Bivariate statistics of wind farm support vessel motions while docking

Abstract

Robust prediction of extreme motions during wind farm support vessel (WFSV) operation is an important safety concern. In particular, it is important to study safety of operation in random sea conditions during WFSV docking against the wind tower, while workers are able to get on to the tower. Docking is performed by thrusting the vessel fender against the wind tower (the alternative docking maneuver by hinging is not studied here). In this paper, the finite element software AQWA has been used to analyze the vessel response due to hydrodynamic wave loads, acting on a specific maintenance ship under actual sea conditions. Excessive motions may occur during certain sea conditions, posing a risk to the crew transfer operation. The authors have primarily focused on the statistical analysis rather than the dynamics of the problem. This paper presents a novel method for estimating bivariate statistics, based on Monte Carlo simulations (or measurements if available). The bivariate average conditional exceedance rate (ACER2D) method is briefly outlined. The ACER2D method offers an accurate estimation of bivariate statistics, utilizing the available data efficiently. Two dimensional probability contours, corresponding to large return periods, are obtained by the ACER2D method. Based on the overall performance of the presented method, it is seen that the ACER2D method provides an efficient and accurate prediction of extreme return period contours. The described approach may serve as a useful tool for vessel design, facilitating optimization of boat parameters in order to minimize excessive vessel motions.

A novel method for prediction of extreme wind speeds across parts of Southern Norway

“…Note that Eq. 5 is similar to the well-known mean upcrossing rate equation for the probability of exceedance (Gaidai et al, 2020;Gao et al, 2020;Naess and Gaidai, 2009). There is evident convergence with respect to the conditioning parameterk:…”

“…Note that the authors have successfully verified the accuracy of the Naess-Gaidai extrapolation model in previous years for a large variety of one-dimensional dynamic systems (Gaidai et al, 2020;Gao et al, 2020;Naess and Gaidai, 2009;Sun et al, 2022).…”

“…} for j ≥ k will be independent of j but only dependent on conditioning level k. Thus non-exceedance probability can be approximated as in the Naess-Gaidai method, see (Naess and Gaidai, 2009;Gaidai et al, 2018;Gaidai et al, 2020;Gao et al, 2020) where:…”

“…However, the experimental or computational cost may be unaffordable for many complex dynamic systems in which the long-term statistics of their responses can only be accurately captured using huge data sets. Motivated by the latter argument, the authors have introduced a novel reliability method for environmental systems that uses the average conditional exceedance rate (ACER) method (Naess and Gaidai, 2009;Gaidai et al, 2020;Gao et al, 2020;Sun et al, 2022) for statistical extrapolation to reduce either measurement or computational costs. Extreme value statistics has been a topical matter for some time now, and there are some excellent reviews on the topic, see (Hansen, 2020;Majumdar et al, 2020).…”

“…The weight function ω can be defined as ω(λ) {ln CI + (λ) − ln CI − (λ)} −2 with (CI − (λ), CI + (λ)) being a confidence interval (CI), empirically estimated from the simulated or measured dataset, see (Gaidai et al, 2020;Gao et al, 2020;Naess and Gaidai, 2009). When the parameter c lim k → ∞ c k is equal or close to 1, the distribution approaches to the Gumbel distribution.…”