Bayesian Hankel dynamic mode decomposition for ship motion digital twinning

Digital twins are widely considered enablers of groundbreaking changes in the development, operation, and maintenance of novel generations of products. They are meant to provide reliable and timely predictions to inform decisions along the entire product life cycle. One of the relevant applications in the naval domain is the digital twinning of ship performance in waves, a crucial aspect in operational efficiency and safety. In this paper, a Bayesian extension of the Hankel dynamic mode decomposition is proposed for ship motion nowcasting and compared with its deterministic counterpart. The proposed method meets all the requirements for formulations devoted to digital twinning, being able to adapt the resulting model based on the data from the physical system, using a limited amount of data, producing real-time predictions, and estimating their reliability. Results are presented and discussed for the course-keeping of the 5415M model in beam-quartering sea state 7 irregular waves at Fr = 0.33, using benchmark data from three different CFD solvers, used as a proxy to real vessel operations. The results show reasonably accurate predictions up to five wave encounters, with the Bayesian formulation improving the deterministic forecasts. In addition, a promising relationship between uncertainty and accuracy is found.