Solution of linear dynamic systems with uncertain properties by stochastic reduced order models

Abstract

A novel method, referred to as the stochastic reduced order model (SROM) method, is proposed for finding statistics of the state of linear dynamic systems with random properties subjected to random noise. The method is conceptually simple, accurate, computationally efficient, and non-intrusive in the sense that it uses existing solvers for deterministic differential equations to find state properties.Bounds are developed on the discrepancy between the exact and the SROM solutions under some assumptions on system properties. The bounds show that the SROM solutions converge to the exact solutions as the SROM representation of the vector of random system parameters is refined. Numerical examples are presented to illustrate the implementation of the SROM method and demonstrate its accuracy and efficiency.