Uncertainty propagation using polynomial chaos and centre manifold theories

This paper proposes a new methodology for uncertainty quantification in the field of nonlinear dynamic system analysis. It consists in combining both the centre manifold theory and the polynomial chaos approach. The first one is known to be a powerful tool for model reduction of nonlinear dynamic systems in Hopf bifurcation point neighbourhood while the polynomial chaos approach is an efficient tool for uncertainty propagation. Therefore, to couple the two methods can help to overcome computational difficulties due to both the complexity of nonlinear dynamic systems and the cost of the uncertainty propagation with the prohibitive Monte Carlo method. The feasibility and efficiency of the proposed methodology is investigated. So, a two degree of freedom model describing a drum brake system subject to uncertain initial conditions is considered.