On Prediction of Extreme Values

Abstract

This paper discusses the prediction of the extreme values of a stationary random process having an arbitrary bandwidth spectrum. Formulas to predict the extreme values are derived for a given number of observations and time by applying order statistics, and the effect of bandwidth of spectrum on the extreme values is discussed. The most probable extreme value and the extreme value for a preassigned probability of being exceeded are obtained. The estimation formulas are applied to predict the extreme value of the pitching motion and acceleration of a ship in irregular seas and waves generated in a towing tank. It is found that the extreme values observed in model experiments fall fairly well in the vicinity of the predicted most probable values. Theoretically, however, the chance that the extreme value will exceed the most probable value is rather high. Hence, the extreme value for a preassigned probability of being exceeded appears to be appropriate for ship (or marine structure) design consideration.