Deriving the absolute wave spectrum from an encountered distribution of wave energy spectral densities

The objective of ship motion-based wave spectrum estimation is to provide the distribution of wave energy densities in absolute domain. However, as a ship generally advances relative to the progressing waves, any spectrum estimate inherently dates back to the encounter domain and, consequently, the spectrum estimate must be transformed to absolute domain. In following sea conditions, spectrum transformation from encounter to absolute domain has no unique (mathematical) solution. This article presents an optimisation-based technique to carry out the particular transformation in following sea conditions. The optimisation relies on an object function established using (wave) spectral moments; calculated directly using the estimated encounter-wave spectrum on the one side and by using a parameterised wave spectrum valid in absolute domain on the other side. The simplicity of the transformation technique is a strength in itself as it leads to an insignificant computational effort in the transformation to absolute domain. Equally important, the specific technique proves capable to provide accurate results in the majority of cases, when comprehensive testings with numerically simulated data of following sea conditions are performed. Furthermore, the technique is tested successfully using experimental full-scale sea trials data.