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An environment–kinetic compound space–time prism-based approach for assessing multi-ship collision risk in confined water

Published online by Cambridge University Press:  14 July 2025

Hongchu Yu Open the ORCID record for Hongchu Yu [Opens in a new window] ,
Zheng Guo ,
Zhixiang Fang ,
Lei Xu  and
Jing Xu
Hongchu Yu*
Affiliation:
School of Navigation, Wuhan University of Technology (WUT), Wuhan, China State Key Laboratory of Maritime Technology and Safety, Wuhan University of Technology, Wuhan, China
Zheng Guo
Affiliation:
School of Navigation, Wuhan University of Technology (WUT), Wuhan, China
Zhixiang Fang
Affiliation:
State Key Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing (Liesmars), Wuhan University, Wuhan, China
Lei Xu
Affiliation:
National Engineering Research Center for Geographic Information System, China University of Geosciences (Wuhan), Wuhan, China
Jing Xu
Affiliation:
Department of Geography, University of California, Santa Barbara, CA, USA
*
Corresponding author: Hongchu Yu; Emails: hcyu@whut.edu.cn, hongshuxifan8140@163.com
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Abstract

Vessel collision risk estimation is crucial in navigation manoeuvres, route planning, risk control, safety management and forewarning issues. The interaction possibility is a good method to quantify the near-miss collision risks of multi-ships. Current models, however, are mostly concerned about the movements in an unrestricted isotropic travel environment or network environment. This article simultaneously addresses these issues by developing a novel environment–kinetic compound space–time prism to capture potential spatial–temporal interactions of multi-ships in constrained dynamic environments. The approach could significantly reduce the overestimation of the individual vessel’s potential travel area and the interaction possibility of encountering vessels in restricted water. The proposed environmental–kinetical compound space–time prism (EKC-STP)-based method enables identifying where and when multi-ships possibly interacted in the constraint water area, as well as how the interaction possibility pattern changed from day to day. The collision risk evaluation results were validated through comparison with other methods. The full picture of hierarchical collision risk distribution in port areas is determined and could be employed to provide quantifiable references for efficient and practical anti-collision measures establishment.

Keywords

confined waterenvironment–kinetic compound space–time prismmulti-ships encounteringpotential collision risktemporal-spatial interaction probability

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Type
Research Article
Information
The Journal of Navigation , Volume 78 , Issue 1 , January 2025 , pp. 58 - 79
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Institute of Navigation

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References

Alessandrini, A., Mazzarella, F. and Vespe, M. (2018). Estimated time of arrival using historical vessel tracking data. IEEE Transactions on Intelligent Transportation Systems, 20(1), 7–15.CrossRefGoogle Scholar
Ali, F., Kim, E. K. and Kim, Y. G. (2015). Type-2 fuzzy ontology-based semantic knowledge for collision avoidance of autonomous underwater vehicles. Information Sciences, 295, 441–464.CrossRefGoogle Scholar
Anderson, J. H., Downs, J. A., Loraamm, R. and Reader, S. (2017). Agent-based simulation of Muscovy duck movements using observed habitat transition and distance frequencies. Computers, Environment and Urban Systems, 61, 49–55.CrossRefGoogle Scholar
Asmara, I. P. S., Kobayashi, E., Artana, K. B., Masroeri, A. A. and Wakabayashi, N. (2014). Simulation-Based Estimation of Collision Risk During Ship Maneuvering in Two-Lane Canal Using Mathematical Maneuvering Group Model and Automatic Identification System Data. In International Conference on Offshore Mechanics and Arctic Engineering (Vol. 45424, p. V04AT02A055).CrossRefGoogle Scholar
Celik, M., Lavasani, S. M. and Wang, J. (2010). A risk-based modelling approach to enhance shipping accident investigation. Safety Science, 48 (1), 18–27.CrossRefGoogle Scholar
Chen, B. Y., Li, Q., Wang, D., Shaw, S. L., Lam, W. H., Yuan, H. and Fang, Z. (2013). Reliable space–time prisms under travel time uncertainty. Annals of the Association of American Geographers, 103 (6), 1502–1521.CrossRefGoogle Scholar
Chen, D., Dai, C., Wan, X. and Mou, J. (2015). June. A research on AIS-based embedded system for ship collision avoidance. In 2015 International Conference on Transportation Information and Safety (ICTIS). IEEE, 512–517.Google Scholar
Chen, P., Huang, Y., Mou, J. and Van Gelder, P. H. A. J. M. (2019). Probabilistic risk analysis for ship-ship collision: State-of-the-art. Safety Science, 117, 108–122.CrossRefGoogle Scholar
Chen, P., Mou, J. and van Gelder, P. H. A. J. M. (2017). Risk assessment methods for ship collision in estuarine waters using AIS and historical accident data. In Maritime Transportation and Harvesting of Sea Resources, 213–221.Google Scholar
Christian, R. and Kang, H. G. (2017). Probabilistic risk assessment on maritime spent nuclear fuel transportation (Part II: Ship collision probability). Reliability Engineering & System Safety, 164, 136–149.CrossRefGoogle Scholar
d’Afflisio, E., Braca, P. and Willett, P. (2021). Malicious AIS spoofing and abnormal stealth deviations: A comprehensive statistical framework for maritime anomaly detection. IEEE Transactions on Aerospace and Electronic Systems, 57(4), 2093–2108.CrossRefGoogle Scholar
Delafontaine, M., Neutens, T. and Van de Weghe, N. (2011). Modelling potential movement in constrained travel environments using rough space–time prisms. International Journal of Geographical Information Science, 25(9), 1389–1411.CrossRefGoogle Scholar
Downs, J. A. and Horner, M. W. (2012). Probabilistic potential path trees for visualizing and analyzing vehicle tracking data. Journal of Transport Geography, 23, 72–80.CrossRefGoogle Scholar
Downs, J. A., Horner, M. W., Hyzer, G., Lamb, D. and Loraamm, R. (2014b). Voxel-based probabilistic space-time prisms for analysing animal movements and habitat use. International Journal of Geographical Information Science, 28(5), 875–890.CrossRefGoogle Scholar
Downs, J. A., Lamb, D., Hyzer, G., Loraamm, R., Smith, Z. J. and O’Neal, B. M. (2014a). Quantifying spatio-temporal interactions of animals using probabilistic space–time prisms. Applied Geography, 55, 1–8.CrossRefGoogle Scholar
Dzikowski, R. and Ślączka, W. (2014). Analysis of IWRAP mk2 application for oil and gas operations in the area of the Baltic Sea in view of fishing vessel traffic. Zeszyty Naukowe/Akademia Morska w Szczecinie, 40(112), 58–66.Google Scholar
Evmides, N., Odysseos, L., Michaelides, M. P. and Herodotou, H. (2022). An Intelligent Framework for Vessel Traffic Monitoring Using AIS Data. In 2022 23rd IEEE International Conference on Mobile Data Management (MDM). IEEE, 413–418.CrossRefGoogle Scholar
Fang, Z., Yu, H., Ke, R., Shaw, S. L. and Peng, G. (2018a). Automatic identification system-based approach for assessing the near-miss collision risk dynamics of ships in ports. IEEE Transactions on Intelligent Transportation Systems, 20(2), 534–543.CrossRefGoogle Scholar
Fang, Z., Yu, H., Lu, F., Feng, M. and Huang, M. (2018b). Maritime network dynamics before and after international events. Journal of Geographical Sciences, 28, 937–956.CrossRefGoogle Scholar
Felski, A. and Jaskólski, K. (2012). Information unfitness as a factor constraining Automatic Identification System (AIS) application to anti-collision manoeuvring. Polish Maritime Research, 19(3), 60–64.CrossRefGoogle Scholar
Felski, A., Jaskólski, K. and Banyś, P. (2015). Comprehensive assessment of automatic identification system (AIS) data application to anti-collision manoeuvring. The Journal of Navigation, 68(4), 697–717.CrossRefGoogle Scholar
Fujii, Y. and Tanaka, K. (1971). Traffic capacity. The Journal of navigation, 24 (4), 543–552.CrossRefGoogle Scholar
Goerlandt, F. and Kujala, P. (2014). On the reliability and validity of ship–ship collision risk analysis in light of different perspectives on risk. Safety science, 62, 348–365.CrossRefGoogle Scholar
Goerlandt, F., Montewka, J., Lammi, H. and Kujala, P. (2012). Analysis of near collisions in the Gulf of Finland. Advances in Safety, Reliability and Risk Management, 2880–2886.Google Scholar
Hansen, M. G., Jensen, T. K., Lehn-Schiøler, T., Melchild, K., Rasmussen, F. M. and Ennemark, F. (2013). Empirical ship domain based on AIS data. The Journal of Navigation, 66(6), 931–940.CrossRefGoogle Scholar
He, Z., Liu, C., Chu, X., Negenborn, R. R. and Wu, Q. (2021). Dynamic anti-collision A-star algorithm for multi-ship encounter situations. International Journal of Geographical Information Science, 118, 102995.Google Scholar
Hu, S., Fang, Q., Xia, H. and Xi, Y. (2007). Formal safety assessment based on relative risks model in ship navigation. Reliability Engineering & System Safety, 92(3), 369–377.CrossRefGoogle Scholar
Hu, Y., Janowicz, K. and Chen, Y. (2016). Task-oriented information value measurement based on space-time prisms. International Journal of Geographical Information Science, 30(6), 1228–1249.CrossRefGoogle Scholar
Im, N. and Luong, T. N. (2019). Potential risk ship domain as a danger criterion for real-time ship collision risk evaluation. Ocean Engineering, 194, 106610.CrossRefGoogle Scholar
Johansen, T. A., Perez, T. and Cristofaro, A. (2016). Ship collision avoidance and COLREGS compliance using simulation-based control behavior selection with predictive hazard assessment. IEEE Transactions on Intelligent Transportation Systems, 17(12), 3407–3422.CrossRefGoogle Scholar
Kaluza, P., Kölzsch, A., Gastner, M. T. and Blasius, B. (2010). The complex network of global cargo ship movements. Journal of the Royal Society Interface, 7(48), 1093–1103.CrossRefGoogle ScholarPubMed
Karahalios, H. (2014). The contribution of risk management in ship management: The case of ship collision. Safety Science, 63, 104–114.CrossRefGoogle Scholar
Kuijpers, B., Grimson, R. and Othman, W. (2011). An analytic solution to the alibi query in the space–time prisms model for moving object data. International Journal of Geographical Information Science, 25(2), 293–322.CrossRefGoogle Scholar
Kuijpers, B., Miller, H. J. and Othman, W. (2017). Kinetic prisms: incorporating acceleration limits into space–time prisms. International Journal of Geographical Information Science, 31(11), 2164–2194.CrossRefGoogle Scholar
Kuijpers, B. and Othman, W. (2009). Modeling uncertainty of moving objects on road networks via space–time prisms. International Journal of Geographical Information Science, 23(9), 1095–1117.CrossRefGoogle Scholar
Last, P., Hering-Bertram, M. and Linsen, L. (2019). Interactive history-based vessel movement prediction. IEEE Intelligent Systems, 34(6), 3–13.CrossRefGoogle Scholar
Lazarowska, A. (2015). Ship’s trajectory planning for collision avoidance at sea based on ant colony optimisation. The Journal of Navigation, 68(2), 291–307.CrossRefGoogle Scholar
Lee, J. and Miller, H. J. (2019). Analyzing collective accessibility using average space-time prisms. Transportation Research Part D: Transport and Environment, 69, 250–264.CrossRefGoogle Scholar
Lee, M. K., Park, Y. S., Park, S., Lee, E., Park, M. and Kim, N. E. (2021). Application of collision warning algorithm alarm in fishing vessel’s waterway. Applied Sciences, 11(10), 4479.CrossRefGoogle Scholar
Leung, Y., Zhao, Z. and Ma, J. H. (2016). Uncertainty analysis of space–time prisms based on the moment-design method. International Journal of Geographical Information Science, 30(7), 1336–1358.CrossRefGoogle Scholar
Li, S., Meng, Q. and Qu, X. (2012). An overview of maritime waterway quantitative risk assessment models. Risk Analysis: An International Journal, 32(3), 496–512.CrossRefGoogle ScholarPubMed
Liao, F. (2019). Space–time prism bounds of activity programs: A goal-directed search in multi-state supernetworks. International Journal of Geographical Information Science, 33(5), 900–921.CrossRefGoogle Scholar
Liu, W. R., Hu, K., Liang, M., Li, Y., Liu, X. and Yang, D. (2023). QSD-LSTM: Vessel trajectory prediction using long short-term memory with quaternion ship domain. Applied Ocean Research, 136, 103592.CrossRefGoogle Scholar
Liu, Z., Wu, Z. and Zheng, Z. (2019). A cooperative game approach for assessing the collision risk in multi-vessel encountering. Ocean Engineering, 187, 106175.CrossRefGoogle Scholar
Loraamm, R. W. and Downs, J. A. (2016). A wildlife movement approach to optimally locate wildlife crossing structures. International Journal of Geographical Information Science, 30(1), 74–88.CrossRefGoogle Scholar
Lyu, H., Hao, Z., Li, J., Li, G., Sun, X., Zhang, G., Yin, Y., Zhao, Y. and Zhang, L. (2023). Ship autonomous collision-avoidance strategies—A comprehensive review. Journal of Marine Science and Engineering, 11(4), 830.CrossRefGoogle Scholar
Lyu, H., Liu, W., Guo, S., Tan, G., Fu, C., Sun, X., Zhao, Y., Zhang, L. and Yin, Y. (2024). Autonomous collision avoidance method for MASSs based on precise potential field modelling and COLREGs constraints in complex sailing environments. Ocean Engineering, 292, 116530.CrossRefGoogle Scholar
Lyu, H. and Yin, Y. (2019). COLREGS-constrained real-time path planning for autonomous ships using modified artificial potential fields. The Journal of Navigation, 72(3), 588–608.CrossRefGoogle Scholar
Mandal, S., Nagarajan, V. and Sha, O. P. (2018). Navigational safety and traffic pattern analysis using AIS data on the western coast of India. Current Science, 114(12), 2473–2481.CrossRefGoogle Scholar
Mazurek, J., Lu, L., Krata, P., Montewka, J., Krata, H. and Kujala, P. (2022). An updated method identifying collision-prone locations for ships. A case study for oil tankers navigating in the Gulf of Finland. Reliability Engineering & System Safety, 217, 108024.CrossRefGoogle Scholar
Miller, H. J. (1991). Modelling accessibility using space-time prism concepts within geographical information systems. International Journal of Geographical Information System, 5(3), 287–301.CrossRefGoogle Scholar
Miller, J. A. (2015). Towards a better understanding of dynamic interaction metrics for wildlife: a null model approach. Transactions in GIS, 19(3), 342–361.CrossRefGoogle Scholar
Mou, J. M., Van der Tak, C. and Ligteringen, H. (2010). Study on collision avoidance in busy waterways by using AIS data. Ocean Engineering, 37(5–6), 483–490.CrossRefGoogle Scholar
Murray, B. and Perera, L. P. (2020). A dual linear autoencoder approach for vessel trajectory prediction using historical AIS data. Ocean Engineering, 209, 107478.CrossRefGoogle Scholar
Murray, B. and Perera, L. P. (2021). An AIS-based deep learning framework for regional ship behavior prediction. Reliability Engineering & System Safety, 215, 107819.CrossRefGoogle Scholar
Murray, B. and Perera, L. P. (2022). Ship behavior prediction via trajectory extraction-based clustering for maritime situation awareness. Journal of Ocean Engineering and Science, 7(1), 1–13.CrossRefGoogle Scholar
Neutens, T., Van de Weghe, N., Witlox, F. and De Maeyer, P. (2008). A three-dimensional network-based space–time prism. Journal of Geographical Systems, 10, 89–107.CrossRefGoogle Scholar
Nguyen, M., Zhang, S. and Wang, X. (2018). A novel method for risk assessment and simulation of collision avoidance for vessels based on AIS. Algorithms, 11(12), 204.CrossRefGoogle Scholar
Nguyen, X. T., Park, Y. S., Park, J. S. and Jeong, J. Y. (2013). Developing a Program to Pre-process AIS Data and applying to Vung Tau Waterway in Vietnam-Based on the IWRAP Mk2 program. Journal of the Korean Society of Marine Environment & Safety, 19(4), 345–351.CrossRefGoogle Scholar
Nyman, T., Porthin, M., Sassi, J., Sonninen, S., Huhta, H. K. and Hänninen, S. (2009). Åland Sea FSA study. In VTT Research Report VTT.Google Scholar
Otoi, O. S., Park, Y. S. and Park, J. S. (2016). A basic study on marine traffic assessment in Mombasa Approach Channel-I. Journal of Navigation and Port Research, 40(5), 257–263.CrossRefGoogle Scholar
Ozbas, B. (2013). Safety risk analysis of maritime transportation: review of the literature. Transportation Research Record, 2326(1), 32–38.CrossRefGoogle Scholar
Öztürk, Ü., Boz, H. A. and Balcisoy, S. (2021). Visual analytic based ship collision probability modeling for ship navigation safety. Expert Systems with Applications, 175, 114755.CrossRefGoogle Scholar
Pedersen, P. T. (1995). Collision and grounding mechanics. Proceedings of WEMT, 95(1995), 125–157.Google Scholar
Qu, X., Meng, Q. and Suyi, L. (2011). Ship collision risk assessment for the Singapore Strait. Accident Analysis & Prevention 43(6), 2030–2036.CrossRefGoogle ScholarPubMed
Rong, H., Teixeira, A. P. and Soares, C. G. (2022). Ship collision avoidance behaviour recognition and analysis based on AIS data. Ocean Engineering, 245, 110479.CrossRefGoogle Scholar
Rothmund, S. V., Haugen, H. E., Veglo, G. D., Brekke, E. F. and Johansen, T. A. (2023, June). Validation of ship intention model for maritime collision avoidance control using historical AIS data. In 2023 European Control Conference (ECC). IEEE, 1–8.CrossRefGoogle Scholar
Seepersad, D., Eriksson, O. F., Greenland, A. and Miller, K. (2020). Benefits of Assessing Risk in Maritime Navigation Using IALA and LINZ Methods. The International Hydrographic Review, 23, 7–33.Google Scholar
Silveira, P., Teixeira, A. P. and Soares, C. G. (2022). A method to extract the Quaternion Ship Domain parameters from AIS data. Ocean Engineering, 257, 111568.CrossRefGoogle Scholar
Silveira, P. A. M., Teixeira, A. P. and Soares, C. G. (2013). Use of AIS data to characterize marine traffic patterns and ship collision risk off the coast of Portugal. The Journal of Navigation, 66(6), 879–898.CrossRefGoogle Scholar
Simsir, U., Amasyalı, M. F., Bal, M., Çelebi, U. B. and Ertugrul, S. (2014). Decision support system for collision avoidance of vessels. Applied Soft Computing, 25, 369–378.CrossRefGoogle Scholar
Sutrisno, J. (2018) Bachelor Thesis & Colloquium–ME141501 Risk assessment of Ship Collision and Grounding in Surabaya West Access Channel due to the Existence of Shipwrecks.Google Scholar
Szłapczyński, R. and Niksa-Rynkiewicz, T. (2018). A framework of a ship domain-based near-miss detection method using Mamdani neuro-fuzzy classification. Polish Maritime Research, 25(s1), 14–21.CrossRefGoogle Scholar
Thanh, N. X., Park, Y. S., Park, J. S. and Kim, T. G. (2015). A study on the Marine Traffic Assessment based on Traffic Distribution in the strait of Malacca. Journal of the Korean Society of Marine Environment & Safety, 21(1), 25–33.CrossRefGoogle Scholar
Tsou, M. C. (2016). Multi-target collision avoidance route planning under an ECDIS framework. Ocean Engineering, 121, 268–278.CrossRefGoogle Scholar
Tu, E., Zhang, G., Rachmawati, L., Rajabally, E. and Huang, G. B. (2017). Exploiting AIS data for intelligent maritime navigation: A comprehensive survey from data to methodology. IEEE Transactions on Intelligent Transportation Systems, 19 (5), 1559–1582.CrossRefGoogle Scholar
Vessel, F. (2008). Risk analysis of sea traffic in the area around Bornholm. COWI A/S, Kongens Lyngby, Denmark, Tech. Rep. P-65775-002.Google Scholar
Vestre, A., Bakdi, A., Vanem, E. and Engelhardtsen, Ø. (2021). AIS-based near-collision database generation and analysis of real collision avoidance Manoeuvres. The Journal of Navigation, 74(5), 985–1008.CrossRefGoogle Scholar
Wang, N. (2010). An intelligent spatial collision risk based on the quaternion ship domain. The Journal of Navigation, 63(4), 733–749.CrossRefGoogle Scholar
Wang, T., Yan, X., Wang, Y. and Wu, Q. (2017). August. A distributed model predictive control using virtual field force for multi-ship collision avoidance under COLREGs. In 2017 4th International Conference on Transportation Information and Safety (ICTIS), 296–305.Google Scholar
Wang, Y., Zhang, J., Chen, X., Chu, X. and Yan, X. (2013). A spatial–temporal forensic analysis for inland–water ship collisions using AIS data. Safety science, 57, 187–202.CrossRefGoogle Scholar
Weng, J., Meng, Q. and Qu, X. (2012). Vessel collision frequency estimation in the Singapore Strait. The Journal of Navigation, 65(2), 207–221.CrossRefGoogle Scholar
Wołejsza, P. (2012). Statistical analysis of real radar target course and speed changes for the needs of multiple model tracking filter. Zeszyty Naukowe/Akademia Morska w Szczecinie, 30 (102), 166–169.Google Scholar
Wright, D., Janzen, C., Bochenek, R., Austin, J. and Page, E. (2019). Marine observing applications using AIS: automatic identification system. Frontiers in Marine Science, 6, 537.CrossRefGoogle Scholar
Wu, X., Mehta, A. L., Zaloom, V. A. and Craig, B. N. (2016). Analysis of waterway transportation in Southeast Texas waterway based on AIS data. Ocean Engineering, 121, 196–209.CrossRefGoogle Scholar
Xiao, Y., Li, X., Yao, W., Chen, J. and Hu, Y. (2022). Bidirectional data-driven trajectory prediction for intelligent maritime traffic. IEEE Transactions on Intelligent Transportation Systems, 24(2), 1773–1785.Google Scholar
Xiao, Z., Fu, X., Zhang, L. and Goh, R. S. M. (2019). Traffic pattern mining and forecasting technologies in maritime traffic service networks: A comprehensive survey. IEEE Transactions on Intelligent Transportation Systems, 21(5), 1796–1825.CrossRefGoogle Scholar
Xin, X., Liu, K., Loughney, S., Wang, J., Li, H. and Yang, Z. (2023a). Graph-based ship traffic partitioning for intelligent maritime surveillance in complex port waters. Expert Systems with Applications, 231, 120825.CrossRefGoogle Scholar
Xin, X., Yang, Z., Liu, K., Zhang, J. and Wu, X. (2023b). Multi-stage and multi-topology analysis of ship traffic complexity for probabilistic collision detection. Expert Systems with Applications, 213, 118890.CrossRefGoogle Scholar
Xu, L., Chen, N., Chen, Z., Zhang, C. and Yu, H. (2021). Spatiotemporal forecasting in earth system science: Methods, uncertainties, predictability and future directions. Earth-Science Reviews, 222, 103828.CrossRefGoogle Scholar
Xu, Q. (2014). Collision avoidance strategy optimization based on danger immune algorithm. Computers & Industrial Engineering, 76, 268–279.CrossRefGoogle Scholar
Xu, X., Wu, B., Xie, L., Teixeira, Â. P. and Yan, X. (2023). A novel ship speed and heading estimation approach using radar sequential images. IEEE Transactions on Intelligent Transportation Systems, 24(10), 11107–11120.CrossRefGoogle Scholar
Yu, H., Bai, X. and Liu, J. (2023b). Ship behavior pattern analysis based on graph theory: A case study in Tianjin Port. Journal of Marine Science and Engineering, 11(12), 2227.CrossRefGoogle Scholar
Yu, H., Fang, Z., Fu, X., Liu, J. and Chen, J. (2021b). Literature review on emission control-based ship voyage optimization. Transportation Research Part D: Transport and Environment, 93, 102768.CrossRefGoogle Scholar
Yu, H., Fang, Z., Murray, A. T. and Peng, G. (2021a). A direction-constrained space-time prism-based approach for quantifying possible multi-ship collision risks. IEEE Transactions on Intelligent Transportation Systems, 22(1), 131–141.CrossRefGoogle Scholar
Yu, H., Meng, Q., Fang, Z., Liu, J. and Xu, L. (2023a). A review of ship collision risk assessment, hotspot detection and path planning for maritime traffic control in restricted waters. The Journal of Navigation, 75(6), 1337–1363.CrossRefGoogle Scholar
Yu, H., Murray, A. T., Fang, Z., Liu, J., Peng, G., Solgi, M. and Zhang, W. (2022). Ship path optimization that accounts for geographical traffic characteristics to increase maritime port safety. IEEE Transactions on Intelligent Transportation Systems, 23(6), 5765–5776.CrossRefGoogle Scholar
Zaman, M. B., Kobayashi, E., Wakabayashi, N., Khanfir, S., Pitana, T. and Maimun, A. (2014). Fuzzy FMEA model for risk evaluation of ship collisions in the Malacca Strait: based on AIS data. Journal of Simulation, 8 (1), 91–104.CrossRefGoogle Scholar
Zhang, W., Goerlandt, F., Kujala, P. and Wang, Y. (2016). An advanced method for detecting possible near miss ship collisions from AIS data. Ocean Engineering, 124, 141–156.CrossRefGoogle Scholar
Zhang, W., Goerlandt, F., Montewka, J. and Kujala, P. (2015). A method for detecting possible near miss ship collisions from AIS data. Ocean Engineering, 107, 60–69.CrossRefGoogle Scholar
Zhao, L. and Fu, X. (2021). A method for correcting the closest point of approach index during vessel encounters based on dimension data from AIS. IEEE Transactions on Intelligent Transportation Systems, 23(8), 13745–13757.CrossRefGoogle Scholar
Zhou, K., Chen, J. and Liu, X. (2018). Optimal collision-avoidance manoeuvres to minimise bunker consumption under the two-ship crossing situation. The Journal of Navigation, 71(1), 151–168.CrossRefGoogle Scholar