In 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 physical background. We construct NN models with circular motion test (CMT) data. We also compare the predictive values with NN and the conventional polynomial approximation method.


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 the hydrodynamic 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 background based on wing theory and momentum theory, but the hydrodynamic force acting on the hull is the most complex and is given by the polynomial approximation representation which depends on the hull form. The approximation is sometimes not accurate enough.

Recently, a lot of research using AI has been done in this field. For example, 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 hydrodynamic forces are assumed to be polynomials, which is called parametric modeling. For nonparametric modeling, see Ouyang, Z. and Zou, Z. (2021), for example.

Therefore, in this research, we develop a new maneuvering hydrodynamic force representation method that overcomes the shortcomings 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 directions) are learned by NN. NN is implemented by scikit-learn and TensorFlow. The effect of changing the parameters of NN and the number of the training data is examined with optimization software. As the result, how to decide hyperparameters of NN such as the number of layers, optimizer, and learning rate will be revealed. As the first step, the easy way to get a similar result to the conventional polynomial approximation, putting MMG polynomials to the input data of NN is demonstrated, for example, the power of the yaw rate, that of the drift angle, or the product of them. On the other hand, we consider the possibility of abstraction about the input data to NN. Thus, we will also propose a more flexible way to choose the input data.

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