The improvement of a variance-based sensitivity analysis method and its application to a ship hull optimization model

Increasingly, more parameters to express and modify ship hull forms are used as variables to identify better designs; however, such proliferation of parameters may result in inefficient and impractical optimization. Dimension reduction by sensitivity analysis (SA) is a feasible way to alleviate this problem. The widely applied variance-based SA is able to determine uninfluential variables for the descending dimension. Sobol and kriging model-based tensor-product basis function (TPBF) methods are studied as representatives of the classical and metamodeling approach of variance-based SA, respectively. The Sobol method is improved by new integrals with less variance and quasi-random numbers with lower star discrepancy for increasing SA accuracy. New integrals reduce the variance of estimation for conditional variance, which results in higher accuracy as demonstrated from the perspective of the Monte Carlo method. More uniform quasi-random numbers generated by uniform design instead of a conventional Sobol sequence potentially improve the accuracy of the quasi Monte Carlo method. A function indicates that both measures can effectively increase the accuracy of SA. The kriging model-based TPBF method is extended from the original ordinary kriging model to linear and quadratic kriging models to extend its application in hull form optimization. A numerical example demonstrates that the accuracy of the kriging model-based TPBF method is higher than that of the improved Sobol method. Nevertheless, it is vulnerable to ill-conditioned correlation matrices. Finally, both methods are implemented in a ship hull form optimization model, and an uninfluential variable for dimension reduction is determined. Both methods should be applied simultaneously if possible due to the higher accuracy of the kriging model-based TPBF method and better robustness of the improved Sobol method.