On the effects of non-linearities in DP systems

Abstract

In offshore operations a trend is forming where vessels are more often required to do multiple short operations within a small-time frame. Traditional mooring systems require execution time far beyond the operation time. Dynamic positioning systems offer great advantages for short time span operations such as crew transfer or lift operations.

Currently operations are planned based on DP capability plots and experience of captain and DPO. DP capability plots have little operational value as this is a static calculation and only provide information for average station keeping capability. During operations, the displacements made by the vessel around the DP set-point, also referred to as DP offset, are of great importance to determine the operability of an operation. Currently, the only way of calculating the DP offset is by conducting extensive time domain simulations, which are hard to integrate in the operational workflow of a DP vessel involved in walk-to-work operations. Therefore, a new approach is developed which predicts the vessel’s DP offset in the frequency domain, which enables a quick and robust calculation of the DP offset which is suited to merge into the on-board workflow. A frequency domain model is per definition a linear model. This leads to the main challenge of this research. A vessel operating on DP is non-linear. Currently there is no insight in what the effect is of non-linear components present in a DP system, on the linear approximation of a frequency domain model.

To investigate the effect of non-linear components onto the DP frequency domain model, a time domain model is developed that is capable of systematically enabling/disabling different non-linear components. The time domain model will serve as the ’truth’ in this research as no actual vessel data is available. Furthermore, this helps identify the effects more easily, as the input for both models are identical. From the time domain model transfer functions can be derived that serve as the basis for the frequency domain model. The transfer function is a linear relation between two variables. In this case, between second order wave drift forces and displacement of the vessel in surge, sway and yaw direction. The following non-linear components are investigated in this research: Thruster ramp up, thruster turning rate, forbidden zones, saturation and thruster allocation. Thruster allocation is present in each model that will be tested, as this is an essential part of a DP system.

Using two methods of determining transfer functions the model and the effects of all non-linear components are tested. The model is subjected to a variety sea-state, with different wave directions. Both methods offer similar results even though different approaches to determine the transfer functions are used. The selected method is capable of accurately predicting vessel offsets, although some extreme offsets are not captured.

It is concluded that the presence of non-linear components have little to no effect on the DP offset as calculated by the time domain model. Because natural frequencies characteristic to these non-linear components are expected to exist at much higher frequencies that naturally present in second order wave drift forces. Thus, making a linear frequency domain model suitable for DP offset forecasting. It is advised to investigate the effect of including 2D input spectra as this is expected to improve the current model.