Variation in short-term ice-induced load amplitudes on a shipʹs hull and related probability distributions

The ice conditions, together with the physical and mechanical properties of the ice encountered by a ship, can change rapidly. As these affect the ship–ice interaction process, the magnitude of the ice-induced loads changes significantly even in the short term. Therefore the ice-breaking process is known to be a stochastic process, which should be studied statistically. Earlier studies indicate that the exponential, lognormal, and Weibull probability distributions would be the best probability distributions to describe the short-term ice-induced load measurements on the shipʹs hull. Furthermore, the standard deviation of the measured ice-induced load histograms has been observed to increase in linear fashion as a function of the mean value of the measured ice-induced load histograms. In addition, the inverse coefficient of variation of these histograms has been observed to decrease exponentially as a function of the measured maximum ice-induced loads. udy in this paper focuses on the statistical analysis of ice-induced loads. At first, the effect of the inverse coefficient of variation on the behaviour of the exponential, lognormal, and Weibull probability distributions is presented briefly. Then it is shown that the close-to-linear relation that exists between the mean value and standard deviation of the measured ice-induced load histograms can be explained by analysing the calculation methods for mean values and standard deviations. In addition, it is shown that the exponential-type relation between the inverse coefficient of variation and the measured maximum value can be explained similarly using the defined nature of the standard deviation and mean value. The effect of the threshold used in the full-scale measurements on these values is also studied and discussed in the paper.