New extreme statistics strategy for the extreme value predictions of ship parametric rolling motions through limited model test observations

Abstract

This work proposes a new extreme statistics strategy to predict the extreme parametric rolling angle through minimal observations from model tests. The core of this strategy is a new synthetic moment method. Based on the Hermite transformation and the Markov chain, the synthetic moment method can provide extreme value predictions for stationary processes. Besides, this work introduces one specific simplification to solve the problem induced by the non-stationarity of the parametric roll. With the help of the new extreme statistics strategy, this work obtains the CDF and PDF of the extreme parametric rolling angle for the C11 container ship. These predictions are derived from only one observed model test time history. The data statistics of other model tests and a vast amount of numerical simulations verify the validities of these predictions. Compared with other methods, the new strategy shows advantages for small sampling predictions. It is possible to replace the widely used ACER method in case of insufficient samples. In addition, further research confirms that the new strategy's intrinsic probability model differs from the widely used GEV model, which is more reasonable for extreme value predictions in a finite time range. The newly presented strategy should effectively predict the extreme value for other complicated stochastic responses.