Non-intrusive generalized polynomial chaos for the robust stability analysis of uncertain nonlinear dynamic friction systems

This paper is devoted to the stability analysis of uncertain nonlinear dynamic dry friction systems. The stability property of dry friction systems is known to be very sensitive to the variations of friction laws. Moreover, the friction coefficient admits dispersions due to the manufacturing processes. Therefore, it becomes necessary to take this uncertainty into account in the stability analysis of dry friction systems to ensure robust predictions of stable and instable behaviors. The generalized polynomial chaos formalism is proposed to deal with this challenging problem treated in most cases with the prohibitive Monte Carlo based techniques. Two equivalent methods presented here combine the non-intrusive generalized polynomial chaos with the indirect Lyapunov method. Both methods are shown to be efficient in the estimation of the stability and instability regions with high accuracy and high confidence levels and at lower cost compared with the classic Monte Carlo based method.