Long-term Distributions of Extremes on Ship Motions in Ocean Waves

Abstract

In this paper, various types of the long-term distribution of extremes are re-examined by the analysis of the actual ship's data. Authors try to applicate the following probability distributions.1) Logarithmic normal distribution with upper limit.2) Gumbel's extreme distribution with upper limit.(Type III), used by Watanabe2), 3).3) Weibull distribution, used by Nordenström4) etc.Moreover, the estimated extreme values of ship motions are compared with the long-term prediction values calculated by the theoretical method.Data used in this paper are measured by the several full container ships, in North Pacific Ocean, in winter. Consequently, next results are obtained.a) Long-term distribution can be expressed properly by the logarithmic normal distribution with upper limit or the Gumbel distribution with upper limit.b) The logarithmic normal distributions without upper limit give clearely large estimated values compared with the actual ship data. Then, this distribution is not suitable for the estimation of long-term ship motions in ocean waves.c) Obtained extreme values in 100 years, are about ±9 degrees on pitch angle, about ±0.96 g on bow vertical acceleration, about ±31 deg. on roll angle.d) Long-term predictions taking into consideration on the ship operations, coincide with the long-term extreme value estimated from the measured data of short terms.