Ship Motion Predictions in the Time Domain

Abstract

Deterministic predictions of wave induced ship motion are increasingly often used to enlarge the oper- ational envelope of ships that perform complex operations at open sea. The large amount of complex operations performed nowadays, motivates the relevance of motion predictions. The company Next Ocean provides these forecasts, based on linear seakeeping theory. While highly linear degrees of freedom are predicted accurately, roll motion predictions prove to be more demanding and are less accurate. This research aims to improve roll prediction accuracy by adding (non)linear damping to the equations of motion. The prediction optimization is performed on data of the platform supply vessel Acta Auriga.

To enable the use of nonlinear forces, the equations of motions are first implemented in the time domain using Cummins’ equations. The linear coefficients in this equation are determined from the frequency dependent coefficients in Acta Auriga’s hydrodynamic database. To ensure the correctness and investigate the limitations of the implemented Cummins equation, the results from the time and frequency domain are extensively compared. Both monochromatic excitations, as well as spectrum (JONSWAP) excitations are considered. In contrast to linear force coefficients, nonlinear force coefficients are generally not known for a given vessel. Implementing these forces into the equations of motion imposes the need for an approximation of these coefficients. Estimates for the linear, quadratic and cubic viscous damping forces are made, using both the measured motions of a vessel operating at sea and the predictions of the corresponding excitation force, made by Next Ocean. A multivariate regression algorithm is used for the identification.

The Cummins equation was successfully implemented. However, the translation from frequency to time domain was more error prone than anticipated; the frequency dependent coefficients need to meet requirements that are typically not met by databases meant for frequency domain calculations only. Furthermore, degrees of freedom without a restoring force showed running away behaviour that could not be negated without adding extra damping. The roll motion was susceptible to instabilities. The exact origin of this instability was looked for, but could not be found. Adding damping resolved the instability. Furthermore, the interpolation in the roll response amplitude operator introduced errors in the initialisation of time domain calculations, which led to inaccurate results when spectrum excitations corresponding to more severe sea states were used. Only under specific conditions, these high energy spectra led to accurate roll predictions. Adding damping made for a close match between frequency and time domain calculation for all degrees of freedom. The complexities mentioned made that an easily scalable algorithm could not be obtained using time domain calculations. Easy scalability be- ing important to Next Ocean means that running time domain simulations in Next Ocean’s product is deemed unrealistic. This also means that no nonlinear forces can be used in real time applications.

In an attempt to improve linear predictions, coefficients in the linear seakeeping model, including the linear damping coefficient, are identified and vessel motions are re-predicted with the added damping and updated linear force coefficients, using the Cummins equation. None of the identified parameters led to better predictions than were obtained by Next Ocean. Identifying and updating parameters was therefore concluded to be not beneficial to the quality of the motion predictions. Adding a fixed amount of linear roll damping, which was not identified from the field data, did lead to improved prediction quality; correlations between predictions and measurements increased by 9.6%.

While the motion prediction could not be improved using the Cummins equation, valuable information on the time domain simulations was obtained. The finding that better predictions were consistently obtained by adding a fixed amount of damping, sparks an opportunity for further research into the ideal amount of damping. This, and more elaborate identification schemes could provide meaningful insight to improve motion predictions.