Design loads for wave impacts -- introducing the Probabilistic Adaptive Screening (PAS) method for predicting extreme non-linear loads on maritime structures

Abstract

Wave impact loads on maritime structures can cause casualties, damage, pollution and operational delays. Consequently, their extreme values should be accounted for in the design of these structures. However, this is challenging, as wave impact events are both rare and highly complex, requiring both high-fidelity simulations and long analysis durations to reliably quantify the associated design loads. Moreover, existing extreme value prediction methods are neither specifically developed nor adequately validated for wave impact phenomena. We therefore introduce the new Probabilistic Adaptive Screening (PAS) method for predicting extreme non-linear loads on maritime structures. The method integrates copula-based statistical dependence modelling with multi-fidelity screening and adaptive sampling. This framework enables efficient extreme value prediction by statistically mapping low-fidelity indicator variables to high-fidelity impact loads. The method allows for efficient linear potential flow indicators to be used in the low-fidelity stage, even for strongly non-linear cases. Its statistical framework is validated against four non-linear test cases, including non-linear waves, ship vertical bending moments, green water impact loads, and slamming loads. It is concluded that PAS with optimal settings accurately estimates both the short-term distributions and extreme values in these test cases, with most probable maximum (MPM) values within 2-15% of the reference brute-force Monte-Carlo Simulation (MCS) results. In addition, PAS achieves this performance very efficiently, requiring in the order of 1-3% of the high-fidelity simulation time needed for conventional MCS. These results demonstrate that PAS can reliably reproduce the statistics of both weakly and strongly non-linear extreme load problems, while significantly reducing the associated computational cost compared to MCS.

Figures (19)

• Figure 1: Two examples of wave impacts on marine structures: a wind turbine foundation near Fécamp in 2023 (left, photo: K. King) and research vessel Discoverer on the Bering Sea in 1979 (right, photo: R. Behn / NOAA).
• Figure 2: Some of the possible statistical levels where multi-fidelity methods can derive or learn the relation between an LF indicator variables (black) and HF non-linear loads (red), including the location of AS and PAS. Modified from VS2025.
• Figure 3: Schematic illustration of PAS, where the numbers roughly correspond to the method steps in \ref{['sec:pas_steps']}. The left plot only shows a small part of the MCS time traces, and only a few HF samples are included in the middle and right distributions to illustrate the principle.
• Figure 4: Example copula-fitting procedure, with from left to right: scatter diagram of LF-HF data in real space, the corresponding empirical pseudo-observations in uniform U,V-space, the fitted copula model in U,V-space, and the transformed data from the copula model in real space (transformed back using fitted marginal distributions).
• Figure 5: MARIN ferry 2 and the relevant instrumentation around the bow before the CRS SCREAM experiments (left), example green water impact (middle) and example bow-flare slamming impact (right).