A Vine Copula-Based Hierarchical Framework for Multiscale Uncertainty Analysis

Uncertainty analysis is an effective methodology to acquire the variability of composite material properties. However, it is hard to apply hierarchical multiscale uncertainty analysis to the complex composite materials due to both quantification and propagation difficulties. In this paper, a novel hierarchical framework combined R-vine copula with sparse polynomial chaos expansions is proposed to handle multiscale uncertainty analysis problems. According to the strength of correlations, two different strategies are proposed to complete the uncertainty quantification and propagation. If the variables are weakly correlated or mutually independent, Rosenblatt transformation is used directly to transform non-normal distributions into the standard normal distributions. If the variables are strongly correlated, the multidimensional joint distribution is obtained by constructing R-vine copula, and Rosenblatt transformation is adopted to generalize independent standard variables. Then, the sparse polynomial chaos expansion is used to acquire the uncertainties of outputs with relatively few samples. The statistical moments of those variables that act as the inputs of next upscaling model can be gained analytically and easily by the polynomials. The analysis process of the proposed hierarchical framework is verified by the application of a 3D woven composite material system. Results show that the multidimensional correlations are modeled accurately by the R-vine copula functions, and thus uncertainty propagations with the transformed variables can be done to obtain the computational results with consideration of uncertainties accurately and efficiently.