Accurate ship-motion prediction is important because it is directly related to the design, control, and economic operation of ships. Many methods are available for studying and predicting ship motions, including time-domain, strip-theory, and system-identification-based predictions. Time-domain and strip-theory predictions suffer from several physical and computational limitations. In this work, we use system-identification techniques to predict ship motions. We establish an identification methodology that can handle general finite-degree-of-freedom (FDOF) models of ship motions.

To establish this methodology, we derive the correct form of the equations of motion. This form contains all relevant linear and nonlinear terms.

Moreover, it explicitly specifies the dependence of the linear and nonlinear parameters on the forward speed. The energy-formulation approach is utilized to obtain full nonlinear ship-motion equations. The advantages of using this formulation are that self-sustained motions are not allowed and the dependence of the parameters on the forward speed is derived explicitly.

The data required for the identification techniques are generated using the Large Amplitude Motions Program (LAMP) developed by the Science Applications International Corporation (SAIC). The ship studied in this work is a Series 60 ship, which is a military cargo ship. LAMP data for different sea states and forward speeds are used to identify and predict the ship motions.

For linear parametric identification, we use the Eigensystem Realization Algorithm (ERA) to determine the coefficients in the linearly coupled equations and the effects of the forward speed on these coefficients.

For linear nonparametric identification, we present a new analysis technique, namely, the circular-hyperbolic decomposition (CHD), which avoids the leakage effects associated with the discrete Fourier transform (DFT). The CHD is then utilized to determine transfer functions and response amplitude operators (RAOs).

For nonlinear parametric identification, we present a methodology that is a combination of perturbation techniques and higher-order spectral moments.

We apply this methodology to identify the nonlinear parameters that cause parametric roll resonance. The level of accuracy of the models and the parameter estimates are determined by validations of the predicted ship motions with the LAMP data.