Non-intrusive generalized polynomial chaos approach to the stability analysis of uncertain nonlinear dynamic systems

Abstract

This paper is devoted to the stability analysis of uncertain nonlinear dynamic systems. The generalized polynomial chaos formalism is proposed to deal with this challenging problem treated in most cases by using the prohibitive Monte Carlo based techniques. Two equivalent methods combining the non-intrusive generalized polynomial chaos with the indirect Lyapunov method are presented. Both methods are shown to be efficient in the estimation of the stability and instability regions of nonlinear dynamic systems with probabilistic uncertainties. Indeed, it is illustrated that the proposed methods give results of high accuracy and high confidence levels at lower cost compared with the classic Monte Carlo based method.Index Terms-Uncertain nonlinear dynamic system, stability analysis, generalized polynomial chaos, nonintrusive approach, Lyapunov indirect method