# Causality-Network-Based Critical Hazard Identification for Railway Accident Prevention: Complex Network-Based Model Development and Comparison

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## Abstract

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## 1. Introduction

#### 1.1. Background

#### 1.2. Related Studies

#### 1.3. Contributions and Organization

- (1)
- We propose an improved ACN model (WLDACN) to model the relationship between hazards and accidents. The shortest distances from hazards to accidents can be obtained based on the proposed new length metrics of edges in WLDACN, which is proven to be superior to other previous methods.
- (2)
- Given the proposed length metrics of WLDACN, the network efficiency is used to represent the difficulty of hazards causing accidents. Therefore, the accident prevention problem is transferred to successfully minimize the WLDACN efficiency.
- (3)
- To support the hazard management of railway systems, we propose a high centrality adaptive and integer programming method to identify critical hazards that greatly contribute to railway accidents. A heuristic algorithm is proposed to solve the integer programming model. The comparison results show that the integer programming method can help prevent accidents better than other models.

## 2. Problem Description and Formulation

#### 2.1. ACN Model

#### 2.1.1. Edge Weight Metrics

#### 2.1.2. Edge Length Metrics

#### 2.2. CHI Method Development

#### 2.2.1. Objective of CHI

#### 2.2.2. High Centrality Adaptive Methods

#### 2.2.3. Integer Programming Method

#### 2.3. Model Performance Comparison

## 3. Case Studies

#### 3.1. Data Description

#### 3.2. ACN Construction and Analysis

#### 3.3. CHI Model Application and Comparison

#### 3.4. ACN Model Comparison

#### 3.5. Limitation of the Method

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Accident causation network. (

**a**) WDACN, (

**b**) DACN (

**c**) ACN after reversing the weight of the edge, (

**d**) Normalized WDACN, (

**e**) WLDACN.

Variable | Description |
---|---|

Abbreviations | |

CHI | critical hazard indentification |

ACN | accident causality network |

WDACN | weighted direct accident causality network |

DACN | direct accident causality network |

SCP | shortest causation path |

MPCP | most probable causation path |

WLDACN | directed ACN with weights and length metrics |

HDA | high degree adaptive |

HBA | high betweenness adaptive |

HCA | high closeness adaptive |

HPA | high pagerank adaptive |

ASCP | average SCP |

IPM | Integer Programming method |

Notations | |

$h$ | hazard node |

a | accident node |

$w\left(i,j\right)$ | the weight of the edge from node $i$ to $j$ |

${F}_{k}\left(h,a\right)$ | The frequencies of the causation route $k$ from hazard node $h$ to accident node $a$ |

${S}_{k}^{h,a}$ | the set of points on causation route $k$ |

$p\left(i,j\right)$ | the normalized weight of the edge from node $i$ to $j$ |

${P}_{k}\left(h,a\right)$ | the active probability of causation route $k$ |

$l\left(i,j\right)$ | the length of the edge from node $i$ to $j$ |

$E$ | the ACN efficiency |

${D}_{h}$ | degree centrality of hazard node $h$ |

${B}_{h}$ | betweenness centrality of hazard node $h$ |

${C}_{h}$ | closeness centrality of hazard node $h$ |

${R}_{h}$ | PageRank of hazard node $h$ |

Accident Type | A01 | A02 | A03 | A04 | A05 | A06 | A07 | A08 | A09 |
---|---|---|---|---|---|---|---|---|---|

H-type hazard | 4.19 | 4.35 | -- | 3.42 | 5.73 | 3.50 | 4.89 | 3.71 | 5.98 |

EM-type hazard | 4.54 | 5.16 | 598 | 3.54 | 5.98 | 5.47 | 5.07 | 3.83 | 7.04 |

E-type hazard | 5.80 | 5.98 | 5.98 | 5.62 | 9.03 | 6.90 | 5.98 | 5.91 | 7.37 |

M-type hazard | 5.88 | 6.09 | -- | 5.19 | 8.34 | 4.78 | 5.58 | 5.47 | 8.47 |

All types | 5.10 | 5.39 | 5.98 | 4.44 | 7.27 | 5.16 | 5.38 | 4.73 | 7.22 |

Accident type | A10 | A11 | A12 | A13 | A14 | A15 | A16 | A17 | A18 |

H-type hazard | 3.71 | 3.71 | 5.73 | 5.04 | 5.73 | 5.73 | 5.04 | -- | 5.76 |

EM-type hazard | 3.83 | 3.82 | 7.58 | 6.89 | 7.58 | 5.29 | 5.92 | 5.98 | 5.98 |

E-type hazard | 5.91 | 5.91 | 9.03 | 8.34 | 9.03 | 5.98 | 8.34 | 5.98 | 8.06 |

M-type hazard | 5.47 | 5.47 | 8.34 | 7.64 | 8.34 | 8.29 | 7.37 | -- | 9.21 |

All types | 4.73 | 4.73 | 7.67 | 6.98 | 7.67 | 6.32 | 6.67 | 5.98 | 7.25 |

**Table 3.**Difficulty of hazards causing accidents under different ACN models and CHI methods. (Bold represent the optimal values).

Models | HBA | HCA | HDA | HPA | IPM |
---|---|---|---|---|---|

DACN | 27.3342 | 72.3560 | 32.4598 | 31.8879 | 27.1856 |

WDACN | 25.8917 | 70.3325 | 31.8904 | 30.0392 | 25.3462 |

WLDACN | 22.9560 | 67.7097 | 31.8904 | 30.0392 | 21.6170 |

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**MDPI and ACS Style**

Li, Q.; Zhang, Z.; Peng, F.
Causality-Network-Based Critical Hazard Identification for Railway Accident Prevention: Complex Network-Based Model Development and Comparison. *Entropy* **2021**, *23*, 864.
https://doi.org/10.3390/e23070864

**AMA Style**

Li Q, Zhang Z, Peng F.
Causality-Network-Based Critical Hazard Identification for Railway Accident Prevention: Complex Network-Based Model Development and Comparison. *Entropy*. 2021; 23(7):864.
https://doi.org/10.3390/e23070864

**Chicago/Turabian Style**

Li, Qian, Zhe Zhang, and Fei Peng.
2021. "Causality-Network-Based Critical Hazard Identification for Railway Accident Prevention: Complex Network-Based Model Development and Comparison" *Entropy* 23, no. 7: 864.
https://doi.org/10.3390/e23070864