What question did this study set out to answer?

The goal is to accurately predict ship roll motion by using new computational algorithms for nonlinear damping models.

May 8, 2026

Two Robust Computational Algorithms for a Few Nonlinear Roll Damping Models In Ocean Engineering: A Novel Graph Polynomial Approach

Key Points

The goal is to accurately predict ship roll motion by using new computational algorithms for nonlinear damping models.
Introduced SPBA and CPCA for estimating ship roll responses over short intervals.
Transformed nonlinear damping equations into sparse algebraic systems using spectral polynomial representations.
Compared results with HPM and MATLAB to validate efficiency and reliability.
SPBA and CPCA achieved lower RMSE compared to HPM, indicating improved accuracy in roll prediction.
Algorithms enhanced roll motion forecasting stability with significant performance metrics.
Validation through heatmaps demonstrated consistent predictive capability over short time frames.

Abstract

Abstract Predicting ship roll motion accurately is a challenging task due to the nonlinear nature of roll damping, which is crucial for the safety of smart and autonomous ships. This study, to the best of our knowledge, is the first to introduce graph-theoretic spectral algorithms specifically, the Stable Set Polynomial of the Complete Bipartite Graph Algorithm (SPBA) and the Clique Polynomial of the Complete Graph Algorithm (CPCA) to estimate ship roll motion responses over short time intervals. By employing short time evolution initial conditions, the nonlinear damping equations are transformed into sparse algebraic systems using spectral polynomial representations. A comparison with the Homotopy Perturbation Method (HPM) and MATLAB solutions highlights the efficiency and reliability of the proposed algorithms. Furthermore, the short time evolution is extrapolated using an MLP with a sigmoid activation function to enhance predictive capability. The effectiveness of SPBA and CPCA is validated with HPM through RMSE heatmaps, which underscore improved accuracy and stability in roll motion forecasting.

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Cite This Study

J et al. (Sat,) studied this question.

synapsesocial.com/papers/69fd7f86bfa21ec5bbf0801b https://doi.org/https://doi.org/10.1115/1.4071844

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