# A Velocity Obstacle-Based Real-Time Regional Ship Collision Risk Analysis Method

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Overview of the Research

#### 2.2. TCR-Based Collision Risk Modelling

_{A},P

_{A}(t),V

_{A}(t)}, and obstacle B is denoted as B{L

_{B},P

_{B}}, where L is the dimensions of them; P is the position of A and B at time t, and V is the their velocity in the time step t.

_{c}) denotes the position of A and B at collision time t

_{c}and $\oplus $ is the Minkowski addition. $\mathrm{P}$ denotes the position of A and B at the given time t after the observation timestep t

_{0}.

#### 2.3. Spatial Clustering of Maritime Traffic

## 3. Model Design

#### 3.1. Data Acquisition and Process

#### 3.2. TCR-Based Risk Analysis

_{ConfP}, which is the TCR measured with circular ConfP with the radius of the length of the ship of interest; (2) R

_{domain}, which is the TCR measured with ConfP determined by the ship of interest’s QSD, denoted as QSD-TCR; and (3) R

_{complexity}, which is the additional VO induced by the simple union of each individual VO. The objective of these indicators is to measure the complexity of the encounter situation. The calculation process of the three indicators is shown in Equation (4):

_{dimension}, VO

_{QSD}, VO

_{individual}, are the intersection regions between the VO and the velocity region of the ship of interest, and V

_{region}is the area of the velocity region of the ship of interest, which indicates all the possible velocities that the ship could take. A major assumption is proposed here to simplify the calculation process, which is that only the changes of course and reduction of velocity are considered as possible collision avoidance measures to construct the velocity region of the ship of interest. With this design, the function of the TCR-based risk analysis can be conducted.

#### 3.3. Spatial Clustering for Traffic Characteristic Analysis

#### 3.4. Result Visualisation

## 4. Case Study

#### 4.1. Data Description and Parameter Setting

#### 4.2. Results and Visualisation

## 5. Discussion

#### 5.1. Comparison between Risk Measurement and Complexity

#### 5.2. Comparison between TCR-Based Approach and CPA-Based Approach

#### 5.3. Implications and Limitations of the Method

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Variable | Setting |
---|---|

Data period | 08:00 7th to 08:00 8th March 2018 (UTC + 8) |

Data boundary | Latitude: 29.8475-30.2733° N, Longitude: 122.6157-123.1313° E |

Update frequency | 15 s |

Eps | 6 nm |

MinPt | 2 |

TCR time | 45 min |

ConfP | Length (own ship + target ship) |

Ship Length (if no data available) | 200 m |

Original Time | Interpolation Timespot | MMSI | Critical TCR | Domain TCR | Complexity | Group | Collision Candidate |
---|---|---|---|---|---|---|---|

16:13:59 | 58439 | 218XXX000 | 0.0552 | 0.4670 | 1.1350 | 1 | Yes |

16:13:56 | 58439 | 356XXX000 | 0.1420 | 0.9129 | 1.6281 | 3 | Yes |

16:13:48 | 58439 | 412XXX830 | 0.1711 | 0.9640 | 1.0014 | 2 | Yes |

18:56:41 | 68204 | 371XXX000 | 0.0238 | 0.2836 | 1 | Noise | No |

18:56:37 | 68204 | 538XXX848 | 0.0446 | 0.7938 | 1.2922 | 1 | Yes |

18:56:37 | 68204 | 667XXX873 | 0.0163 | 0.5926 | 1 | 2 | Yes |

**Table 3.**Results of collision risk analysis using the method proposed by [8].

Original Time | Interpolation Timespot | MMSI (Maritime Mobile Service Identify) | M2 [8] | Complexity | Group (DBSCAN) |
---|---|---|---|---|---|

16:13:59 | 58440 | 218XXX000 | 0.10189 | 1.127 | 1 |

16:13:56 | 58440 | 356XXX000 | 0.60342 | 2.289 | 3 |

16:13:48 | 58440 | 412XXX830 | 0.32578 | 1 | 2 |

18:56:41 | 68204 | 371XXX000 | 0.072746 | 1.244 | Noise |

18:56:37 | 68204 | 414XXX000 | 0.19505 | 1.158 | 1 |

18:56:37 | 68204 | 667XXX873 | 0.77214 | 1.003 | 2 |

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**MDPI and ACS Style**

Chen, P.; Li, M.; Mou, J.
A Velocity Obstacle-Based Real-Time Regional Ship Collision Risk Analysis Method. *J. Mar. Sci. Eng.* **2021**, *9*, 428.
https://doi.org/10.3390/jmse9040428

**AMA Style**

Chen P, Li M, Mou J.
A Velocity Obstacle-Based Real-Time Regional Ship Collision Risk Analysis Method. *Journal of Marine Science and Engineering*. 2021; 9(4):428.
https://doi.org/10.3390/jmse9040428

**Chicago/Turabian Style**

Chen, Pengfei, Mengxia Li, and Junmin Mou.
2021. "A Velocity Obstacle-Based Real-Time Regional Ship Collision Risk Analysis Method" *Journal of Marine Science and Engineering* 9, no. 4: 428.
https://doi.org/10.3390/jmse9040428