This paper presents a novel two-step hydrodynamic coefficients identification method to identify the damping and restoring moment coefficients of ship roll motion in irregular waves. The random decrement technique (RDT) is first used to convert the responses into random decrement signatures. Then, a Hilbert transform (HT)-based nonlinear system identification method is used to identify the damping and restoring moment coefficients from the obtained random decrement signatures. Numerical studies were performed on two ship models with simulated data. The results show that the proposed method can successfully identify the hydrodynamic coefficients of roll motion using the vibration responses of ships in irregular waves.


The rolling motion of a ship under wave excitation is an important factor affecting the safety and operability of the ship; therefore, accurately determining the nonlinear characteristics of the rolling motion is the key to ship design. Researchers have done a lot of research on the rolling motion of ships, and established various hypothetical models using the nonlinear terms of the determined damping and return moments (Wright and Marshfield, 1979; Morrall, 1980; Chan et. al, 1995.). However, different formulations of nonlinear damping and restoring moment may lead to completely different roll amplitudes (Taylan, 2000), which may result in different ship stability characteristics. Non-parametric methods are non-linear recovery and damping moment models that are not based on any assumptions. This approach reduces many uncertainties. Therefore, it is necessary to develop some non-parametric methods to identify the rolling motion equations.

Inverse techniques are used to solve this problem. For example, Mahfouz (2004) uses Random Decrement Technique (RDT) and neural networks to identify the parameters related to the description of the ship rolling motion. Jang et. al (2010) identified the functional form of the nonlinear roll damping and restoring moment using a deterministic inverse method. In these studies, the roll motion problem is transformed into an identification problem, which aims to identify the parameters that control the characteristics of a given dynamic system.

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