Improved stochastic averaging method using Hamiltonian for parametric rolling in irregular longitudinal waves

Using the stochastic averaging method, the probability density function (PDF) of roll motion for parametric rolling in irregular waves is obtained. In this paper, the stochastic averaging method using Hamiltonian proposed by Dostal is used, and the PDF of roll amplitude and Hamiltonian are derived from the equations of roll motion. In addition, the asymptotic behavior of PDF is investigated to improve the accuracy of the calculation. Furthermore, to improve the applicability of this method, the simulation-based stochastic method is proposed. Compared to the results of the stochastic averaging method proposed by Roberts and Dostal, the results using this improved method show a good agreement. The results are examined for parametric excitation using white noise as well as colored noise. Moreover, the relationship between the scale parameter and the PDF is theoretically analyzed and formulated.