Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Time-Domain 3-DOF Ship Motion Modeling By
A Self-Organizing State-Space Model With Measured Data
Takaaki Hanaki1 and Munehiko Minoura1
1

Department of Naval Architecture and Ocean Engineering, Osaka University, Osaka, Japan

ABSTRACTThe seakeeping of a ship is estimated precisely by linear potential theory(e.g., slender ship theory) as a practical calculation method (Kashiwagi,1995). Recently, the Rankine Panel Method (RPM) has been studied well(e.g., Kim et al., 2011; Shao et al., 2012), but most of the studies using
RPM have been conducted for the head wave; it is still unreliable forlow-frequency waves. Kashiwagi (2020) pointed out that the calculation
cost is high for all the wave directions and frequencies needed to predictthe response of a ship to irregular waves. There are also advanced computational methods such as Computational Fluid Dynamics (CFD), andthis method can consider large amplitude motions and nonlinear eﬀects
related to ﬂuid viscosity. However, the calculation cost is higher than thatof RPM. In addition, it may be hard to understand each component physically because the CFD considers all the possible physical phenomena.
Navigation of a ship with predicting the future performance in actual seasneeds to predict the ship’s motions in real-time. Considering the computational power of current computers, the Impulse Response Function
Method (Fonseca and Soares, 1998) based on the method of Cummins(1962) using numerical results in the frequency domain is eﬀective, instead of the computationally expensive time-domain three-dimensional
panel method and CFD. However, the simulation and observation in tanktests and actual seas have some discrepancies due to errors in modelingand observation. In addition, the ship’s motions are greatly aﬀected not
only by wind and waves but also by sinkage and trim due to changes inthe draft and center of gravity caused by loading. Therefore, it is hardto calculate seakeeping comprehensively under various operating conditions.

The seakeeping of a ship is estimated precisely at design time. However, its reliability has declined with the enlargement of the ship’s hull.
Also, computing the performance comprehensively under all operating
conditions is unrealistic. Therefore, it is practical to estimate the performance using numerical calculations and measurements in actual seas.
In this paper, a self-organizing state-space model is realized based on
the 3-degree-of-freedom equation of motion. This model can estimate
the state variables and parameters of the model simultaneously. Applying the ensemble Kalman ﬁlter with Monte Carlo approximation to themodel updates the model via measured data in real-time to predict the actual phenomena. As a result, the prediction capability of a ship’s motion
improves, and the ship’s added mass and damping coeﬃcients are evaluated directly through the ﬁltering step. This paper reports on validationsof the proposed method using experimental data in tank tests.

KEY WORDS: Seakeeping; Time-Domain; Self-Organizing StateSpace Model; 3-DOF Coupled Motions; Data Assimilation; Ensemble
Kalman Filter.

INTRODUCTION
In recent years, the analysis of the on-board monitoring data has been
attractive for researchers to evaluate the ship performances in actual seasof a full-scale ship (Minoura et al., 2019). This tendency depends largelyon the Energy Eﬃciency Design Index (EEDI) regulation introduced by
the International Maritime Organization (IMO) to reduce Green House
Gas (GHG) emissions from ships in operation. It is necessary to use newfuels such as hydrogen and ammonia that do not emit GHG or develop
new systems that can control the production and consumption of propulsion energy to achieve zero emissions. However, these operational costs
are high. Not only hull forms and devices for energy-saving but also eﬃcient operations with control of the ship’s motion are required to improvefuel eﬃciency while ensuring safety. Since oceangoing ships often sailin severe sea states, short-term and long-term predictions of the ship’s
responses in actual seas are necessary. Therefore, it is essential to establish a method to accurately evaluate the seakeeping of a full-scale ship in
actual seas by analyzing the on-board monitoring data.

One of the approaches to solving this problem is to utilize measured
data. The combination of digital technology capable of analyzing big
data with mathematical and numerical methods is expected to improve
the accuracy of existing theories and overcome their limitations (Kimet al., 2021). It is practical to obtain some performances under simple conditions by numerical calculation and estimate the performancesin the actual seas by analyzing the measured time-series data. However, such a uniﬁed method has not yet been established. The authors(Hanaki and Minoura, 2021) focus on data assimilation (Evensen, 1994)
as an analysis method to combine simulation models and measured data.
Data assimilation is a method to improve the ”certainty” of a simulation
model (state-space model) by comparing its estimation with actual ob-3539