A Computationally Efficient Procedure for Tuning of Ship Transfer Functions

The analysis of wave-ship interactions is highly relevant for the safety – as well as the energy efficiency – of the maritime operations. One application is the onboard estimation of the ship’s responses in incoming seaways, which requires regular and accurate updates of the vessel’s seakeeping model, accounting for possible changes in the operational conditions.

This paper presents a simple approach for fast estimation of the wave-to-motion transfer functions of vessels. Prior information of the wave spectrum, characterizing the sea state, and ship motion measurements, i.e. time series sequences from onboard sensors, are supposed to be available. Semi-empirical closed-form expressions derived for a box-shaped vessel define Parameterized Response Amplitude Operators (P-RAOs) for the heave and pitch motions.

The five input parameters, namely the ship speed, length, breadth, draught and block coefficient, are regarded as  optimization variables. An optimization problem is established to minimize the spectral discrepancy between, on one hand, the measured responses, and, on the other hand, the theoretical responses computed with the wave spectrum and P-RAOs.

Numerical simulations of measured motions in a predefined long-crested sea state are carried out in the frequency domain for two different ships, a small research vessel and a container ship, using a set of RAOs obtained by a commercial potential flow code. The simulated measurements are considered as the ground truth.

Tuning of the P-RAOs is carried out, and the results show a fairly good agreement between the tuned P-RAOs and the true RAOs over a wide portion of the frequency range. Moreover, the normalized error between the true and estimated response spectra is significantly decreased after tuning the P-RAOs.