Second-order derivatives for geometrical uncertainties

Abstract

The paper presents a method for handling geometrical uncertainties. In this case, discretization of continuous uncertainty field leads to a large set of correlated uncertainties/random variables. In order to reduce dimensionality of the problem, the authors propose a method that takes advantage of both the probabilistic information (covariance) and the local behavior of the objective (up to a second-order derivatives). The proposed method is verified for the UMRIDA BC-03 test case (UMRIDA Consortium, Test case description innovative database for UQ and RDM, 2014). The method is shown to outperform the Karhunen-Loeve decomposition and the analysis based purely on the Hessian matrix. The method allows to keep the same level of accuracy with a significant reduction of the number of uncertainties.