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

Prediction of Hydrodynamic Forces by Neural Network with CMT data
Toru Nakanishi, Takuya Omori
National Maritime Research Institute.

Mitaka-shi, Tokyo, Japan

directions) are learned by NN. NN is implemented by scikit-learn andTensorFlow. The effect of changing the parameters of NN and thenumber of the training data is examined with optimization software. Asthe result, how to decide hyperparameters of NN such as the number oflayers, optimizer, and learning rate will be revealed. As the first step, theeasy way to get a similar result to the conventional polynomial
approximation, putting MMG polynomials to the input data of NN isdemonstrated, for example, the power of the yaw rate, that of the drift
angle, or the product of them. On the other hand, we consider thepossibility of abstraction about the input data to NN. Thus, we will also
propose a more flexible way to choose the input data.

ABSTRACTIn this paper, we develop a new maneuvering hydrodynamic force
representation method by Neural Network (NN). We focus on the forces
and moment acting on a hull because they are not modeled with physicalbackground. We construct NN models with circular motion test (CMT)
data. We also compare the predictive values with NN and theconventional polynomial approximation method.

KEY WORDS:
Hydrodynamic forces; Neural Network;
polynomial approximation; circular motion test data.

MATHEMATICAL MODELINTRODUCTION
The maneuvering motion of a ship is simulated by solving the motion
equation. In the case of MMG model, see Yasukawa, H. and Yoshimura,Y. (2015), the external force term of this equation is separated into thehydrodynamic forces and interference components that act on the hull,rudder, and propeller. Among these hydrodynamic forces, the forces
acting on the rudder and propeller are modeled with physical backgroundbased on wing theory and momentum theory, but the hydrodynamicforce acting on the hull is the most complex and is given by thepolynomial approximation representation which depends on the hullform. The approximation is sometimes not accurate enough.
Recently, a lot of research using AI has been done in this field. Forexample, Zhang, X. and Zou, Z. (2012) and Woo, J. and Kim, N. (2013)
use NN to obtain hydrodynamic derivatives from time series data. Zhang,
X. and Zou, Z. (2013) and Xu, H., Hassani, V., and C. G, Soares. (2020)
use support vector machine (SVM). In both cases, the hydrodynamicforces are assumed to be polynomials, which is called parametricmodeling. For nonparametric modeling, see Ouyang, Z. and Zou, Z.
(2021), for example.
Therefore, in this research, we develop a new maneuveringhydrodynamic force representation method that overcomes theshortcomings of the polynomial approximation by SVM or NN. Training
data is acquired by the circular motion test, and the hydrodynamic force
representation of the conventional polynomial approximation and that of
NN are compared and verified. The relationships between the input
variables (drift angle and non-dimensional yaw rate value) and output
variables (hydrodynamic forces and moment of surge, sway, and yaw

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Coordinate system

Fig. 1 Coordinate system
We adopt Earth Fixed Axes System O-𝑋 𝑌 and Body Axes System
originated from the mid-ship point of the centerline (Fig.1). In this figure,𝜓 denotes the heading angle, 𝛽 the drift angle, and 𝛿 the rudder angle.
𝑢, 𝑣, and 𝑟 denote the surge velocity, sway velocity, and rotational
velocity, respectively. 𝑋, 𝑌, and 𝑁 are the hydrodynamic forces andmoment of the surge, sway, and yaw directions at the mid-ship,respectively.