Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Balancing for nonlinear systems
Systems & Control Letters
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Interval analysis and fuzzy set theory
Fuzzy Sets and Systems - Special issue: Interfaces between fuzzy set theory and interval analysis
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Application of polynomial chaos in stability and control
Automatica (Journal of IFAC)
WSEAS TRANSACTIONS on SYSTEMS
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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.