Analytical Systems Engineering Advanced Mathematics

摘要

This effort was concerned with identifying and assessing the primary technical barriers and risks that must be overcome to establish fast computational methods for uncertainty analysis in large models of interconnected components in which the shape of system-level dynamics is important. The results of this study show tremendous promise for computationally efficient methods for propagating uncertainty. Numerous approaches were investigated on problems ranging from the control of afterburner combustion instabilities to modeling organic molecules and DNA. This contract also resulted in a highly successful workshop on the Design of Dynamical Systems Robust to Uncertainty, engaging experts from international communities. The following papers are appended to this report: 'Propagation of Uncertain Inputs through Networks of Nonlinear Components;' 'Graph Decomposition Methods for Uncertainty Propagation in Complex, Nonlinear Interconnected Dynamical Systems;' 'Spectral Balance: A frequency Domain Framework for Analysis of Nonlinear Dynamical Systems;' 'An Iterative Method for Propagation of Probability Distributions in Feedback Systems;' 'Uncertainty in the Dynamics of Conservative Maps;' 'Dynamics in Molecular Modelling and the Scope for Uncertainty Analysis by Dellnitz-Preis and Polynomial Chaos Methods;' and 'Symmetry-Breaking and Uncertainty Propagation in a Reduced Order Thermo-acoustic Model.' (51 refs. following main report).