Application of linear filter and moment equation for parametric rolling in irregular longitudinal waves

Publikationstyp
Journal Article
Date Issued
2022-09-12
Sprache
English
Author(s)
Maruyama, Yuuki  
Maki, Atsuo  
Dostal, Leo  
Umeda, Naoya  
Institut
Mechanik und Meerestechnik M-13  
TORE-URI
http://hdl.handle.net/11420/13655
Journal
Journal of marine science and technology  
Volume
27
Issue
4
Start Page
1252
End Page
1267
Citation
Journal of Marine Science and Technology (Japan) 27 (4): 1252-1267 (2022)
Publisher DOI
10.1007/s00773-022-00903-8
Scopus ID
2-s2.0-85137941599
Publisher
Springer
Parametric rolling is one of the dangerous dynamic phenomena. To discuss the safety of a vessel when a dangerous phenomenon occurs, it is important to estimate the probability of certain dynamical behavior of the ship with respect to a certain threshold level. In this paper, the moment values are obtained by solving the moment equations. Since the stochastic differential equation (SDE) is needed to obtain the moment equations, the autoregressive moving average (ARMA) filter is used. The effective wave is modeled using the 6th-order ARMA filter. In addition, the parametric excitation process is modeled using a non-memory transformation obtained from the relationship between GM and wave elevation. The resulting system of equations is represented by the 8th-order Itô stochastic differential equation, which consists of a second-order SDE for the ship motion and a 6th-order SDE for the effective wave. This system has nonlinear components. Therefore, the cumulant neglect closure method is used as higher-order moments need to be truncated. Furthermore, the probability density function of roll angle is determined using moment values obtained from the SDE and the moment equation. Here, two types of the probability density function are suggested and have a good agreement.
Subjects
Cumulant neglect
Linear filter
Moment equation
Parametric rolling
Stochastic differential equation
DDC Class
600: Technik