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Prediction of Extreme Responses from Limited Data


Report No. : 
RMS-36
Authors: 
P.R. de Jong
Authors: 
S.R. Winterstein
Published: 
May 1999
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The main objective of this thesis is to study procedures to estimate statistics of extreme responses to random excitation. Various methods are applied to predict the extreme statistics of the horizontal offset of a spar buoy, consisting of 3 dominant frequency bands; resonant surge, resonant pitch, and wave frequency response. In order to study the effect of limited data, both 1 hour of model test data and 36 hours of computer simulated data were analyzed. Gumbel, standard Weibull, quadratic Weibull, and Hermite models were fitted using the method of moments. The local peaks of the components of the response appeared to be well described by the Rayleigh model (of which the Weibull is a generalization) when fitted to the simulated data. The distribution of the total response being a mixture of 3 Rayleigh distributed variables was better described by the Hermite (local peaks) and Gumbel distributions (global peaks). For the observed 1 hour of data, the distributions of the components seemed considerably more narrow and "pinched". We show this to be largely due to the effect of limited data, which biases the higher moments in particular. However, it is not unlikely that limitations of the computational model account partly for this discrepancy. Estimates of the uncertainty in our predictions were made using non-parametric bootstrapping, which were compared to results from simulation. The results suggest that computer simulations provide good results, while non-parametric bootstrapping appears to be less suitable to estimate statistics of extremes. In addition, it appears that for all models the uncertainty in the predictions of the mean max can be reduced by dividing the limited data into short-duration segments, from which many estimates of the mean max can be made by extrapolating a fitted model.