Decoupled approach to Multidisciplinary system analysis and Design under epistemic uncertainty

Abstract

An efficient probabilistic approach is developed for uncertainty propagation in multidisciplinary system analysis under epistemic uncertainty. A decoupled approach is used in this thesis to un-nest the multidisciplinary system analysis from the probabilistic analysis to achieve better computational efficiency. This study proposes a moment matching based approach to estimate the first four moments of the coupling variables (variables that couple two or more sub-systems/ disciplines). The estimated first four moments are used as the uncertainty descriptors of the coupling variables. The probability density functions of the coupling variables are determined using the estimated first four moments. The proposed moment matching approach uses Taylor series expansion, tensor product quadrature, and univariate dimension reduction methods to estimate the moments of the coupling variables. Once the uncertainty in the coupling variables is quantified, the system level uncertainty propagation analysis is similar to single discipline problems which is available in the literature. The proposed methods are equally applicable to both sampling and analytical approximation-based reliability analysis methods. The proposed approach does not require any repeated sampling by Monte Carlo simulation, and yet can generate results similar to a sampling-based approach by Monte Carlo simulation; thus relieves us of the time consuming computationally prohibitive nature of Monte Carlo simulation. A mathematical problem and a real-life engineering problem are used to illustrate the proposed methods. The accuracy of the proposed decoupled approach is also verified by Monte Carlo simulation.