Vessel maneuvering model identification using multi-output dynamic radial-basis-function networks

In this paper, a vessel maneuvering model (VMM) based on multi-output dynamic radial-basis-function network (MDRBFN) is proposed. Data samples used for training and testing are obtained from the vessel maneuvering dynamics based on a group of nonlinear differential equations. In order to identify the vessel maneuvering model, the differential equations are transformed into nonlinear state-space form. Considering that the desired states are not only dependent on system inputs, i.e., rudder defection and propeller revolution, but also previous states, the proposed MDRBFN is focus on the multi-input multi-output (MIMO) case. The structure of traditional fixed-size RBF networks is difficult to determine, so the growing and pruning algorithm is introduced to multi-output RBF networks to realize RBF networks with dynamic structure. The MDRBFN starts with no hidden neurons, and during the learning process, hidden neurons are recruited automatically according to hidden nodes generation criteria and parameters estimation. In addition, insignificant hidden nodes would be deleted if the node significance is lower than the predefined threshold. As a consequence, the proposed MDRBFN-based VMM (MDRBFN-VMM) reasonably captures the essential maneuvering dynamics with a compact structure. Finally, simulation results indicate that the proposed MDRBFN-VMM achieves promising performance in terms of approximation and prediction.