Session: 06-07-01 Metocean, Measurement and Data Interpretation

Submission Number: 155197

Deep Learning Joint Extremes of Metocean Variables Using the SPAR Model 

This paper presents a novel method for estimating joint extremes of metocean variables in two or more dimensions. The method is based on the semi-parametric angular-radial (SPAR) model, introduced at OMAE 2024 [1]. After a transformation to angular-radial coordinates, the problem of modelling multivariate extremes is transformed to one of modelling an angular density, and the tail of a radial variable, modelled conditional on angle. In the SPAR approach, the tail of the radial variable is modelled using a generalised Pareto (GP) distribution, providing a natural extension of univariate extreme value theory to multivariate settings. In this work we show how the method can be applied in higher dimensions, using a case study for five metocean variables: wind speed, wind direction, wave height, wave period and wave direction. The angular density is modelled using a mixture of von Mises-Fisher distributions, fitted using an expectation-maximisation (EM) algorithm. The parameters of the GP model for the conditional radial distribution, are estimated using a neural network. This provides great flexibility in the dependence structures that can be represented, together with computationally efficient routines for training the model. The application of the method requires fewer assumptions about the properties of the distributions of the variables, compared to other available methods. Using various diagnostic plots, we show that the fitted models provide an excellent description of the joint extremes of the dataset. The uncertainties in the predicted extreme conditions are also discussed.

[1] E Mackay, CJR Murphy-Barltrop, P Jonathan. "The SPAR Model: A New Paradigm for Multivariate Extremes. Application to Joint Distributions of Metocean Variables". Proc OMAE 2024, Singapore

Presenting Author: Edward Mackay University of Exeter

Presenting Author Biography: Ed Mackay is a member of the Renewable Energy Group at the University of Exeter. His research interests include statistical modelling of extreme environments and the interaction with offshore structures.