Bayesian dynamic mode decomposition for real-time 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 their most interesting applications in the naval field is the digital twinning of ship performances in waves, a crucial aspect in design and operation safety. In this paper, a Bayesian extension of the Hankel dynamic mode decomposition method is proposed for ship motion's nowcasting as a prediction tool for naval digital twins. The proposed algorithm meets all the requirements for formulations devoted to digital twinning, being able to adapt the resulting models with the data incoming 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 data from three different CFD solvers. The results show predictions keeping good accuracy levels up to five wave encounter periods, with the Bayesian formulation improving the deterministic forecasts. In addition, a connection between the predicted uncertainty and prediction accuracy is found.

Analysis and Forecasting of the Dynamics of a Floating Wind Turbine Using Dynamic Mode Decomposition

This article presents a data-driven equation-free modeling of the dynamics of a hexafloat floating offshore wind turbine based on the Dynamic Mode Decomposition (DMD). The DMD is here used to provide a modal analysis and extract knowledge from the dynamic system. A forecasting algorithm for the motions, accelerations, and forces acting on the floating system, as well as the height of the incoming waves, the wind speed, and the power extracted by the wind turbine, is developed by using a methodological extension called Hankel-DMD, that includes time-delayed copies of the states in an augmented state vector. All the analyses are performed on experimental data collected from an operating prototype. The quality of the forecasts obtained varying two main hyperparameters of the algorithm, namely the number of delayed copies and the length of the observation time, is assessed using three different error metrics, each analyzing complementary aspects of the prediction. A statistical analysis exposed the existence of optimal values for the algorithm hyperparameters. Results show the approach's capability for short-term future estimates of the system's state, which can be used for real-time prediction and control. Furthermore, a novel Stochastic Hankel-DMD formulation is introduced by considering hyperparameters as stochastic variables. The stochastic version of the method not only enriches the prediction with its related uncertainty but is also found to improve the normalized root mean square error up to 10% on a statistical basis compared to the deterministic counterpart.