Applycation of Statistics of Extremes to Predict the Extreme Value of a Response to Ocean Waves from Result of Full Scale Measurement

Abstract

It has been proposed in some papers to apply statistics of extremes to prediction of the extreme value in a long-term distribution of such response as wave induced load from result of full scale measurement. But there is no discussion on the difference between the conventional extremal distribution and that of the largest value among peak values measured by the experiment.Though a short-term distribution of peak values of the response is approximately described by the Rayleigh distribution, a distribution of the largest value is not equal to that of the Rayleigh distribution with a constant parameter. At first, authors study on it and clarify that it is described by the double exponential distribution, which has another character than that of the extremal distribution for the Rayleigh distribution.The extremal distribution of the conventional theory puts the base on the result of random sampling. This sampling condition is not the same as that of measured peak values in the experiment. Considering the difference in sampling, authors lead equations, by which we can calculate the accurate extremal distribution. Supposing such a model which is a group of numberless Rayleigh distributions with parameters described by the Weibull distribution, authors investigate the characteristics of the extremal distribution. The following characters are find out by our study.Speaking strictly, the distribution dose not fit to the double exponential distribution and the Weibull distribution except a limited condition. In general it is approximated by the latter.The distribution varies with sample size of the largest values measured during the experiment. In the case when we predict the extreme value in a long-term distribution from result of a shorter period measurement, it is required to correct the distribution counting for the sample size.Regarding the above result, authors propose two prediction methods which can estimate the value accurately.