Currently there are three methods of calculating the Dynamic Positioning capability of a vessel namely: static calculations, real-time time domain simulations and fast-time time domain simulations, although the outcome of the last two should be identical. In each of these methods a set of input variables is required to perform the calculations. These inputs are not always exactly known and are therefore sometimes estimated or taken from databases. It is not always clear how big the uncertainty in these estimated inputs is, and on top of that: how big the effect on the predicted DP capability is. To be able to quantify how certain a DP capability calculation is and which input data contribute most to the output uncertainty, in this thesis the input uncertainties for both static and fast-time dynamic calculations are investigated. Each method is subdivided in three different design stages which are: conceptual design, preliminary design and as built design. For the static calculations all three design stages are evaluated but for the fast-time dynamic simulations only the as built stage is considered.

The static calculation part of the analysis consists of determining the input uncertainties, the input sensitivities to the output and finally calculating the output uncertainty. The method used for this calculation assumes that either the relation between input and output is linear or can be linearised at the point of interest. The input uncertainties are calculated using historical data of the Bibby Wavemaster 1 which is the vessel used as case study throughout this thesis and is specifically designed for the purpose of servicing offshore wind farms. It is observed that the input uncertainties of the main dimensions of the vessel are clearly reducing when moving through the design stages. Furthermore it is concluded that the environmental coefficients of wind, waves and current are the most uncertain, even in the conceptual design stage where input parameters of the main dimensions of the vessel vary the most. When considering the sensitivity in the three design stages no big changes were observed, meaning that in all design stages the main dimensions of the vessel are most sensitive to the output. Finally the uncertainty in the output was evaluated were it was observed that for the as built stage still a standard deviation of 4% uncertainty of the output is present, resulting in a calculated 99.7% confidence interval of either 12% too high or too low.

In the dynamic calculation part only the as built stage is considered. Again the uncertain parameters are defined but due to the PID controller in the dynamic model some new input parameters are now present. The gains of this PID controller are assumed to be uncertain and are therefore taken into account during the dynamic uncertainty analysis. Due to a limitation in the aNySIM licence bought by Damen it is impossible to change the wave coefficients which causes their uncertainty not to be taken into account. Since the dynamic simulations are considered to have strong non linearities and possibly even discontinuities due to thruster saturation, the calculation method used for the static part is not applicable anymore. Therefore it is decided to use Monte Carlo simulations to quantify the uncertainty in dynamic DP calculations. Due to the large computational time required to perform large amounts of Monte Carlo simulations with aNySIM, a machine learning method is used to capture the dynamic behaviour of the vessel. A small number of simulations performed by aNySIM is required to train the model which are selected using the Sobol design of experiments technique. This technique optimises the choice of the simulation points to make sure the complete space of possible inputs is covered. By using the machine learning model to obtain an output of a dynamic simulation only a fraction of a second is required instead of 17 minutes when using aNySIM. By running the Monte Carlo simulation on the created machine learning model it was observed that the 97.7% confidence interval for offset can either be calculated up to 8.7% too low or too high whereas the prediction for heading up to 23.1% too low or too high when compared to the base case. It is concluded that using DP for the purpose of people transferring by means of a "Walk To Work" bridge, uncertainties should be taken into account to reduce both safety and contractual requirements risks.