# Inundation Resilience Analysis of Metro-Network from a Complex System Perspective Using the Grid Hydrodynamic Model and FBWM Approach: A Case Study of Wuhan

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## Abstract

**:**

## 1. Introduction

## 2. Methodology and Materials

#### 2.1. Study Area

#### 2.2. Network Modeling: Simplified Three-Dimensional Model of Metro Network under Flood Evolution Scenario

#### 2.2.1. Basic Network

#### 2.2.2. Node Characteristics

- Node Degree

**out**) or j → i(

**in**), as shown in Figure 5a. The node-out degree ${d}_{i}^{o}$ represents the number of nodes that flood flows from node i to other nodes, and the node-in degree ${d}_{i}^{i}$ is described by the number of nodes where the flood flows into node i. The parameter ${\delta}_{ij}$, whose values were all assigned as 1, denotes the flood flow between node i and node j. The inflow was marked as ${\delta}_{ij}^{i}$ and the outflow was specified as ${\delta}_{ij}^{o}$. The node degree ${d}_{i}$ is the sum of node input degree and node output degree. The calculation formula is as follows:

- 2.
- Node Strength

- 3.
- Node Betweenness

- 4.
- Closeness Centrality

- 5.
- Passenger Flow

- 6.
- GDP Density

#### 2.2.3. Node Toughness Strength

#### 2.3. Flood Hazard Simulation

#### 2.3.1. Surface Flooding Simulation: Identification of Flood-Prone Metro Nodes

- Inundation simulation

- 2.
- Rain design

^{2})].

#### 2.3.2. Inundation Sequence Simulation of Stations: Dynamic Node Breakdown Algorithm

**Step 1:**Initialization parameters. Input node-in degrees, node-out degrees, edge lengths, edge weights, node passenger flow, and GDP density to form six $n\times n$ initial matrices.

**Step 2:**Calculation of flood diffusion length based on flood velocity and interval time.

**Step 3:**The characteristics matrix of each node is calculated.

**Step 4:**Based on the set of breakdown node points at the previous moment, we determined the breakdown nodes at the next moment.

**Step 5:**Record the ${f}_{i}\left(t\right)$ of the breakdown node as 0 and clear it. Then, start searching for the breakdown node of the next moment.

#### 2.4. Resilience Assessment Model of Metro Network

#### 2.4.1. Toughness Strength Assessment Model for Metro Network

- ①
- Calculation of node toughness strength index weights: FBWM

**Step 1**: Determine the best and worst indicators. In this step, the importance of each indicator is compared. The best indicator B and the worst indicator W are decided.

**Step 2**: Compare the importance of other evaluation indicators with the best indicator B and the worst indicator W and record them as ${a}_{BW}$, as shown in Figure 11.

**Step 3**: Determine the optimal fuzzy weight value (${\tilde{w}}_{B},{\tilde{w}}_{W},{\tilde{w}}_{j}$) of the best indicator, the worst indicator, and each other indicator, of which, ${\tilde{w}}_{B}=\left({L}_{B}^{w},{M}_{B}^{w},{U}_{B}^{w}\right)$, ${\tilde{w}}_{W}=\left({L}_{W}^{w},{M}_{W}^{w},{U}_{W}^{w}\right)$, ${\tilde{w}}_{j}=\left({L}_{j}^{w},{M}_{j}^{w},{U}_{j}^{w}\right)$. In the previous step, the importance ${a}_{BW}$ of each indicator compared with the best indicator B and the worst indicator W is obtained. To obtain the optimal fuzzy weight, we needed to minimize the maximum value of $\left|\frac{{\tilde{w}}_{B}}{{\tilde{w}}_{W}}-{\tilde{a}}_{BW}\right|$. Therefore, an optimization model was developed to solve this problem.

**Step 4**: The fuzzy weights ${\tilde{w}}_{B},{\tilde{w}}_{W}$ can be refined using GMIR, as shown in Equations (27) and (28).

- ②
- Toughness Strength of Metro Network

#### 2.4.2. Organization Recovery Capacity of Metro Network

## 3. Results and Discussion

#### 3.1. Data Source

#### 3.2. Flood Hazard Analysis of Metro Network

#### 3.2.1. Flooded Node Breakdown Analysis

#### 3.2.2. Node Dynamic Breakdown Process

#### 3.3. Resilience Assessment of Metro Network

#### 3.3.1. Evaluation of Node Toughness Strength Weights

#### 3.3.2. Node Toughness Strength Analysis

#### 3.3.3. Toughness Strength Analysis of Network

#### 3.3.4. Organization Recovery Capacity Evaluation

#### 3.4. Resilience Enhancement Discussion of Metro Network

- Improve node toughness strength

- 2.
- Determine the priority of rescue and evacuation nodes

## 4. Conclusions

- The article establishes a simplified three-dimensional model of a complex metro network by topological methods while considering the slope directions between stations. The simplified dynamic network of metro nodes combines the topological characteristics of the metro system with the features of flood evolution. This paper presents research on urban metro flood risk from regional metro network resilience.
- The grid hydrodynamic is modeled to fully utilize high-precision DEM data for inundation prediction without preprocessing and meshing, significantly reducing processing time. This alternative model provides comparable results to conventional software for regional maximum flood extent, depth, and inundation duration. The grid hydrodynamic model perfectly identified the surface flood-prone points in this paper.
- The dynamic node breakdown algorithm was developed to obtain the subsurface flooding node sequence by inputting the node adjacency matrix and the distance between nodes. The principle of the algorithm is easy to understand. The calculation results are accurate and conform to the law of flood dispersion. The dynamic node breakdown algorithm finally obtains the whole metro network flooded process and the change of node toughness strength.
- The node toughness strength was estimated by combining the natural and social attributes of the nodes through the FBWM method. As a newer multi-criteria decision-making method, FBWM optimizes the minimum error by nonlinear programming equations and preserves the fuzzy information using fuzzy triangular numbers.
- Based on the above conclusions, the resilience of the Wuhan metro network was assessed. The rate of decline in the toughness strength of the metro network is higher than 0.079 and is maximum within the first 40 min. Organization recovery capacity during this period could reach 94.64%, achieving the rescue of most flooded nodes. In response to the evaluated resilience results, this paper proposes a resilience enhancement proposal based on improving the node toughness strength and determining the priority of rescue and evacuation nodes.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

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**Figure 1.**The metro stations were flooded. (

**a**) Shenzhoulu station of Guangzhou metro line 21 on 30 July 2021. (

**b**) Station of metro line 5 flooded during heavy rainfall on 18 July 2021, in Zhengzhou. (

**c**) The New York metro station was attacked on 2 September 2021.

**Figure 3.**Climate and location information for Wuhan. (

**a**) Administrative region of Wuhan with the metro system. (

**b**) Temperature of Wuhan. (

**c**) Rainfall. (

**d**) Rainfall days.

**Figure 4.**Urban metro diagram. (

**a**) Remote sensing image of the Wuhan city. (

**b**) Two-dimensional map of urban metro. (

**c**) Three-dimensional map of urban metro.

**Figure 12.**The prediction and identification of flood-prone stations. (

**a**) Submerged water depth of the metro network. (

**b**) Enlarged view of the flooded Yangluo Development Zone station. (

**c**) Enlarged view of the flooded Renhe Road station.

**Figure 14.**Node Characteristics. (

**a**) Node degree. (

**b**) Node strength. (

**c**) Node betweenness. (

**d**) Closeness centrality. (

**e**) Passenger flow. (

**f**) GDP density.

**Figure 16.**Diagram of inundation time and toughness strength of nodes at T = 20 min (

**a**) and T = 40 min (

**b**).

Difference of Terrain (m) | Weights from Low to High Terrain Nodes | Weights from High to Low Terrain Nodes |
---|---|---|

0–6 | 0.5 | 0.6 |

6–12 | 0.4 | 0.7 |

12–18 | 0.3 | 0.8 |

18–24 | 0.2 | 0.9 |

24–30 | 0.1 | 1 |

**Table 2.**Transformation rules of Linguistic variables [57].

Linguistic Terms | Membership Function (L,M,N) |
---|---|

Equally important (EI) | (1,1,1) |

Weakly important (WI) | (2/3,1,3/2) |

Fairly important (FI) | (3/2,2,5/2) |

Very important (VI) | (5/2,3,7/2) |

Absolutely important (AI) | (7/2,4,9/2) |

Data | Source |
---|---|

Remote-sensing data | http://eds.ceode.ac.cn/nuds/freedataquery (accessed on 15 December 2021) |

DEM (30 m × 30 m) | http://www.gscloud.cn (accessed on 20 November 2021) |

Design Formula of Rainstorm Intensity | Wuhan local standards DB4201/T 641 2020 (accessed on 6 December 2021) |

Metro passenger flow in Wuhan | https://iwuhan.org/webapps/WuhanMetroFlowDetail/ (accessed on 12 January 2022) |

GDP density | http://tjj.hubei.gov.cn/tjsj/ (accessed on 15 December 2021) |

Number of metro stations | https://www.wuhanrt.com/public_forward.aspx (accessed on 15 December 2021) |

Distance between metro stations | https://www.wuhanrt.com/public_forward.aspx (accessed on 7 November 2021) |

Elevation within the metro network. | https://www.wuhanrt.com/public_forward.aspx (accessed on 7 January 2022) Fieldwork estimation(Estimated from subway floors) |

Indicators\Category | The Ability to Receive Flood (25%) | The Ability to Transmit Flood (25%) | The Risk of Casualties (20%) | The Risk of Economic Loss (20%) | The Importance of Location (10%) | Best Indicators/B_{j} |
---|---|---|---|---|---|---|

Node degree | 25% | 25% | - | - | - | EI |

Node strength | - | 25% | - | - | - | FI |

Node betweenness | 20% | 20% | - | - | WI | |

Closeness centrality | - | - | - | - | 10% | AI |

Passenger flow | - | - | 20% | - | - | VI |

GDP density | - | - | - | 20% | - | VI |

Indicators | Fuzzy Weight | Comprehensive Weight |
---|---|---|

Node degree | (0.3046, 0.3088, 0.3489) | 0.3148 |

Node strength | (0.1420, 0.1420, 0.1829) | 0.1488 |

Node betweenness | (0.2382, 0.2382, 0.3152) | 0.2510 |

Closeness centrality | (0.0830, 0.0834, 0.0951) | 0.0853 |

Passenger flow | (0.0919, 0.1051, 0.1130) | 0.1042 |

GDP density | (0.0919, 0.1051, 0.1130) | 0.1042 |

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**MDPI and ACS Style**

Sun, H.; Li, M.; Jiang, H.; Ruan, X.; Shou, W.
Inundation Resilience Analysis of Metro-Network from a Complex System Perspective Using the Grid Hydrodynamic Model and FBWM Approach: A Case Study of Wuhan. *Remote Sens.* **2022**, *14*, 3451.
https://doi.org/10.3390/rs14143451

**AMA Style**

Sun H, Li M, Jiang H, Ruan X, Shou W.
Inundation Resilience Analysis of Metro-Network from a Complex System Perspective Using the Grid Hydrodynamic Model and FBWM Approach: A Case Study of Wuhan. *Remote Sensing*. 2022; 14(14):3451.
https://doi.org/10.3390/rs14143451

**Chicago/Turabian Style**

Sun, Hai, Meixin Li, Hui Jiang, Xuejing Ruan, and Wenchi Shou.
2022. "Inundation Resilience Analysis of Metro-Network from a Complex System Perspective Using the Grid Hydrodynamic Model and FBWM Approach: A Case Study of Wuhan" *Remote Sensing* 14, no. 14: 3451.
https://doi.org/10.3390/rs14143451