Abstract
The methodology proposed in this paper considers the uncertainty present in modeling the probability of collision between ships on a route. The proposal allows representing and quantifying uncertainty, and ensures rigorous propagation of this uncertainty from the input variables to the output variable.
This proposal complements the analysis of risk and helps the decision maker to know the degree of confidence associated with the results of the analysis.
Pedersen’s model has been selected to estimate the probability of collision, using the information provided by the AIS, and Dempster-Shafer Theory has been selected for the treatment of uncertainty.
This methodology has been applied to maritime traffic in the Canary Islands and has been validated using the Kullback-Leibler divergence. The results are consistent with those obtained with the software IWRAP recommended by IALA.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Dempster, A.P.: Upper and lower probabilities induced by a multi-valued mapping. Annals of Mathematical Statistics 38, 325–339 (1967)
Yager, R.R.: Arithmetic and other operations on Dempster-Shafer structures. International Journal of Man-Machine Studies 25, 357–366 (1986)
Fuji, Y., Yamanouchi, H., Mizuki, N.: Some factors affecting the frequency of accidents in marine traffic. II: The probability of stranding. III: The effect of darkness on the probability of stranding. Journal of Navigation 27 (1974)
Mac Duff, T.: The probability of vessel collisions. Ocean Industry, 144–148 (1974)
Pedersen, P.T.: Collision and grounding mechanics. In: Proceedings of WEMT 1995. The Danish Society of Naval Architects and Marine Engineers, pp. 461–474 (1995)
Friis-Hansen, P., Engberg, P.C.: Basic modeling principles for prediction of collision and grounding frequencies. Technical University of Denmark (2008)
Montewka, J., Hinz, T., Kujala, P., Matusiak, J.: Probability Modelling of vessel collisions. Reliability Engineering and System Safety 95, 573–589 (2010)
Montewka, J., Goerlandt, F., Kujala, P.: Determination of collision criteria and causation factors appropriate to a model for estimating the probability of maritime accidents. Ocean Engineering 40, 50–61
Goerlandt, F., Kujala, P.: Traffic simulation based ship collision probability modeling. Reliability Engineering and System Safety 96(1), 91–107 (2011)
Fowler, T.G., Sorgard, E.: Modeling ship transportation risk. Risk Analysis 20(2), 225–244 (2000)
Sofartsstyrelsen. Risk analysis of sea traffic in the area around Bornholm. Technical report, COWI, Kongens Lyngby (2008)
Merrick, J., Van Dorp, J., Blackford, J., Shaw, G., Harrald, J., Mazzuchi, T.: A traffic density analysis of proposed ferry service expansion in San Francisco bay using a maritime simulation model. Reliability Engineering and System Safety 81, 119–132 (2003)
Merrick, J., Van Dorp, J.: Modeling risk in the dynamic environment of maritime transportation. In: Proceedings of the Winter Simulation Conference, pp. 1090–1098 (2001)
Gucma, L.: Models of ship’s traffic flow for the safety of marine engineering structures evaluation. In: Proceedings of the ESREL, pp. 713–718 (2003)
Przywarty, M.: Probabilistic model of ships navigational safety assessment on large sea areas. In: Proceedings of the 16th International Symposium on Electronics in Transport (2008)
Shafer, G.: A mathematical theory of evidence. Princeton University Press (1976)
Sentz, K., Ferson, S.: Combination of evidence in Dempster-Shafer theory. Technical report. Sandia National Laboratories (2002)
Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)
Neumann, T.: A simulation environment for modeling and analysis of the distribution of shore observatory stations. International Journal on Marine Navigation and Safety of Sea Transportation 5(4) (2011)
Filipowicz, W.: An application of mathematical theory of evidence in navigation. International Journal on Marine Navigation and Safety of Sea Transportation 3(4) (2009)
Filipowicz, W.: Belief structures in position fixing. Communications in Computer and Information Science 104, 434–446 (2010)
Sii, H.S., Ruxton, T., Wang, J.: Synthesis using fuzzy set theory and a Dempster-Shafer based approach to compromise decision-making with multiple-attributes applied to risk control options selection. Proceedings Institution of Mechanical Engineers 216, 15–29 (2002)
Helton, J.C.: Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. Journal of Statistical Computation and Simulation 57, 3–76 (1997)
Ferson, S., Kreinovich, V., Ginzburg, L., Myers, D., Sentz, K.: Constructing probability boxes and Dempster-Shafer structures. Technical report. Sandia National Laboratories (2003)
Miller, L.H.: Table of percentage points of Kolmogorov statistics. Journal of the American Statistical Association 51, 111–121 (1956)
Ferson, S., Hajagos, J.: Arithmetic with uncertain numbers: rigorous and (often) best possible answers. Reliability Engineering and System Safety 85, 135–152 (2004)
Ferson, S., Tucker, W.T.: Sensitivity in Risk analyses with uncertain numbers. Technical report. Sandia National Laboratories (2006)
Zona marítima especialmente sensible. Secretaría General de Transporte. Dirección General de la Marina Mercante. Capitanía Marítima en Las Palmas. Ministerio de Fomento. Gobierno de España (2007)
Lilliefors, H.: On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association 62, 399–402 (1967)
IALA Recommendation O-134 on the IALA Risk Management tool for ports and restricted waterways (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Talavera Ortiz, A., Aguasca Colomo, R., Galván González, B.J. (2013). Dempster-Shafer Theory Based Ship-Ship Collision Probability Modelling. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory - EUROCAST 2013. EUROCAST 2013. Lecture Notes in Computer Science, vol 8112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53862-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-53862-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-53861-2
Online ISBN: 978-3-642-53862-9
eBook Packages: Computer ScienceComputer Science (R0)