Research Papers: Polar and Arctic Engineering

A Finite Element Method-Based Potential Theory Approach for Optimal Ice Routing

[+] Author and Article Information
Henry Piehl

Department of Marine Technology,
Norwegian University of Science and
Technology, NTNU,
Trondheim 7491, Norway
e-mail: henry.piehl@ntnu.no

Aleksandar-Saša Milaković

Department of Marine Technology,
Norwegian University of Science and
Technology, NTNU,
Trondheim 7491, Norway

Sören Ehlers

Department of Ship Structural
Design and Analysis,
Hamburg University of Technology, TUHH,
Hamburg 21073, Germany

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received June 10, 2016; final manuscript received June 7, 2017; published online August 8, 2017. Assoc. Editor: Marcelo R. Martins.

J. Offshore Mech. Arct. Eng 139(6), 061502 (Aug 08, 2017) (7 pages) Paper No: OMAE-16-1059; doi: 10.1115/1.4037141 History: Received June 10, 2016; Revised June 07, 2017

Shipping in ice-covered regions has gained high attention within recent years. Analogous to weather routing, the occurrence of ice in a seaway affects the selection of the optimal route with respect to the travel time or fuel consumption. The shorter, direct path between two points—which may lead through an ice-covered area—may require a reduction of speed and an increase in fuel consumption. A longer, indirect route, could be more efficient by avoiding the ice-covered region. Certain regions may have to be avoided completely, if the ice thickness exceeds the ice-capability of the ship. The objective of this study is to develop a computational method that combines coastline maps, route cost information (e.g., ice thickness), transport task, and ship properties to find the optimal route between port of departure, A, and port of destination, B. The development approach for this tool is to formulate the transport task in the form of a potential problem, solve this equation with a finite element method (FEM), and apply line integration and optimization to determine the best route. The functionality of the method is first evaluated with simple test problems and then applied to realistic transport scenarios.

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Piehl, H. , von Bock und Polach, R. U. F. , Erceg, S. , Polic, D. , Bambulyak, A. , Das, J. , Erceg, B. , Tõns, T. , Bergström, M. V. , Myland, D. , Milakovic, A.-S. , and Ehlers, S. , 2015, “ A Framework for a Design and Optimization Platform for Ships in Arctic Conditions,” International Conference on Port and Ocean Engineering Under Arctic Conditions (POAC), Trondheim, Norway, June 14–18, Paper No. 198. https://www.researchgate.net/publication/283106632_A_framework_for_a_design_and_optimization_platform_for_ships_in_arctic_conditions
Bertoia, C. , Manore, M. , Steen Andersen, H. , OConnors, C. , Hansen, K. , and Evanego, C. , 2004, “ Synthetic Aperture Radar for Operational Ice Observation and Analysis,” Synthetic Aperture Radar Marine User's Manual, C. R. Jackson and J. R. Apel , eds., National Oceanic and Atmospheric Administration, Washington, DC, pp. 417–442.
Khvorostovsky, K. , and Rampal, P. , 2016, “ On Retrieving Sea Ice Freeboard From Icesat Laser Altimeter,” Cryosphere, 10(5), pp. 2329–2346. [CrossRef]
Kovacs, A. , Valleau, N. C. , and Holladay, J. S. , 1987, “ Airborne Electromagnetic Sounding of Sea-Ice Thickness and Subice Bathymetry,” Cold Reg. Sci. Technol., 14(3), pp. 289–311. [CrossRef]
Suominen, M. , Kulovesi, J. , Lensu, M. , Lehtiranta, J. , and Kujala, P. , 2014, “ A Comparison of Shipborne Methods for Ice Thickness Determination,” 22nd IAHR International Symposium on Ice, Singapore, Aug. 11–15.
Williams, E. , Swithinbank, C. , and Robin, G. , 1975, “ A Submarine Sonar Study of Arctic Pack Ice,” J. Glaciol., 15(73), pp. 349–362. [CrossRef]
Melling, H. , Johnston, P. H. , and Riedel, D. A. , 1995, “ Measurements of the Underside Topography of Sea Ice by Moored Subsea Sonar,” J. Atmos. Oceanic Technol., 12(3), pp. 589–602. [CrossRef]
WMO, 1968, “ WMO Sea Ice Nomenclature, Terminology and Codes,” World Meteorological Organization, Geneva, Switzerland, Vol. 1, Report No. 259.
Choi, M. , Chung, H. , Yamaguchi, H. , and Nagakawa, K. , 2015, “ Arctic Sea Route Path Planning Based on an Uncertain Ice Prediction Model,” Cold Reg. Sci. Technol., 109, pp. 61–69. [CrossRef]
Dijkstra, E. W. , 1959, “ A Note on Two Problems in Connexion With Graphs,” Numer. Math., 1(1), pp. 269–271. [CrossRef]
Hart, P. E. , Nilsson, N. J. , and Raphael, B. , 1968, “ A Formal Basis for the Heuristic Determination of Minimum Cost Paths,” IEEE Trans. Syst. Sci. Cybern. SSC4, 4(2), pp. 100–107. [CrossRef]
Björnsson, Y. , and Halldorsson, K. , 2006, “ Improved Heuristics for Optimal Path-Finding on Game Maps,” Second AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment (AIIDE), Marina del Rey, CA, June 20–23, Paper No. 6. http://www.aaai.org/Papers/AIIDE/2006/AIIDE06-006.pdf
Young, T. , 2001, “ Optimizing Points-of-Visibility Pathfinding,” Game Programming Gems 2, M. DeLoura , ed., Vol. 2., Charles River Media, Hingham, MA, pp. 324–329.
Open Source, 2017, “ Python Programming Language,” Python Software Foundation, Wilmington, DE, accessed July 1, 2017, http://www.python.org/
Topf, J. , and Hormann, C. , 2016, “ OpenStreetMapData,” Jochen Topf, Dresden, Germany, accessed July 1, 2017, http://openstreetmapdata.com/data/coastlines
Andreas Kloeckner, 2008, “ MeshPy,” Andreas Klöckner, accessed July 1, 2017, https://mathema.tician.de/software/meshpy/
Shewchuk, J. R. , 1996, “ Triangle: Engineering a 2d Quality Mesh Generator and Delaunay Triangulator,” Applied Computational Geometry: Towards Geometric Engineering (Lecture Notes in Computer Science), Vol. 1148, Springer-Verlag, Berlin, pp. 203–222. [CrossRef]
Bathe, K.-J. , 1996, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ. [PubMed] [PubMed]
SciPy.org, 2014, “ Spsolve,” The Scipy Community, accessed July 1, 2017, http://docs.scipy.org/doc/scipy/reference/sparse.linalg.html
SciPy.org, 2016, “ Fmin,” The Scipy Community, accessed July 1, 2017, http://docs.scipy.org/doc/scipy-0.16.1/reference/generated/scipy.optimize.fmin.html


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Fig. 1

Test case setup for routing around the island of Fehmarn

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Fig. 2

Finite element mesh around island of Fehmarn

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Fig. 4

FEM potential field solution

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Fig. 9

Route-straightening procedure

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Fig. 10

Initial and improved northern route around the island if an ice field is present

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Fig. 11

Initial and improved southern route through the strait between island and mainland

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Fig. 5

Gradient vector field

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Fig. 6

Magnitude of gradient vector field

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Fig. 7

Collection of initial routes computed from vector field

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Fig. 8

Relative route costs for possible paths through gradient vector field



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