Non-standard stochastic averaging of large-amplitude ship rolling in random seas

L. Dostal, E. Kreuzer, N. Sri Namachchivaya

Research output: Contribution to journalArticlepeer-review


The current intact stability criteria for ships do not account for their dynamic behaviour in irregular waves sufficiently. We provide analytical criteria for ship and sea state parameters that indicate large roll amplitudes or capsizing and determine the mean time for these events. These results can be used to formulate vulnerability criteria for the occurrence of parametric roll. We use reduced order models in order to perform an analytical analysis to this complicated problem. Therefore, we study the dynamics of a ship in random seas as a perturbation of a Hamiltonian system. The random process across the energy levels of the Hamiltonian system is approximated by a Markov process, which is obtained by stochastic averaging. The noise owing to wave excitation is a nonwhite stationary stochastic process. This is an extension to previous results, where white noise excitation was used.

Original languageEnglish (US)
Pages (from-to)4146-4173
Number of pages28
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2148
StatePublished - Dec 8 2012


  • Duffing oscillator
  • Parametric roll
  • Random seas
  • Ship dynamics
  • Stochastic averaging

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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