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
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
Statistical approach in complex circuits by a wavelet based Thevenin's theorem
ICC'07 Proceedings of the 11th Conference on Proceedings of the 11th WSEAS International Conference on Circuits - Volume 11
Uncertainty propagation using polynomial chaos and centre manifold theories
ISPRA'10 Proceedings of the 9th WSEAS international conference on Signal processing, robotics and automation
Application of polynomial chaos in stability and control
Automatica (Journal of IFAC)
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A new methodology for a robust analysis of uncertain nonlinear dynamic systems is presented in this paper. The originality of the method proposed lies in the combination of the centre manifold theory with the polynomial chaos approach. The first one is known to be a powerful tool for model reduction of nonlinear dynamic systems in the neighbourhood of the Hopf bifurcation point 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.