Consistent State Space Modelling of Hydrodynamic Memory

Abstract

The conventional way to model hydrodynamic memory or radiation force is to use retardation functions. These functions are usually derived from frequency-dependent damping functions that are calculated by a diffraction-radiation code using potential theory. Calculating the retardation functions can be challenging due to lack of information at high frequency. In simulation of wave-driven vessel motion the retardation function is convolved with the velocity to give the wave radiation force, which is time-consuming. The paper describes how the memory effects can be modelled consistently by linear differential equations, such that coupled modes of motion share one set of poles. The coefficients of the differential equations are found by least squares fitting of a certain rational function to the numerical damping function. One advantage of this is that no assumption need to be made about the added mass at infinite frequency. Nor is any conditioning of the given data necessary. Using the fitted model in time-domain simulation is much quicker than using retardation functions. The method is applied to data representing the sway, roll and yaw motions of an FPSO of 238 m length. It was found that a sixth-order differential equation model fitted the given numeric radiation function well. It is shown how the high frequency asymptote for added mass can be estimated with high accuracy, which is valuable when it is not known in advance.