Abstract
The aim of the present chapter is to advocate for a very effective stochastic procedure based on the First-Order Reliability method (FORM) and Monte Carlo simulations (MCS), for prediction of parametric rolling in stationary stochastic seaways. Due to efficient optimization procedures implemented in standard FORM codes and the short duration of the time domain simulations needed, the calculation of the mean out-crossing rates of any given roll response is very fast. Thus complicated nonlinear effects can be included. Furthermore, the FORM analysis also identifies the most probable wave episodes leading to given roll responses. Because of the linearization in the FORM procedure the results are, however, only asymptotically exact and thus MCS often also needs to be performed. Here a scaling property inherent in the FORM procedure is investigated for use in MCS in order to reduce the necessary simulation time. More specifically, the MCS results for the reliability index β for parametric rolling of a ship suggest that the relation \(\beta = a + b/{H}_{\mathrm{s}}\) can provide an accurate scaling of the reliability index with significant wave height Hs. MCS can therefore be performed for sea states higher than the design sea state and thereafter be scaled down. From the reliability index the mean out-crossing rate and the probability of exceedance are then readily obtained.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Adegeest, L. J. M, Braathen, A. Løseth, R. M.: Use of non-linear sea-loads nimulations in design of ships. Proc. PRADS’1998, Delft, pp. 53–58 (1998)
Alford, K. A., Troesch, A. W., McCue, L.: LS design wave elevations leading to extreme roll motions. Proc. STAB’2005, Istanbul, Turkey (2005)
Borge, J., Gonzáles, R., Hessner, K., Reichert, K., Soares, C. G.: Estimation of sea state directional spectra by using marine radar imaging of sea surface. Proc. ETCE/OMAE2000 Joint Conference, New Orleans, Louisiana, USA (2000)
Bulian, G., Francescutto, A. A.: Simplified modular approach for the prediction of the roll motion due to the combined action of wind and waves. Proc Instn Enggrs, Part M: J. Engineering for the Maritime Environment 218:189–212 (2004)
Bulian, G.: Nonlinear parametric rolling in regular waves – a general procedure for the analytical approximation of the GZ curve and its use in time domain simulations. Ocean Engineering 32:309–330 (2005)
Daalen, E. F. G., Boonstra, H., Blok, J. J.: Capsize probability analysis of a small container vessel. Proc- 8th Int. Workshop on Stability and Operational Safety of Ships, Istanbul, October 6–7 (2005)
Der Kiureghian, A.: The geometry of random vibrations and solutions by FORM and SORM. Probabilistic Engineering Mechanics 15:81–90 (2000)
Det Norske Veritas: General purpose probabilistic analysis program, Version 4.4 (2003)
Dietz, J. S., Friis-Hansen, P., Jensen, J. J.: Most likely response waves for estimation of extreme value ship response statistics. Proc PRADS’2004, Travemünde, September, Germany (2004)
Ditlevsen, O., Arnbjerg-Nielsen, T.: Model-correction-factor method in structural reliability. Journal of Engineering 120:1–10 (1994)
France, W. N., Levadou, M., Treakle, T. W., Paulling, J. R., Michel, R. K., Moore, C.: An investigation of head-sea parametric rolling and its influence on container lashing systems. Marine Technology 40:1–19 (2003)
Fujimura, K., Der Kiureghian, A.: Tail-equivalent linearization method for nonlinear random vibration. Probabilistic Engineering Mechanics 22: 63–76 (2007)
Hsieh, S.-R., Troesch. A. W., Shaw, S. W.: A nonlinear probabilistic method for predicting vessel capsize in random beam seas. Proc Royal Society London, Part A, 446:195–211 (1994)
IMO submission (SLF 50) by Germany: Proposal for an additional intact stability regulations. Subcommittee on Stability, Loadlines and on Fishing Vessels (2007)
de Kat, J. O.: ITTC specialist committee on stability in waves (2005)
Jensen, J. J., Mansour, A. E., Olsen, A. S.: Estimation of ship motions using closed-form expressions. Ocean Engineering 31:61–85 (2004)
Jensen, J. J., Capul, J.: Extreme response predictions for jack-up units in second-order stochastic waves by FORM. Probabilistic Engineering Mechanics 21:330–337 (2006)
Jensen, J. J., Olsen, A. S.: On the assessment of parametric roll in random sea. Proc. World Maritime Technology Conference, London, 6–10 March (2006)
Jensen, J. J., Pedersen, P. T.: Critical wave episodes for assessment of parametric roll Proc. IMDC’06, Ann Arbor, May, pp. 399–411 (2006)
Jensen, J. J.: Efficient estimation of extreme non-linear roll motions using the first-order reliability method (FORM). J. Marine Science and Technology 12:191–202 (2007)
Jensen, J. J.: Extreme value predictions using Monte Carlo simulations with artificially increased load spectrum. Probabilistic Engineering Mechanics, 26:399–404 (2010)
Koo, H., Der Kiureghian, A., Fujimura, K.: Design point excitation for nonlinear random vibrations. Probabilistic Engineering Mechanics. 20:136–147 (2005)
Krüger, S., Hinrichs, R., Cramer, H.: Performance based approaches for the evaluation of intact stability problems. Proc. PRADS’2004, Travemünde, September, Germany (2004)
Kroeger, H.-P.: Roll Simulation von Schiffen im seegang. Schiffstechnik 33:187–216 (in German) (1986)
Lindgren, G.: Some properties of a normal process near a local maximum. Ann. Math. Stat. 41:1870–1883 (1970)
Ness, O. B., McHenry, G., Mathisen, J., Winterstein, S. R.: Nonlinear analysis of ship rolling in random beam waves. Proc. STAR Symposium on 21st Century Ship and Offshore Vessel Design, Production and Operation, April 12–15, pp. 49–66 (1989)
Neves, M. A. S., Rodriquez, C. A.: A coupled third-order model of roll parametric resonance. Proc Maritime Transportation and Exploitation of Ocean and Coastal Resources, pp. 243–253, Taylor and Francis, London, UK (2005)
Nielsen, J. K., Hald, N. H., Michelsen, J., Nielsen, U. D., Baatrup, J., Jensen, J. J., Petersen, E. S.: Seasense – real-time onboard decision Support. Proc. World Maritime Technology Conference, London, 6-10 March (2006)
Nielsen, U. D.: Estimations of on-site directional wave spectra from measured ship responses. Marine Structures 19:33–69 (2006)
Nielsen, U. D., Jensen, J. J.: Numerical simulations of the rolling of a ship in a stochastic sea – Evaluations by Use of MCS and FORM. Proc of 28th International Conference on Offshore Mechanics and Arctic Engineering (OMAE’09), Honolulu, USA, June, Paper No. 79765 (2009)
Pereira, R.: Simulation nichtlinearer Seegangslasten. Schiffstechnik 35:173-193 (in German) (1988)
Rathje, H.: Impact of Extreme Waves on Ship Design and Ship Operation. Proc Design & Operation for Abnormal Conditions, Royal Institution of Naval Architects, London, 26–27 January (2005)
Shin, Y. S., Belenky, V. L., Paulling, J. R., Weems, K. M., Lin, W. M.: Criteria for parametric roll of large container ships in head seas. Transactions of SNAME 112:14–47 (2004)
Spanos, D., Papanikolaou, A. A numerical simulation of a fishing vessel in parametric roll in head sea. Proc. 8th Int. Workshop on Stability and Operational Safety of Ships, Istanbul, October 6–7 (2005)
Spanos, D., Papanikolaou, A., Papatzanakis, G.: Risk-based onboard guidance to the master for avoiding dangerous seaways. 6th OSAKA Colloquium on Seakeeping and Stability of Ships, Osaka University, Japan, March 26–28 (2008)
Spyrou, K. J.: Designing against parametric instability in following seas. Ocean Engineering 26:625–653 (2000)
Spyrou, K., Themelis, N.: Development of probabilistic procedures and validation – Alternative 2: Capsize mode analysis. Deliverables D235, SAFEDOR-D-235-2006-11-9-NTUA–rev-1 (2006)
Themelis, N., Spyrou, K., Niotis, S.: Implementation and application of probabilistic Procedures. Deliverables D236, SAFEDOR-D-236-2007-06-15-NTUA–rev-1 (2007)
Tonguc, E., Söding, H.: Computing capsizing frequencies of ships in a seaway. Proc. 3rd Int. Conf. on Stability of Ships and Ocean Vehicles STAB’86, Gdansk (1986)
Tromans, P. S., Anaturk, A. R., Hagemeijer, P.: A New Model for the Kinematics of Large Ocean Waves - Application as a Design Wave. Proc 1st Offshore and Polar Engineering Conference (ISOPE), Vol. 3, pp. 64–71 (1991)
Vidic-Perunovic, J., Jensen, J. J.: Parametric roll due to instantaneous volumetric changes and speed variations. Ocean Engineering 36:891–899 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Jensen, J.J. (2012). Probability of Parametric Roll in Random Seaways. In: Fossen, T., Nijmeijer, H. (eds) Parametric Resonance in Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1043-0_5
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1043-0_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1042-3
Online ISBN: 978-1-4614-1043-0
eBook Packages: EngineeringEngineering (R0)