Statistical analysis of parametric roll in irregular seas on clusters with large roll amplitudes

Abstract

The statistical evaluations on the numerical and experimental parametric roll time series in long-crest irregular heading waves are conducted. In the time series of parametric roll under irregular seas, strong “grouping phenomenon” or “cluster structures” can be observed. A pick-out procedure based on parametric roll detection scheme is applied to get the clusters with large roll amplitudes to form the truncated realizations. The statistical properties of the truncated realizations are investigated and compared with those of the original realizations. It is found that the confidence bands of variances of the truncated realizations are significantly larger than those of the original realizations, which indicates that the truncated realizations, i.e. the clusters with large roll amplitudes, are more dependent and narrow-banded than the original realizations. The distribution of the truncated realization is close to normal distribution with the kurtosis slightly larger than the normal distribution, while the distribution of the original realization is leptokurtic with sharp peak and thick tail. The kurtosis of the truncated realizations can be viewed as the lower limit of kurtosis for the possible distribution of the parametric roll. The estimated lower limit of kurtosis with 95% confidence interval can be given approximately as 3.650 ± 0.127.