A JOINT PROBABILITY DISTRIBUTION FOR MULTIVARIATE WIND-WAVE CONDITIONS AND DISCUSSIONS ON UNCERTAINTIES

Erik Vanem, E. Fekhari, Nikolay K. Dimitrov, Mark Kelly, Alexis Cousin, Martin Guiton
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Abstract

This paper presents a joint statistical model that has been fitted to data of wind and wave conditions for an offshore location off South Brittany. The data are from a numerical model and contain hourly values for several wind and wave variables over a period of 32 years. The joint distribution presented in this paper considers the variables wind direction, mean wind speed, significant wave height, wave direction and peak period. A conditional model for turbulence given wind speed is introduced to yield an additional variable for the joint model. The joint model is constructed as a product of marginal and conditional models for the various variables. Additionally, the fitted models will be used to construct environmental contours for some of the variables. For significant wave height, various models are used to obtain different extreme value estimates, illustrating the uncertainties involved in extrapolating statistical models beyond the support of the data, and a discussion on the use of non-parametric copulas for the joint distribution is presented. Moreover, bootstrap has been performed to estimate the uncertainty in estimated model parameters from sampling variability. The effect of changing which variable to model as the marginal in a conditional model is illustrated by switching from wind speed to significant wave height. Such joint distribution models are important inputs for design of offshore structures, and in particular for offshore wind turbines, and the influence of the joint model in design is illustrated by a simple case study.
多元风浪条件的联合概率分布及不确定性讨论
本文介绍了一个联合统计模型,该模型与南布列塔尼近海的风浪条件数据相匹配。这些数据来自一个数值模型,包含 32 年间多个风力和海浪变量的小时值。本文提出的联合分布考虑了风向、平均风速、显著波高、波向和峰值周期等变量。在风速条件下,引入了湍流条件模型,为联合模型增加了一个变量。联合模型是各种变量的边际模型和条件模型的乘积。此外,拟合模型将用于构建某些变量的环境等值线。对于巨浪高度,将使用各种模型来获得不同的极值估计值,以说明在数据支持范围之外推断统计模型所涉及的不确定性,并讨论在联合分布中使用非参数共线的问题。此外,还进行了自举法,以估计抽样变异性对估计模型参数的不确定性。通过从风速到显著波高的转换,说明了在条件模型中改变哪个变量作为边际模型的效果。这种联合分布模型是海上结构,特别是海上风力涡轮机设计的重要输入,并通过一个简单的案例研究说明了联合模型在设计中的影响。
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