# Predicting Hidden Danger Quantity in Coal Mines Based on Gray Neural Network

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Principle of Hidden Danger Quantity Prediction

#### 2.2. GM (1,1) Model Predicting Hidden Danger Quantity

#### 2.2.1. Mean GM (1,1) Prediction Model

^{(1)}(t) of ${X}^{\left(1\right)}\left(t\right)$, and

#### 2.2.2. Buffer Operator Improvement GM (1,1)

#### 2.3. Residual Error Modified Model for Hidden Danger Prediction Based on PSO-RELM

#### 2.3.1. ELM

_{i}= [x

_{i}

_{1}, x

_{i}

_{1}, ⋯ x

_{in}]

^{T}∈ R

^{n}is the input value, and t

_{i}= [t

_{i}

_{1}, t

_{i}

_{1}, ⋯ t

_{in}]

^{T}∈ R

^{n}is the output value, then the regression model of the neuron function $f\left(x\right)$ of which the hidden node number is L can be expressed as [30]:

^{+}is the generalized inverse of matrix $H$, and

#### 2.3.2. Regular Learning Machine RELM

#### 2.3.3. PSO-RELM

## 3. Results and Analysis

#### 3.1. Predicting the Hidden Danger Quantity by GM (1,1) with Weakened Buffer Operator

#### 3.2. Modification of Residual Error Based on PSO-ELM

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Li, T. Study On investigation and management system for safety hidden dangers and internal control processes in coal mines. China Coal
**2012**, 2, 26–29. [Google Scholar] - Liang, Z.; Xin, G.; Guanglong, L.; Jian, J. Discussion on three works relationships of hidden trouble investigation and control and safety quality standardization and safety risk prevention and control management system. China Coal
**2015**, 7, 116–119. [Google Scholar] - Zhang, D.W. Analysis of Coal Mine Safety Hidden Danger Trends Based on OLAM. Coal Eng.
**2015**, 5, 139–142. [Google Scholar] - Zhang, S.Y. Research and Practice of Coal Mine Safety Hidden Trouble Investigation and Control. Zhongzhou Coal
**2010**, 11, 113–114. [Google Scholar] - General Office of State Security supervision. Circular of the General Office of the State Administration of Work Safety on Further Doing Hidden Danger Elimination and Control Normalization Mechanism Construction Pilot Work. For. Labor Saf.
**2013**, 26, 26–27. [Google Scholar] - Chen, Y.Q. Application of data mining technology in coal mine hidden hazard management. Ind. Mine Autom.
**2016**, 42, 27–30. [Google Scholar] - Zhang, C.L. Study On big data processing and knowledge discovery analysis method for safety hazard in coal mine. J. Saf. Sci. Technol.
**2016**, 09, 176–181. [Google Scholar] - Wang, X.Y. The Study of Evaluation and Prediction on the Governance Capability for Safety Hidden Danger of Coal Mine. Ph.D. Thesis, China University of Mining and Technology (Beijing), Beijing, China, 2013. [Google Scholar]
- Chen, Q. Analysis on Accident Causation Factors and Hazard Theory. China Saf. Sci. J.
**2009**, 19, 67–71. [Google Scholar] - Wang, L.K. The Hierarchy Analysis for Hidden Danger and Research on Early Warning Method in Coal Mine. Ph.D. Thesis, China University of Mining and Technology (Beijing), Beijing, China, 2015. [Google Scholar]
- Zhang, D. Studies on the Identification of Mine Safety Hidden Danger and The Closed-Loop Management Model. Ph.D. Thesis, China University of Mining and Technology (Beijing), Beijing, China, 2009. [Google Scholar]
- Fan, Y. Research on Neural Network Prediction. Master’s Thesis, Southwest Jiao Tong University, Chengdu, China, 2005. [Google Scholar]
- Gao, W.; Farahani, M.R.; Aslam, A.; Hosamani, S. Distance learning techniques for ontology similarity measuring and ontology mapping. Clust. Comput. J. Netw. Softw. Tools Appl.
**2017**, 20, 959–968. [Google Scholar] [CrossRef] - Xiong, Z.G.; Wu, Y.; Ye, C.H.; Zhang, X.M.; Xu, F. Color image chaos encryption algorithm combining CRC and nine palace map. Multimed. Tools Appl.
**2019**, 78, 31035–31055. [Google Scholar] [CrossRef] - Zhao, N.; Xia, M.J.; Mi, W.J. Modeling and solution for inbound container storage assignment problem in dual cycling mode. Discret. Contin. Dyn. Syst. S
**2020**. [Google Scholar] [CrossRef] [Green Version] - Yu, K.; Zhou, L.; Cao, Q.; Li, Z. Evolutionary Game Research on Symmetry of Workers’ Behavior in Coal Mine Enterprises. Symmetry
**2019**, 11, 156. [Google Scholar] [CrossRef] [Green Version] - Chen, B.Z.; Wu, M. Etiologies of accident and Safety concepts. J. Saf. Sci. Technol.
**2008**, 4, 42–46. [Google Scholar] - Tian, S.C.; Li, H.X.; Wang, L.; Chen, T. Probe into the Frequency of Coal Mine Accidents Based on the Theory of Three Types of Hazards. China Saf. Sci. J.
**2007**, 17, 177–179. [Google Scholar] - Den, J.L. Brief Introduction of Grey System Theory. Inn. Mong. Electr. Power
**1993**, 3, 51–52. [Google Scholar] - Liu, S.F.; Zeng, B.; Liu, J.F.; Xie, N.M. Several Basic Models of GM (1,1) and Their Applicable Bound. J. Syst. Eng. Electron.
**2014**, 3, 501–508. [Google Scholar] - Liu, S.F.; Yang, Y.J.; Wu, L.F. Grey System Theory and Its Application; Science Press: Beijing, China, 2014. [Google Scholar]
- Chen, L.; Lin, W.; Li, J.; Tian, B.; Pan, H. Prediction of lithium-ion battery capacity with metabolic grey model. Energy
**2016**, 106, 662–672. [Google Scholar] [CrossRef] - Kumar, U.; Jain, V.K. Time Series Models (Grey-Markov, Grey Model with Rolling Mechanism and Singular Spectrum Analysis) to Forecast Energy Consumption in India. Energy
**2010**, 35, 1709–1716. [Google Scholar] [CrossRef] - Shaikh, F.; Ji, Q.; Shaikh, P.H.; Mirjat, N.H.; Uqaili, M.A. Forecasting China’s Natural Gas Demand Based on Optimised Nonlinear Grey Models. Energy
**2017**, 140, 941–951. [Google Scholar] [CrossRef] - Zhou, H.P. The Research and Application of Death Rate Per Million-Ton Coal Prediction Method. Ph.D. Thesis, China University of Mining and Technology (Beijing), Beijing, China, 2012. [Google Scholar]
- Jiao, L.C.; Yang, S.Y.; Liu, F.; Wang, S.G.; Feng, Z.X. Seventy Years Beyond Neural Networks: Retrospect and Prospect. Chin. J. Comput.
**2016**, 8, 1697–1716. [Google Scholar] - Chen, J.H.; Liu, L.; Zhou, Z.Y.; Yong, X.Y. Optimization of mining methods based on combination of principal component analysis and neural networks. J. Cent. South Univ.
**2010**, 41, 1967–1972. [Google Scholar] - Wu, A.X.; Guo, L.; Yu, J.; Yang, Y.P.; Xiao, X. Neural network model construction and its application in fuzzily optimization of mining method. Min. Met. Eng.
**2003**, 23, 6–11. [Google Scholar] - Kennedy, J. Particle Swarm Optimization. In Encyclopedia of Machine Learning; Sammut, C., Webb, G.I., Eds.; Springer: Boston, MA, USA, 2011. [Google Scholar]
- Huang, G.B.; Zhu, Q.Y.; Siew, C.K. Extreme Learning Machine: Theory and Applications. Neurocomputing
**2006**, 70, 489–501. [Google Scholar] [CrossRef] - Lan, Y.; Yeng, C.S.; Huang, G.B. Ensemble of Online Sequential Extreme Learning Machine. Neurocomputing
**2009**, 72, 3391–3395. [Google Scholar] [CrossRef] - Bartlett, P.L. The Sample Complexity of Pattern Classification with Neural Networks: The Size of the Weights Is More Important Than the Size of the Network. Ieee Trans. Inf. Theory
**1998**, 44, 525–536. [Google Scholar] [CrossRef] [Green Version] - Deng, W.Y.; Zheng, Q.H.; Lin, C. Regularized Extreme Learning Machine. In Proceedings of the 2009 IEEE Symposium on Computational Intelligence and Data Mining, Nashville, TN, USA, 30 March–2 April 2009; pp. 389–395. [Google Scholar]
- Xue, H.B.; Lun, S.X. A Review on Application of PSO in Multi Objective Optimization. J. Bohai Univ. (Nat. Sci. Ed.)
**2009**, 3, 265–269. [Google Scholar] - Zhang, Y.; Le, J.; Liao, X.; Zheng, F.; Liu, K.; An, X. Multi-objective hydro-thermal-wind coordination scheduling integrated with large-scale electric vehicles using IMOPSO. Renew. Energy
**2018**, 128, 91–107. [Google Scholar] - Yang, X.Y.; Guan, W.Y.; Liu, Y.Q.; Xiao, Y.Q. Prediction Intervals Forecasts of Wind Power Based on PSO-KELM. Proc. Chin. Soc. Electr. Eng.
**2015**, S1, 146–153. [Google Scholar] - Wang, J.; Bi, H.Y. A New Extreme Learning Machine Optimized by PSO. J. Zhengzhou Univ. (Nat. Sci. Ed.)
**2013**, 1, 100–104. [Google Scholar] - Box, G.E.P.; Jenkins, G. Time Series Analysis, Forecasting and Control; Holden-Day, Incorporated: San Francisco, CA, USA, 1990; pp. 238–242. [Google Scholar]
- Bajić, S.; Bajić, D.; Gluščević, B.; Ristić Vakanjac, V. Application of Fuzzy Analytic Hierarchy Process to Underground Mining Method Selection. Symmetry
**2020**, 12, 192. [Google Scholar] [CrossRef] [Green Version] - Tsolaki-Fiaka, S.; Bathrellos, G.D.; Skilodimou, H.D. Multi-Criteria Decision Analysis for an Abandoned Quarry in the Evros Region (NE Greece). Land
**2018**, 7, 43. [Google Scholar] [CrossRef] [Green Version]

**Figure 2.**Hidden danger quantity prediction principle. GM, gray model; ELM, extreme learning machine.

No. | Original Sequence | Buffer Operator Sequence | ||||||
---|---|---|---|---|---|---|---|---|

Actual Value | Fitted Value | Residual Error | Relative Error | Actual Value | Fitted Value | Residual Error | Relative Error | |

1 | 777 | — — | — — | — — | — — | — — | — — | — — |

2 | 681 | 680.68 | −0.32 | 0.05% | — — | — — | — — | — — |

3 | 715 | 673.19 | −41.81 | 5.85% | — — | — — | — — | — — |

4 | 500 | 665.78 | −165.78 | 33.16% | 668.25 | — — | — — | — — |

5 | 762 | 658.45 | −103.55 | 14.20% | 664.5 | 673.303 | 8.803 | 1.325% |

6 | 759 | 651.20 | −107.80 | 14.20% | 684 | 665.669 | −18.331 | 2.680% |

7 | 627 | 644.03 | −17.03 | 2.72% | 662 | 658.122 | −3.878 | 0.586% |

8 | 609 | 636.94 | 27.94 | 4.59% | 689.25 | 650.660 | −38.590 | 5.599% |

9 | 392 | 629.93 | 237.93 | 60.70% | 596.75 | 643.283 | 46.533 | 7.798% |

10 | 730 | 623.00 | −107.00 | 14.66% | 589.5 | 635.989 | 46.489 | 7.886% |

11 | 690 | 616.14 | −73.86 | 10.70% | 605.25 | 628.779 | 23.529 | 3.887% |

12 | 643 | 609.36 | −33.64 | 5.23% | 613.75 | 621.650 | 7.900 | 1.287% |

13 | 550 | 602.65 | 52.65 | 9.57% | 653.25 | 614.601 | −38.649 | 5.916% |

14 | 602 | 596.02 | −5.98 | 0.99% | 621.25 | 607.633 | −13.617 | 2.192% |

15 | 604 | 589.46 | −14.54 | 2.41% | 599.75 | 600.744 | 0.994 | 0.166% |

16 | 629 | 582.97 | −46.03 | 7.32% | 596.25 | 593.933 | −2.317 | 0.389% |

17 | 611 | 576.55 | −34.45 | 5.64% | 611.5 | 587.199 | −24.301 | 3.974% |

18 | 649 | 570.21 | −78.79 | 12.14% | 623.25 | 580.541 | −42.709 | 6.853% |

19 | 493 | 563.93 | 70.93 | 14.39% | 595.5 | 573.959 | −21.54 | 3.617% |

20 | 510 | 557.72 | 47.72 | 9.36% | 565.75 | 567.451 | 1.701 | 0.301% |

21 | 466 | 551.59 | 85.59 | 18.37% | 529.5 | 561.018 | 31.518 | 5.952% |

22 | 603 | 545.51 | −57.49 | 9.53% | 518 | 554.657 | 36.657 | 7.077% |

No. | Prediction Value of Original Sequence | Prediction Value of Buffer Operator Sequence | ||||||
---|---|---|---|---|---|---|---|---|

Actual Value | Fitted Value | Residual Error | Relative Error | Actual Value | Fitted Value | Residual Error | Relative Error | |

1 | 581 | 539.51 | −41.49 | 7.14% | 540 | 548.37 | 8.37 | 1.55% |

2 | 621 | 533.57 | −87.43 | 14.08% | 567.75 | 542.15 | −25.6 | 4.51% |

Swarm number | 15 | 20 | 25 | 30 | 35 |

Ultimate error | 0.0658 | 0.0717 | 0.0579 | 0.0608 | 0.0573 |

Time consumed (s) | 3.028 | 3.905 | 4.207 | 4.862 | 6.067 |

Number of Hidden Layer Nodes | Mean Square Error of Training | Predicted Mean Square Error | Consumed Time |
---|---|---|---|

5 | 23.28 | 2.44 | 2.924s |

6 | 23.22 | 2.35 | 2.928s |

7 | 22.88 | 2.46 | 2.931s |

8 | 22.43 | 2.68 | 2.938s |

9 | 21.78 | 2.36 | 2.938s |

10 | 21.48 | 2.546 | 3.233s |

11 | 21.01 | 2.40 | 3.499s |

12 | 21.02 | 2.52 | 3.067s |

No. | Actual Value | Fitted Value of GM | Residual Error | Optimized ELM | Fitted Value of Combination Model | Residual Error of Combination Model | Relative Error |
---|---|---|---|---|---|---|---|

1 | 668.25 | — — | — — | — — | — — | — — | — — |

2 | 664.5 | 673.303 | 8.803 | — — | — — | — — | — — |

3 | 684 | 665.669 | −18.331 | — — | — — | — — | — — |

4 | 662 | 658.122 | −3.878 | — — | — — | — — | — — |

5 | 689.25 | 650.660 | −38.590 | 32.80 | 683.46 | −5.79 | 0.84% |

6 | 596.75 | 643.283 | 46.533 | −27.01 | 616.27 | 19.52 | 3.27% |

7 | 589.5 | 635.989 | 46.489 | −44.16 | 591.83 | 2.33 | 0.39% |

8 | 605.25 | 628.779 | 23.529 | −20.96 | 607.82 | 2.57 | 0.42% |

9 | 613.75 | 621.650 | 7.900 | −9.71 | 611.94 | −1.81 | 0.29% |

10 | 653.25 | 614.601 | −38.649 | 39.46 | 654.06 | 0.81 | 0.12% |

11 | 621.25 | 607.633 | −13.617 | 9.76 | 617.39 | −3.86 | 0.62% |

12 | 599.75 | 600.744 | 0.994 | 8.48 | 609.22 | 9.47 | 1.58% |

13 | 596.25 | 593.933 | −2.317 | −9.00 | 584.93 | −11.32 | 1.90% |

14 | 611.5 | 587.199 | −24.301 | 24.49 | 611.69 | 0.19 | 0.03% |

15 | 623.25 | 580.541 | −42.709 | 24.54 | 605.08 | −18.17 | 2.92% |

16 | 595.5 | 573.959 | −21.54 | 18.22 | 592.18 | −3.32 | 0.56% |

17 | 565.75 | 567.451 | 1.701 | −4.06 | 563.39 | −2.36 | 0.42% |

18 | 529.5 | 561.018 | 31.518 | −13.80 | 547.22 | 17.72 | 3.35% |

19 | 518 | 554.657 | 36.657 | −34.95 | 519.71 | 1.71 | 0.33% |

No. | Actual Mean | GM(1,1) Prediction Value | Correction Value of Optimized ELM | Prediction Value of Combination Model | Residual Error | Relative Error |
---|---|---|---|---|---|---|

1 | 540 | 548.37 | −4.07 | 544.3 | 4.3 | 0.79% |

2 | 567.75 | 542.15 | 20.14 | 562.29 | −5.46 | 0.96% |

No. | Actual Value | Prediction Value | Residual Error | Relative Error |
---|---|---|---|---|

1 | 581 | 598.2 | 17.2 | 2.96% |

2 | 621 | 599.16 | −21.84 | 3.52% |

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## Share and Cite

**MDPI and ACS Style**

Zhao, H.; He, Q.; Wei, Z.; Zhou, L.
Predicting Hidden Danger Quantity in Coal Mines Based on Gray Neural Network. *Symmetry* **2020**, *12*, 622.
https://doi.org/10.3390/sym12040622

**AMA Style**

Zhao H, He Q, Wei Z, Zhou L.
Predicting Hidden Danger Quantity in Coal Mines Based on Gray Neural Network. *Symmetry*. 2020; 12(4):622.
https://doi.org/10.3390/sym12040622

**Chicago/Turabian Style**

Zhao, Hongze, Qiao He, Zhao Wei, and Lilin Zhou.
2020. "Predicting Hidden Danger Quantity in Coal Mines Based on Gray Neural Network" *Symmetry* 12, no. 4: 622.
https://doi.org/10.3390/sym12040622