# A Chronological Overview of Scientific Research on Ship Grounding Frequency Estimation Models

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## Abstract

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## 1. Introduction

## 2. Science Articles Which Contributed to Estimating Ship Grounding Frequency

## 3. Analytical Models

_{RG}) results is calculated from the geometric probability (P

_{G}) and causation probability (P

_{C}). The geometric probability of a vessel’s grounding by hitting the edge of the canal was calculated by using the Buffon’s needle problem:

- Grounding due to errors in navigation: a type of event when a tanker collides with the shoreline while making way due to navigational errors and lack of crew vigilance;
- Grounding due to leeway/drift: a type of event when a tanker loses its maneuverability, through loss of steering or propulsion, and drifts towards the shoreline before it is taken in tow or repaired.

_{pg}represents the frequency of powered grounding (number of powered grounding events per year); n

_{pg}is the critical situation when a vessel using its own propulsion sails towards a waypoint and runs aground within 20 min unless a critical alteration of the course is performed; Pc is the probability of clear visibility (more than 4 km); P

_{f}is the probability of reduced visibility (less than 4 km); p

_{pg}

_{,c}represents the corresponding probability of the powered grounding given a critical situation in clear visibility (causation factor); p

_{pg}

_{,f}is the corresponding probability of powered grounding given a critical situation in reduced visibility (causation factor).

_{dg}represents the frequency of drift grounding (number of drift grounding events per year); f

_{p}

_{,l}is the frequency of propulsion breakdown (number of ships experiencing propulsion breakdowns per year related to all lanes {l} within 50 nm from the grounding location); p

_{d}is the probability of leeway/drift tracks leading to the location of grounding (drifts towards the shoreline); p

_{w}is the probability of the wind speed category; p

_{sr}

_{,w}is the probability of saving the vessel through self-repairing, depending on wind speeds; p

_{t}

_{,w}is the probability of saving the vessel through towing assistance, depending on wind speeds; p

_{a}

_{,w}is the probability of saving the vessel by anchoring, depending on wind speeds.

- Step 1. Identify hazards from the elements of organization, man, ship and environment to define impact factors;
- Step 2: Grounding accident statistics are used to identify scenarios and influencing factors;
- Step 3: Define variables (nodes) and dependencies (arrows) to construct the structure of the BN model;
- Step 4: Conditional Probability Tables (CPT). Factors are derived from the history database. In addition, vessel condition and waterway complexity were introduced to facilitate the modeling process;
- Step 5: Validate the model. Three axioms were introduced to verify that the BN model works properly as intended.

## 4. Statistical Models

_{I}is the expected number of grounding events per year in Category I; N

_{II}is the expected number of grounding events per year in Category II; P

_{C,i}is the causation probability—i.e., the ratio between the ships aground and the ships on a grounding course; Q

_{i}is the number of ships in class i passing a cross section of the route per year; FCat is the expected number of collisions or groundings per year; z is the coordinate in the direction perpendicular to the route; (Zmin,Zmax) are the transverse coordinates for an obstacle.; e

^{−d/a}is the factor representing the probability of the navigator to fail to check the ship’s position from the bend in the channel to the obstacle, assuming that the position check event can be described as the Poisson procedure.

_{C}) and the distance between each position check, ai.

- When a vessel sails towards a shoal and its course should be altered;
- When a vessel’s course follows the coastline and must not be changed, but the vessel turns towards the coastline;
- When a vessel sails along the coastline and deviates from its course; the vessel should alter the course but it fails to do so;
- When a vessel’s position is incorrect with regard to an obstacle; the vessel should alter the course but it fails to do so;
- In a meeting situation, a vessel gives way but the new course leads towards the shoal.

_{G}was calculated for the whole length of the sea lane, and expressed as the one-dimensional probability matrix:

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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Grounding Frequencies | ||||||||||||||||
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1974 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2002 | 2005 | 2006 | 2007 | 2008 | 2010 | 2011 | 2013 | 2018 | 2021 |

[12,13] | [14] | [1] | [3] | [15] | [16] | [17] | [18] | [19] | ||||||||

[20] | [21] | [22] | [23] | [24,25] | [26] | [27] | [30] | [31] | [32] | |||||||

[14] | [22] | [3] | [15,23] | [17] | [18] | [32] | [19] | |||||||||

[24] | [17] | [27] | [30] | [32] | ||||||||||||

[13] | [20] | [14] | [24] | [17,26] | [32] | |||||||||||

Sub Categories | ||||||||||||||||

Models that do not use the distribution of ships to build the model | ||||||||||||||||

Models that use the distribution of ships to build the model | ||||||||||||||||

Taking historical data into account | ||||||||||||||||

Using AIS data | ||||||||||||||||

Involves meteorological conditions |

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**MDPI and ACS Style**

Galić, S.; Lušić, Z.; Mladenović, S.; Gudelj, A. A Chronological Overview of Scientific Research on Ship Grounding Frequency Estimation Models. *J. Mar. Sci. Eng.* **2022**, *10*, 207.
https://doi.org/10.3390/jmse10020207

**AMA Style**

Galić S, Lušić Z, Mladenović S, Gudelj A. A Chronological Overview of Scientific Research on Ship Grounding Frequency Estimation Models. *Journal of Marine Science and Engineering*. 2022; 10(2):207.
https://doi.org/10.3390/jmse10020207

**Chicago/Turabian Style**

Galić, Stipe, Zvonimir Lušić, Saša Mladenović, and Anita Gudelj. 2022. "A Chronological Overview of Scientific Research on Ship Grounding Frequency Estimation Models" *Journal of Marine Science and Engineering* 10, no. 2: 207.
https://doi.org/10.3390/jmse10020207