Multi-level optimisation and global sensitivity analysis of the probabilistic damage stability method for single hold ships

Abstract

The probabilistic damage stability method offers great design freedom when used as a base of design. However, due to the complexity of the calculation and amount of parameters that influence the attained index, much of this freedom is not being harnessed by designers. This research tries to give the designer more insight in where to look when trying to comply with the regulations, by providing an initial subdivision design and create an overview of the influence of the parameters on the attained index. Many parameters have been found that either direct or indirect influence the damage stability calculation. A selection of parameters is chosen from this list as a starting point that are commonly used in the subdivision of large single hold vessels. A parameterised base ship has been made in the DELFTship program that is used for the execution of the optimisation and sensitivity analysis. The exploration for a suitable optimisation method and sensitivity analysis is based on the properties of these methods and method requirements that apply to this specific research. The most important requirement for both methods is the number of iterations needed to obtain a reasonable result, as the damage stability calculation can take up to 15 minutes. This resulted in the choice for the SACOBRA optimisation algorithm. To guarantee the effectiveness of the design, a second level to the optimisation is added where, the number of bulkheads is optimised, while simultaneously optimising the steel weight. During the research, the cargo hold volume was added as this proved to be an effective objective to ensure the efficiency of the design. This resulted in the change to the SAMO-COBRA algorithm, where the single objective SACOBRA algorithm was still used as a verification method and to investigate if it could be used for experimenting with certain design choices. For the sensitivity analysis the Morris method was chosen, mainly for its low number of sample points needed to converge. This method can be applied to a broad range of models and is characterised by its simplicity. However, this simplicity resulted in a relatively low amount of insight generated regarding the influence of the parameters on both the objectives as well as each other. A correlation matrix was added to further provide knowledge and insight. A sensitivity analysis by hand was performed to verify the results of both analysis methods.

The first optimisation stage showed to be a relatively fast way to determine the amount of bulkheads compared to the attained index that can be expected. However, a relatively large margin of error is observed in this stage and more information is needed to be able to make a decision on how many bulkheads is used to further optimise. The use of the SAMO-COBRA method in the second optimisation stage proved to be effective at providing the naval architect with a range of design proposals, where the probabilistic damage stability regulations were used as a base of design. Furthermore, it is shown that for single hold ships in general, the priority of the algorithm followed the influence of the parameters on the distance they were able to create between the cargo hold and the outer hull. The influence of the parameters, resulting from the sensitivity analyses endorse these claims. The Morris method showed the high non-linear and non-monotonic behaviour of the parameters that were investigated. This made it difficult to distinguish the level of influence between the parameters. The combination of the Morris method, Pearson correlation matrix and the sensitivity by hand proved to be sufficient for determining the behaviour of the probabilistic damage stability calculation. In the end, this research proposes a new foundation of designing a ship with the probabilistic damage stability regulations as a base of design. After the initial design from the two stage optimisation all other design requirements are implemented in the design. If the ship then fails to comply with the regulations, the knowledge and insight from this research can be used to increase the survivability of the ship in order for it to comply again.