Grey-box models for wave loading prediction

TL;DR

This paper introduces a physics-informed machine learning approach combining Morison's equation with Gaussian process NARX models to improve wave loading predictions on offshore structures, achieving significant accuracy gains.

Contribution

It develops and compares two grey-box modeling strategies integrating physics and data-driven methods, enhancing prediction accuracy and extrapolative capabilities.

Findings

Residual GP-NARX model reduces NMSE by 29.13% over Morison's equation.

Grey-box models improve extrapolation in low-data scenarios.

The best model combines physics and data for superior wave force prediction.

Abstract

The quantification of wave loading on offshore structures and components is a crucial element in the assessment of their useful remaining life. In many applications the well-known Morison's equation is employed to estimate the forcing from waves with assumed particle velocities and accelerations. This paper develops a grey-box modelling approach to improve the predictions of the force on structural members. A grey-box model intends to exploit the enhanced predictive capabilities of data-based modelling whilst retaining physical insight into the behaviour of the system; in the context of the work carried out here, this can be considered as physics-informed machine learning. There are a number of possible approaches to establish a grey-box model. This paper demonstrates two means of combining physics (white box) and data-based (black box) components; one where the model is a simple summation of the two components, the second where the white-box prediction is fed into the black box as an additional input. Here Morison's equation is used as the physics-based component in combination with a data-based Gaussian process NARX - a dynamic variant of the more well-known Gaussian process regression. Two key challenges with employing the GP-NARX formulation that are addressed here are the selection of appropriate lag terms and the proper treatment of uncertainty propagation within the dynamic GP. The best performing grey-box model, the residual modelling GP-NARX, was able to achieve a 29.13\% and 5.48\% relative reduction in NMSE over Morison's Equation and a black-box GP-NARX respectively, alongside significant benefits in extrapolative capabilities of the model, in circumstances of low dataset coverage.