Abstract
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.
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Notes
- 1.
The acronym NARMAX stands for Nonlinear Auto-Regressive Moving Average with e(X)ogenous inputs. The model accounts for process dynamics via the AR part, and noise dynamics via the MA. If one neglects the noise model by assuming that the noise is white Gaussian, the overall model is denoted NARX.
- 2.
Within other sectors of the system identification community, a different terminology is commonly adopted; it is often the case that computing the OSA predictions is simply referred to as prediction, while computing the MPO predictions is referred to as simulation. This is a little unfortunate, but the authors will continue with the OSA/MPO terminology to ensure consistency with their previous work.
- 3.
The coefficients of the noise model terms are not included in the table. The noise terms are only included in the model as a means of reducing parameter estimation bias, they are not used in making predictions.
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Acknowledgements
The authors would like to thank Ramboll Oil and Gas, Denmark, for financial support for TR; they would also like to specifically thank Dr Ulf Tyge Tygeson for various useful discussions regarding wave loading.
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Worden, K., Rogers, T., Cross, E.J. (2017). Identification of Nonlinear Wave Forces Using Gaussian Process NARX Models. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-54404-5_22
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