A hybrid dimensional reduction method for uncertainty analysis of structures

Abstract

In order to address the issue of uncertainty analysis of large scale structures with high-dimensional input variables in the engineering, a hybrid dimensional reduction method (H-DRM) is pro-posed in this work. The method can be seen as an improvement on the multiplicative dimensional reduc-tion method (M-DRM). First, the original response function is approximated by the univariate M-DRM, based on which the variance contribution to the output variance can be estimated by three point estimate. The significant variables are thereby identified and further extended to the bivariate M-DRM. The final approximation of the original response function can be seen as a hybrid combination of univariate M-DRM of all variables and bivariate M-DRM of significant variables. The proposed H-DRM is then used for the calculation of moments and structural reliability, with the help of three point estimate. The pro-posed method can adaptively achieve the balance of computational efficiency and accuracy, and is able to avoid the curse of dimension when using three point estimate. Several examples are studied to demonstrate the feasibility of the proposed method.