Stochastic Multidisciplinary Analysis with High Dimensional Coupling

1. Abstract This paper combines efficient uncertainty propagation and sampling techniques for uncertainty quantification of aerospace structures. A new method is developed for including uncertainty quantification in multi-disciplinary system analysis (MDA) that usually requires iterative analyses with a large number of coupling variables. The methodology for MDA estimates the probability distributions of the coupling variables based on computing the probability of satisfying the inter-disciplinary compatibility equations. This idea is used to develop a joint distribution approach for multidisciplinary analysis. Using the distributions of the feedback variables, the bi-directional coupling can be reduced to unidirectional coupling, while still preserving the mathematical relationship between the coupling variables. In realistic structures, the number of coupling variables is potentially large. Therefore, principal component analysis (PCA) is adopted to decrease the number of coupling variables. For computational efficiency, a copula-based sampling is employed to implement probabilistic multi-disciplinary analysis. The proposed methods are illustrated using 3-D aero-elasticity analysis of an aircraft wing. 2.