Theoretical estimation of roll acceleration in beam seas using PDF line integral method

Abstract

The prevention of excessive roll acceleration is one of the fundamental requirements of an oceangoing vessel at sea. In this paper, aiming at this requirement, we propose a new theoretical method for calculating roll angular acceleration, called “PDF line integral method.”. This paper presents the derivation of this method and a numerical comparison with Monte Carlo simulation (MCS) results; also, its validity is shown. Although the utilized GZ curve (restoring curve) exhibits strong asymmetricity, the proposed method can provide for such a condition. With only the information of roll and roll rate joint probability density function (PDF), this method can approximately calculate the roll angular acceleration, which is a high-order differential property. In addition, a relatively good agreement is achieved between the theory and MCS results.