Stochastic Multidisciplinary Analysis with High-Dimensional Coupling

Abstract

This paper presents a novel approach for efficient uncertainty quantification and propagation in multidisciplinary analysis with a large number of coupling variables. The proposed methodology has three elements: Bayesian network, copula-based sampling, and principal component analysis. The Bayesian network represents the joint distribution of multiple variables through marginal distributions and conditional probabilities, and it updates the distributions based on new data. This paper uses this concept to develop a novel approach for probabilistic multidisciplinary analysis, that is, inference of distributions of the coupling variables by enforcing the interdisciplinary compatibility condition (which is treated similar to data for updating). The Bayesian network is built using only a few iterations of the coupled multidisciplinary analysis, without iterating until convergence. A copula-based sampling technique is employed for efficient sampling from the joint and conditional distributions. Further savings are achieved through dimension reduction using principal component analysis. A mathematical example and an aeroelastic analysis of an aircraft wing are used to demonstrate the proposed probabilistic multidisciplinary analysis methodology.