Identification of Nonlinear Wave Forces Using Gaussian Process NARX Models

It has long been known that the standard equation-Morisons equation-for the prediction of fluid loading forces on slender members, is inadequate outside a fairly narrow regime of wave conditions. There have been many attempts to improve on Morisons equation over the years, including a number based on nonlinear system identification. Some years ago, the current first author, together with collaborators, proposed an identification methodology based on polynomial NARMAX/NARX models. The objective of the current paper is to update that methodology, taking into account modern practice in machine learning. In particular, an approach based on Gaussian process NARX models will be demonstrated, which has the advantage of bypassing the polynomial structure detection problem and also of providing natural confidence intervals for predictions. The approach will be demonstrated on real data for wave forces in a directional sea. The current paper will also take the opportunity to critically highlight a number of weaknesses of the original study in the light of modern best practice in machine learning.