The Time Prediction of Ship Motions at Sea
Authors: Broome D.R. , Pittaras A. 
Published: October 2008

ABSTRACT
The work described in this paper is related to the time prediction of ship motions under wind, wave and current excitation. The prediction is based on mathematical models generated in real time by using system identification techniques. The applications of ship motion prediction are numerous. The potential improvement in safety of landing aircraft and helicopters on carriers and other naval and commercial ships is of particular interest. A case study is included in the paper. Roll measurements obtained from the sea trials of a frigate are analysed and actual and predicted ship responses are compared. The results demonstrate that prediction of ship motions using on-line system identification methods is feasible.

INTRODUCTION
The short-term prediction of ship motion has always been of interest, because it can be used to improve the performance of certain marine operations. In the commercial field for example heave prediction could be used as a feed forward signal for diving bell heave compensation. In naval operations the applications are numerous. Roll and heave predictions could be used to make helicopter landing on aircraft carriers safer. Sea keeping could also be improved under certain operating conditions.
This paper outlines research work carried out on adaptive ship motion prediction. The prediction is based on mathematical models generated in real time by using system identification techniques. Thus no previous knowledge about the ship and the mathematical model describing its response to sea waves is necessary. Changes in operating conditions such as ship loading or sea state do not necessitate any modifications to the predictor software. This work is thus fundamentally different from previous approaches to the problem, where a model had to be assumed for the ship response and the solutions of the associated differential equations propagated in the time domain. A case study is included to demonstrate the application of adaptive predictors in ship motion prediction. The data analysed are from the sea trials of a frigate and roll predictions are compared to actual ship roll motions.
Ship motion prediction has been a subject of study by various researchers. The Response Amplitude Operator (RAO) technique is described in some detail by O'Reilly [1]. An energy index based on the ship motions in six degrees of freedom is used as an aid to helicopter landing. The success of the method relies on the fact that the energy index may indicate the onset of relatively quiescent deck motion intervals. However there is no apparent method to calculate how long these intervals will be. In addition AO's can only be obtained by model testing and the technique suggested to calculate the energy index is computationally expensive and complicated.
The Kalman-Bucy filter in predictor form is used by Sidar and Doolin [2] and Triantafyllou et al [3] among others. Mathematical models for ship motions in state-space form are obtained by fitting second-order transfer functions to experimentally derived power spectral densities for aircraft carrier heave and pitch motions [2]. By arguing that heave and pitch motions are in fact narrow-band processes, the Kalman filter is shown to give results similar to that of a predictor for the state of a harmonic oscillator.