A Model to Predict Crosscut Stress Based on an Improved Extreme Learning Machine Algorithm

: The analysis of crosscut stability is an indispensable task in underground mining activities. Crosscut instabilities usually cause geological disasters and delay of the project. On site, mining engineers analyze and predict the crosscut condition by monitoring its convergence and stress; however, stress monitoring is time-consuming and expensive. In this study, we propose an improved extreme learning machine (ELM) algorithm to predict crosscut’s stress based on convergence data, for the ﬁrst time in literature. The performance of the proposed technique is validated using a crosscut response by means of the FLAC 3D ﬁnite difference program. It is found that the improved ELM algorithm performs higher generalization performance compared to traditional ELM, as it eliminates the random selection for input weights. Furthermore, a crosscut construction project in an underground mine, Yanqianshan iron mine, located in Liaoning Province (China), is selected as the case study. The accuracy and efﬁciency of the improved ELM algorithm has been demonstrated by comparing predicted stress data to measured data on site. Additionally, a comparison is conducted between the improved ELM algorithm and other commonly used artiﬁcial neural network algorithms.


Introduction
Surrounding rock stability in crosscuts has always been a major concern in underground mining activities. Crosscut accidents such as roof failures, rib falls, and rock blasts primarily resulted from stress concentration and could lead to casualties and huge economic loss [1][2][3][4]. For example, major roof failures in Australian underground mines have been known to result in the stoppage of crosscut construction for several months, causing a production loss of more than a hundred million dollars in some cases [5]. Generally, the crosscut stability can be monitored and predicted by analyzing stress and displacement in surrounding rock. In situ, the displacement of surrounding rock can be measured efficiently and economically by convergence instruments, such as tape extensometers, laser scanners (profilometers), and geodetic surveying (total stations) [6]. These instruments are usually placed at intervals between 5 m and 50 m relying on the rock properties. The convergence data of surrounding rock is processed manually or automatically as digital data and then transmitted to the data processing unit [7,8]. However, it is time-consuming and expensive to obtain the stress data of surrounding rock in crosscuts. Additionally, the stress-deformation relationship for surrounding rock in crosscuts is full of uncertainty, as it is affected by many factors such as lithology, rock mass structure, and groundwater [9,10]. Hence, it is of great practical significance to seek a commercially available way to obtain the stress distribution of surrounding rock in crosscuts.
A comparison between improved ELM and other existing ANN algorithms is also conducted in Section 5. Finally, the conclusion drawn from the present study is summarized in Section 6.

A Brief Introduction to Traditional ELM
ELM is a typical single-hidden-layer feedforward neural network (SLFN). Unlike traditional learning algorithms in feedforward neural network where the parameters are tuned iteratively, ELM calculates the hidden layer node parameters mathematically, resulting in good generalization ability at extremely fast learning speed [30]. Structure of ELM is illustrated in Figure 1.
Energies 2019, 12, x FOR PEER REVIEW 3 of 16 conducted in Section 5. Finally, the conclusion drawn from the present study is summarized in Section 6.

A Brief Introduction to Traditional ELM
ELM is a typical single-hidden-layer feedforward neural network (SLFN). Unlike traditional learning algorithms in feedforward neural network where the parameters are tuned iteratively, ELM calculates the hidden layer node parameters mathematically, resulting in good generalization ability at extremely fast learning speed [30]. Structure of ELM is illustrated in Figure 1. Equation (1) can be written compactly as: where H is the hidden-layer output matrix of the neural network. The ith column of H is the ith hidden nodes output vector corresponding to inputs x1, …, xN, and the jth row of H is the output vector of the hidden layer with respect to inputs xj.
The input weight w i and hidden biases bi is chosen randomly without knowing the training datasets. The output weight L is then solved with matrix computation formula =H + T, where H + is Moore-Penrose of H and standard SFLN withN hidden neurons and activation function g(x) are mathematically modelled as [30] where w i = [w i1 , w i2 , · · · , w in ] T is the weight of the connection from the input neurons to the ith hidden neuron; β i = [β i1 , β i2 , · · · , β in ] T is the weight vector connecting the ith output neurons and hidden neuron; o i = [o i1 , o i2 , . . . , o in ] T is the jth output vector of SLFN; b i is the threshold of the ith hidden neuron; and w i · x j presents the inner product of w i and x j . Equation (1) can be written compactly as: where where H is the hidden-layer output matrix of the neural network. The ith column of H is the ith hidden nodes output vector corresponding to inputs x 1 , . . . , x N , and the jth row of H is the output vector of the hidden layer with respect to inputs x j . The input weight w i and hidden biases b i is chosen randomly without knowing the training datasets. The output weight L is then solved with matrix computation formula = H + T, where H + is Moore-Penrose of H and T = [t 1 , t 2 , · · · , t N ] T is the target value matrix. ELM not only tends to find the smallest norm weights, but also the smallest training error, and its pseudo code is shown in Algorithm 1 [20].

Improved ELM Algorithm
As discussed earlier, the input weight of traditional ELM is random usually causing low generalization ability. Therefore, the greedy algorithm is firstly employed into this study to improve the generalization performance of traditional ELM. When solving the problem greedy algorithm always makes the best choice at present step and will consider local optimal solution rather than the overall optimization. The procedure of greedy algorithm includes four steps, e.g., (a) establishing a mathematical model to describe the problem, (b) dividing the problem into several sub-problems, (c) determining local optimal solution for each sub-problem, and (d) combining the all local optimal solutions [31]. The iteration process for greedy algorithm is summarized as follows. In the given dataset D and objective function f, the initial approximating value f 0 is set at 0. The approximating value at kth iteration f k is determine based on f k−1 , and the approximating error at (k − 1)th iteration τ k−1 is calculated as f − f k . For each iteration, one is expected to reduce τ k as much as possible. The analytical formula is expressed as The incorporated greedy algorithm makes the traditional ELM system move in the direction of reducing the error when the error obtained from system cannot meet the requirement. Once the local minimum point is found, the searching step will be ended and then work on the rest data. Thus, the whole hidden layer can be changed with reducing the error significantly. Based on the traditional ELM model, the computational process for the improved ELM algorithm is shown in Figure 2.
The steps of constructing the crosscut stress prediction model are described as follows: (1) Establish relational model of stress-displacement based on traditional ELM.
(2) Calculate the error E and determine the searching step t.
(3) Modify input weight w ij in hidden layer with t and get new input weight w ij .
(4) Update the new output layer weight β'.  To illustrate the effectiveness of the proposed improved ELM algorithm, two studies including the numerical study and case study are presented in the following sections.

Numerical Model
FLAC 3D , which is a numerical software based on finite-difference method, has been widely used in mining engineering to analyze the ground subsidence and deformation and stress distribution of surrounding rock [32,33]. Based on FLAC 3D , a three-dimensional model according to the mining condition was established to obtain stress-displacement data for ELM use, as shown in Figure 3, since the change of displacement in crosscuts is inconspicuous and difficult to get a lot of data in a short time [28].

Numerical Model
FLAC 3D , which is a numerical software based on finite-difference method, has been widely used in mining engineering to analyze the ground subsidence and deformation and stress distribution of surrounding rock [32,33]. Based on FLAC 3D , a three-dimensional model according to the mining condition was established to obtain stress-displacement data for ELM use, as shown in Figure 3, since the change of displacement in crosscuts is inconspicuous and difficult to get a lot of data in a short time [28].
As shown in Figure 3a  semi-circle part is 2.0 m. Six sampling points located in cross section between y = 5 m and y = 6 m to obtain stress-displacement data are illustrated in Figure 3c.   Figure 3b, the yellow part in the model middle is the tunnel which will be excavated. The width of tunnel is 4 m with a height of 3.8 m in a central line, and the radius in upper semi-circle part is 2.0 m. Six sampling points located in cross section between y = 5 m and y = 6 m to obtain stress-displacement data are illustrated in Figure 3c.
Another important part of numerical modelling is assigning the constitutive model, which describes the mechanical behaviour including yielding and post-crack of geomaterial [34]. In FLAC 3D , elastic, strain softening, and Mohr-coulomb (mohr) models are often used for mining engineering. In this simulation, the mohr model is used to simulate the behaviour of surrounding rock (e.g., magnetite), since it can describe the granular materials with loose cementation in an ideal situation. Mechanical properties of magnetite simulated in this study are given in Table 1, based on laboratory tests and field investigations.  Another important part of numerical modelling is assigning the constitutive model, which describes the mechanical behaviour including yielding and post-crack of geomaterial [34]. In FLAC 3D , elastic, strain softening, and Mohr-coulomb (mohr) models are often used for mining engineering. In this simulation, the mohr model is used to simulate the behaviour of surrounding rock (e.g., magnetite), since it can describe the granular materials with loose cementation in an ideal situation. Mechanical properties of magnetite simulated in this study are given in Table 1, based on laboratory tests and field investigations.

Data Collection
After crosscut excavation, the stress state balance in surrounding rock is disturbed. The displacement and stress will change with time until it reaches equilibrium. During the computational process, FLAC 3D could record the displacement and stress information of monitoring points automatically. The displacement distribution in crosscut surrounding rock after excavation is shown in  . It can be noticed that the biggest settlement existed in the middle roof, which is corresponding to the monitoring point ID 21461 and ID 6061. Considering the difference of stress-displacement state between ID 21461 and ID 6061 is unremarkable, ID 21461 is chosen for ELM training and validation. The vertical stress and X, Y, and Z-direction displacements of ID 21461 are given in Figure 5. As shown, the displacement of ID 21461 in Y-direction is not significant compared to that in X and Z-directions. Additionally, the stability of a crosscut is usually influenced by the overlaying rock gravity and horizontal displacement in side-walls. Thus, the displacements in X and Z-directions of ID 21461 are taken as input, while the vertical stress of ID 21461 is considered as output.
displacement and stress will change with time until it reaches equilibrium. During the computational process, FLAC 3D could record the displacement and stress information of monitoring points automatically. The displacement distribution in crosscut surrounding rock after excavation is shown in Figure 4. It can be noticed that the biggest settlement existed in the middle roof, which is corresponding to the monitoring point ID 21461 and ID 6061. Considering the difference of stress-displacement state between ID 21461 and ID 6061 is unremarkable, ID 21461 is chosen for ELM training and validation. The vertical stress and X, Y, and Z-direction displacements of ID 21461 are given in Figure 5. As shown, the displacement of ID 21461 in Y-direction is not significant compared to that in X and Z-directions. Additionally, the stability of a crosscut is usually influenced by the overlaying rock gravity and horizontal displacement in side-walls. Thus, the displacements in X and Z-directions of ID 21461 are taken as input, while the vertical stress of ID 21461 is considered as output.
To improve the accuracy of the ELM model, the displacement and stress data of the elements in the same position as ID 21461 along the Y axis in different cross sections, e.g., 10 < y < 11, 15 < y < 16, 20 < y < 25, 30 < y < 31 are chosen as training samples. The total number of training samples is 3000.    Vs.

Traditional and Improved ELM Validation
After training, the model is used to validate the vertical stress of elements in cross-sections 7 < y < 8, 13 < y < 14 and 17 < y < 18 according to their displacement data. By putting the displacement data obtained from X and Z-directions into the prediction model including traditional and improved ELM models, the relevant predictive vertical stress of elements can be obtained. Figure 6 compares the vertical stress obtained from two predictive models with measured data obtained from FLAC 3D in three different cross-sections. It is worth noting that the vertical stress obtained from improved To improve the accuracy of the ELM model, the displacement and stress data of the elements in the same position as ID 21461 along the Y axis in different cross sections, e.g., 10 < y < 11, 15 < y < 16, 20 < y < 25, 30 < y < 31 are chosen as training samples. The total number of training samples is 3000.

Traditional and Improved ELM Validation
After training, the model is used to validate the vertical stress of elements in cross-sections 7 < y < 8, 13 < y < 14 and 17 < y < 18 according to their displacement data. By putting the displacement data obtained from X and Z-directions into the prediction model including traditional and improved ELM models, the relevant predictive vertical stress of elements can be obtained. Figure 6 compares the vertical stress obtained from two predictive models with measured data obtained from FLAC 3D in three different cross-sections. It is worth noting that the vertical stress obtained from improved ELM model matches well with the results calculated by FLAC 3D , regardless of the position of cross-section, especially for the residual stress. However, there is significant difference between traditional ELM predictions and numerical results.

Traditional and Improved ELM Validation
After training, the model is used to validate the vertical stress of elements in cross-sections 7 < y < 8, 13 < y < 14 and 17 < y < 18 according to their displacement data. By putting the displacement data obtained from X and Z-directions into the prediction model including traditional and improved ELM models, the relevant predictive vertical stress of elements can be obtained. Figure 6 compares the vertical stress obtained from two predictive models with measured data obtained from FLAC 3D in three different cross-sections. It is worth noting that the vertical stress obtained from improved ELM model matches well with the results calculated by FLAC 3D , regardless of the position of cross-section, especially for the residual stress. However, there is significant difference between traditional ELM predictions and numerical results. To further validate the effectiveness and validity of the improved ELM model, additional vertical stress of 0.38 MPa was applied on the top surface of the numerical model to simulate increasing 10 m depth of the crosscut. Increasing depth leads to higher displacement and vertical stress in crosscut surrounding rock. During excavation of the crosscut, displacement information of elements in the middle roof in cross-sections 5 < y < 6, 10 < y < 11, 15 < y < 16, 20 < y < 21 was recorded and then employed into the improved ELM model. Figure 7 compares the vertical stress predicted by improved ELM model with that obtained from FLAC 3D in four different cross-sections. As seen, the improved ELM model still predicts the vertical stress in high accuracy after changing the depth of excavated crosscut. Therefore, it may be concluded that the improved ELM algorithm is a promising technique to predict stress of surrounding rock in crosscut based on the displacement data. The improved ELM model will be applied in a case study of an underground crosscut in Yanqianshan Iron Mine. To further validate the effectiveness and validity of the improved ELM model, additional vertical stress of 0.38 MPa was applied on the top surface of the numerical model to simulate increasing 10 m depth of the crosscut. Increasing depth leads to higher displacement and vertical stress in crosscut surrounding rock. During excavation of the crosscut, displacement information of elements in the middle roof in cross-sections 5 < y < 6, 10 < y < 11, 15 < y < 16, 20 < y < 21 was recorded and then employed into the improved ELM model. Figure 7 compares the vertical stress predicted by improved ELM model with that obtained from FLAC 3D in four different cross-sections. As seen, the improved ELM model still predicts the vertical stress in high accuracy after changing the depth of excavated crosscut. Therefore, it may be concluded that the improved ELM algorithm is a promising technique to

Application to Yanqianshan Iron Mine
To illustrate its capability in engineering application, the improved ELM algorithm was used to predict the crosscut stress in Yanqianshan underground mine. The predictions from the improved ELM model were compared with the measured field data to evaluate the robustness of the proposed technique. In addition, the prediction performance of BP, ELM, genetic algorithm-based ELM (GA-ELM), and improved ELM were compared and discussed.

Engineering Background of Yanqianshan Iron Mine
Yanqianshan iron mine (YIM), located 22 km west of Anshan City, Liaoning Province, China, was commissioned in the 1960s. YIM includes three main orebodies (e.g., Fe1, Fe2, and Fe3) distributed in exploration lines from XVI to IX+100 as shown Figure 8. Fe1 is the main orebody with a strike length of 1600 m in the trans-meridional direction. Extraction procedure of YIM includes three parts, such as surface mining, transition stage mining, and underground mining. As shown in Figure 9, open-pit mining method with an annual production of 2.

Application to Yanqianshan Iron Mine
To illustrate its capability in engineering application, the improved ELM algorithm was used to predict the crosscut stress in Yanqianshan underground mine. The predictions from the improved ELM model were compared with the measured field data to evaluate the robustness of the proposed technique. In addition, the prediction performance of BP, ELM, genetic algorithm-based ELM (GA-ELM), and improved ELM were compared and discussed.

Engineering Background of Yanqianshan Iron Mine
Yanqianshan iron mine (YIM), located 22 km west of Anshan City, Liaoning Province, China, was commissioned in the 1960s. YIM includes three main orebodies (e.g., Fe1, Fe2, and Fe3) distributed in exploration lines from XVI to IX+100 as shown Figure 8. Fe1 is the main orebody with a strike length of 1600 m in the trans-meridional direction. Extraction procedure of YIM includes three parts, such as surface mining, transition stage mining, and underground mining. As shown in Figure 9, open-pit mining method with an annual production of 2. Currently, YIM is in the transition stage and mining the orebody in West hanging wall, which is also the case study in this paper. Drift-ramp and block caving method are selected to develop and extract the orebody in the West hanging wall. Two main haulages are constructed in level −51 m and −123 m, and the structural openings are in open-pit platform. The orebody is divided into 8 levels and each sublevel with a height of 18 m. Level +21 m is used to form the ore overburden layer. Considering the low stability of the hanging wall, there is a 20 m pillar between each ore layer and open-pit boundary.

Filed Data Collection
According to the geological condition and construction progress of West hanging wall, three monitoring areas were placed at #4, #5 and #6 crosscuts respectively on −33 m level, as shown in Figure 10a. Figure 10 also illustrates the drilling process for installing monitoring equipment. YHY200 borehole stress meter was used to record the stress variation. JSS30A Digital Display Convergence Meter with high precision was chosen to monitor the roof displacement, and tunnel section convergence continuous the monitoring system (TSCCMS) with a precision of 0.01 mm was used to record the horizonal displacement of surrounding rock. JSS30A and TSCCMS were placed near the location of borehole stress meter. The observation elapsed from January 2018 to March 2018, and data recorded every five days. A total number of 108 observations including 36 horizontal displacement values, 36 roof subsidence values, and 33 stress values were recorded, as shown in Figure 11. Currently, YIM is in the transition stage and mining the orebody in West hanging wall, which is also the case study in this paper. Drift-ramp and block caving method are selected to develop and extract the orebody in the West hanging wall. Two main haulages are constructed in level −51 m and −123 m, and the structural openings are in open-pit platform. The orebody is divided into 8 levels and each sublevel with a height of 18 m. Level +21 m is used to form the ore overburden layer. Considering the low stability of the hanging wall, there is a 20 m pillar between each ore layer and open-pit boundary.

Filed Data Collection
According to the geological condition and construction progress of West hanging wall, three monitoring areas were placed at #4, #5 and #6 crosscuts respectively on −33 m level, as shown in Figure 10a. Figure 10 also illustrates the drilling process for installing monitoring equipment. YHY200 borehole stress meter was used to record the stress variation. JSS30A Digital Display Convergence Meter with high precision was chosen to monitor the roof displacement, and tunnel section convergence continuous the monitoring system (TSCCMS) with a precision of 0.01 mm was used to record the horizonal displacement of surrounding rock. JSS30A and TSCCMS were placed near the location of borehole stress meter. The observation elapsed from January 2018 to March 2018, and data recorded every five days. A total number of 108 observations including 36 horizontal displacement values, 36 roof subsidence values, and 33 stress values were recorded, as shown in Figure 11. Currently, YIM is in the transition stage and mining the orebody in West hanging wall, which is also the case study in this paper. Drift-ramp and block caving method are selected to develop and extract the orebody in the West hanging wall. Two main haulages are constructed in level −51 m and −123 m, and the structural openings are in open-pit platform. The orebody is divided into 8 levels and each sublevel with a height of 18 m. Level +21 m is used to form the ore overburden layer. Considering the low stability of the hanging wall, there is a 20 m pillar between each ore layer and open-pit boundary.

Filed Data Collection
According to the geological condition and construction progress of West hanging wall, three monitoring areas were placed at #4, #5 and #6 crosscuts respectively on −33 m level, as shown in Figure 10a. Figure 10 also illustrates the drilling process for installing monitoring equipment. YHY200 borehole stress meter was used to record the stress variation. JSS30A Digital Display Convergence Meter with high precision was chosen to monitor the roof displacement, and tunnel section convergence continuous the monitoring system (TSCCMS) with a precision of 0.01 mm was used to record the horizonal displacement of surrounding rock. JSS30A and TSCCMS were placed near the location of borehole stress meter. The observation elapsed from January 2018 to March 2018, and data recorded every five days. A total number of 108 observations including 36 horizontal displacement values, 36 roof subsidence values, and 33 stress values were recorded, as shown in Figure 11. As shown in the Figure 11a, it is clear that the convergence of these three crosscuts was between 4.9 mm and 8.2 mm. While there is slightly difference in convergence rate, the overall deformation law is similar, that is the crosscuts trend to convergent. The convergence rate is significantly dependent on mining progress. After drift blasting and excavation, the convergence value increases obviously. It is worth noting from Figure 11b, the roofs of these three monitored crosscuts performed deformation in different degrees, and the deformation value ranges from 0.77 mm to 2.47 mm. The monitoring points in #4 and #5 are influenced by mining activities, resulting in higher deformation in roof compared to that in #6. During the monitoring period, there were no extracting activities in #6. As shown in Figure 11c, the stress in monitored crosscuts has not changed distinctly with observed values between 0.18 MPa and 1.20 MPa. In general, the surrounding rock in the −33 m level could be kept stable during mining activities. As shown in the Figure 11a, it is clear that the convergence of these three crosscuts was between 4.9 mm and 8.2 mm. While there is slightly difference in convergence rate, the overall deformation law is similar, that is the crosscuts trend to convergent. The convergence rate is significantly dependent on mining progress. After drift blasting and excavation, the convergence value increases obviously. It is worth noting from Figure 11b, the roofs of these three monitored crosscuts performed deformation in different degrees, and the deformation value ranges from 0.77 mm to 2.47 mm. The monitoring points in #4 and #5 are influenced by mining activities, resulting in higher deformation in roof compared to that in #6. During the monitoring period, there were no extracting activities in #6. As shown in Figure 11c, the stress in monitored crosscuts has not changed distinctly with observed values between 0.18 MPa and 1.20 MPa. In general, the surrounding rock in the −33 m level could be kept stable during mining activities.  Figure 11. Variation of (a) convergence displacement, (b) roof displacement, and (c) stress with monitoring time.

Training and Validation
The total number of collected vertical stress on the roof of crosscuts is 36 expressed as Z36. Accordingly, the measured convergence and roof displacements as shown in Figure 11a,b are named as X36 and Y36, respectively. The data is divided into training group (X24, Y24, and Z24) and As shown in the Figure 11a, it is clear that the convergence of these three crosscuts was between 4.9 mm and 8.2 mm. While there is slightly difference in convergence rate, the overall deformation law is similar, that is the crosscuts trend to convergent. The convergence rate is significantly dependent on mining progress. After drift blasting and excavation, the convergence value increases obviously. It is worth noting from Figure 11b, the roofs of these three monitored crosscuts performed deformation in different degrees, and the deformation value ranges from 0.77 mm to 2.47 mm. The monitoring points in #4 and #5 are influenced by mining activities, resulting in higher deformation in roof compared to that in #6. During the monitoring period, there were no extracting activities in #6. As shown in Figure 11c, the stress in monitored crosscuts has not changed distinctly with observed values between 0.18 MPa and 1.20 MPa. In general, the surrounding rock in the −33 m level could be kept stable during mining activities.

Training and Validation
The total number of collected vertical stress on the roof of crosscuts is 36 expressed as Z 36 . Accordingly, the measured convergence and roof displacements as shown in Figure 11a,b are named as X 36 and Y 36 , respectively. The data is divided into training group (X24, Y24, and Z24) and validation group (X 12 , Y 12 , and Z 12 ). After finishing training, X 12 is incorporated into prediction models to obtain predictive results. For example, when validating the roof stress in #4 crosscut, the deformation including convergence and roof subsidence and roof stress of #5 and #6 crosscuts are selected as training data, while deformation of #4 crosscut is used as input. For comparison, the commonly used BP algorithms and GA-ELM are also used to predict crosscut stress.
To evaluate the prediction performance, three loss functions, namely root mean square error (RMSE), maximum relative error (MRE), and mean absolute percentage error (MAPE) are introduced as the evaluation criteria, as defined by Reference [23] where ρ is the number of predictions; e t = s t −Ŝ t , S n is the in-situ data for time t, andŝ n is the predictive values for the same period. The predicted stress of BP, ELM, GA-ELM, and improved ELM algorithms with the measured data in situ are compared in Figure 12 and Table 2. The training time, RMSE, MRE and MAPE of each algorithm are listed in Table 2 as well. As shown in Figure 12, we can find that predictions from the improved ELM model agree well with the field data in all crosscuts. GA-ELM model generally performs acceptable predictions on only #5 crosscut, but the prediction on the first 10 days still overestimate the field data significantly. The predictions of both BP and traditional ELM show are not accurate in all three cases. In general, four algorithms can predict the stress in crosscuts precisely at the beginning of monitoring. However, with times going by the predictions of BP, ELM, and GA-ELM gradually deviate the measured data in situ.  The results obtained from Table 2 obviously indicate that the prediction performance of the improved ELM model, is better than BP, ELM, and GA-ELM. The prediction precision of improved ELM has a significant improvement to traditional ELM where the RMSE, MRE, and MAPE reduce by 0.12MPa, 32.23%, and 15.94%, respectively. As expected the ELM shows the highest speed in prediction with a training time of 0.05 s, however, its performance is only slightly superior compared with BP. As for GA-ELM, although it performs acceptable precision with low RMSE (e.g., 0.13MPa), it is time-consuming compared with other three algorithms. In addition, the MRE obtained from GA-ELM is three times higher than that obtained from the improved ELM. The improved ELM algorithm computes quickly with a training time of only 1.70 s. Therefore, it can be concluded that the improved ELM algorithm is superior in predicting crosscut stress compared to BP, ELM, and GA-ELM.

Conclusions
Crosscut stability analysis has gained worldwide interests due to its importance in underground engineering projects. Stability analysis and prediction are commonly based on the crosscut convergence and stress data. However, it is time-consuming and expensive to monitor the crosscut stress. Therefore, an improved ELM algorithm is proposed in this paper to predict the  The results obtained from Table 2 obviously indicate that the prediction performance of the improved ELM model, is better than BP, ELM, and GA-ELM. The prediction precision of improved ELM has a significant improvement to traditional ELM where the RMSE, MRE, and MAPE reduce by 0.12MPa, 32.23%, and 15.94%, respectively. As expected the ELM shows the highest speed in prediction with a training time of 0.05 s, however, its performance is only slightly superior compared with BP. As for GA-ELM, although it performs acceptable precision with low RMSE (e.g., 0.13MPa), it is time-consuming compared with other three algorithms. In addition, the MRE obtained from GA-ELM is three times higher than that obtained from the improved ELM. The improved ELM algorithm computes quickly with a training time of only 1.70 s. Therefore, it can be concluded that the improved ELM algorithm is superior in predicting crosscut stress compared to BP, ELM, and GA-ELM.

Conclusions
Crosscut stability analysis has gained worldwide interests due to its importance in underground engineering projects. Stability analysis and prediction are commonly based on the crosscut convergence and stress data. However, it is time-consuming and expensive to monitor the crosscut stress. Therefore, an improved ELM algorithm is proposed in this paper to predict the crosscut stress using its convergence displacement. The capability of the improved ELM algorithm is then verified using a numerical model and a case study. The results show that traditional algorithm assigns input weight randomly leading to a fast computation speed, but unsatisfactory precision in stress prediction. The prediction accuracy and quality of ELM model was improved significantly by introducing greedy algorithm. In terms of different criteria, RMSE, MRE, and MAPE, it is found that for the test case of Yanqianshan Iron Mine, the improved ELM performs the best compared with BP, ELM, and GA-ELM algorithms. GA-ELM also shows acceptable prediction for #5 crosscut, however, it is time-consuming with a training time of 15.38 s, which is 14.37 times higher than that of the improved ELM algorithm. In conclusion, the improved ELM model can effectively improve the crosscut stress prediction and provide stability analysis for engineering projects, which is of great practical significance for future underground mining activities in Yanqianshan Iron Mine.

Conflicts of Interest:
The authors declare that there is no conflict of interests regarding the publication of this paper.