In this paper we show how a new idea for how to calculate the derivatives of extrapolated 50-year return values, used in extreme load safety criteria, can be used to estimate the uncertainty in these return values resulting from uncertainty in the simulations and in the load extrapolation procedure itself. The method yields uncertainty estimates with a high degree of accuracy. Additionally, to highlight one of the subtler uncertainties involved in this setting, we also make a small study of how changing the block size used in the extraction of maxima from load time series affects the 50-year return value.


Finding ways to reduce the cost of offshore wind turbine support structures is one of the main objectives of current research on this topic. One of the main challenges involved in cost reduction of structures is the balance between measures that reduce the resistance to loading (like e.g. lighter designs) and the safety requirements. A primary reason for the difficulty posed by this balance is the large amount of uncertainties in the analysis. On the load side there are a lot of uncertainties coming from various sources such as measurements, local variations within windfarms and simplified modeling of the environment. In the structure there are uncertainties such as those related to the production of components and to simplified structural models. The usual solution to this issue is to make designs that are very conservative, scaling preliminary designs as dictated by analysis by large safety factors. Hence, increased knowledge about uncertainty could potentially enable designers to be less conservative and make more economical choices.

Extreme load, or Ultimate Limit State (ULS), criteria present a particular challenge for uncertainty analysis due to the way these are evaluated. Chiefly, this is because of the requirement (Det Norske Veritas, 2014) that extreme loads should be the 50-year return values calculated from the loads obtained by simulations. While this is a standard procedure in the design of wind turbines, it is not trivial. It entails fitting the short term maximum loads to extreme value distributions and then extrapolating from these distributions to the 50-year return value. A considerable amount of work has gone into the study of various aspects of the load extrapolation procedure for wind turbines. A comparison of three different approaches, including a process model, was made by Cheng (2002). A study of the effect of turbulence level on the predicted extreme load was performed by Moriarty et al. (2002). A report discussing, among other things, several aspects of extreme load extrapolation, including selection of threshold values, the statistical uncertainty of the fits, details of both short term and long term statistics and possibilities for model simplification was made by Moriarty et al. (2004). Further studies and discussion of various standard and alternative methods for short term fitting and long term extrapolation methods, as well as details of uncertainty, can be found in, e.g., Saranyasoontorn and Manuel (2006), Ragan and Manuel (2007), Agarwal and Manuel (2007), Fogle et al. (2008), Toft and Sørensen (2009), Agarwal and Manuel (2010) and Dimitrov (2016).

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