Matteo Diez

Giorgio Palma, Andrea Serani, Matteo Diez

In this study, we present and validate an ensemble-based Hankel Dynamic Mode Decomposition with control (HDMDc) for uncertainty-aware seakeeping predictions of a high-speed catamaran, namely the Delft 372 model. Experimental measurements (time histories) of wave elevation at the longitudinal center of gravity, heave, pitch, notional flight-deck velocity, notional bridge acceleration, and total resistance were collected from irregular wave basin tests on a 1:33.3 scale replica of the Delft 372 model under sea state 5 conditions at Fr = 0.425, and organized into training, validation, and test sets. The HDMDc algorithm constructs an equation-free linear reduced-order model of the seakeeping vessel by augmenting states and inputs with their time-lagged copies to capture nonlinear and memory effects. Two ensembling strategies, namely Bayesian HDMDc (BHDMDc), which samples hyperparameters considered stochastic variables with prior distribution to produce posterior mean forecasts with confidence intervals, and Frequentist HDMDc (FHDMDc), which aggregates multiple model obtained over data subsets, are compared in providing seakeeping prediction and uncertainty quantification. The FHDMDc approach is found to improve the accuracy of the predictions compared to the deterministic counterpart, also providing robust uncertainty estimation; whereas the application of BHDMDc to the present test case is not found beneficial in comparison to the deterministic model. FHDMDc-derived probability density functions for the motions closely match both experimental data and URANS results, demonstrating reliable and computationally efficient seakeeping prediction for design and operational support.

Andrea Serani, Matteo Diez

The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature mapping synthesis borrowed from clinical medicine, delving into the field of design-space dimensionality reduction techniques tailored for shape optimization, bridging traditional methods and cutting-edge technologies. Dissecting the spectrum of these techniques, from classical linear approaches like principal component analysis to more nuanced nonlinear methods such as autoencoders, the discussion extends to innovative physics-informed methods that integrate physical data into the dimensionality reduction process, enhancing the physical relevance and effectiveness of reduced design spaces. By integrating these methods into optimization frameworks, it is shown how they significantly mitigate the curse of dimensionality, streamline computational processes, and refine the design exploration and optimization of complex functional surfaces. The survey provides a classification of methods and highlights the transformative impact of these techniques in simplifying design challenges, thereby fostering more efficient and effective engineering solutions.

Giorgio Palma, Andrea Bardazzi, Alessia Lucarelli et al.

This article presents the data-driven equation-free modeling of the dynamics of a hexafloat floating offshore wind turbine based on the application of dynamic mode decomposition (DMD). All the analyses are performed on experimental data collected from an operating prototype. The DMD has here used i) to extract knowledge from the dynamic system through its modal analysis, ii) for short-term forecasting from the knowledge of the immediate past of the system state, and iii) for the system identification and reduced order modeling. The forecasting method for the motions, accelerations, and forces acting on the floating system is developed using Hankel-DMD, a methodological extension that includes time-delayed copies of the states in an augmented state vector. The system identification task is performed by applying Hankel-DMD with control (Hankel-DMDc), which models the system including the effect of forcing terms. The influence of the main hyperparameters of the methods, namely the number of delayed copies in the state and input vector and the length of the observation time, is investigated with a full factorial analysis using three error metrics analyzing complementary aspects of the prediction: the normalized root mean square error, the normalized average minimum-maximum absolute error, and the Jensen-Shannon divergence. A Bayesian extension of the Hankel-DMD and Hankel-DMDc is introduced by considering the hyperparameters as stochastic variables varying in suitable ranges defined after the full factorial analysis, enriching the predictions with uncertainty quantification. Results show the capability of the approaches for short-term forecasting and system identification, suggesting their potential for real-time continuously-learning digital twinning and surrogate data-driven reduced order modeling.

Giorgio Palma, Andrea Serani, Shawn Aram et al.

This study introduces and compares the Hankel dynamic mode decomposition with control (Hankel-DMDc) and a novel Bayesian extension of Hankel-DMDc as model-free (i.e., data-driven and equation-free) approaches for system identification and prediction of free-running ship motions in irregular waves. The proposed DMDc methods create a reduced-order model using limited data from the system state and incoming wave elevation histories, with the latter and rudder angle serving as forcing inputs. The inclusion of delayed states of the system as additional dimensions per the Hankel-DMDc improves the representation of the underlying non-linear dynamics of the system by DMD. The approaches are statistically assessed using data from free-running simulations of a 5415M hull's course-keeping in irregular beam-quartering waves at sea state 7, a highly severe condition characterized by nonlinear responses near roll-resonance. The results demonstrate robust performance and remarkable computational efficiency. The results indicate that the proposed methods effectively identify the dynamic system in analysis. Furthermore, the Bayesian formulation incorporates uncertainty quantification and enhances prediction accuracy. Ship motions are predicted with good agreement with test data over a 15 encounter waves observation window. No significant accuracy degradation is noted along the test sequences, suggesting the method can support accurate and efficient maritime design and operational planning.

Giorgio Palma, Andrea Serani, Kevin McTaggart et al.

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.

Danny D'Agostino, Andrea Serani, Frederick Stern et al.

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.