Maximum roll angle estimation of a ship in confused sea waves via a quasi-deterministic approach

This paper considers the maximum roll motion of a ship in confused sea waves. The ship motion is described by a nonlinear differential equation including quadratic damping and cubic restoring force. The excitation of the ship is represented by a stationary mean-zero Gaussian process of a given power spectral density function. It is shown that a reliable estimate of the maximum roll motion is found considering the ship response to an approximate deterministic representation of an appropriately large and adequately rich (frequency-wise) load. Specifically, the time variation of the load is approximated by a normalized autocovariance function; the maximum amplitude of the load is taken as a certain multiple of the standard deviation of the stochastic load process. This approximation relates to the method of quasi-deterministic representation of extreme realizations of a stationary Gaussian process; the method is interpreted as a tool for generating deterministic time histories of the load which are compatible with a certain power spectral density function. The efficacy of this perspective is shown by comparison with the results from pertinent Monte Carlo simulations. Next, the paper addresses the ship stability problem in the space of initial conditions. In this context, it shows that the proposed approximation can be adequately utilized for a ship safety assessment.