# Predicting the Mine Friction Coefficient Using the GSCV-RF Hybrid Approach

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}. The results show that, among the three models, the GSCV-RF model’s prediction result for α was the best, the RF model performed well and the BP model performed worst. In the prediction for all the datasets obtained by GSCV-RF model, all the values of MAE and RMSE were less than 0.5, the values of R

^{2}were more than 0.85 and the value of R

^{2}of the passive and active support test sets were 0.8845 and 0.9294, respectively. This proved that the GSCV-RF model can offer a more accurate α and aid in the reasonable design and the safe operation of a ventilation system.

## 1. Introduction

## 2. Predictive Model Construction

#### 2.1. RF Prediction Models

- 1.
- Input conditions for forest growth: RF prediction results are heavily influenced by three hyperparameters: the number of decisions, the maximum number of features and the maximum depth of the decision tree, which are, respectively, defined as x
_{1}, x_{2}and x_{3}and used as the input growth conditions (x_{1}, x_{2}, x_{3}). - 2.
- The dataset containing N samples with O input features is sampled N times using put-back sampling, and o features are selected randomly to serve as the input features. This process is repeated N times to generate N training datasets including N samples with o input features (o ≤ O):$${D}_{1}={x}_{11},{y}_{11},\left({x}_{12},{y}_{12}\right),\cdots ,\left({x}_{1N},{y}_{1N}\right)\phantom{\rule{0ex}{0ex}}{D}_{2}={x}_{21},{y}_{21},\left({x}_{22},{y}_{22}\right),\cdots ,\left({x}_{2N},{y}_{2N}\right)\phantom{\rule{0ex}{0ex}}\cdots \phantom{\rule{0ex}{0ex}}{D}_{N}={x}_{N1},{y}_{N1},\left({x}_{N2},{y}_{N2}\right),\cdots ,\left({x}_{NN},{y}_{NN}\right)$$
_{N}is the Nth dataset of training numbers; x_{NN}is the input data under the Nth sample of the Nth training dataset; and y_{NN}is the output data under the Nth sample of the Nth training dataset.

_{NNj}is the jth input data under the Nth sample in the Nth training dataset.

- 3.
- Choose one of the datasets, select the appropriate cut variable j and cut point s, and ensure the segmentation effect using Equation (3).$$\underset{j,s}{\mathrm{min}}\left[\underset{{c}_{1}}{\mathrm{min}}{\displaystyle \sum}_{{x}_{i}\in {R}_{1}\left(j,s\right)}{\left({y}_{i}-{c}_{1}\right)}^{2}+\underset{{c}_{2}}{\mathrm{min}}{\displaystyle \sum}_{{x}_{i}\in {R}_{2}\left(j,s\right)}{\left({y}_{i}-{c}_{2}\right)}^{2}\right]$$
- 4.
- The optimal (j, s) is partitioned into regions to obtain ${R}_{1}$ and ${R}_{2}$, and the output value of the corresponding region ${\hat{c}}_{m}$ is determined:$${R}_{1}\left(j,s\right)=\left\{x|{x}^{\left(j\right)}\le s\right\},\hspace{1em}\hspace{1em}{R}_{2}\left(j,s\right)=\left\{x|{x}^{\left(j\right)}>s\right\}\phantom{\rule{0ex}{0ex}}{\widehat{c}}_{m}=\frac{1}{{N}_{m}}{\displaystyle \sum}_{{x}_{i}\in {R}_{m}\left(j,s\right)}{y}_{i},\hspace{1em}\hspace{1em}\hspace{1em}x\in {R}_{m},\hspace{1em}\hspace{1em}m=1,2$$
- 5.
- Until the requirements for the decision tree’s growth are satisfied, repeat steps 2 and 3 for the divided subregions.
- 6.
- To construct a decision tree, divide the input space into M regions, R
_{1}, R_{2}, $\cdots $, R_{M}.$$f\left(x\right)={\displaystyle \sum}_{m=1}^{M}{\widehat{c}}_{m}I\left(x\in {R}_{m}\right)$$ - 7.
- Repeat steps 2, 3, 4 and 5 until the forest’s growth requirements are satisfied and an equal number of decision trees are formed so as to form a random forest.

- Select the appropriate input and output properties to build a prediction indicator system.
- Use numerical and clustering methods to process the data such that it satisfies the RF model’s requirements.
- Adopting a given percentage, divide the dataset into a training set for training the model and a test set for testing the prediction.
- Input the model parameters (growth conditions), such as the number of decisions, maximum number of features and maximum depth of the decision tree.
- Train the training set’s α prediction model.
- Predict the α of the test set.
- According to the predictions to evaluation the constructed RF forecasting model. The evaluation indicators include mean absolute error (MAE), root mean square error (RMSE) and model goodness of fit (R
^{2}):$$MAE=\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}\left|\widehat{{y}_{i}}-{y}_{i}\right|$$$$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}{\left|\widehat{{y}_{i}}-{y}_{i}\right|}^{2}}$$$${R}^{2}=1-\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left(\widehat{{y}_{i}}-{y}_{i}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left(\overline{{y}_{i}}-{y}_{i}\right)}^{2}}$$

#### 2.2. GSCV Optimization Algorithm

- Set the range of each hyperparameter and set range of RF’s hyperparameter (growth condition) as an example:$${x}_{1}\in \left[1,n\right]\phantom{\rule{0ex}{0ex}}{x}_{2}\in \left[1,m\right]\phantom{\rule{0ex}{0ex}}{x}_{3}\in \left[1,z\right]$$
_{1}; m is the upper limit of the value of the hyperparameter x_{2}; and z is the upper limit of the value of the hyperparameter x_{3}. - To obtain a hyperparameter combination, set each hyperparameter individually. Assuming that each hyperparameter step is 1, n × m × z hyperparameter combinations (x
_{n}, x_{m}, x_{z}) are created. Hence, each hyperparameter combination represents one of the growth conditions of RF. - To avoid the chance of outcomes owing to dataset partitioning, the dataset is divided into K mutually exclusive subsets of the same size, d
_{1}, d_{2}, $\cdots $, d_{k}, and each subset is utilized as a separate validation set once, and the remaining K-1 subsets are used to produce K new datasets. - Each hyperparameter combination (x
_{n}, x_{m}, x_{z}) is trained once on each of the K new datasets, the goodness-of-fit ${R}_{1}^{2}{,R}_{2}^{2},\cdots {,R}_{\mathrm{k}}^{2}$ under each dataset is produced, and the output of the hyperparameter combination is the mean value $\overline{{R}_{{(\mathrm{x}}_{\mathrm{n}}{,\mathrm{x}}_{\mathrm{m}}{,\mathrm{x}}_{\mathrm{z}})}^{2}}$ of the corresponding goodness-of-fit for each dataset.$$\overline{{R}_{\left({x}_{n},{x}_{m},{x}_{z}\right)}^{2}}=\frac{1}{k}{\displaystyle \sum}_{i=1}^{k}{R}_{i}^{2}$$ - Repeat step 4 for each combination of hyperparameters in order to identify the optimal output as an input parameter for the algorithm combined with GSCV. The following is an expression of the optimal output:$$\underset{{x}_{n},{x}_{m},{x}_{z}}{\mathrm{max}}[\overline{{R}_{\left({x}_{n},{x}_{m},{x}_{z}\right)}^{2}}]$$

#### 2.3. GSCV-RF Prediction Model

- The range and step size of the three hyperparameters, including the number of decision trees, the maximum number of features and the maximum decision tree depth, are established.
- Combining the values of each hyperparameter to individually yields all the possible hyperparameter combinations.
- The α dataset is divided into K equal parts, with K-1 parts serving as the training set and the remaining 1 part serving as the test set. After K repetitions, each sample serves as one test set, resulting in K new datasets.
- Using the new dataset, each combination of hyperparameters is subjected to K-fold cross-validation.
- The results produced for each hyperparameter combination are scored, and the combination with the highest score is used as the model’s input parameter.

## 3. Example Analysis

#### 3.1. Constructing a Forecasting Indicator System

#### 3.2. Data Selection and Processing

No. | Indicator | Data Type |
---|---|---|

1 | Support Type | Character type |

2 | Cross-Section Profile | Character type |

3 | Bracket Size | Numerical type |

4 | Roadway Cross-Sectional Area | Numerical type |

5 | Lane Circumference | Numerical type |

6 | Perimeter of Unsupported Section | Numerical type |

7 | Bracket Longitudinal Bore | Numerical type |

8 | Cross-Bore of Bracket | Numerical type |

9 | Equivalent Radius | Numerical type |

10 | Effective Ventilation Area Factor | Numerical type |

11 | Coefficient of frictional resistance | Numerical type |

#### 3.3. Data Statistics

Indicators | Min. | Max. | Avg. | St. D. | Med. | S. Var. | St. E. | Kurt. | Skew. | Range | Mode |
---|---|---|---|---|---|---|---|---|---|---|---|

Training Datasets | |||||||||||

Support Type | 1 | 2 | 1.5 | 0.503 | 1.5 | 0.253 | 0.05 | −2.041 | 0 | 1 | |

Bracket Size | 10 | 26 | 15.68 | 4.126 | 15 | 17.028 | 0.413 | 0.002 | 0.592 | 16 | 10 |

Roadway Cross-Sectional Area | 4 | 10 | 6.94 | 2.247 | 6 | 5.047 | 0.225 | −1.366 | 0.033 | 6 | 4 |

Lane Circumference | 8.32 | 13.16 | 10.812 | 1.816 | 10.19 | 3.297 | 0.182 | −1.358 | −0.13 | 4.84 | 8.32 |

Perimeter of Unsupported Section | 2.13 | 3.37 | 2.712 | 0.509 | 2.61 | 0.259 | 0.051 | −1.668 | 0.021 | 1.24 | 2.13 |

Bracket Longitudinal Bore | 3 | 8 | 4.97 | 1.85 | 5 | 3.423 | 0.185 | −1.218 | 0.416 | 5 | 3 |

Cross-Bore of Bracket | 0.033 | 0.135 | 0.065 | 0.021 | 0.062 | 0 | 0.002 | 0.69 | 0.816 | 0.102 | 0.059 |

α | 0.071 | 0.261 | 0.121 | 0.042 | 0.106 | 0.002 | 0.004 | 1.049 | 1.291 | 0.19 | 0.137 |

Testing Datasets | |||||||||||

Support Type | 1 | 2 | 1.667 | 0.482 | 2 | 0.232 | 0.098 | −1.568 | −0.755 | 1 | 2 |

Bracket Size | 10 | 24 | 15.708 | 4.059 | 16 | 16.476 | 0.829 | −0.294 | 0.32 | 14 | 16, 18 |

Roadway Cross-Sectional Area | 4 | 10 | 6.542 | 1.865 | 6 | 3.476 | 0.381 | −0.927 | 0.39 | 6 | 5 |

Lane Circumference | 8.32 | 13.16 | 10.538 | 1.51 | 10.19 | 2.281 | 0.308 | −1.058 | 0.196 | 4.84 | 9.30 |

Perimeter of Unsupported Section | 2.13 | 3.37 | 2.702 | 0.386 | 2.61 | 0.149 | 0.079 | −1.052 | 0.188 | 1.24 | 2.39 |

Bracket Longitudinal Bore | 3 | 8 | 4.75 | 1.622 | 4 | 2.63 | 0.331 | −0.049 | 0.976 | 5 | 4 |

Cross-Bore of Bracket | 0.035 | 0.094 | 0.066 | 0.018 | 0.066 | 0 | 0.004 | −1.347 | −0.164 | 0.059 | 0.084 |

α | 0.092 | 0.273 | 0.134 | 0.047 | 0.118 | 0.002 | 0.01 | 1.735 | 1.407 | 0.181 | 0.916 0.118 0.143 |

Indicators | Min. | Max. | Avg. | St. D. | Med. | S. Var. | St. E. | Kurt. | Skew. | Range | Mode |
---|---|---|---|---|---|---|---|---|---|---|---|

Training Datasets | |||||||||||

Support Type | 1 | 2 | 1.367 | 0.49 | 1 | 0.24 | 0.089 | −1.784 | 0.583 | 1 | 1 |

Cross-Section Profile | 1 | 2 | 1.433 | 0.504 | 1 | 0.254 | 0.092 | −2.062 | 0.283 | 1 | 1 |

Equivalent Radius | 0.828 | 2.3 | 1.389 | 0.505 | 1.158 | 0.255 | 0.092 | −1.372 | 0.539 | 1.472 | 0.835 2.000 |

Effective Ventilation Area Factor | 0.84 | 1 | 0.954 | 0.044 | 0.96 | 0.002 | 0.008 | 0.927 | −1.122 | 0.16 | 1.00 |

α | 0.01 | 0.045 | 0.021 | 0.01 | 0.017 | 0 | 0.002 | −0.139 | 0.91 | 0.035 | 0.029 |

Testing Datasets | |||||||||||

Support Type | 1 | 2 | 1.333 | 0.516 | 1 | 0.267 | 0.211 | −1.875 | 0.968 | 1 | 1 |

Cross-Section Profile | 1 | 2 | 1.5 | 0.548 | 1.5 | 0.3 | 0.224 | −3.333 | 0 | 1 | |

Equivalent Radius | 0.884 | 2.05 | 1.283 | 0.482 | 1.048 | 0.232 | 0.197 | −0.697 | 1.064 | 1.166 | |

Effective Ventilation Area Factor | 0.87 | 1 | 0.962 | 0.047 | 0.975 | 0.002 | 0.019 | 4.225 | −1.967 | 0.13 | |

α | 0.01 | 0.042 | 0.023 | 0.012 | 0.02 | 0 | 0.005 | −0.089 | 0.802 | 0.032 |

**Figure 6.**Violin plots showing the distribution of the passive support dataset. (

**a**) Violin plot of the support-type data; (

**b**) violin plot of the bracket size data; (

**c**) violin plot of the roadway cross-sectional area data; (

**d**) violin plot of the lane circumference data; (

**e**) violin plot of the perimeter of the unsupported section data; (

**f**) violin plot of the bracket longitudinal bore data; (

**g**) violin plot of the cross-bore of bracket data; (

**h**) violin plot of the friction resistance coefficient (passive support) data.

**Figure 7.**Violin plots showing the distribution of the active support dataset. (

**a**) Violin plot of the support-type data; (

**b**) violin plot of the cross-section profile data; (

**c**) violin plot of the equivalent radius data; (

**d**) violin plot of the effective ventilation area factor data; (

**e**) violin plot of the perimeter of friction resistance coefficient (active support) data.

#### 3.4. RF Model Prediction

^{2}were 0.0019, 0.0029 and 0.9952, respectively, and in the passive support test sets, the values were 0.0112, 0.0159 and 0.8814, respectively. In the active support training sets, the values were 0.0010, 0.0015 and 0.9775, respectively, and in the active support test sets, the values were 0.0027, 0.0031 and 0.9165, respectively. All the values of the MAE and RMSE of the datasets were less than 0.05, and the value of R

^{2}was more than 0.85.

No. | Parameter Name | Value (Passive Support) | Value (Active Support) |
---|---|---|---|

1 | n_estimators | 100 | 100 |

2 | max_features | Auto | Auto |

3 | max_depth | None | None |

**Figure 8.**The passive support RF model prediction results. (

**a**) Correlation evaluation of the measured and predicted values of α; (

**b**) curves of the measured and predicted values of the samples; (

**c**) sample prediction error curve; (

**d**) sample error frequency distribution.

**Figure 9.**The active support RF model prediction results. (

**a**) Correlation evaluation of the measured and predicted values of α; (

**b**) curves of the measured and predicted values of the samples; (

**c**) sample prediction error curve; (

**d**) sample error frequency distribution.

#### 3.5. GSCV-RF Model Predictions

#### 3.5.1. Searching for the Optimal Input Parameters

#### 3.5.2. Model Training and Prediction

^{2}were 0.0018, 0.0025 and 0.9965, respectively, and in the passive support test sets, the values were 0.0112, 0.01597 and 0.8845, respectively. In the active support training sets, the values were 0.0014, 0.0019 and 0.9641, respectively, and in the active support test sets, the values were 0.0024, 0.0028 and 0.9294, respectively. All the values of the MAE and RMSE of datasets were less than 0.05, and the value of R

^{2}was more than 0.85.

**Figure 10.**The passive support GSCV-RF model prediction results. (

**a**) Correlation evaluation of the measured and predicted values of α; (

**b**) curves of the measured and predicted values of the samples; (

**c**) sample prediction error curve; (

**d**) sample error frequency distribution.

**Figure 11.**The active support GSCV-RF model prediction results. (

**a**) Correlation evaluation of the measured and predicted values of α; (

**b**) curves of the measured and predicted values of the samples; (

**c**) sample prediction error curve; (

**d**) sample error frequency distribution.

#### 3.6. BP Model Prediction

_{h}is the number of hidden layer nodes, and I is the number of hidden layer nodes.

^{2}were 0.0111, 0.0136 and 0.8945, respectively, and in the passive support test sets, the values were 0.0127, 0.0182 and 0.8455, respectively. In the active support training sets, the values were 0.0038, 0.0050 and 0.7533, respectively, and in the active support test sets, the values were 0.0041, 0.0056 and 0.7235, respectively. All the values of the MAE and RMSE of datasets was less than 0.05. Besides, except for the passive support training sets, the value of R

^{2}for the remaining three datasets was less than 0.85.

^{2}for the remaining sets was too low, indicating that the model’s prediction accuracy was inferior.

No. | Parameter Name | Value (Passive Support) | Value (Active Support) |
---|---|---|---|

1 | Number of nodes in the input layer | 7 | 4 |

2 | Number of nodes in the output layer | 15 | 9 |

3 | Number of nodes in the implicit layer | 1 | 1 |

**Figure 12.**The passive support BP model prediction results. (

**a**) Correlation evaluation of the measured and predicted values of α; (

**b**) curves of the measured and predicted values of the samples; (

**c**) sample prediction error curve; (

**d**) sample error frequency distribution.

**Figure 13.**The active support BP model prediction results. (

**a**) Correlation evaluation of the measured and predicted values of α; (

**b**) curves of the measured and predicted values of the samples; (

**c**) sample prediction error curve; (

**d**) sample error frequency distribution.

#### 3.7. Prediction Result Comparison

^{2}increased by 0.13%. With respect to the prediction results of the passive support test sets provided by the GSCV-RF model, the value of MAE remained unchanged, the value of RMSE decreased by 1.26% and the value of R

^{2}increased by 0.35%. With respect to the prediction results of the active support training sets provided by the GSCV-RF model, the value of MAE increased by 40%, the value of RMSE increased by 26.67% and the value of R

^{2}decreased by 1.37%. Even though the rate of the increase in MAE and RMSE was greater, their respective indicator magnitude order was lower, and the error was still at a lower level. With respect to the prediction results of the active support test sets provided by the GSCV-RF model, the value of MAE decreased by 11.11%, the value of RMSE decreased by 9.68% and the value of R

^{2}increased by 1.41%. Consequently, we realized that, compared to the RF model, the GSCV-RF model is superior in its prediction ability, yielding more accurate and reliable data.

^{2}decreased by 10.24%. With respect to the prediction results of the passive support test sets provided by the BP model, the value of MAE increased by 13.39%, the value of RMSE increased by 15.92% and the value of R

^{2}decreased by 4.41%. With respect to the prediction results of the active support training sets provided by the BP model, the value of MAE increased by 171.43%, the value of RMSE increased by 163.16% and the value of R

^{2}decreased by 21.86%. With respect to the prediction results of the active support test sets provided by the BP model, the value of MAE increased by 70.83%, the value of RMSE increased by 100% and the value of R

^{2}decreased by 22.15%.

Predictive Models | MAE | RMSE | R^{2} | |
---|---|---|---|---|

RF | Passive Support Training Set | 0.0019 | 0.0029 | 0.9952 |

GSCV-RF | 0.0018 | 0.0025 | 0.9965 | |

BP | 0.0111 | 0.0136 | 0.8945 | |

RF | Passive Support Test Set | 0.0112 | 0.0159 | 0.8814 |

GSCV-RF | 0.0112 | 0.0157 | 0.8845 | |

BP | 0.0127 | 0.0182 | 0.8455 | |

RF | Active Support Training Set | 0.0010 | 0.0015 | 0.9775 |

GSCV-RF | 0.0014 | 0.0019 | 0.9641 | |

BP | 0.0038 | 0.0050 | 0.7533 | |

RF | Active Support Test Set | 0.0027 | 0.0031 | 0.9165 |

GSCV-RF | 0.0024 | 0.0028 | 0.9294 | |

BP | 0.0041 | 0.0056 | 0.7235 |

## 4. Conclusions

^{2}, and a graphical representation of the relationship between the actual sample measurement value and the prediction value and errors was provided. Therefore, the conclusion of the paper is as follows:

- The paper began with the roadway support type, and after classifying the roadways as passive support or active support, the passive support α prediction indicator system and the active support α prediction indicator system were developed, respectively. The study demonstrated that the accuracy of these two support systems combined with machine learning, which can successfully predict α, is dependent on the algorithm employed.
- The paper introduced the RF algorithm to solve the problem of α determination. To avoid the super parameter’s influence, the GSCV algorithm was also introduced, and the GSCV-RF prediction model was constructed to predict the passive support training sets. The results were MAE = 0.0018, RMSE = 0.0025 and R
^{2}= 0.9965. In the prediction of the passive support test sets, the results were MAE = 0.0112, RMSE = 0.0157 and R^{2}= 0.8845. In the prediction of the active support training sets, the results were MAE = 0.0014, RMSE = 0.0019 and R^{2}= 0.964. In the prediction of the active support test sets, the results were MAE = 0.0024, RMSE = 0.0028 and R^{2}= 0.9294. The smaller MAE and RMSE, as well as the larger R^{2}, demonstrated that the GSCV-RF model can produce more accurate and reliable predictions of α. - After comparing and analyzing the three models, we concluded that the GSCV-RF model was superior in α prediction, followed by the RF model and the BP model. The BP model’s R
^{2}was too low, proving that the GSCV-RF model was superior in α prediction.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Gao, K.; Qi, Z.; Liu, Y.; Zhang, J. Calculation Model for Ventilation Friction Resistance Coefficient by Surrounding Rock Roughness Distribution Characteristics of Mine Tunnel. Sci. Rep.
**2022**, 12, 3193. [Google Scholar] [CrossRef] [PubMed] - Wu, C. Mine Ventilation and Air Conditioning, 1st ed.; Zhongnan University Press: Changsha, China, 2008; pp. 63–68. [Google Scholar]
- Shao, B. Research on Fuzzy Querying System for Mine Roadway’s Frictional Resistance Coefficient; Liaoning Technical University: Fuxin, China, 2015. [Google Scholar]
- Song, Y.; Zhu, M.; Wei, N.; Deng, L.J. Regression analysis of friction resistance coefficient under different support methods of roadway based on PSO-SVM. J. Phys. Conf. Ser.
**2021**, 1941, 012046. [Google Scholar] [CrossRef] - Liang, J.; Wang, Q. Design and Implementation of Friction Coefficient Database for Roadway Ventilation. Saf. Coal Mines.
**2019**, 50, 99–101. [Google Scholar] - Hamdia, K.M.; Zhuang, X.; Rabczuk, T. An Efficient Optimization Approach for Designing Machine Learning Models Based on Genetic Algorithm. Neural Comput. Appl.
**2021**, 33, 1923–1933. [Google Scholar] [CrossRef] - Zhang, P. The Research of New Methods to Compute Coefficient of Mine Roadway’s Frictional Resistance; Liaoning Technical University: Fuxin, China, 2004. [Google Scholar]
- Wang, S. Calculation of Mine Tunnel Friction Coefficient Based on Multilayer Feedforward Neural Networks; Liaoning Technical University: Fuxin, China, 2014. [Google Scholar]
- Wei, N.; Liu, J. Prediction of Mine Frictional Resistance Coefficient Based on BP Neural Network. Mine Saf. Environ. Prot.
**2018**, 45, 7–10. [Google Scholar] - Zhang, J.; Yin, G.; Ni, Y.; Chen, J. Prediction of Industrial Electric Energy Consumption in Anhui Province Based on GA-BP Neural Network. IOP Conf. Ser. Earth Environ. Sci.
**2018**, 108, 052061. [Google Scholar] [CrossRef] - Qian, K.; Hou, Z.; Sun, D. Sound Quality Estimation of Electric Vehicles Based on GA-BP Artificial Neural Networks. Appl. Sci.
**2020**, 10, 5567. [Google Scholar] [CrossRef] - Breiman, L. Random Forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef] [Green Version] - Tao, H.; Salih, S.Q.; Saggi, M.K.; Dodangeh, E.; Voyant, C.; Al-Ansari, N.; Yaseen, Z.M.; Shahid, S. A Newly Developed Integrative Bio-Inspired Artificial Intelligence Model for Wind Speed Prediction. IEEE Access
**2020**, 8, 83347–83358. [Google Scholar] [CrossRef] - Furqan, F.; Muhammad, N.A.; Kaffayatullah, K.; Muhammad, R.S.; Muhammad, F.J.; Fahid, A.; Rayed, A. A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC). Appl. Sci.
**2020**, 10, 7330. [Google Scholar] - Li, S.; Gao, K.; Liu, Y.; Zhou, H.; Liu, Z. Random Forest Inversion Method for Mine Ventilation Resistance Coefficient. Mod. Min.
**2020**, 36, 205–207. [Google Scholar] - Zhu, Y.; Huang, L.; Zhang, Z.; Behzad, B. Estimation of Splitting Tensile Strength of Modified Recycled Aggregate Concrete Using Hybrid Algorithms. SSRN Electron. J.
**2021**, 3, 389–406. [Google Scholar] - Fu, Y.; Pan, L.; Wang, Q. Simulation and Optimization of Boiler Air Supply Control System Based on Machine Learning. J. Eng. Thermophys.
**2022**, 43, 1777–1782. [Google Scholar] - Li, L.; Liang, T.; Ai, S.; Tang, X. An Improved Random Forest Algorithm and Its Application to Wind Pressure Prediction. Int. J. Intell. Syst.
**2021**, 36, 4016–4032. [Google Scholar] - Sudhakar, S.; Srinivas, P.; Soumya, S.S.; Rambabu, S.; Suresh, K. Prediction of Groundwater Quality Using Efficient Machine Learning Technique. Chemosphere
**2021**, 276, 130265. [Google Scholar] - Sarkhani Benemaran, R.; Esmaeili-Falak, M.; Javadi, A. Predicting Resilient Modulus of Flexible Pavement Foundation Using Extreme Gradient Boosting Based Ptimised OModels. Int. J. Pavement Eng.
**2022**, 1–20. [Google Scholar] [CrossRef] - Lu, H. Statistical Learning Method, 1st ed.; Tsinghua University Press: Beijing, China, 2012; pp. 67–72. [Google Scholar]
- Nguyen, H.; Drebenstedt, C.; Bui, X.N.; Bui, D.T. Prediction of Blast-Induced Ground Vibration in an Open-Pit Mine by a Novel Hybrid Model Based on Clustering and Artificial Neural Network. Nat. Resour. Res.
**2020**, 29, 691–709. [Google Scholar] - Shan, R.; Peng, Y.; Kong, X.; Xiao, Y.; Yuan, H.; Huang, B.; Zheng, Y. Research Progress of Coal Roadway Support Technology at Home and Abroad. Chin. J. Rock Mech. Eng.
**2019**, 38, 2377–2403. [Google Scholar] - Liu, Y. Study on The Air Quantity of Mine Ventilation Network Based on BP Neural Network Prediction Model of Friction Resistance Coefficient in Roadway. Min. Saf. Environ. Prot.
**2021**, 48, 101–106. [Google Scholar] - Pi, Z. Study on the Clustering Analysis of Ventilation Resistance Characteristics and Supporting Pattern of Mine Roadway; Liaoning Technical University: Fuxin, China, 2012. [Google Scholar]
- Bao, W.; Ren, C. Research on Prediction Method of Battery Soc Based on GWO-BP Network. Comput. Appl. Softw.
**2022**, 39, 65–71. [Google Scholar]

No. | Parameter Name | Parameter Range | Step Length |
---|---|---|---|

1 | n_estimators | [10, 150] | 1 |

2 | max_features | [0.1, 1.0] | 0.1 |

3 | max_depth | [3, 50] | 1 |

No. | Parameter Name | Optimum Value (Passive Support) | Optimum Value (Active Support) |
---|---|---|---|

1 | n_estimators | 67 | 110 |

2 | max_features | 0.9 | 1.0 |

3 | max_depth | 9 | 3 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guo, C.; Wang, X.; He, D.; Liu, J.; Li, H.; Jiang, M.; Zhang, Y.
Predicting the Mine Friction Coefficient Using the GSCV-RF Hybrid Approach. *Appl. Sci.* **2022**, *12*, 12487.
https://doi.org/10.3390/app122312487

**AMA Style**

Guo C, Wang X, He D, Liu J, Li H, Jiang M, Zhang Y.
Predicting the Mine Friction Coefficient Using the GSCV-RF Hybrid Approach. *Applied Sciences*. 2022; 12(23):12487.
https://doi.org/10.3390/app122312487

**Chicago/Turabian Style**

Guo, Chenyang, Xiaodong Wang, Dexing He, Jie Liu, Hongkun Li, Mengjiao Jiang, and Yu Zhang.
2022. "Predicting the Mine Friction Coefficient Using the GSCV-RF Hybrid Approach" *Applied Sciences* 12, no. 23: 12487.
https://doi.org/10.3390/app122312487