“Nonlinear Time-Domain Strip Theory Formulation for Low-Speed Manoeuvering and Station-Keeping”

Authors: Thor I. Fossen and Øyvind N. Smogeli,
Affiliation: NTNU, Centre for Ships and Ocean Structures
Reference: 2004, Vol 25, No 4, pp. 201-221.

Keywords: Ship, rig, modeling, strip theory, seakeeping

Abstract: This paper presents a computer effective nonlinear time-domain strip theory formulation for dynamic positioning (DP) and low-speed manoeuvring. Strip theory or 2D potential theory, where the ship is divided in 20 to 30 cross sections, can be used to compute the potential coefficients (added mass and potential damping) and the exciting wave loads (Froude-Krylov and diffraction forces). Commercially available programs are ShipX (VERES) by Marintek (Fathi, 2004) and SEAWAY by Amarcon (Journée & Adegeest, 2003), for instance. The proposed method can easily be extended to utilize other strip theory formulations or 3-D potential programs like WAMIT (2004). The frequency dependent potential damping, which in classic theory results in a convolution integral not suited for real-time simulation, is compactly represented by using the state-space formulation of Kristiansen & Egeland (2003). The separation of the vessel model into a low-frequency model (represented by zerofrequency added mass and damping) and a wave-frequency model (represented by motion transfer functions or RAOs), which is commonly used for simulation, is hence made superfluous. Transformations of motions and coefficients between different coordinate systems and origins, i.e. data frame, hydrodynamic frame, body frame, inertial frame etc., are put into the rigid framework of Fossen (1994, 2002). The kinematic equations of motion are formulated in a compact nonlinear vector representation and the classical kinematic assumption that the Euler angles are small is removed. This is important for computation of accurate control forces at higher roll and pitch angles. The hydrodynamic forces in the steadily translating hydrodynamic reference frame (equilibrium axes) are, however, assumed tobe linear. Recipes for computation of retardation functions are presented and frequency dependent viscous damping is included. Emphasis is placed on numerical computations and representation of the data from VERES and SEAWAY in Matlab/Simulink. For this purpose a Simulink add-in to the Marine Systems Simulator (MSS) at the Norwegian University of Science and Technology has been developed (Fossen et al., 2004).

PDF PDF (963 Kb)        DOI: 10.4173/mic.2004.4.1

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[1] Peter Gu, Ahmed Ahmed Walid, Yousef Iskandarani and Hamid Reza Karimi (2013), doi:10.1007/s13042-012-0076-x
[2] Gullik A. Jensen, Niklas Säfström, Tu Duc Nguyen and Thor I. Fossen (2010), doi:10.1016/j.oceaneng.2009.12.009
[3] Atul Thakur, Petr Svec and Satyandra K. Gupta (2012), doi:10.1016/j.robot.2012.07.009
[4] THOR I. FOSSEN (2005), doi:10.1142/S0218127405013691
[5] Keum-Shik Hong and Quang Hieu Ngo (2012), doi:10.1016/j.oceaneng.2012.06.013
[6] (2011), doi:10.1002/9781119994138.refs
[7] Xuetao Chen and Woei Wan Tan (2013), doi:10.1016/j.oceaneng.2013.05.021
[8] Atul Thakur and Satyandra K. Gupta (2011), doi:10.1115/1.3617443
[9] Haizhi Liang, Luyu Li and Jinping Ou (2015), doi:10.1007/s00773-015-0322-5
[10] Zhongli Wang and Yunhui Liu (2009), doi:10.1109/ROBIO.2009.4913162
[11] A. Pereira, J. Das and G.S. Sukhatme (2008), doi:10.1109/IROS.2008.4650991
[12] K. Unneland, E. Kristiansen and O. Egeland (2005), doi:10.1109/OCEANS.2005.1639784
[13] I.F. Ihle, R. Skjetne and T.I. Fossen (2005), doi:10.1109/.2005.1469806
[14] I.-A.F. Ihle, R. Skjetne and T.I. Fossen (2004), doi:10.1109/CDC.2004.1428723
[15] Daniel Leite, Fernando Gomide, Rosangela Ballini and Pyramo Costa (2011), doi:10.1109/FUZZY.2011.6007452
[16] I.-A.F. Ihle, J. Jouffroy and T.I. Fossen (2005), doi:10.1109/CDC.2005.1582247
[17] Yusuke Kobashi, Genma Sano, Tsuyoshi Nakamura and Masayoshi Kanoh (2011), doi:10.1109/FUZZY.2011.6007480
[18] G. Torsetnes, J. Jouffroy and T.I. Fossen (2004), doi:10.1109/CDC.2004.1429657
[19] I.-A.F. Ihle, J. Jouffroy and T.I. Fossen (2005), doi:10.1109/OCEANS.2005.1639888
[20] A.K. Bondhus and K.Y. Pettersen (2005), doi:10.1109/OCEANS.2005.1639986
[21] Xue Tao Chen and Woei Wan Tan (2012), doi:10.1109/FUZZ-IEEE.2012.6251243
[22] Xue Tao Chen and Woei Wan Tan (2012), doi:10.1109/FUZZ-IEEE.2012.6251244
[23] Kari Unneland, Paul Van Dooren and Olav Egeland (2007), doi:10.1109/ACC.2007.4282863
[24] Ye Zhao, Min Zhang, Hui Chen and Xiao-Feng Yuan (2014), doi:10.1109/TAP.2014.2322893
[25] Quang Hieu Ngo, Giyong Hong and Keum-Shik Hong (2011), doi:10.1109/SII.2011.6147652
[26] Yongping Jin, Buyan Wan, Deshun Liu, Youduo Peng and Yong Guo (2016), doi:10.1016/j.oceaneng.2016.03.056
[27] Benjamin Golding, Andrew Ross and Thor I. Fossen (2006), doi:10.3182/20060329-3-AU-2901.00048
[28] Yongping Jin, Buyan Wan, Deshun Liu, Youduo Peng, Zhihua Cai and Jianghui Dong (2016), doi:10.21595/jve.2016.16955
[29] Owen Thorp, George Piper and Roger Cortesi (2014), doi:10.1177/1077546312468926
[30] P. Du, A. Ouahsine, K.T. Toan and P. Sergent (2017), doi:10.1016/j.oceaneng.2017.07.013
[31] Gyoung-Hahn Kim, Mingxu Piao and Keum-Shik Hong (2017), doi:10.1109/ASCC.2017.8287600
[32] V. A. Golikov, V. V. Golikov, Ya. Volyanskaya, O. Mazur and O. Onishchenko (2018), doi:10.1088/1755-1315/172/1/012010
[33] Sondre Sanden Tørdal and Geir Hovland (2019), doi:10.1115/1.4041643
[34] Marc Levadou and Riaan van t Veer (2011), doi:10.1007/978-94-007-1482-3_17
[35] Ranjan Vepa (2013), doi:10.1007/978-1-4471-5400-6_4
[36] (2015), doi:10.1002/9781119140931.biblio
[37] Shahrokh Sepehrirahnama, Eng Teo Ong, Heow Pueh Lee and Kian-Meng Lim (2019), doi:10.1016/j.jfluidstructs.2019.102756
[38] Mohamid Salih Noorazlina, Md Salim Kamil, Mohammad Amiruddin Hashim, Nordiana Jamil and Hanisah Johor (2018), doi:10.1007/978-3-319-72697-7_50
[39] M. Daniele, G. Quaranta, P. Masarati and A. Zanoni (2020), doi:10.1007/s42496-020-00037-3
[40] Nedeleg Bigi, Kostia Roncin, Jean-Baptiste Leroux and Yves Parlier (2020), doi:10.3390/jmse8070486
[41] (2021), doi:10.1002/9781119575016.ref
[42] Taavi Salumae, Ahmed Chemori and Maarja Kruusmaa (2019), doi:10.1109/JOE.2017.2774318
[43] Zhenpeng Dong, Xiao Liang, Yuanhang Hou and Zhao Zhang (2022), doi:10.1016/j.oceaneng.2022.110915
[44] Yong-ping Jin, Kun Xie, Guang-ping Liu, Bu-yan Wan and You-duo Peng (2022), doi:10.1007/s13344-022-0013-z
[45] Yongping Jin, Kun Xie, Guangping Liu, Youduo Peng and Buyan Wan (2022), doi:10.1016/j.oceaneng.2022.112031
[46] Bilgin Bozkurt and Melek Ertogan (2023), doi:10.1016/j.oceaneng.2022.113309
[47] Qu Yang and Lilong Cai (2023), doi:10.1016/j.oceaneng.2022.113311
[48] Henning Overaas, Hakon S. Halvorsen, Olav Landstad, Vidar Smines and Tor Arne Johansen (2023), doi:10.1109/JOE.2023.3288969
[49] Bilgin Bozkurt, Melek Ertogan and Sebnem Helvacioglu (2022), doi:10.1109/ICCMA56665.2022.10011458
[1] BAILEY, P. A., PRICE, W. G. TEMAREL, P. (1998). A Unified Mathematical Model Describing the Maneuvering of A Ship Travelling in a Seaway, Trans. RINA 140, pp. 131-149.
[2] BOESE, P. (1970). Eine Einfache Methode zur Berechnung der Wiederstandserhohlung eines Schiffes in Seegang, Technical Report Technical Report 258. Institut für Schiffbau der Universität Hamburg, Germany. In German.
[3] CUMMINS, W. E. (1962). The Impulse Response Function and Ship Motions, .
[4] DENIS, M. ST. PIERSON, W. J. (1953). On the Motions of Ships in Confused Seas, Trans. SNAME 61, pp. 280-357.
[5] FALTINSEN, O. M. (1990). Sea Loads on Ships and Offshore Structures, Cambridge University Press.
[6] FALTINSEN, O. M. SVENSEN, T. (1990). Incorporation of Seakeeping Theories in CAD, International Symposium on CFD and CAD in Ship Design, MARIN, Wageningen, The Netherlands.
[7] FATHI, D. (2004). ShipX Vessel Responses ´VERES´, Marintek AS, Trondheim. ShipX Vessel Responses.VERES.
[8] FATHI, D.and HOFF, J. R. (2004). ShipX Vessel Responses ´VERES´ Theory Manual, Marintek AS, February 13, 2004.
[9] FOSSEN, T. I. (1994). Guidance and Control of Ocean Vehicles, John Wiley and Sons. Ltd. ISBN 0-471-94113-1.
[10] FOSSEN, T. I. (2002). Marine Control Systems: Guidance, Navigation and Control of Ships, Rigs and Underwater Vehicles, Marine Cybernetics AS. Trondheim, Norway. ISBN 82-92356-00-2.
[11] FOSSEN, T. I., PEREZ, T., SMOGELI, O. SØRENSEN, A. J. (2004). Marine Systems Simulator, Norwegian University of Science and Technology, Trondheim, www.cesos.ntnu.no/mss.
[12] FRANK, W. (1967). Oscillation of Cylinders in or below the Free Surface of Deep Fluids, Technical Report 2375. Naval Ship Research and Development Centre, Washington DC, USA.
[13] GERRITSMA, J. (1960). Ship Motions in Longitudinal Waves, International Shipbuilding Progress, 7, pp. 49-76.
[14] GERRITSMA, J. BEUKELMAN, W. (1972). Analysis of the Resistance Increase in Waves of a Fast Cargo-Ship, International Shipbuilding Progress.
[15] GRIM, O. (1953). Berechnung der durch Schwingungen eines Schiffskörpers Erzeugten Hydrodynamischen Kräfte, Jahrbuch der Schiffsbautechnischen Gesellschaft 47, pp. 277-299. In German.
[16] IKEDA, Y, HIEMNO, Y. TANAKA, N. (1978). A Prediction Method for Ship Rolling, Technical Report 00405. Department of Naval Architecture, University of Osaka Prefecture, Japan.
[17] JOURNÉE, J. M. J. (1993). Hydromechanic Coefficients for Calculating Time Domain Motions of Cutter Suction Dredges by Cummins Equations, Technical Report DUT-SHL Report 0968. Delft University of Technology.
[18] JOURNÉE¸, J. M. J. ADEGEEST, L. J. M. (2003). Theoretical Manual of Strip Theory Program ´SEAWAY for Windows´, Amarcon. Delft University of Technology. DUT-SHL Report 1370.
[19] KEIL, H. (1974). Die Hydrodynamische Kräfte bei der periodischen Bewegung zweidimensionaler Körper an der Oberfläche flacher Gewasser, Technical Report 305. Institut für Schiffbau der Universität Hamburg, Deutschland. In German.
[20] KORVIN-KROUKOVSKY, B. V. JACOBS, W. R. (1957). Pitching and Heaving Motions of a Ship in Regular Waves, Transactions SNAME, 65, pp. 590-632.
[21] KRISTIANSEN, E. EGELAND, O. (2003). Frequency-Dependent Added Mass in Models for Controller Design for Wave Motion Damping, Proc. of the IFAC Conference on Maneuvering and Control of Marine Systems.MCMC´03. Girona, Spain.
[22] OGILVIE, T. (1964). Recent Progress towards the Understanding and Prediction of Ship Motions, Proc. of the 5th Symposium on Naval Hydrodynamics.
[23] SALVESEN, N., TUCK, E. O. FALTINSEN, O. M. (1970). Ship Motions and Sea Loads, Trans. SNAME, 78, pp. 250-287.
[24] TASAI, F. (1959). On the Damping Force and Added Mass of Ships Heaving and Pitching, Technical Report 26, Research Institute for Applied Mechanics, Kyushu University. Japan.
[25] TASAI, F. (1960). Formula for Calculating Hydrodynamic Force on a Cylinder Heaving in the Free Surface, N-Parameter Family. Technical Report 31. Research Institute for Applied Mechanics, Kyushu University. Japan.
[26] TASAI, F. (1961). Hydrodynamic Force and Moment Produced by Swaying and Rolling Oscillation of Cylinders on the Free Surface, Technical Report 35. Research Institute for Applied Mechanics, Kyushu University. Japan.
[27] URSELL, F. (1949). On the Heaving Motion of a Circular Cylinder on the Surface of a Fluid, Quarterly Journal of Mechanics and Applied Mathematics.
[28] WAMIT (2004). User manual, www.wamit.com, WAMIT, Inc. 822 Boylston St. Suite 202 Chestnut Hill, MA 02467-2504 USA.

  title={{Nonlinear Time-Domain Strip Theory Formulation for Low-Speed Manoeuvering and Station-Keeping}},
  author={Fossen, Thor I. and Smogeli, Øyvind N.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}