# A Machine Learning Method for Engineering Risk Identification of Goaf

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Principal Component Analysis

#### 2.1. Basic Principles

#### 2.2. Mathematical Model

_{1}, x

_{2}, ..., x

_{m}, are included in the n samples, the original data matrix can be obtained, as follows:

_{ij}represents the data before standardization; x* ij represents the data after standardization; max(x

_{j}) and min(x

_{j}) are the maximum and minimum values in the column j data, respectively.

_{1}, x

_{2},..., x

_{m})

^{T}are denoted as the m new ones, and the new variables can be linearly expressed by the original ones as x

_{1}, x

_{2},..., x

_{m}, that is:

_{1m}, y

_{2m},..., y

_{nm}signifies the variables sourced through PCA, and u is the correlation coefficient matrix among the variables, which need to satisfy the following conditions:

- (1)
- (1) ${u}_{k1}^{2}+{u}_{k2}^{2}+\cdots +{u}_{km}^{2}=1(k=1,2,\cdots ,n)$;

- (2)
- cov(y
_{i}, y_{j}) = 0(i ≠ j; i, j = 1, 2,…, m), namely, the components of principal analysis are independent and there is no overlapping information; - (3)
- var(y
_{1}) ≥ var(y_{2}) ≥ … ≥ var(y_{m}), namely, the principal components are sorted according to the standard deviation, where: y_{1}, y_{2},…, y_{m}, obtained through the above process, can be determined as the principal components of 1, 2,…, m of the original variables.

#### 2.3. Geometric Interpretation

## 3. Multi-Classification Support Vector Machine (SVM)

#### 3.1. Basic Principles of SVM

_{1}’ and ‘H

_{2}’ is signified as ‘interval’, the size of which is related to the normal vector ‘w’ of line ‘H

_{0}’, and where the value is equal to 2/||w||.

_{i}≥ 0′. Thus, the interval maximization at this moment can be signified as ‘soft interval maximization’, the corresponding convex quadratic programming problem of which is:

_{i}refers to the ‘Lagrange multiplier’; α

_{i}≥ 0 (i = 1, 2, ..., N); μ

_{i}≥ 0.

^{*}= (α* 1, α* 2, ..., α* N)

^{T}is the solution of the dual problem, if there is a component α* j of α

^{*}that satisfies 0 < α* j < C, then the optimal solution of the original problem can be determined as:

#### 3.2. Constructing a Multi-Classification Support Vector Machine

#### 3.3. Cross-Validation

#### 3.4. Parameter Optimization of the Differential Evolution Algorithm

_{1}, M

_{2},..., M

_{N}), where n denotes the size of the population. Note that the upper and lower bounds of the parameters should be set before initialization, then afterward the intermediate population can be accessibly obtained by mutating and crossing the parameters. Moreover, a greedy strategy is adopted to select the method of one-against-one between the two populations to obtain the new generation.

_{1}, a

_{2}, a

_{3}∈{1, 2,…, N}, and a

_{1}≠ a

_{2}≠ a

_{3}; N is the size of the population; F refers to the scaling factor, the value of which is a positive real number and also generally a random one between (0, 1), which can control the evolution rate of the population; G represents the current population, and G + 1 denotes the next generation.

_{rand}signifies an integer that is randomly generated in {1, 2} to ensure that at least one optimization parameter will mutate; C refers to the crossover factor, which is normally a random number between [0, 1].

## 4. Engineering Examples

Y2 = −0.751X1 + 0.519X2 + 0.766X3 − 0.158X4 + 0.638X5 − 0.019X6 + 0.583X7 − 0.001X8 − 0.123X9;

Y3 = −0.031X1 + 0.219X2 + 0.211X3 + 0.110X4 − 0.454X5 − 0.065X6 + 0.191X7 + 0.405X8 + 0.846X9;

Y4 = 0.296X1 − 0.363X2 + 0.451X3 − 0.173X4 + 0.367X5 + 0.103X6 − 0.246X7 − 0.288X8 + 0.413X9;

Y5 = 0.117X1 − 0.251X2 − 0.182X3 − 0.043X4 − 0.067X5 + 0.060X6 + 0.697X7 − 0.343X8 + 0.096X9.

## 5. Conclusions

- (1)
- The ‘one-against-one’ method is used to construct a multi-classification SVM. In order to prevent the overfitting of the model, the K-fold cross-validation method will be employed to select it. Above all, the research results reveal that the SVM has the desirable ability of generalization. Compared with the neural network, the apparent advantages lie in solving the problems of overfitting and it is easy to fall into the local minimum that can be detected in the SVM under the conditions of small samples.
- (2)
- PCA is used to preprocess the original data of multi-source impact indicators for goaf risk identification, which can realize the dimensionality reduction and data denoising, and can simultaneously improve the prediction accuracy and classification efficiency while retaining the most information.
- (3)
- Using the strategy of DE and a global optimization search mechanism, the optimal solution of the problems to be optimized will be automatically obtained, namely, the kernel function parameter of SVM, ‘γ’, and the penalty factor, ‘C’. Moreover, the engineering calculation example further verifies that the DE has the characteristics of clear logic, strong convergence, and good robustness.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Yi, H.; Zhang, X.; Yang, H.; Li, M.; Gao, Q.; Jinke. Goaf collapse vibration analysis and disposal based on a experiment of heavy ball touchdown. Explos. Shock Waves
**2019**, 39, 91–103. [Google Scholar] - Zhao, Y.; Tang, J.; Chen, Y.; Zhang, L.; Wang, W.; Wan, W.; Liao, J. Hydromechanical coupling tests for mechanical and permeability characteristics of fractured limestone in complete stress-strain process. Environ. Earth Sci.
**2017**, 76, 24. [Google Scholar] [CrossRef] - Zhao, Y.; Luo, S.; Wang, Y.; Wang, W.; Zhang, L.; Wan, W. Numerical Analysis of Karst Water Inrush and a Criterion for Establishing the Width of Water-resistant Rock Pillars. Mine Water Environ.
**2017**, 36, 508–519. [Google Scholar] [CrossRef] - Liao, Y.; Yu, G.; Liao, Y.; Jiang, L.; Liu, X. Environmental Conflict Risk Assessment Based on AHP-FCE: A Case of Jiuhua Waste Incineration Power Plant Project. Sustainability
**2018**, 10, 4095. [Google Scholar] [CrossRef] [Green Version] - Wu, H.; Jia, Q.; Wang, W.; Zhang, N.; Zhao, Y. Experimental Test on Nonuniform Deformation in the Tilted Strata of a Deep Coal Mine. Sustainability
**2022**, 13, 13280. [Google Scholar] [CrossRef] - Du, K.; Li, X.; Liu, K.; Zhao, X.; Zhou, Z.; Dong, L. Comprehensive evaluation of underground goaf risk and engineering application. J. Cent. South Univ.
**2011**, 42, 2802–2811. [Google Scholar] - Yuan, Z.; Zhai, J.; Li, S.; Jiang, Z.; Huang, F. A Unified Solution for Surrounding Rock of Roadway Considering Seepage, Dilatancy, Strain-Softening and Intermediate Principal Stress. Sustainability
**2022**, 14, 8099. [Google Scholar] [CrossRef] - Liu, Y.; Hao, Y.; Lu, Y. Improved Design of Risk Assessment Model for PPP Project under the Development of Marine Architecture. J. Coast. Res.
**2021**, 9, 74–80. [Google Scholar] [CrossRef] - Liu, S.; Nie, Y.; Hu, W.; Ashiru, M.; Li, Z.; Zou, J. The Influence of Mixing Degree between Coarse and Fine Particles on the Strength of Offshore and Coast Foundations. Sustainability
**2022**, 14, 9177. [Google Scholar] [CrossRef] - Chen, W.; Wan, W.; Zhao, Y.; Peng, W. Experimental Study of the Crack Predominance of Rock-Like Material Containing Parallel Double Fissures under Uniaxial Compression. Sustainability
**2020**, 12, 5188. [Google Scholar] [CrossRef] - Zhang, Y.; Chang, X.; Liang, J. Comparison of different algorithms for calculating the shading effects of topography on solar irradiance in a mountainous area. Environ. Earth Sci.
**2017**, 76, 295. [Google Scholar] [CrossRef] - Feng, T.; Chen, H.; Wang, K.; Nie, Y.; Zhang, X.; Mo, H. Assessment of underground soil loss via the tapering grikes on limestone hillslopes. Agric. Ecosyst. Environ.
**2020**, 5, 297. [Google Scholar] [CrossRef] - Chen, J.; Liu, L.; Zhou, Z.; Yong, X. Optimization of mining methods based on combination of principal component analysis and neural networks. J. Cent. South Univ.
**2010**, 41, 1967–1972. [Google Scholar] - Wang, X.; Duan, Y.; Peng, X. Fuzzy Synthetic Assessment of the Danger Degree of Mined-out Area Disaster. Min. Res. Dev.
**2005**, 25, 83–85. [Google Scholar] - Zhou, J.; Shi, X. Evaluation of the alternatives for mined out area disposal based on the identical degree of set pair analysis. Met. Mine
**2009**, 396, 10–13. [Google Scholar] - Wang, X.; Ding, D.; Duan, Y. Applications of the grey relation analysis in the evaluation of the risk degree of the underground mined-out stopes. J. Saf. Sci. Technol.
**2006**, 2, 35–39. [Google Scholar] - Gong, F.; Li, X.; Dong, L.; Liu, X. Underground goaf risk evaluation based on uncertainty measurement theory. Chin. J. Rock Mech. Eng.
**2008**, 27, 323–330. [Google Scholar] - Hu, Y.; Li, X. Bayes discriminant analysis method to identify risky of complicated goaf in mines and its application. Trans. Nonferrous Met. Soc. China
**2012**, 22, 425–431. [Google Scholar] [CrossRef] - Feng, Y.; Wang, X.; Cheng, A.; Zhang, Q.; Zhao, J. Method optimization of underground goaf risk evaluation. J. Cent. South Univ.
**2013**, 44, 2881–2888. [Google Scholar] - Wang, Z.; Guo, J.; Wang, L. Recognition of goaf risk based on support vector machines method. J. Chongqing Univ.
**2015**, 38, 85–90. [Google Scholar] - Wang, H.; Li, X.; Dong, L.; Liu, K.; Tong, H. Classification of goaf stability based on support vector machine. J. Saf. Sci. Technol.
**2014**, 10, 154–159. [Google Scholar] - Fang, X.; Ding, Z.; Shu, X. Hydrogen yield prediction model of hydrogen production from low rank coal based on support vector machine optimized by genetic algorithm. J. China Coal Soc.
**2010**, 35, 205–209. [Google Scholar] - Hsu, C.-W.; Lin, C.-J. A comparison of methods for multi-class support vector machines. IEEE Trans. Neural Netw.
**2002**, 13, 415–425. [Google Scholar] [PubMed] - Kebel, U. Pairwise Classification and Support Vector Machines. In Advances in Kernel Methods-Support Vector Learning; MIT Press: Cambridge, MA, USA, 1999; pp. 255–258. [Google Scholar]
- Platt, J.C.; Cristianini, N.; Shawe-Taylor, J. Large Margin DAGs for Multi-class Classification. Adv. Neural Inf. Process. Syst.
**2000**, 12, 547–553. [Google Scholar] - Bennett, K.P.; Blue, J.A. A support vector machine approach to decision tree. Rensselaer Polytech. Inst.
**1997**, 3, 2396–2401. [Google Scholar] - Zhou, Z. Machine Learning; Tsinghua University Press: Beijing, China, 2017; pp. 121–139. [Google Scholar]
- Liang, N.; Tuo, Y.; Deng, Y.; Jia, Y. Classification model of ice transport and accumulation in front of channel flat sluice based on PCA-SVM. Chin. J. Theor. Appl. Mech.
**2021**, 53, 703–713. [Google Scholar] - Chen, X.; Yang, G.; Huang, M. Real-coded Quantum Differential Evolution Algorithm. J. Chin. Comput. Syst.
**2013**, 34, 1141–1146. [Google Scholar] - Xu, Z.; Zhou, D.; Luo, Y. Fuzzy Neural Network Based on Principal Component. Comput. Eng. Appl.
**2006**, 42, 34–36. [Google Scholar]

Sample Serial Number | Exploitation Depth X1/m | Mining Methods X2 | Goaf Mining Height X3/m | Maximum Exposure Area X4/m^{2} | Maximum Exposure Height X5/m | Maximum Exposed Span X6/m | Pillar Situation X7 | Measured Volume X8 /m ^{3} | Governance Rate X9 | Risk Rank |
---|---|---|---|---|---|---|---|---|---|---|

1 | 130 | 1 | 35 | 3589 | 35 | 39 | 0 | 57,481.1 | 0.0 | 2 |

2 | 130 | 1 | 20 | 1208 | 0.99 | 24 | 1 | 12,141.3 | 94.4 | 1 |

3 | 130 | 1 | 35 | 1735 | 5.97 | 28 | 0 | 31,595.7 | 96.3 | 1 |

4 | 130 | 1 | 35 | 1644 | 35 | 32 | 2 | 17,144.4 | 100.0 | 1 |

5 | 130 | 1 | 25 | 2489.5 | 25 | 39 | 2 | 19,377.7 | 100.0 | 1 |

…… | ||||||||||

119 | 220 | 1 | 15 | 349 | 15 | 17 | 0 | 3200 | 0.0 | 1 |

120 | 220 | 1 | 15 | 259 | 15 | 10 | 0 | 2867 | 0.0 | 1 |

Index | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 |
---|---|---|---|---|---|---|---|---|---|

X1 | 1.000 | ||||||||

X2 | −0.366 | 1.000 | |||||||

X3 | −0.389 | 0.273 | 1.000 | ||||||

X4 | 0.001 | −0.432 | −0.084 | 1.000 | |||||

X5 | −0.325 | −0.045 | 0.512 | 0.089 | 1.000 | ||||

X6 | −0.050 | −0.465 | 0.097 | 0.695 | 0.227 | 1.000 | |||

X7 | −0.342 | 0.163 | 0.296 | 0.086 | 0.236 | 0.103 | 1.000 | ||

X8 | −0.046 | −0.150 | 0.098 | 0.594 | 0.019 | 0.370 | 0.110 | 1.000 | |

X9 | 0.104 | 0.010 | 0.153 | −0.039 | −0.309 | −0.093 | −0.005 | 0.061 | 1.000 |

Component | Initial Characteristic Value | Sum of Squares of Extracted Loads | ||||
---|---|---|---|---|---|---|

Total | Percentage Variance | Accumulation/% | Total | Percentage Variance | Accumulation/% | |

1 | 2.444 | 27.150 | 27.150 | 2.444 | 27.150 | 27.150 |

2 | 2.208 | 24.528 | 51.678 | 2.208 | 24.528 | 51.678 |

3 | 1.233 | 13.698 | 65.377 | 1.233 | 13.698 | 65.377 |

4 | 0.911 | 10.127 | 75.504 | 0.911 | 10.127 | 75.504 |

5 | 0.733 | 8.139 | 83.643 | 0.733 | 8.139 | 83.643 |

6 | 0.584 | 6.493 | 90.136 | |||

7 | 0.402 | 4.470 | 94.607 | |||

8 | 0.290 | 3.217 | 97.824 | |||

9 | 0.196 | 2.176 | 100.000 |

Index | Principal Component | ||||
---|---|---|---|---|---|

Y1 | Y2 | Y3 | Y4 | Y5 | |

X1 | −0.059 | −0.751 | −0.031 | 0.296 | 0.117 |

X2 | −0.565 | 0.519 | 0.219 | −0.363 | −0.251 |

X3 | 0.100 | 0.766 | 0.211 | 0.451 | −0.182 |

X4 | 0.884 | −0.158 | 0.110 | −0.173 | −0.043 |

X5 | 0.321 | 0.638 | −0.454 | 0.367 | −0.067 |

X6 | 0.858 | −0.019 | −0.065 | 0.103 | 0.060 |

X7 | 0.188 | 0.583 | 0.191 | −0.246 | 0.697 |

X8 | 0.664 | −0.001 | 0.405 | −0.288 | −0.343 |

X9 | −0.118 | −0.123 | 0.846 | 0.413 | 0.096 |

Sample Serial Number | Y1 | Y2 | Y3 | Y4 | Y5 | Risk Rank |
---|---|---|---|---|---|---|

1 | 0.9692 | 1.8113 | 0.1422 | 0.3396 | −0.6124 | 2 |

2 | −0.1286 | 1.0236 | 1.2293 | 0.1273 | 0.0872 | 1 |

3 | 0.0849 | 1.2046 | 1.2507 | 0.5023 | −0.4067 | 1 |

4 | 0.5255 | 2.3128 | 1.0500 | 0.6140 | 0.2771 | 1 |

5 | 0.6189 | 1.8470 | 1.1160 | 0.3447 | 0.3573 | 1 |

…… | ||||||

119 | −0.2744 | 0.6973 | 0.0772 | 0.0678 | −0.2842 | 1 |

120 | −0.4014 | 0.7017 | 0.0838 | 0.0565 | −0.2910 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Yuan, H.; Cao, Z.; Xiong, L.; Li, H.; Wang, Y.
A Machine Learning Method for Engineering Risk Identification of Goaf. *Water* **2022**, *14*, 4075.
https://doi.org/10.3390/w14244075

**AMA Style**

Yuan H, Cao Z, Xiong L, Li H, Wang Y.
A Machine Learning Method for Engineering Risk Identification of Goaf. *Water*. 2022; 14(24):4075.
https://doi.org/10.3390/w14244075

**Chicago/Turabian Style**

Yuan, Haiping, Zhanhua Cao, Lijun Xiong, Hengzhe Li, and Yixian Wang.
2022. "A Machine Learning Method for Engineering Risk Identification of Goaf" *Water* 14, no. 24: 4075.
https://doi.org/10.3390/w14244075