

The forms of the roll damping force and restoring force need to be known a priori the corresponding coefficients in the roll damping force are determined by the free roll decay model test. Various models of roll motion containing nonlinear terms in the damping force and restoring force have been studied by many researchers, such as Taylan (2000), De Kat and Paulling (1989), and Ahmed et al. Roll damping is too complex to be solved analytically because of viscous effects. The roll motion has more influence on capsizing and is significantly influenced by fluid viscosity compared with the other motions. A ship can experience three types of displacement motions (surge, sway, and heave) and three types of angular motions (roll, pitch, and yaw). Introduction Safety against the capsizing of a ship is very important. Results show that the MCMC method is an effective way to identify roll damping and nonlinear restoring forces from free roll decay. Reconstructed roll histories are compared with ones from both the earlier work of the authors and the computational fluid dynamics method. The conditional expectation and covariance of the conditional component distribution used in the Gibbs sampler are derived directly in the matrix-vector form by using an analytic inversion formula. In the nonparametric identification of roll damping and nonlinear restoring forces, the nonlinear Volterra integral equation of the first kind is solved by the Markov chain Monte Carlo (MCMC) method. Here, the stochastic inverse method is introduced, and a new nonparametric approach is adopted to identify roll damping and nonlinear restoring forces from a free roll decay simulation, which is carried out by the Reynolds-averaged Navier-Stokes method and overset mesh technology. To identify them from free roll decay behaviors, the models are generally assumed to be known a priori.

Roll damping and nonlinear restoring forces have an important influence on ship roll motion.

