Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Data-driven uncertainty-aware seakeeping prediction of the Delft 372 catamaran using ensemble Hankel dynamic mode decomposition

Giorgio Palma, Andrea Serani, Matteo Diez

TL;DR

This work develops and validates an ensemble Hankel Dynamic Mode Decomposition with control (HDMDc) framework to predict seakeeping responses of the Delft 372 catamaran under irregular waves while quantifying uncertainty. By augmenting states and inputs with time delays, and employing regularized regression, the method yields an equation-free reduced-order model usable in real time. Among the two ensemble strategies, Frequentist HDMDc (FHDMDc) markedly improves prediction accuracy and robustly captures peak motions, with predicted distributions closely matching high-fidelity data. Bayesian HDMDc (BHDMDc) provides limited benefits and often underestimates uncertainty, while FHDMDc demonstrates strong potential for design and operational support due to its low computational footprint and distributional fidelity. The study also identifies resistance predictions as a remaining challenge and points to extensions such as two-stage modeling and extended observables to better capture nonlinear input–output effects.

Abstract

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.

Data-driven uncertainty-aware seakeeping prediction of the Delft 372 catamaran using ensemble Hankel dynamic mode decomposition

TL;DR

This work develops and validates an ensemble Hankel Dynamic Mode Decomposition with control (HDMDc) framework to predict seakeeping responses of the Delft 372 catamaran under irregular waves while quantifying uncertainty. By augmenting states and inputs with time delays, and employing regularized regression, the method yields an equation-free reduced-order model usable in real time. Among the two ensemble strategies, Frequentist HDMDc (FHDMDc) markedly improves prediction accuracy and robustly captures peak motions, with predicted distributions closely matching high-fidelity data. Bayesian HDMDc (BHDMDc) provides limited benefits and often underestimates uncertainty, while FHDMDc demonstrates strong potential for design and operational support due to its low computational footprint and distributional fidelity. The study also identifies resistance predictions as a remaining challenge and points to extensions such as two-stage modeling and extended observables to better capture nonlinear input–output effects.

Abstract

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.

Paper Structure

This paper contains 11 sections, 23 equations, 8 figures, 4 tables.

Table of Contents

  1. Test Case
  2. Methods
  3. HDMDc
  4. Uncertainty quantification in HDMDc through ensembling
  5. Bayesian HDMDc
  6. Frequentist HDMDc
  7. Performance metrics
  8. Numerical setup for HDMDc
  9. Results
  10. Discussion
  11. Conclusions

Figures (8)

  • Figure 1: Delft 372 catamaran model: geometry and body plan.
  • Figure 2: CNR-INM 2554 model for towing-tank seakeeping experiments.
  • Figure 3: Average value of NRMSE for HDMDc over validation sequences varying hyperparameters' values, full factorial analysis.
  • Figure 4: Interquartile range of NRMSE for HDMDc over validation sequences varying hyperparameters' values, full factorial analysis.
  • Figure 5: Time series prediction, EFD vs HDMDc vs BHDMDc, randomly selected test sequence.
  • ...and 3 more figures