# Risk Reasoning from Factor Correlation of Maritime Traffic under Arctic Sea Ice Status Association with a Bayesian Belief Network

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Risk Definition of Maritime Traffic under Status Association

_{n}refers to the n-th risk factor, S

^{i}

_{n}refers to the i-th state of the n-th risk factor, t refers to the occurrences of DA effects of risk factor S

_{n}, and the number of states of T is i

^{t}.

#### 2.2. Risk Factors Network Structure on Ship-Ice Collision

#### 2.3. Status Dynamic Association on Ship-Ice Collision

#### 2.4. Reasoning Method of Node Parameter in Factors Correlation Network

#### 2.4.1. Bayesian Inference Method of Ship-Ice Collision Risk

_{n})) called PPD, P(S

_{n}|parents(S

_{n})) refers to the probability of S

_{n}obtained under certain evidence information parents(S

_{n}), called CPD, which is used to describe the process of generating data S

_{n}.

#### 2.4.2. Bayesian Method of Risk Inference under Evidence Information

_{n})|S

_{n}) is called posterior probability distribution (PoD), which represents the probability of occurrence of risk event parents(S

_{n}) after the evidence update, which is the required event probability. P(S

_{n}) represents the probability of event S

_{n}under any hypothesis, which called standardized constant.

_{1}

^{i=yes}, so as to find the state that has a greater impact on the collision accident. Since N1 and X1 are indirect relationships in the Bayesian network structure and cannot be solved directly, they need to be solved jointly with the Equation (6) on the basis of Equation (8). The calculation process is shown in Equation (9), where the solution of P(N1) is referred to Equation (7):

#### 2.4.3. The Calculation Approach of Factors Network Parameters

_{n}) and likelihood P(S

_{n}

_{−1}|S

_{n}). Other parameters can be calculated after these two parameters are known. In addition to the method of mathematical statistics, the solution of S

_{n}needs to be solved by subjective judgment in most cases. Among them, the calculation of mathematical statistics method is shown in Equation (10):

_{n}, and i = h represents the h-th state among all i states of the risk factor S.

_{n−}

_{1}|S

_{n}) is the CPD calculation under certain information. In Bayesian analysis, it is usually judged based on experience. Since experts often come from different fields, they are different in age, experience, and knowledge reserves, and judgments on the results are also different. The Dempster-Shafer (D-S) theory has great advantages in dealing with the joint solution of multi-source information fusion, so, a CPD calculation method based on the D-S theory is proposed. First, define the universe of discourse in the form of a combination of CPD between the states of two directly related nodes in the Bayesian network, as shown in Equation (11), α represents the CPD function between two states of two nodes:

_{1}, m

_{2}, …, m

_{n}and their synthesis rules are denoted by Equation (12). By combining the opinions of multiple experts, a CPD between two nodes with mutual dependence is obtained:

#### 2.5. Data Collection

#### 2.5.1. Prior Probability Distribution of Factors Network Parameters

#### 2.5.2. Conditional Probability Distribution of Factors Network Parameters

## 3. Result

#### 3.1. Comparative Analysis of Maritime Traffic Risk

#### 3.2. The Impact of Ice Condition on Maritime Traffic Risk

- (a)
- When the evidence information in AM and CM are P(NAI-NAI) = 1 and P(NAI) = 1, the risk assessment results are basically the same, and the risk assessment result in the AM is slightly higher than those in the CM.
- (b)
- When the evidence information in AM and CM are P(NAI-HAI) = 1 and P(HAI) = 1, the risk assessment result in the AM is significantly higher than that in the CM.
- (c)
- When the evidence information in AM and CM are P(HAI-NAI) = 1 and P(NAI) = 1, P(HAI-HAI) = 1 and P(HAI) = 1 respectively, the risk assessment results in the AM are lower than those in the CM.

- When the ship at station A, the state with a higher probability of SDA is NAI-HAI, which is close to the state of scenario b), so the risk assessment result of the AM is significantly higher than that of the CM.
- When the ship is at station B, C, D, and E respectively, the state with a higher probability of SDA is HAI-HAI, which is close to the state of scenario c), so the risk assessment result in the CM is higher than AM.

#### 3.3. Model Validation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Burgherr, P. In-depth analysis of accidental oil spills from tankers in the context of global spill trends from all sources. J. Hazard. Mater.
**2007**, 140, 245–256. [Google Scholar] [CrossRef] [PubMed] - Hansen, H.L.; Jepsen, J.R.; Hermansen, K. Factors influencing survival in case of shipwreck and other maritime disasters in the Danish merchant fleet since 1970. Saf. Sci.
**2012**, 50, 1589–1593. [Google Scholar] [CrossRef] - Annual Overview of Marine Casualties and Incidents 2019. Available online: http://www.emsa.europa.eu/ (accessed on 11 July 2019).
- Chen, Y.M.; Huang, W.R.; Xu, S.D. Frequency Analysis of Extreme Water Levels Affected by Sea-Level Rise in East and Southeast Coasts of China. J. Coast. Res.
**2014**, 68, 105–112. [Google Scholar] [CrossRef] - Eyring, V.; Isaksen, I.S.A.; Berntsen, T. Transport impacts on atmosphere and climate: Shipping. Atmos. Environ.
**2010**, 44, 4735–4771. [Google Scholar] [CrossRef] - Borja, N.A. Growth in the docks: Ports, metabolic flows and socio-environmental impacts. Sustain. Sci.
**2020**, 15, 11–30. [Google Scholar] - Chen, X.Q.; Wang, S.Z.; Shi, C.J.; Wu, H.; Zhao, J.; Fu, J. Robust Ship Tracking via Multi-view Learning and Sparse Representation. J. Navig.
**2019**, 72, 176–192. [Google Scholar] [CrossRef] - Chen, X.Q.; XU, X.Q.; Yang, Y.S.; Wu, H.; Tang, J.; Zhao, J. Augmented Ship Tracking Under Occlusion Conditions from Maritime Surveillance Videos. IEEE Access
**2020**, 8, 42884–42897. [Google Scholar] [CrossRef] - Smith, L.C.; Stephenson, S.R. New Trans-Arctic shipping routes navigable by midcentury. Proc. Natl. Acad. Sci. USA
**2013**, 110, 1191–1195. [Google Scholar] [CrossRef] [Green Version] - De Silva, L.W.A.; Yamaguchi, H.; Ono, J. Ice-ocean coupled computations for sea-ice prediction to support ice navigation in Arctic sea routes. Polar Res.
**2015**, 34, 25008. [Google Scholar] [CrossRef] [Green Version] - Eddy, B.; Francois, J.F.; Hugo, R.R. Melting Ice Caps and the Economic Impact of Opening the Northern Sea Route. Econ. J.
**2018**, 1307, 1–45. [Google Scholar] - Silber, G.K.; Adams, J.D. Vessel Operations in the Arctic, 2015–2017. Front. Mar. Sci.
**2019**, 6, 573. [Google Scholar] [CrossRef] - Wei, T.; Yan, Q.; Qi, W.; Ding, M.; Wang, C. Projections of Arctic sea ice conditions and shipping routes in the twenty-first century using CMIP6 forcing scenarios. Environ. Res. Lett.
**2020**, 15, 10. [Google Scholar] [CrossRef] - Melia, N.; Haines, K.; Hawkins, E. Sea ice decline and 21st century trans-Arctic shipping routes. Geophys. Res. Lett.
**2016**, 43, 9720–9728. [Google Scholar] [CrossRef] - Zhang, Z.; Huisingh, D.; Song, M. Exploitation of trans-Arctic maritime transportation. J. Clean. Prod.
**2019**, 212, 960–973. [Google Scholar] [CrossRef] - Marchenko, N.; Andreassen, N.; Borch, O.J.; Kuznetsova, S.; Jakobsen, U. Arctic Shipping and Risks: Emergency Categories and Response Capacities. TransNav Int. J. Mar. Navig. Saf. Sea Transp.
**2018**, 12, 107–114. [Google Scholar] [CrossRef] [Green Version] - Kum, S.; Sahin, B. A root cause analysis for Arctic Marine accidents from 1993 to 2011. Saf. Sci.
**2015**, 74, 206–220. [Google Scholar] [CrossRef] - Huang, L.; Tuhkuri, J.; Igrec, B.; Li, M.; Thomas, G. Ship resistance when operating in floating ice floes: A combined CFD&DEM approach. Mar. Struct.
**2020**, 74, 102817. [Google Scholar] - Li, F.; Kõrgesaar, M.; Kujala, P.; Goerlandt, F. Finite element based meta-modeling of ship-ice interaction at shoulder and midship areas for ship performance simulation. Mar. Struct.
**2020**, 71, 102736. [Google Scholar] [CrossRef] - Chai, W.; Leira, B.J.; Naess, A.; Høyland, K.; Ehlers, S. Development of environmental contours for first-year ice ridge statistics. Struct. Saf.
**2020**, 87, 101996. [Google Scholar] [CrossRef] - Chai, W.; Leira, B.J.; Høyland, K.V.; Sinsabvarodom, C.; Yu, Z. Statistics of thickness and strength of first-year ice along the Northern Sea Route. J. Mar. Sci. Technol.
**2020**. [Google Scholar] [CrossRef] - Valdez Banda, O.A.; Goerlandt, F.; Montewka, J.; Kujala, P. A risk analysis of winter navigation in Finnish sea areas. Accid. Anal. Prev.
**2015**, 79, 100–116. [Google Scholar] [CrossRef] [PubMed] - Montewka, J.; Goerlandt, F.; Kujala, P.; Lensu, M. Towards probabilistic models for the prediction of a ship performance in dynamic ice. Cold Reg. Sci. Technol.
**2015**, 112, 14–28. [Google Scholar] [CrossRef] - Afenyo, M.; Khan, F.; Veitch, B.; Yang, M. Arctic shipping accident scenario analysis using Bayesian Network approach. Ocean Eng.
**2017**, 133, 224–230. [Google Scholar] [CrossRef] - Zhang, M.; Zhang, D.; Fu, S.; Yan, X.; Goncharov, V. Safety distance modeling for ship escort operations in Arctic ice-covered waters. Ocean Eng.
**2017**, 146, 202–216. [Google Scholar] [CrossRef] - Fu, S.; Zhang, D.; Montewka, J.; Zio, E.; Yan, X. A quantitative approach for risk assessment of a ship stuck in ice in Arctic waters. Saf. Sci.
**2018**, 107, 145–154. [Google Scholar] [CrossRef] - Goerlandt, F.; Montewka, J.; Zhang, W.; Kujala, P. An analysis of ship escort and convoy operations in ice conditions. Saf. Sci.
**2017**, 95, 198–209. [Google Scholar] [CrossRef] - Eguíluz, V.M.; Fernández-Gracia, J.; Irigoien, X.; Duarte, C.M. A quantitative assessment of arctic shipping in 2010–2014. Sci. Rep.
**2016**, 6, 30682. [Google Scholar] - Fedi, L.; Faury, O.; Etienne, L. Mapping and analysis of maritime accidents in the Russian Arctic through the lens of the Polar Code and POLARIS system. Mar. Policy
**2020**, 118, 103984. [Google Scholar] [CrossRef] - Sarhadi, A.; Burn, D.H.; Concepción, A.M.; Wiper, M.P. Time-varying nonstationary multivariate risk analysis using a dynamic bayesian copula. Water Resour. Res.
**2016**, 52, 2327–2349. [Google Scholar] [CrossRef] - Aziz, A.; Ahmed, S.; Khan, F.; Stack, C.; Lind, A. Operational risk assessment model for marine vessels. Reliab. Eng. Syst. Saf.
**2019**, 185, 348–361. [Google Scholar] [CrossRef] - Ung, S.T. Evaluation of human error contribution to oil tanker collision using fault tree analysis and modified fuzzy Bayesian Network based CREAM. Ocean Eng.
**2019**, 179, 159–172. [Google Scholar] [CrossRef] - Chai, T.; Weng, J.X.; Xiong, D.Q. Development of a quantitative risk assessment model for ship collisions in fairways. Saf. Sci.
**2017**, 91, 71–83. [Google Scholar] [CrossRef] - Endrina, N.; Rasero, J.C.; Konovessis, D. Risk analysis for RoPax vessels: A case of study for the Strait of Gibraltar. Ocean Eng.
**2018**, 151, 141–151. [Google Scholar] [CrossRef] - Sahin, B. Risk Assessment of Arctic Navigation by Using Improved Fuzzy-AHP. Int. J. Marit. Eng.
**2015**, 157, 241–250. [Google Scholar] - Karahalios, H. A Risk Assessment of Ships Groundings in Rivers: The Case of Parana River. J. Navig.
**2019**, 73, 833–845. [Google Scholar] [CrossRef] - Zhang, J.; Teixeira, N.P.; Guedes, S.C.; Yan, X.P. Quantitative assessment of collision risk influence factors in the Tianjin port. Saf. Sci.
**2018**, 110, 363–371. [Google Scholar] [CrossRef] - Mazaheri, A.; Montewka, J.; Kujala, P. Towards an evidence-based probabilistic risk model for ship-grounding accidents. Saf. Sci.
**2016**, 86, 195–210. [Google Scholar] [CrossRef] - Fu, S.; Zhang, D.; Montewka, J.; Yan, X.P.; Zio, E. Towards a probabilistic model for predicting ship besetting in ice in Arctic waters. Reliab. Eng. Syst. Saf.
**2016**, 155, 124–136. [Google Scholar] [CrossRef] [Green Version] - Baksh, A.A.; Abbassi, R.; Garaniya, V.; Khan, F. Marine transportation risk assessment using Bayesian Network: Application to Arctic waters. Ocean Eng.
**2018**, 159, 422–436. [Google Scholar] [CrossRef] - Khan, B.; Khan, F.; Veitch, B.; Yang, M. An operational risk analysis tool to analyze marine transportation in arctic waters. Reliab. Eng. Syst. Saf.
**2018**, 169, 485–502. [Google Scholar] [CrossRef] - Khan, B.; Khan, F.; Veitch, B. A Dynamic Bayesian Network model for ship-ice collision risk in the Arctic waters. Saf. Sci.
**2020**, 130, 104858. [Google Scholar] [CrossRef] - Aven, T. The risk concept—historical and recent development trends. Reliab. Eng. Syst. Saf.
**2012**, 99, 33–44. [Google Scholar] [CrossRef] - Hu, S.P.; Li, Z.; Xi, Y.T.; Gu, X.Y.; Zhang, X.X. Path Analysis of Causal Factors Influencing Marine Traffic Accident via Structural Equation Numerical Modeling. J. Mar. Sci. Eng.
**2019**, 7, 96. [Google Scholar] [CrossRef] [Green Version] - Kujala, P.; Hänninen, M.; Arola, T.; Ylitalo, J. Analysis of the marine traffic safety in the Gulf of Finland. Reliab. Eng. Syst. Saf.
**2009**, 94, 1349–1357. [Google Scholar] [CrossRef] - Eliopoulou, E.; Papanikolaou, A.; Voulgarellis, M. Statistical analysis of ship accidents and review of safety level. Saf. Sci.
**2016**, 85, 282–292. [Google Scholar] [CrossRef] - Sotiralis, P.; Ventikos, N.P.; Hamann, R.; Golyshev, P.; Teixeira, A.P. Incorporation of human factors into ship collision risk models focusing on human centred design aspects. Reliab. Eng. Syst. Saf.
**2016**, 156, 210–227. [Google Scholar] [CrossRef] - Kontovas, C.A.; Psaraftis, H.N. Formal safety assessment: A critical review. Mar. Technol.
**2009**, 46, 45–59. [Google Scholar] - International Code for Ships Operating in Polar Waters. Available online: http://www.imo.org/ (accessed on 2 February 2016).
- Wang, Z.J.; Silberman, J.A.; Corbett, J.J. Container vessels diversion pattern to trans-Arctic shipping routes and GHG emission abatement potential. Marit. Policy Manag.
**2020**. [Google Scholar] [CrossRef] - Stevenson, T.C.; Davies, J.; Huntington, H.P.; Sheard, W. An examination of trans-Arctic vessel routing in the Central Arctic Ocean. Mar. Policy
**2019**, 100, 83–89. [Google Scholar] [CrossRef] - Zhang, X.; Zhang, Q.; Yang, J.; Cong, Z.; Chen, H. Safety risk analysis of unmanned ships in inland rivers based on a fuzzy Bayesian network. J. Adv. Transp.
**2019**. [Google Scholar] [CrossRef] - Wang, T.; Wu, Q.; Diaconeasa, M.A.; Yan, X.; Mosleh, A. On the use of the hybrid causal logic methodology in ship collision risk assessment. J. Mar. Sci. Eng.
**2020**, 8, 485. [Google Scholar] [CrossRef] - Peng, Y.; Boyle, L.N. Driver’s adaptive glance behavior to in-vehicle information systems. Accid. Anal. Prev.
**2015**, 85, 93–101. [Google Scholar] [CrossRef] [PubMed] - Dotzauer, M.; Waard, D.D.; Caljouw, S.R.; Gloria, P.; Brouwer, W.H. Behavioral adaptation of young and older drivers to an intersection crossing advisory system. Accid. Anal. Prev.
**2015**, 74, 24–32. [Google Scholar] [CrossRef] [PubMed] - Ding, J.F.; Shyu, W.H. Key Factors Influencing the Building of Arctic Shipping Routes. J. Navig.
**2016**, 69, 1261–1277. [Google Scholar]

**Figure 6.**The change of PoD in M1 and M2 under the variation of SDA. Among them, (

**a**–

**d**) means that the SDA states of NAI-NAI, NAI-HAI, HAI-NAI, and HAI-HAI increase by 10% respectively, (

**e**–

**h**) means that the SDA states of NAI-NAI, NAI-HAI, HAI-NAI, and HAI-HAI increase by 30% respectively.

No | Symbol | Description |
---|---|---|

1 | X1 | ice condition |

2 | X2 | radar failure |

3 | X3 | environmental obstruction |

4 | X4 | wind speed effect |

5 | X5 | wave height effect |

6 | X6 | process failure |

7 | X7 | navigation function failure |

8 | X8 | electronic chart error |

9 | X9 | the insufficient chart not been updated |

10 | X11 | the inappropriate route selection |

11 | X12 | the fuel measurement system failure |

12 | X13 | engine failure |

13 | X14 | propeller failure |

14 | M1 | serious ice condition |

15 | M2 | human error |

16 | M3 | Restricted visibility |

17 | M4 | operation failure |

18 | M5 | wind and wave effects |

19 | M6 | navigation failure |

20 | M7 | navigation system failure |

21 | M8 | the engine’s fuel supply is contaminated |

22 | M9 | power failure |

23 | M10 | engine shutdown |

24 | N1 | ship-ice collision accident |

Data Source | Content | Usability | Format | Value Range | Data Processing Tool |
---|---|---|---|---|---|

https://nsidc.org/data | Daily SIC change data | Open access | bin | [0, 1] | Python (NumPy, pyproj) |

State | PPD | ||||
---|---|---|---|---|---|

A | B | C | D | E | |

NAI-NAI | 0 | 0 | 0.232 | 0 | 0 |

NAI-HAI | 0.931 | 0 | 0 | 0.299 | 0 |

HAI-NAI | 0 | 0.232 | 0.079 | 0 | 0 |

HAI-HAI | 0.069 | 0.768 | 0.689 | 0.701 | 1 |

Nodes | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 | X10 | X11 | X12 | X13 | X14 | |

yes | 0.036 | 0.03 | 0.053 | 0.056 | 0.029 | 0.004 | 0.038 | 0.025 | 0.024 | 0.032 | 0.022 | 0.004 | 0.029 |

no | 0.964 | 0.97 | 0.947 | 0.944 | 0.971 | 0.996 | 0.962 | 0.975 | 0.976 | 0.968 | 0.988 | 0.996 | 0.971 |

Data source | OL | OL | EJ | EJ | OL | OL | OL | OL | OL | EJ | EJ | OL | EJ |

State | expert1 | expert2 | expert3 | expert4 | expert5 |
---|---|---|---|---|---|

increase | 0.69 | 0.64 | 0.72 | 0.85 | 0.91 |

constant | 0.28 | 0.33 | 0.28 | 0.13 | 0.08 |

decrease | 0.03 | 0.03 | 0.04 | 0.02 | 0.01 |

State | NAI-NAI | NAI-HAI | HAI-NAI | HAI-HAI |
---|---|---|---|---|

increase | 0 | 0.999 | 0 | 0.348 |

constant | 0.982 | 0.001 | 0.017 | 0.652 |

decrease | 0.018 | 0 | 0.983 | 0 |

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**MDPI and ACS Style**

Li, Z.; Hu, S.; Gao, G.; Xi, Y.; Fu, S.; Yao, C.
Risk Reasoning from Factor Correlation of Maritime Traffic under Arctic Sea Ice Status Association with a Bayesian Belief Network. *Sustainability* **2021**, *13*, 147.
https://doi.org/10.3390/su13010147

**AMA Style**

Li Z, Hu S, Gao G, Xi Y, Fu S, Yao C.
Risk Reasoning from Factor Correlation of Maritime Traffic under Arctic Sea Ice Status Association with a Bayesian Belief Network. *Sustainability*. 2021; 13(1):147.
https://doi.org/10.3390/su13010147

**Chicago/Turabian Style**

Li, Zhuang, Shenping Hu, Guoping Gao, Yongtao Xi, Shanshan Fu, and Chenyang Yao.
2021. "Risk Reasoning from Factor Correlation of Maritime Traffic under Arctic Sea Ice Status Association with a Bayesian Belief Network" *Sustainability* 13, no. 1: 147.
https://doi.org/10.3390/su13010147