Black-box modeling of ship manoeuvring motion based on feed-forward neural network with Chebyshev orthogonal basis function

Abstract

Based on polynomial interpolation and approximation theory, a novel feed-forward neural network, the feed-forward neural network with Chebyshev orthogonal basis function, is proposed for black-box modeling of ship manoeuvring motion. The neural model adopts a three-layer structure, in which the hidden layer neurons are activated by a group of Chebyshev orthogonal polynomial activation functions and the other two layers’ neurons use identity mapping as activation functions. Weight update formulas are derived by employing the standard back-propagation (BP) training method. With the simulated 15o/15o zigzag test data as input and calculated values of the hydrodynamic forces and moment as output, the feed-forward neural network with Chebyshev orthogonal basis function and the BP neural network are applied to identify the nonlinear functions in the nonlinear hydrodynamic model of ship manoeuvring motion. With the simulated 20o/20o zigzag test data and 35o turning test data as input, the hydrodynamic forces and moment are predicted by using the identified nonlinear functions. Comparison between the calculated and predicted hydrodynamic forces and moment shows that the feed-forward neural network with Chebyshev orthogonal basis function is superior to the BP neural network in identifying the nonlinear functions of the nonlinear hydrodynamic model of ship manoeuvring motion and is an effective method to conduct the black-box modeling of ship manoeuvring motion.