Maximum Likelihood Method as a Means to Estimate the Directional Wave Spectrum and the Mean Wave Drift Force on a Dynamically Positioned Vessel

Abstract

Feed forward in control theory is a method in which real time information about system disturbance is fed into the controller to improve its performance. As such, feed forward of the wave drift forces would improve DP behavior of a ship in terms of fuel consumption as well as position keeping. In the present study the wave drift forces have been divided in a constant part and a low frequent oscillating part. The constant part directly depends on the directional wave energy spectrum. In this paper the directional spectrum and mean drift force will be estimated from six relative wave height measurements on a dynamically positioned vessel. The Extended Maximum Likelihood Method (EMLM) is known to make a reliable estimate of the directional wave spectrum from wave measurements at fixed locations in the wave field. For a wave feed forward application the EMLM had to be implemented on a moving ship. Six relative wave height probes have been installed on board of a shuttle tanker. The EMLM has been applied to these relative motions and the low frequent yawing motion has been taken into account to calculate an earth bound spectral estimate. The estimate for the spectrum is based on a 30min average and is updated every minute in a moving average algorithm. Finally, the mean wave drift force is calculated for the actual heading of the ship.