Adaptive approximation in multi-objective optimization for full stochastic fatigue design problem

Abstract As the size of ship has grown rapidly, the importance of exact fatigue strength assessment has been recognized more and more. High concern about fatigue crack often raises target fatigue life to two or three times of ship lifetime. This leads to the use of very thick plates to reduce dynamic stress range or the application of weld toe grinding to reduce stress concentration or removing weld defects. However, such measures can cause some troubles in fabrication process. As a fatigue strength assessment procedure, full stochastic fatigue analysis based on wave loads analysis has been recommended due to its high accuracy and straightforward approach. However, its huge computing time hinders a ship designer from making iterative explorations for a better design to minimize the use of aforementioned measures. This paper proposes an efficient approach to optimize plate thicknesses around hot spots and the applications of weld toe grinding with meeting the required target fatigue life based on the full stochastic fatigue assessment. Two conflicting objectives are taken into consideration; to minimize steel weight and to minimize total weld toe grinding length. Whether to employ weld toe grinding or not for a hot spot can be seen as a selection variable. In order to treat such selection variables along with continuous variables in the multi-objective optimization, Multi-objective Genetic Algorithm (MOGA) is introduced. This paper also employs adaptive approximation framework to resolve the computational burden of the full stochastic fatigue analysis in the optimization. The strategy to refit approximations iteratively can minimize the required number of analysis. A convergence criterion of the adaptive approximation framework is newly proposed considering the feature of discrete objective function attributed to the introduction of selection variables. One of the objective functions, toe grinding length, is purely depending on how many hot spots toe grindings are applied to. The proposed approach is applied to a liquid dome opening problem of LNG carrier, which is known as one of the most difficult parts to satisfy required fatigue strength due to the stress concentration caused by its large opening and weld attachments on upper deck.