The key to uncertainty design optimization (UDO) is uncertainty quantification (UQ), but the traditionally used Monte Carlo (MC) method can be time-consuming and computationally expensive. Therefore, a ship UDO method based on polynomial chaos expansions (PCE) and the maximum entropy method (MEM) is proposed.

PCE with less computational cost is selected to quantify the stochastic properties of the output under the influence of multiple uncertain parameters. According to the properties of the orthogonal polynomials, an improved probabilistic collocation method (IPCM) based on the linear independence principle is used to solve the polynomial coefficient of PCE. In addition, the first four moments of the constraint obtained by PCE are combined with MEM to solve the probability density function (PDF) of the constraint, and the failure probability of the constraint is obtained by integrating PDF on the failure domain.

The improved probability collocation method based on the principle of linear independence provides the optimal number of probability collocation points and greatly reduces the number of sample points. When solving the failure probability of the constraint based on PCE and MEM, compared with the results of MC, the accuracy of the proposed method can meet the requirements with no additional calculations. The UDO results of bulk carriers verify that PCE has obvious advantages in accuracy and efficiency in engineering applications compared with MC.

The method proposed herein can efficiently and accurately ensure the robustness and reliability of ship design schemes.