Calibration of response amplitude operators based on measurements of vessel motions and directional wave spectra

A vessel's response to waves is dependent on a large number of parameters, some of which are both frequency and direction dependent. To predict vessel response, these parameters are used to construct response amplitude operators (RAOs) that act as transfer functions between the directional wave spectra and the motion spectra of the vessel. In particular situations, however, vessel motions predicted using RAOs calculated with general-purpose radiation-diffraction codes and measured wave spectra are found to deviate from measured vessel responses. To address this problem, a methodology for calibrating RAOs based on measurements of the directional wave spectra and vessel motions is proposed. Use is made of a vector fitting method through which the frequency dependent hydrodynamic properties of the vessel can be approximated by a ratio of two polynomials, thus greatly reducing the number of parameters that need to be calibrated. The reduced set of parameters is subsequently related to previously identified causes of RAO inaccuracy in order to arrive at optimization algorithms for identifying more accurate RAOs from the measurements. It is shown that the RAOs can be improved with accuracy in situations where the discrepancies are caused by imprecise estimates for the vessel's radii of gyration, center of gravity, or viscous damping. When the discrepancies in the RAOs are related to the potential mass, damping and wave forces, however, the problem becomes highly non-convex and it is not possible to find a unique RAO that satisfies the data.