Research on second level of vulnerability criteria of parametric rolling with stochastic stability theory

Abstract

The second level of vulnerability criteria of parametric rolling proposed by the International Maritime Organization (IMO) is aimed to evaluate the probability of roll instability and large roll motion of ships in the designated sea areas. Compared with the numerical simulation in random waves, the stability boundary derived from the criteria has large errors. Some additional checks are required in the key region. A new method is proposed to assess ship parametric roll in the designed sea area based on stochastic stability theory. A nonlinear system has the same stability properties as its equivalent linear system. Therefore, the nonlinear parametric rolling motion equation is linearized in order to study its stochastic stability in random waves. Based on the top Lyapunov exponent and the stochastic averaging theory, the expressions for parametric rolling stability boundary are given. The accuracy of these stability boundaries is verified by comparison with numerical simulation. The new method with the stochastic stability boundary can quickly and accurately evaluate the probability of large roll motion of ships in the designated sea areas which illustrates the possibility of improvement to a certain extent.