# Analytical Modeling for Underground Risk Assessment in Smart Cities

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Problem Formulation

## 4. Approximation Schemes for Underground Risk Index

#### 4.1. Linear Approximation

#### 4.2. Hierarchical Fuzzy Inference System based Approximation

#### 4.2.1. General Hierarchical Fuzzy Inference System

#### 4.2.2. Approximation using Hierarchical Fuzzy Inference System

#### 4.3. Hybrid Approach Based Approximation

## 5. Experimental Design

#### 5.1. Linear Approximation

#### 5.2. Hierarchical Fuzzy Inference System based Approximation

#### Rules definition for Hierarchical Fuzzy Inference System

#### 5.3. Hybrid Approach Based Approximation

- For Case 1, average based scheme result is Low, thus ignoring M4, which may be critical.
- Case 2 and Case 3 are treated as the same by both schemes which is not true.

## 6. Implementation of Approximation Schemes for Underground Risk Index

#### 6.1. Linear Approximation

#### 6.2. Hierarchical Fuzzy Inference System Based Approximation

#### 6.3. Hybrid Approach Based Approximation

## 7. Results and Discussion

## 8. Conclusions and Future Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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Label | Very Low | Low | Medium | High | Very High |
---|---|---|---|---|---|

Value | 1 | 2 | 3 | 4 | 5 |

**Table 2.**Example cases for illustration of rules definition using average and maximum based schemes.

S. No. | Input | Output | ||||
---|---|---|---|---|---|---|

M1 | M2 | M3 | M4 | Max-Based | Avg.-Based | |

Case 1 | V.Low | V.Low | V.Low | V.High | V.High | Low |

1 | 1 | 1 | 5 | 5 | (1 + 1 + 1 + 5)/4 = 2 | |

Case 2 | High | High | High | V.High | V.High | High |

4 | 4 | 4 | 5 | 5 | (4 + 4 + 4 + 5)/4 = 4.25 | |

Case 3 | - | - | Medium | V.High | V.High | High |

3 | 5 | 5 | (3 + 5)/2 = 4 |

FIS Component | Membership Function | Fuzzification | Implication | Aggregation | Defuzzification |
---|---|---|---|---|---|

Method used | Triangular | Min for AND Max for OR | Min | Max | Centroid |

Membership Function Name | Membership Function Labels | Range |
---|---|---|

Very Low | VL | (0.0 to 1.5) |

Low | L | (0.5 to 4.0) |

Medium | M | (3.0 to 7.0) |

High | H | (6.0 to 9.5) |

Very High | VH | (8.5 to 10) |

Risk Contributing Factor | Parameter | Unit | Range |
---|---|---|---|

Water supply risk index (M1) | Length | [m] | (0–300) |

Depth | [mm] | (0–2500) | |

Years of burial | [year] | (0–30) | |

Leakage probability | [%] | (0–100) | |

Pipeline ductability | [cm] | (0–100) | |

Sewerage line risk index (M2) | Length | [m] | (0–300) |

Depth | [mm] | (0–2500) | |

Years of burial | [year] | (0–30) | |

Leakage probability | [%] | (0–100) | |

Pipeline ductability | [cm] | (0–100) | |

Metro structure risk index (M3) | Age | [year] | (0–30) |

Degree of peripheral depression | [%] | (0–100) | |

Ground state risk index (M4) | Granularity | [%] | (0–100) |

Compaction | [%] | (0–100) | |

Ground water level | [m] | (0–10) |

Statistical Measure | Linear Approximation | Basic Hierarchical FIS Model 1 | Integrated Hierarchical FIS Model 2 | ||
---|---|---|---|---|---|

Avg. based | maximum based | Avg. based | maximum based | ||

Mean Absolute Deviation (MAD) | 1.16 | 2.46 | 0.73 | 3.1 | 0.43 |

Mean Square Error (MSE) | 1.71 | 6.72 | 0.82 | 10.67 | 0.33 |

Root Mean Square Error (RMSE) | 1.31 | 2.59 | 0.91 | 3.26 | 0.57 |

Correlation Coefficient (R) | 0.77 | 0.85 | 0.83 | 0.77 | 0.91 |

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**MDPI and ACS Style**

Ullah, I.; Fayaz, M.; Kim, D. Analytical Modeling for Underground Risk Assessment in Smart Cities. *Appl. Sci.* **2018**, *8*, 921.
https://doi.org/10.3390/app8060921

**AMA Style**

Ullah I, Fayaz M, Kim D. Analytical Modeling for Underground Risk Assessment in Smart Cities. *Applied Sciences*. 2018; 8(6):921.
https://doi.org/10.3390/app8060921

**Chicago/Turabian Style**

Ullah, Israr, Muhammad Fayaz, and DoHyeun Kim. 2018. "Analytical Modeling for Underground Risk Assessment in Smart Cities" *Applied Sciences* 8, no. 6: 921.
https://doi.org/10.3390/app8060921