A framework for optimal temporal reduced order modeling of nonlinear dynamical systems

作者：LaBryer A^*; Attar P J; Vedula P

来源：Journal of Sound and Vibration, 2013, 332(4): 993-1010.

DOI：10.1016/j.jsv.2012.10.008

An optimal temporal reduced order modeling framework is proposed for nonlinear dynamical systems. The governing equations are modified for an under-resolved simulation with an arbitrary scheme and a coarse temporal grid. Subgrid-scale models are developed to account for the unresolved temporal structure via inclusion of statistical information on a multi-point temporal stencil. These models are based upon principles of mean-square error minimization, conditional expectations and stochastic estimation. In order to validate the proposed framework, we investigate time-periodic solutions for a canonical Duffing oscillator using a coarse harmonic balance scheme. In order to demonstrate application of the proposed framework to a high dimensional nonlinear dynamical system, we also investigate a simply supported, geometrically nonlinear beam under the influence of time-periodic external forcing. For both problems, the subgrid-scale models are shown to significantly improve the accuracy of coarse-grained solutions.

• 出版日期2013-2-18