A Simplified Estimation of Long-Term Distributions of Various Random Variables Induced by Ocean Waves, and a Study on the Influences of Operating Conditions on the Extremes

Abstract

It has been shown in the previous paper, that the extreme value in the long-term distribution of wave bending moment expected to be exceeded with the probability of 10^-8 or near order is ruled by only probability of encounter of one or at most several severe wave conditions. This is caused by the composition of the long-term distribution of it. The distribution is composed by various short-term distributions which are described by the Rayleigh distribution.
In this paper, it is shown that the extreme values in the long-term distributions of such various random variables as wave shearing force, various wave loads, pitching and rolling angles, heaving amplitude, various accelerations caused by ship motions etc., which have the same composition as that of wave bending moment, have the same character. And a new simplified method of estimating the extreme values with high accuracy is suggested.
The method not only simplifies the calculation, but also can be applied to the analysis of relation between the extreme values and various factors which have influences on the values. As examples of the application of the method, the influences of operating conditions such as change of course or ship speed in rough seas, etc., and wave conditions, on the extreme values are analyzed in detail. Judging from the foregoing studies, it is concluded that the extreme values are to be estimated on assumed operating condition that the ship sails always heading sea course at very low speed (heave to condition) in short crest irregular waves.