Non-intrusive reduced order model for stochastic dynamical systems
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Stochastic dynamical systems have garnered much attention in modern engineering and applied science for modeling complex underlying physical phenomen under uncertainty. This contribution presents a novel method for constructing reduced order model of nonlinear stochastic dynamical systems with both stochastic excitation and random system parameters. The method uses proper orthogonal decomposition (POD) to construct reduced-order model of stochastic dynamical systems in its state space representation. Discrete empirical interpolation method (DEIM) is further used to reduce the number of the nonlinear terms in the state space representation. Kriging model is employed to approximate every nonlinear term selected by DEIM. The effectiveness of the proposed method is validated with a high-dimensional nonlinear hysteretic frame structure.
