Ship design optimization with mixed uncertainty based on evidence theory

With the continuous development of ship design and application requirements, the deterministic design optimization based on design conditions has been difficult to meet the current demands of ship design. Some parameters regarded as fixed values in ship design inevitably fluctuate when sailing in the real marine environment, and the changes of these uncertainties will directly affect the performance of the ship scheme. Therefore, higher requirements are proposed by the designers for the robustness and reliability of the ship scheme under the influence of uncertainty. Generally, uncertainty can be divided into two types, which are aleatory uncertainty an epistemic uncertainty. In most researches, due to the modeling of epistemic uncertainty is not mature, uncertain parameters which might belong to epistemic uncertainty are often modeled as the stochastic distribution belonging to aleatory uncertainty, thus insufficient distribution information will lead to false modeling and result in wrong analysis. Also, few studies have taken the influence of aleatory and epistemic uncertainty into consideration simultaneously in ship design. Therefore, in this research, evidence theory is used to model interval variables of epistemic uncertainty, and the influence of mixed uncertainty on constraints and objective functions is analyzed. By deriving the failure probability of the constraint function and the expectation and standard deviation of the objective function in the framework of evidence theory, and the reliability and robustness expression under mixed uncertainty are completed. Finally, a unified analysis and propagation method of mixed uncertainty is proposed based on evidence theory. By applying this method to the engineering optimization of a bulk carrier, the optimal scheme under mixed uncertainty is obtained, which has better reliability and robustness than the deterministic optimal scheme.