Extreme nonlinear ship response estimations by active learning reliability method and dimensionality reduction for ocean wave

An efficient extreme ship response prediction approach in a given short-term sea state is devised in the paper. The present approach employs an active learning reliability method, named as the active learning Kriging + Markov Chain Monte Carlo (AK-MCMC), to predict the exceedance probability of extreme ship response. Apart from that, the Karhunen-Loève (KL) expansion of stochastic ocean wave is adopted to reduce the number of stochastic variables and to expedite the AK-MCMC computations. Weakly and strongly nonlinear vertical bending moments (VBMs) in a container ship, where the former only accounts for the nonlinearities in the hydrostatic and Froude-Krylov forces, while the latter also accounts for the nonlinearities in the radiation and diffraction forces together with slamming and hydroelastic effects, are studied to demonstrate the efficiency and accuracy of the present approach. The nonlinear strip theory is used for time domain VBM computations. Validation and comparison against the crude Monte Carlo Simulation (MCS) and the First Order Reliability Method (FORM) are made. The present approach demonstrates superior efficiency and accuracy compared to FORM. Moreover, methods for estimating the Mean-out-crossing rate of VBM based on reliability indices derived from the present approach are proposed and are validated against long-time numerical simulations.