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In order to guarantee the safety of payload, crew, and structures, ships must exhibit good seakeeping, maneuverability, and structural-response performance, also when they operate in adverse weather conditions. In this context, the availability of forecasting methods to be included within model-predictive control approaches may represent a decisive factor. Here, a data-driven and equation-free modeling approach for forecasting of trajectories, motions, and forces of ships in waves is presented, based on dynamic mode decomposition (DMD). DMD is a data-driven modeling method, which provides a linear finite-dimensional representation of a possibly nonlinear system dynamics by means of a set of modes with associated frequencies. Its use for ship operating in waves has been little discussed and a systematic analysis of its forecasting capabilities is still needed in this context. Here, a statistical analysis of DMD forecasting capabilities is presented for ships in waves, including standard and augmented DMD. The statistical assessment uses multiple time series, studying the effects of the number of input/output waves, time steps, time derivatives, along with the use of time-shifted copies of time series by the Hankel matrix. The assessment of the forecasting capabilities is based on four metrics: normalized root mean square error, Pearson correlation coefficient, average angle measure, and normalized average minimum/maximum absolute error. Two test cases are used for the assessment: the course keeping of a self-propelled 5415M in irregular stern-quartering waves and the turning-circle of a free-running self-propelled KRISO Container Ship in regular waves. Results are overall promising and show how state augmentation (using from four to eight input waves, up to two time derivatives, and four time-shifted copies) improves the DMD forecasting capabilities up to two wave encounter periods in ..., Comment: arXiv admin note: text overlap with arXiv:2105.13062 submitted to Ocean Engineering

The prediction capability of recurrent-type neural networks is investigated for real-time short-term prediction (nowcasting) of ship motions in high sea state. Specifically, the performance of recurrent neural networks, long-short term memory, and gated recurrent units models are assessed and compared using a data set coming from computational fluid dynamics simulations of a self-propelled destroyer-type vessel in stern-quartering sea state 7. Time series of incident wave, ship motions, rudder angle, as well as immersion probes, are used as variables for a nowcasting problem. The objective is to obtain about 20 s ahead prediction. Overall, the three methods provide promising and comparable results., Comment: 10 pages, 5 figures, to be published in conference proceeding of IX International Conference on Computer Methods in Marine Engineering

A data-driven and equation-free approach is proposed and discussed to model ships maneuvers in waves, based on the dynamic mode decomposition (DMD). DMD is a dimensionality-reduction/reduced-order modeling method, which provides a linear finite-dimensional representation of a possibly nonlinear system dynamics by means of a set of modes with associated oscillation frequencies and decay/growth rates. DMD also allows for short-term future estimates of the system's state, which can be used for real-time prediction and control. Here, the objective of the DMD is the analysis and forecast of the trajectories/motions/forces of ships operating in waves, offering a complementary efficient method to equation-based system identification approaches. Results are presented for the course keeping of a free-running naval destroyer (5415M) in irregular stern-quartering waves and for the free-running KRISO Container Ship (KCS) performing a turning circle in regular waves. Results are overall promising and show how DMD is able to identify the most important modes and forecast the system's state with reasonable accuracy up to two wave encounter periods., Comment: 8 pages, 5 figures, to be published in conference proceeding of IX International Conference on Computer Methods in Marine Engineering

The fast marching method is a widely used numerical method for solving the Eikonal equation arising from a variety of scientific and engineering fields. It is long deemed inherently sequential and an efficient parallel algorithm applicable to large-scale practical applications is not available in the literature. In this study, we present a highly scalable massively parallel implementation of the fast marching method using a domain decomposition approach. Central to this algorithm is a novel restarted narrow band approach that coordinates the frequency of communications and the amount of computations extra to a sequential run for achieving an unprecedented parallel performance. Within each restart, the narrow band fast marching method is executed; simple synchronous local exchanges and global reductions are adopted for communicating updated data in the overlapping regions between neighboring subdomains and getting the latest front status, respectively. The independence of front characteristics is exploited through special data structures and augmented status tags to extract the masked parallelism within the fast marching method. The efficiency, flexibility, and applicability of the parallel algorithm are demonstrated through several examples. These problems are extensively tested on six grids with up to 1 billion points using different numbers of processes ranging from 1 to 65536. Remarkable parallel speedups are achieved using tens of thousands of processes. Detailed pseudo-codes for both the sequential and parallel algorithms are provided to illustrate the simplicity of the parallel implementation and its similarity to the sequential narrow band fast marching algorithm., Comment: v1 submitted to Journal of Computational Physics on January 12, 2015. v2 submitted to Journal of Computational Physics on April 18, 2016. v3 accepted by Journal of Computational Physics (corrected proof). Available online 14 December 2016, ISSN 0021-9991, http://www.sciencedirect.com/science/article/pii/S0021999116306659

Flows around a wedge-shaped bow are simulated with the aim of investigating the wave breaking mechanism and small scale features of ship bow waves. This fluid dynamics video shows the plunging wave breaking process around the wedge including the thin water sheet formation, overturning sheet with surface disturbance, fingering and breaking up into spray, plunging and splashing, and air entrainment., Comment: Two videos included