# Stability Prediction Model of Roadway Surrounding Rock Based on Concept Lattice Reduction and a Symmetric Alpha Stable Distribution Probability Neural Network

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## Abstract

**:**

## 1. Introduction

- (1)
- To combat the uncertainty and concealment of the correlation between the prediction indexes of surrounding rock stability, a model based on grid multi-layer attribute reduction is established to reduce the attributes of the evaluation index, optimize the index, and improve model efficiency.
- (2)
- The synthetic minority over-sampling technique (SMOTE) is used to synthesize new training samples, so that the numbers of training samples are balanced. Introduction of symmetrical alpha stable distribution instead of Gaussian distribution as the basis function of the probabilistic neural network model gives the model a broader meaning of expression.
- (3)
- Concept lattice multi-level attribute reduction involves more efficient index optimization, however its promotion ability and anti-noise ability are poor. Since the probabilistic neural network has advantages in data training, a concept lattice and symmetrical alpha stable distribution probability neural network model for roadway surrounding rock stability prediction should be superior.

## 2. Reduced Concept Lattice

#### 2.1. Basic Notion of the Concept Lattice

#### 2.2. Attribute Reduction Based on the Concept Lattice

## 3. Probabilistic Neural Network Model Based on Symmetric Alpha Stable Distribution

#### 3.1. Alpha Stable Distribution

#### 3.2. Probabilistic Neural Network

#### 3.3. Improved Probabilistic Neural Network

## 4. Prediction Model for Roadway Surrounding Rock Stability

#### 4.1. Selection of Evaluation Indexes for Roadway Surrounding Rock Stability

#### 4.2. Data Discretization

#### 4.3. Construction of Concept Lattice

#### 4.4. Reduction Indexes

#### 4.5. Establishment of Improved Probabilistic Neural Networks Model

## 5. Practical Engineering Applications

## 6. Conclusions

- (1)
- The proposed method uses five indexes: rock quality designation (RQD), uniaxial compressive strength (Rc), the integrity coefficient of rock mass, groundwater seepage, and joint condition as initial evaluation indexes, constructs a concept lattice according to training samples, generates a corresponding Hasse diagram, then uses concept lattice reduction to reduce the initial evaluation indexes. The reduced indexes are RQD, Rc, and groundwater seepage. By calculating correlation coefficients between the evaluation indexes, we prove the effectiveness of reduction.
- (2)
- Our method uses a symmetrical alpha stable distribution to replace the commonly used Gauss distribution in the probabilistic neural network and optimize parameter α, γ of the alpha stable distribution with a genetic algorithm, resulting in α and γ values of 0.2848 and 1.5963. This makes the enhanced probabilistic neural network more adaptable and improves the accuracy rate of the model prediction result.
- (3)
- Taking the roadway of the Jianlinshan mining area in the Daye iron mine as an example, we applied the prediction model for roadway surrounding rock stability based on the concept lattice and improved probabilistic neural network. The accuracy rate was up to 90%, which is 20% higher than the accuracy rate of the prediction model based on the original probabilistic neural network. In other words, the proposed prediction model can meet the demands of practical engineering and provides a new method for predicting the stability of roadway surrounding rock.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Number | Article | Journal |
---|---|---|

1 | Stability classification of adjoining rock of underground engineering based on Hopfield network | Chinese Journal of Geotechnical Engineering |

2 | Research on surrounding rock evaluation of underground engineering based on extension method | Chinese Journal of Rock Mechanics and Engineering |

3 | Set pair analysis—variable fuzzy set model for evaluation of stability of surrounding rock | Chinese Journal of Geotechnical Engineering |

4 | A novel extension evaluation model of surrounding rock stability based on connection cloud | Chinese Journal of Geotechnical Engineering |

5 | Classification of stability of surrounding rock using cloud model | Chinese Journal of Geotechnical Engineering |

6 | A fuzzy comprehensive evaluation methodology for rock burst forecasting using microseismic monitoring | Tunnelling and Underground Space Technology |

7 | Stability and availability evaluation of underground strategic petroleum reserve (SPR) caverns in bedded rock salt of Jintan, China | Energy |

8 | Decoupled explosion in an underground opening and dynamic responses of surrounding rock masses and structures and induced ground motions: A FEM-DEM numerical study | Tunnelling and Underground Space Technology |

…… |

Category | Rock Quality Designation (RQD) | Uniaxial Compressive Strength (Rc/MPa) | Integrity Coefficient of Rock Mass | Groundwater Seepage/(L/(min·10 m)) | Joint Condition |
---|---|---|---|---|---|

Stable, I | [90, 100] | [150, 200] | [0.75, 1.00] | [0, 5) | [9, 10] |

Relatively stable, II | [75, 90) | [100, 150) | [0.55, 0.75) | [5, 10) | [7, 9) |

Basically stable, III | [50, 75) | [60, 100) | [0.30, 0.55) | [10, 25) | [4, 7) |

Unstable, IV | [25, 50) | [30, 60) | [0.15, 0.30) | [25, 125) | [2, 4) |

Extremely unstable, V | [0, 25) | [0, 30) | [0.00, 0.15) | [125, 250] | [0, 2) |

Sequence Number | Rock Quality Designation (Grade) | Uniaxial Compressive Strength (Grade) | Integrity Coefficient of Rock Mass (Grade) | Groundwater Seepage (Grade) | Joint Condition (Grade) | Grade |
---|---|---|---|---|---|---|

1 | 96 (1) | 200.0 (1) | 0.97 (1) | 5 (1) | 9 (1) | I |

2 | 93 (1) | 152.0 (1) | 0.99 (1) | 3 (1) | 8.3 (2) | I |

3 | 98 (1) | 140.0 (2) | 0.95 (1) | 9 (2) | 8 (2) | I |

4 | 90 (1) | 170.0 (1) | 0.96 (1) | 9 (2) | 7.5 (2) | I |

5 | 88 (2) | 185.5 (1) | 0.89 (1) | 6 (2) | 8 (2) | II |

6 | 73 (3) | 176.4 (1) | 0.80 (1) | 8 (2) | 7 (2) | II |

7 | 92 (1) | 158.2 (1) | 0.94 (1) | 6 (2) | 7 (2) | II |

8 | 76 (2) | 181.9 (1) | 0.92(1) | 9 (2) | 8 (2) | II |

9 | 79 (2) | 126.0 (2) | 0.67 (2) | 7 (2) | 7.5 (2) | II |

10 | 74 (3) | 40.0 (4) | 0.38 (3) | 10 (2) | 6 (3) | III |

11 | 59 (3) | 97.0 (3) | 0.43 (3) | 15 (3) | 6.7 (3) | III |

12 | 65 (3) | 70.0 (3) | 0.60 (2) | 9 (2) | 6 (3) | III |

13 | 69 (3) | 65.0 (3) | 0.50 (3) | 9 (2) | 5 (3) | III |

14 | 48 (4) | 25.0 (5) | 0.22 (4) | 20 (3) | 4 (4) | IV |

15 | 74 (3) | 25.0 (5) | 0.15(4) | 20 (3) | 3 (4) | IV |

16 | 33 (4) | 78.0 (3) | 0.27 (4) | 20 (3) | 1.6 (4) | IV |

17 | 35 (4) | 25.0 (5) | 0.40 (3) | 12 (3) | 5 (4) | IV |

18 | 18 (5) | 20.0 (5) | 0.03 (5) | 20 (3) | 1 (5) | V |

19 | 20 (5) | 20.0 (5) | 0.20 (4) | 12 (3) | 3 (5) | V |

20 | 14 (5) | 35.0 (4) | 0.20 (4) | 15 (3) | 3 (5) | V |

Object | a_1 | a_2 | a_3 | a_4 | a_5 | b_1 | b_2 | b_3 | … | f_1 | f_2 | f_3 | f_4 | f_5 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | × | × | × | |||||||||||

2 | × | × | × | |||||||||||

3 | × | × | × | |||||||||||

4 | × | × | × | |||||||||||

5 | × | × | × | |||||||||||

6 | × | × | × | |||||||||||

7 | × | × | × | |||||||||||

8 | × | × | × | |||||||||||

9 | × | × | × | |||||||||||

10 | × | × | ||||||||||||

11 | × | × | × | |||||||||||

12 | × | × | × | |||||||||||

13 | × | × | × | |||||||||||

14 | × | × | ||||||||||||

15 | × | × | ||||||||||||

16 | × | × | × | |||||||||||

17 | × | × | ||||||||||||

18 | × | × | ||||||||||||

19 | × | × | ||||||||||||

20 | × | × |

Sequence Number | Discriminable Concept | Corresponding Loss Attribute |
---|---|---|

1 | ({1,2, …, 20}, Ø) | abcde |

2 | ({11,14,15,16,17,18,19,20}, {d_3}) | abce |

3 | ({10,11,12,13,14,17}, {e_3}) | abcd |

4 | ({6,10,11,12,13,15}, {a_3}) | bcde |

5 | ({10,20}, {b_4}) | acde |

6 | ({11,12,13,16}, {b_3}) | acde |

7 | ({9,12}, {c_2, d_2}) | abe |

8 | ({10,11,13,17}, {c_3,e_3}) | abd |

9 | ({16,18}, {d_3,e_5}) | abc |

10 | ({11,14,17}, {d_3,e_3}) | abc |

11 | ({3,4,5,6,7,8,9}, {d_2,e_2}) | abc |

12 | ({1,2,3,4,7}, {a_1,c_1}) | bde |

13 | ({11,15}, {a_3,d_3}) | cbe |

14 | ({6,10,12,13}, {a_3,d_2}) | bce |

15 | ({14,15,17,18,19}, {b_5,d_3}) | ace |

16 | ({11,16}, {b_3,d_3}) | ace |

17 | ({14,15,16,19,20}, {c_4,d_3}) | abe |

18 | ({3,9}, {b_2,d_2,e_2}) | ac |

19 | ({15,19,20}, {c_4,d_3,e_4}) | ab |

20 | ({11,17}, {c_3,d_3,e_3}) | ab |

21 | ({1,2,4,7}, {a_1,b_1,c_1}) | de |

22 | ({14,15,19}, {b_5,c_4,d_3}) | ae |

23 | ({2,3,4,7}, {a_1,c_1,e_2}) | bd |

24 | ({4,5,6,7,8}, {a_1,c_1,d_2,e_2}) | b |

25 | ({2,4,7}, {a_1,b_1,c_1,e_2}) | d |

26 | ({3,4,7}, {a_1,c_1,d_2,e_2}) | b |

27 | ({15,19}, {b_5,c_4,d_3,e_4}) | a |

28 | ({4,7}, {a_1,b_1,c_1,d_2,e_2}) | Ø |

Number of Roadway | Rock Quality Designation (RQD) | Uniaxial Compressive Strength (Rc/MPa) | Integrity Coefficient of Rock Mass | Groundwater Seepage/(L/(min·10 m) | Joint Condition | Grade |
---|---|---|---|---|---|---|

1 | 55 | 98 | 0.5 | 10 | 5 | III |

2 | 40 | 60 | 0.3 | 12 | 5 | IV |

3 | 20 | 20 | 0.3 | 12 | 3 | V |

4 | 96 | 135 | 0.8 | 9 | 9 | I |

5 | 50 | 100 | 0.5 | 10 | 6 | III |

6 | 42 | 63 | 0.5 | 10 | 3 | III |

7 | 100 | 150 | 0.7 | 10 | 8 | I |

8 | 78 | 125 | 0.6 | 10 | 5 | II |

9 | 30 | 80 | 0.6 | 20 | 6 | IV |

10 | 25 | 35 | 0.3 | 20 | 2 | V |

Name of Prediction Model | Concept Lattice Reduction and Symmetric Alpha Stable Distribution Probability Neural Network | Symmetric Alpha Stable Distribution Probability Neural Network | Probabilistic Neural Network | Mean Value Method |
---|---|---|---|---|

Accuracy of prediction results | 90% | 80% | 70% | 50% |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Ye, Y.; Wang, Q.; Liu, X.
Stability Prediction Model of Roadway Surrounding Rock Based on Concept Lattice Reduction and a Symmetric Alpha Stable Distribution Probability Neural Network. *Appl. Sci.* **2018**, *8*, 2164.
https://doi.org/10.3390/app8112164

**AMA Style**

Liu Y, Ye Y, Wang Q, Liu X.
Stability Prediction Model of Roadway Surrounding Rock Based on Concept Lattice Reduction and a Symmetric Alpha Stable Distribution Probability Neural Network. *Applied Sciences*. 2018; 8(11):2164.
https://doi.org/10.3390/app8112164

**Chicago/Turabian Style**

Liu, Yang, Yicheng Ye, Qihu Wang, and Xiaoyun Liu.
2018. "Stability Prediction Model of Roadway Surrounding Rock Based on Concept Lattice Reduction and a Symmetric Alpha Stable Distribution Probability Neural Network" *Applied Sciences* 8, no. 11: 2164.
https://doi.org/10.3390/app8112164