Extreme Value Estimation of Mooring Lines Top Tension

Abstract

It is known that the mooring system of floating platforms responds non-linearly to environmental loads. Even though the wave-frequency excitation can be assumed as a Gaussian process, the line tension generally is not a Gaussian process due to the second-order slow-drift floater motions and the nonlinearities of the system itself. Distinct short-term time-domain analyses with the same wave spectrum excitation, i.e., distinct realizations of the response process, lead to a set of distinct values for the simulated individual maximum observed line tensions. Therefore, the ideal practice for estimating extreme tension values should be to perform a sufficiently large number of independent simulations along with an extreme statistical analysis considering the sample of the maximum line tension identified in each simulation. However, this process can be very time-consuming and cumbersome for everyday design applications. In this paper, the short-term line tension is assumed to be a non-Gaussian ergodic process. The extreme tension is then estimated based on the peaks sample of just a single simulated tension time-history. A number of known probability distributions are fitted to the peaks of the time series and classic order statistics theory is applied to determine the most probable extreme line tension corresponding to a specified short-time period (3-h) in order to identify the one with best performance. The proposed probability distribution models for the tension peaks are the 3-parameter Weibull distribution, the Weibull distribution fitted to the tail of the data (Weibull-tail) and the Shifted Generalized Lognormal Distribution (SGLD). The estimated extreme values are also prone to uncertainties due to time-domain simulation details. The effects of the major parameters in the dynamic analysis, such as simulation length and discretization level of the wave spectrum, are therefore investigated using several simulated mooring line tension time-histories. Furthermore, the effect of correlation between consecutive line tension peaks in the extreme values estimation is investigated through a Nataf transformation-based model for joint probability distribution for the peaks and the one step Markov chain condition. It is shown that this latter consideration leads to extreme value estimates that are invariably smaller than those obtained by standard order statistics. These estimates are also shown to be closer to the extreme estimates directly obtained from a sample of largest values taken from several distinct numerical simulations. Numerical examples cover two study cases for mooring lines belonging to FPSO (Floating, Production, Storage and Offloading) units to be installed in Brazilian waters.