Efficient Estimation of Temporal Exceeding Probability for Ship Responses in Broad-Band Wave Fields

Calculating extreme ship statistics is critical for ship design. This study aims to determine the temporal exceeding probability, i.e., the percentage of time a ship's response exceeds a threshold, as it navigates through an irregular broad-band wave field. Direct simulations are often infeasible due to the rarity of extreme events, high dimensionality of wave fields, and the computational expense of numerical models. To mitigate these challenges, we parameterize the wave field and simulate only the most informative groups using natural initial conditions (starting the simulation from several cyclic waves ahead). We adopt a Bayesian experimental design approach, leveraging the uncertainty in a Gaussian process surrogate model to define an acquisition function for sequentially selecting the next best sample, thus reducing computational costs. The approach's effectiveness is demonstrated through different wave parametrization thresholds and ship responses' thresholds using a nonlinear roll equation.