Giorgio Palma

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.

Giorgio Palma, Ivan Santic, Andrea Serani et al.

This study addresses the system identification of a small autonomous surface vehicle (ASV) under moored conditions using Hankel dynamic mode decomposition with control (HDMDc) and its Bayesian extension (BHDMDc). Experiments were carried out on a Codevintec CK-14e ASV in the towing tank of CNR-INM, under both irregular and regular head-sea wave conditions. The ASV under investigation features a recessed moon pool, which induces nonlinear responses due to sloshing, thereby increasing the modelling challenge. Data-driven reduced-order models were built from measurements of vessel motions and mooring loads. The HDMDc framework provided accurate deterministic predictions of vessel dynamics, while the Bayesian formulation enabled uncertainty-aware characterization of the model response by accounting for variability in hyperparameter selection. Validation against experimental data demonstrated that both HDMDc and BHDMDc can predict the vessel's response to unseen regular and irregular wave excitations. In conclusion, the study shows that HDMDc-based ROMs are a viable data-driven alternative for system identification, demonstrating for the first time their generalization capability for a sea condition different from the training set, achieving high accuracy in reproducing vessel dynamics.

Andrea Serani, Giorgio Palma, Matteo Diez

Dimensionality reduction is essential in simulation-based shape design, where high-dimensional parameterizations hinder optimization, surrogate modeling, and systematic design-space exploration. Parametric Model Embedding (PME) addresses this issue by constructing reduced variables from geometric information while preserving an explicit backmapping to the original design parameters. However, PME is intrinsically linear and may become inefficient when the sampled design space is governed by nonlinear geometric variability. This paper introduces a nonlinear extension of PME, denoted NLPME. The proposed framework preserves the defining principle of PME -- geometry-driven latent variables and parameter-mediated reconstruction -- while replacing the linear reduced subspace with a nonlinear latent representation. Geometry is not reconstructed directly from the latent variables; instead, the latent representation is decoded into admissible design parameters, and the corresponding geometry is recovered through a forward parametric map. The method is assessed on a bio-inspired autonomous underwater glider with a 32-dimensional parametric shape description and a CAD-based geometry-generation process. NLPME reaches a 5\% reconstruction-error threshold with \(N=5\) latent variables, compared with \(N=8\) for linear PME, and a 1\% threshold with \(N=9\), compared with \(N=15\) for PME. Comparison with a deep autoencoder shows that most of the nonlinear compression gain can be retained while preserving an explicit backmapping to the original design variables. The results establish NLPME as a compact, admissible, and engineering-compatible nonlinear reduced representation for parametric shape design spaces.

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.