Efficient Estimation of Extreme Roll Motion of Ships

Ju Hyuck Choi

Research output: Book/ReportPh.D. thesis

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The main purpose of the thesis is to develop calculation procedures to efficiently estimate the probability associated with the exceedance of roll angles above given threshold values for a ship sailing in waves. According to the second generation intact stability criteria (IMO SLF 51/WP.2, 2008), various failure modes due to rolling must be checked in the design and operation of ships. In the present work, two different failure modes are considered; parametric roll in longitudinal waves and roll motion in dead ship condition.
The First Order Reliability Method (FORM) has previously been found useful for extreme value prediction of stationary stochastic time domain processes (Der Kiureghian, 2000; Jensen, 2007; Jensen et al., 2014), and provides the basis for the present thesis.
In this study, attempts have been made to increase the prediction accuracy, applying a numerical models for time domain roll simulation. Specifically, wave-induced roll motions are analyzed by the application of numerical procedures based on a six-degrees-of-freedom (6-DOF) model and a (simpler) single-degree-of-freedom model. The 6-DOF model using the impulse response function (IRF) approach requires more computational effort compared to the simplified 1-DOF model. Especially for extreme value statistics, this can be prohibitively expensive. However, the advantages of the FORM procedure enable the use of a 6-DOF model and the IRF approach.
Regarding the probabilistic assessment of roll motion, the three most important aspects are: 1) the reliability index β, 2) the Poisson assumption for extreme value statistics and 3) the mean upcrossing rate. The reliability index β is a measure of the point-wise probability. The Poisson assumption makes it possible to express the extreme value statistics through the mean upcrossing rate, and therefore, the mean upcrossing rate can be interpreted as an equivalent measure to ‘probability of exceedance per time unit’. The major effort of the project has been to improve each of the aspects above.
It has been found that the reliability β from the FORM procedure is accurate when compared to the Second Order Reliability Method (SORM) and Monte Carlo Simulation (MCS). In addition, the FORM procedure has been found to be efficient for finding the reliability index β. For dead ship condition, it has been found that the FORM linearization yields accurate extreme value predictions. On the contrary, for parametric roll responses, the mean upcrossing rate and the Vanmarcke’s factor obtained through the FORM linearization may lead to some error in extreme value predictions. Therefore, an alternative expression of the mean upcrossing rate for parametric roll has been suggested. From a statistical analysis using MCS, the alternative model has been validated to be accurate and efficient. It is also validated from the statistical analysis that the extreme roll peaks can be assumed to be un-correlated, hence, the Poisson model can be practically used without applying Vanmarcke’s factor.
As an application example, the capsize probability in dead ship condition for a small ferry was evaluated using the present procedure. Two different GM values were considered, one based on the IMO weather criterion and one using only the standard IMO intact stability rules. It was found that the minimum GM-requirement by the IMO weather criterion is too conservative, and rather ranges of allowable GM values should be applied in agreement with e.g., Erichsen et al. (2015).
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages167
ISBN (Electronic)978-87-7475-537-1
Publication statusPublished - 2018
SeriesDCAMM Special Report


  • Parametric roll
  • Roll motion in dead ship condition
  • 6-DOF
  • IRF approach
  • FORM
  • SORM
  • MCS
  • Mean upcrossing rate
  • Vanmarcke’s factor
  • Poisson model
  • Probabilistic response assessment
  • Extreme value statistics
  • The second generation of intact stability criteria
  • The weather criterion

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