Non-Gaussian buffeting analysis of large structures by means of a Proper Orthogonal Decomposition

Abstract

Proper Orthogonal Decomposition is implemented in a Bispectral Stochastic Analysis of large MDOF structures. Although Higher Order Stochastic Analysis has been introduced few decades ago, its establishment has found place only in a theoretical way, or applied to very small systems. Its heavy computational cost as well as resource consumption burden has let it aside for practical civil engineering applications. Nevertheless, in wind engineering, the community is increasingly considering the importance of non-Gaussian nature of wind induced vibrations. This is of interest for the extreme value analysis, for which many theoretical and empirical models exist for non-Gaussian random processes. In this context, a (bi-)spectral approach is realized in a 2-D frequency space where the bispectrum is computed then the 3rd statistical moment is obtained by means of a twofold integration. These operations are quite heavy as soon as the dimension of the problem increases. A novel algorithm implementation is proposed. It hinges on (i) the use of Proper Orthogonal Decomposition and the (ii) development of an optimized numerical method. The proposed algorithmic arrangement minimizes the number of operations, and consequently saves time and memory, while conserving precision in estimating 3rd order statistical moments of structural responses.