Sensitivity Analysis Based on Polynomial Chaos Expansions and Its Application in Ship Uncertainty-Based Design Optimization

In order to truly reflect the ship performance under the influence of uncertainties, uncertainty-based design optimization (UDO) for ships that fully considers various uncertainties in the early stage of design has gradually received more and more attention. Meanwhile, it also brings high dimensionality problems, which may result in inefficient and impractical optimization. Sensitivity analysis (SA) is a feasible way to alleviate this problem, which can qualitatively or quantitatively evaluate the influence of the model input uncertainty on the model output, so that uninfluential uncertain variables can be determined for the descending dimension to achieve dimension reduction. In this paper, polynomial chaos expansions (PCE) with less computational cost are chosen to directly obtain Sobol' global sensitivity indices by its polynomial coefficients; that is, once the polynomial of the output variable is established, the analysis of the sensitivity index is only the postprocessing of polynomial coefficients. Besides, in order to further reduce the computational cost, for solving the polynomial coefficients of PCE, according to the properties of orthogonal polynomials, an improved probabilistic collocation method (IPCM) based on the linear independence principle is proposed to reduce sample points. Finally, the proposed method is applied to UDO of a bulk carrier preliminary design to ensure the robustness and reliability of the ship.