Application of the polynomial chaos method in global sensitivity analysis of trimaran cross-deck structure

Abstract

An efficient global sensitivity analysis method based on the Polynomial Chaos (PC) method is applied to investigate the strength of a trimaran cross-deck structure. The PC method can reduce the amount of computation and converge faster than the Monte Carlo (MC) method. For the quantitative investigation of the sensitivity of the stresses in the cross-deck to the changes in the cross-deck plate thickness, Latin Hypercube Sampling (LHS) was used to obtain samples, and a Finite Element Method (FEM) model was used to compute the stress based on a load case prescribed by the Rules for the Classification of Trimarans. The PC surrogate models of different degrees of polynomial were trained and validated from the perspective of bias and variance. The third-degree PC model was selected to approximate the response of the stresses to the plate thickness. The global sensitivity indices were computed on the basis of the PC surrogate model, and the results were compared with those obtained by MC. The third-degree PC surrogate model effectively approximates the response of the stresses to the plate thickness, and the sensitivity indices of PC converges much faster than those of MC with respect to the number of samples. The stress at the corner of the cross-deck is the most sensitive to the thickness of the aft web. Meanwhile, the stress at the main-hull connection is the most sensitive to the thickness of the lower panel. Furthermore, the maximum von Mises stress and shear stress at the side-hull connection are the most sensitive to the thickness of the upper panel, and the maximum principal stress at the side-hull connection is the most sensitive to the thickness of the lower panel. The feasibility and efficiency of the PC method is proven, and the influence of the plate thickness on the stress response is described quantitatively.