables showed their effects on the dependent variable under a given set of assumptions. Accordingly, the RMR variable contains many values which have high feature value, and the UCS variable contains medium feature values, but their sensitivity is slightly lower than the RMR variable only.Following variables are the φ and C. The remaining variables seem to be of low significance on the roof displacement predictions.Based on the sensitivity analysis,we can understand how various sources of uncertainty in the proposed SA-ANFIS model contribute to the model’s overall uncertainty.

7. Conclusions

The stability of roadways in underground mines exploited by longwall mining is a great concern of engineers,researchers,as well as mine companies since it can cause severe accidents with the large deformation of surrounding rocks based on the roof displacement.Therefore,a precise forecast of the roof displacement in roadways has significance in mitigating the risks and accidents from surrounding rock deformation and roof displacement in roadways.This study proposed four novel intelligent models based on physics-based optimization algorithms (i.e. SA, EO, MVO and HGSO)and ANFIS,i.e.SA-ANFIS,EO-ANFIS,MVO-ANFIS and HGSOANFIS models, for predicting roof displacement in roadways. The obtained results show that the proposed intelligent models are potential tools for mitigating and early-warning the risks and accidents from the instability of roadways in underground mines.Of those, the SA-ANFIS model was introduced as the most dominant model with the highest accuracy in predicting roadway stability.Based on the accurate predictions from the proposed model, the reinforcement solutions can be suggested to ensure roadways’stability during exploiting minerals,especially in the underground mines exploited by the longwall mining.

In this study, the roadway stability in underground mines was considered and predicted through the roof displacement of roadways.The obtained results are positive,and they are background for future works. However, due to the dataset was collected from different underground mines, thus different buried depths may have great influence on roof displacement and vault settlement.Future works should be performed to consider the effects of different buried depths on roof displacement and vault settlement,as well as survey the accuracy of the proposed AI models in this study with such conditions.

Declaration of competing interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication, and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

This research was funded by the Natural Science Foundation of Hunan Province,China(Grant No.2021JJ30679).The authors would also like to thank the Center for Mining, Electro-Mechanical Research, Hanoi University of Mining and Geology, Hanoi, Vietnam,for the kind supports.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jrmge.2021.07.005.