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Efficient estimation of extreme non-linear roll motions using the first-order reliability method (FORM)

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Abstract

In on-board decision support systems, efficient procedures are needed for real-time estimation of the maximum ship responses to be expected within the next few hours, given online information on the sea state and user-defined ranges of possible headings and speeds. For linear responses, standard frequency domain methods can be applied. For non-linear responses, as exhibited by the roll motion, standard methods such as direct time domain simulations are not feasible due to the required computational time. However, the statistical distribution of non-linear ship responses can be estimated very accurately using the first-order reliability method (FORM), which is well known from structural reliability problems. To illustrate the proposed procedure, the roll motion was modelled by a simplified non-linear procedure taking into account non-linear hydrodynamic damping, time-varying restoring and wave excitation moments, and the heave acceleration. Resonance excitation, parametric roll, and forced roll were all included in the model, albeit with some simplifications. The result is the mean out-crossing rate of the roll angle together with the most probable wave scenarios (critical wave episodes), leading to user-specified specific maximum roll angles. The procedure is computationally very effective and can thus be applied to real-time determination of ship-specific combinations of heading and speed to be avoided in the actual sea state.

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References

  1. Rathje H (2005) Impact of extreme waves on ship design and ship operation. In: Proceedings of the conference on design and operation for abnormal conditions. RINA, London

  2. Nielsen JK, Hald NH, Michelsen J, et al (2006) SeaSense—real-time onboard decision support. In: Proceedings of the world maritime technology conference, London, March 6–10, IMarEST

  3. Borge J, Gonzáles R, Hessner K, et al (2000) Estimation of sea state directional spectra by using marine radar imaging of the sea surface. In: Proceedings of the ETCE/OMAE2000 joint conference, New Orleans, ASME

  4. UD Nielsen (2006) ArticleTitleEstimations of on-site directional wave spectra from measured ship responses Mar Struct 19 33–69 Occurrence Handle10.1016/j.marstruc.2006.06.001

    Article  Google Scholar 

  5. Krüger S, Hinrichs R, Cramer H (2004) Performance-based approaches for the evaluation of intact stability problems. In: Proceedings of PRADS'2004, Travemünde, September 19(1):33–69

  6. van Daalen EFG, Boonstra H, Blok JJ (2005) Capsize probability analysis of a small container vessel. In: Proceedings of the 8th international workshop on stability and operational safety of ships, Istanbul, October 6–7

  7. G Bulian A Francescutto (2004) ArticleTitleA simplified modular approach for the prediction of the roll motion due to the combined action of wind and waves J Eng Marit Environ 218 189–212

    Google Scholar 

  8. MAS Neves CA Rodriquez (2005) A coupled third-order model of roll parametric resonance Proceedings: maritime transportation and exploitation of ocean and coastal resources Taylor and Francis London 243–253

    Google Scholar 

  9. S-R Hsieh AW Troesch SW Shaw (1994) ArticleTitleA nonlinear probabilistic method for predicting vessel capsize in random beam seas Proc R Soc London Part A 446 195–211 Occurrence Handle10.1098/rspa.1994.0099

    Article  Google Scholar 

  10. KJ Spyrou (2000) ArticleTitleDesigning against parametric instability in following seas Ocean Eng 26 625–653 Occurrence Handle10.1016/S0029-8018(99)00019-0

    Article  Google Scholar 

  11. Ness OB, McHenry G, Mathisen J, Winterstein SR (1989) Nonlinear analysis of ship rolling in random beam waves. In: Proceedings of the STAR symposium on 21st century ship and offshore vessel design, production and operation, Society of Naval Architects and Marine Engineers, April 12–15, pp 49–66

  12. Søborg AV, Friis-Hansen P (2004) Reliability analysis of dynamic stability in waves. In: Proceedings of the 23rd international conference on offshore mechanics and arctic engineering (OMAE'04), Vancouver, June, ASME, Paper no. 51591

  13. JJ Jensen J Capul (2006) ArticleTitleExtreme response predictions for jack-up units in second-order stochastic waves by FORM Probab Eng Mech 21 IssueID4 330–337 Occurrence Handle10.1016/j.probengmech.2005.11.007

    Article  Google Scholar 

  14. A Der Kiureghian (2000) ArticleTitleThe geometry of random vibrations and solutions by FORM and SORM Probab Eng Mech 15 81–90 Occurrence Handle10.1016/S0266-8920(99)00011-9

    Article  Google Scholar 

  15. Det Norske Veritas (2003) PROBAN, general purpose probabilistic analysis program, version 4.4. Det Norske Veritas, Høvik

  16. G Lindgren (1970) ArticleTitleSome properties of a normal process near a local maximum Ann Math Stat 41 IssueID6 1870–1883 Occurrence Handle272051 Occurrence Handle0222.60027

    MathSciNet  MATH  Google Scholar 

  17. Tromans PS, Anaturk AR, Hagemeijer P (1991) A new model for the kinematics of large ocean waves—application as a design wave. In: Proceedings of the first offshore and polar engineering conference (ISOPE), vol 3, Heriot-Watt University, Edinburgh UK, 11–16 August, International Society of Offshore and Polar Engineers, pp 64–71

  18. LJM Adegeest A Braathen RM Løseth (1998) Use of non-linear sea-load simulations in the design of ships Proceedings of PRADS'1998 Elsevier Delft 53–58

    Google Scholar 

  19. Dietz JS, Friis-Hansen P, Jensen JJ (2004) Most likely response waves for estimation of extreme value ship response statistics. In: Proceedings of PRADS'2004, Travemünde, September, Seehafen, Hamburg

  20. O Ditlevsen T Arnbjerg-Nielsen (1994) ArticleTitleModel-correction-factor method in structural reliability J Eng 120 1–10 Occurrence Handle10.1061/(ASCE)0733-9399(1994)120:1(1)

    Article  Google Scholar 

  21. Alford KA, Troesch AW, McCue LS (2005) Design wave elevations leading to extreme roll motions. In: Proceedings of the 8th international workshop on stability and operational safety of ships, Istanbul, October 6–7

  22. H Koo A Der Kiureghian K Fujimura (2005) ArticleTitleDesign point excitation for nonlinear random vibrations Probab Eng Mech 20 IssueID2 136–147 Occurrence Handle10.1016/j.probengmech.2005.04.001

    Article  Google Scholar 

  23. Jensen JJ, Pedersen PT (2006) Critical wave episodes for assessment of parametric roll. In: Proceedings of IMDC'06, Ann Arbor, May 16–19, University of Ann Arbor, pp 399–411

  24. ITTC Specialist Committee on Stability in Waves (chaired by de Kat JO) (2005) Final report and recommendation. In: Clarke D, Mesbahi AP (eds) Proceedings of the 24th international towing tank conference, University of Newcastle-upon-Tyne, September 4–10, pp 369–408

  25. WN France M Levadou TW Treakle et al. (2003) ArticleTitleAn investigation of head-sea parametric rolling and its influence on container lashing systems Mar Technol 40 IssueID1 1–19

    Google Scholar 

  26. YS Shin VL Belenky JR Paulling et al. (2004) ArticleTitleCriteria for parametric roll of large containerships in head seas Trans SNAME 112 14–47

    Google Scholar 

  27. H-P Kroeger (1986) ArticleTitleRollsimulation von schiffen im seegang Schiffstechnik 33 187–216

    Google Scholar 

  28. Jensen JJ, Olsen AS (2006) On the assessment of parametric roll in random seas. In: Proceedings of the world maritime technology conference, London, March 6–10, IMarEST

  29. G Bulian (2005) ArticleTitleNonlinear parametric rolling in regular waves—a general procedure for the analytical approximation of the GZ curve and its use in time domain simulations Ocean Eng 32 309–330 Occurrence Handle10.1016/j.oceaneng.2004.08.008

    Article  Google Scholar 

  30. JJ Jensen AE Mansour AS Olsen (2004) ArticleTitleEstimation of ship motions using closed-form expressions Ocean Eng 31 61–85 Occurrence Handle10.1016/S0029-8018(03)00108-2

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Technical University of Denmark, Nils Koppel Allé, Building 403/024, Kgs., Lyngby, DK, 2800, Denmark

    Jørgen Juncher Jensen

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Jensen, J. Efficient estimation of extreme non-linear roll motions using the first-order reliability method (FORM). J Mar Sci Technol 12, 191–202 (2007). https://doi.org/10.1007/s00773-007-0243-z

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  • DOI: https://doi.org/10.1007/s00773-007-0243-z

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