Higher-order Taylor series expansion for uncertainty quantification with efficient local sensitivity

Abstract

An efficient numerical approach for uncertainty quantification using a higher-order Taylor series expansion is presented. Moreover, local sensitivities in the Taylor series are evaluated using a high-accuracy and computationally efficient approach called modified forward finite difference (ModFFD). Once the sensitivities are estimated, with ModFFD, the stochastic response can be obtained for different realizations of the random inputs without incurring additional function evaluations. The main advantage of this approach is that it is applicable for any input distributions and is unrestricted by the nature of random input variables (correlated and uncorrelated). To test the presented approach, several analytical and engineering problems were considered with up to twenty-two random variables. For the engineering problem, a ten-bar truss problem with twenty-two random variables and buckling of a composite laminate with twenty random variables is considered. The comparison of the results with that of a large number of Monte Carlo Simulations demonstrated its high accuracy and computational efficiency for random inputs with non-standard random inputs and varying correlation.