Identification of passive state-space models of strongly frequency dependent wave radiation forces

This paper describes a methodology for obtaining passive state space representations of wave radiation forces for floating bodies with zero forward speed oscillating in multiple degrees of freedom. The method is based on fitting rational transfer functions written on pole-residue form to radiation frequency responses calculated using standard boundary element codes. Determination of poles and residues is facilitated by the vector fitting algorithm, originally developed for fitting of frequency responses of electrical networks. Using the poles and residues as parameters in the fitting has advantages over the more common ratio-of-polynomials transfer function formulation when the model order is high, which is typically required when the frequency dependence is strong and wide-banded such as for multibody floating systems. A methodology for perturbing the residues of slightly non-passive systems such that they become passive is also presented. The method is demonstrated successfully for a five-body wave energy converter, an array of circular cylinders and a single cylinder. A discussion and investigation of the truncation of high frequencies is provided for the wave energy converter, and parameter constraints governing the extrapolation of the rational model above the frequencies present in the dataset are suggested.