Data Assimilation-based Simultaneous Phase-Resolved Ocean Wave and Ship Motion Forecast

TL;DR

This work addresses the challenge of forecasting nonlinear, phase-resolved ocean waves and associated ship motion under data uncertainty. It introduces the EnKF-HOS-CMI framework, which couples the high-order spectral method for wave dynamics, the Cummins-equation-based ship model, and the ensemble Kalman filter for sequential data assimilation, allowing wave data, ship data, or both to constrain the forecast. The approach yields significantly improved long-term forecast accuracy over non-assimilative baselines and enables simultaneous estimation of ship parameters through a parameter-augmented state, demonstrated in synthetic tests with a box-shaped ship and irregular waves. The method promises enhanced robustness for real-time wave-ship forecasting and can inform safe and efficient maritime operations by integrating diverse observation sources.

Abstract

This paper presents a data-assimilation (DA)-based approach to forecast the phase-resolved wave evolution process and ship motion, which is developed by coupling the high-order spectral method (HOS), ensemble Kalman filter (EnKF), and a Cummins-equation-based ship model (CMI). With the developed EnKF-HOS-CMI method, the observation data for wave, ship, or both can be incorporated into the model, therefore producing the optimal analysis results. The developed method is validated and tested based on a synthetic problem on the motions of an irregular wave field and a box-shaped free-floating ship. We show that the EnKF-HOS-CMI method achieves much higher accuracy in the long-term simulation of nonlinear phase-resolved wave field and ship motion in comparison with the HOS-CMI method. Also, the ship parameters are estimated accurately by using a parameter-augmented state space in EnKF.

Figures (7)

• Figure 1: Schematic illustration of the EnKF-HOS-CMI coupled framework. The size of ellipse represents the amount of uncertainty.
• Figure 2: Schematic illustration of the synthetic case.
• Figure 3: Wave forecast errors with HOS-CMI (---~ $\circ$ ---) and EnKF-HOS-CMI by assimilating wave data (-- -- --); heave data ($\cdot\ \cdot\ \cdot$); roll data (---~ $\square$ ---); wave, heave, and roll data ()
• Figure 4: Time histories of heave motion: reference solution () ; w/ DA ($\cdot\ \cdot\ \cdot$); w/o DA (-- -- --).
• Figure 5: Time histories of roll motion: reference solution () ; EnKF-HOS-CMI ($\cdot\ \cdot\ \cdot$); HOS-CMI (-- -- --).