THE SPAR MODEL: A NEW PARADIGM FOR MULTIVARIATE EXTREMES. APPLICATION TO JOINT DISTRIBUTIONS OF METOCEAN VARIABLES

Ed Mackay, Callum Murphy-Barltrop, Philip Jonathan
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Abstract

This paper presents the application of a new multivariate extreme value model for the estimation of metocean variables. The model requires fewer assumptions about the forms of the margins and dependence structure compared to existing approaches, and provides a flexible and rigorous framework for modelling multivariate extremes. The method involves a transformation of variables to polar coordinates. The tail of the radial variable is then modelled using the generalised Pareto distribution, with parameters conditional on angle, providing a natural extension of univariate theory to multivariate problems. The resulting model is referred to as the semi-parametric angular-radial (SPAR) model. We consider the estimation of the joint distributions of (1) wave height and wave period, and (2) wave height and wind speed. We show that the SPAR model provides a good fit to the observations in terms of both the marginal distributions and dependence structures. The use of the SPAR model for estimating long-term extreme responses of offshore structures is discussed, using some simple response functions for floating structures and an offshore wind turbine with monopile foundation. We show that the SPAR model is able to accurately reproduce response distributions, and provides a realistic quantification of uncertainty.
Spar 模型:多变量极值的新范例。应用于海洋变量的联合分布
本文介绍了一种新的多元极值模型在计量海洋变量估算中的应用。与现有方法相比,该模型对边际形式和依赖结构的假设较少,为多元极值建模提供了一个灵活而严谨的框架。该方法涉及将变量转换为极坐标。然后使用广义帕累托分布对径向变量的尾部进行建模,参数以角度为条件,从而将单变量理论自然扩展到多变量问题。由此产生的模型被称为半参数角度-径向(SPAR)模型。我们考虑估算 (1) 波高和波长周期以及 (2) 波高和风速的联合分布。结果表明,SPAR 模型在边际分布和依赖结构方面都能很好地拟合观测结果。我们利用浮动结构和带单桩基础的海上风力涡轮机的一些简单响应函数,讨论了如何利用 SPAR 模型估算海上结构的长期极端响应。我们的研究表明,SPAR 模型能够准确再现响应分布,并对不确定性进行实际量化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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