Nonparametric Identification of Nonlinear Added Mass Moment of Inertia and Damping Moment Characteristics of Large-Amplitude Ship Roll Motion

Abstract

This study aims to investigate the nonlinear added mass moment of inertia and damping moment characteristics of large-amplitude ship roll motion based on transient motion data through the nonparametric system identification method. An inverse problem was formulated to solve the first-kind Volterra-type integral equation using sets of motion signal data. However, this numerical approach leads to solution instability due to noisy data. Regularization is a technique that can overcome the lack of stability; hence, Landweber’s regularization method was employed in this study. The L-curve criterion was used to select regularization parameters (number of iterations) that correspond to the accuracy of the inverse solution. The solution of this method is a discrete moment, which is the summation of nonlinear restoring, nonlinear damping, and nonlinear mass moment of inertia. A zero-crossing detection technique is used in the nonparametric system identification method on a pair of measured data of the angular velocity and angular acceleration of a ship, and the detections are matched with the inverse solution at the same discrete times. The procedure was demonstrated through a numerical model of a full nonlinear free-roll motion system in still water to examine and prove its accuracy. Results show that the method effectively and efficiently identified the functional form of the nonlinear added moment of inertia and damping moment.