PARAMETER IDENTIFICATION OF NONLINEAR ROLLING MOTION IN RANDOM SEAS

The concept of the random decrement has been used successfully in the damping identification of linear systems. The formulation of the random decrement existing in the literature is based on the assumption that the dynamic system if linear, time invariant and subjected to Gaussian white noise excitation. Thus, one can use the principle of superposition if formulating the equation for the random decrement. In this paper, the concept of the random decrement is extended to nonlinear systems. The equation governing the random decrement is derived for a ship performing rolling motion in random beam waves. It is shown that this equation is similar to the equation of free rolling in beam waves. It is also shown that the Gaussian white noise, satisfies a linearized free roll equation. These equations are then used to identify the parameters of the nonlinear rolling equation. This method would be particularly useful in determining the value of the metacentric height for a ship rolling under the action of unknown random excitations effected by random waves. This is the first step towards formulating a procedure for the identification of the parameters in the differential equation describing the nonlinear rolling of a ship subjected to an unknown realistic sea.