Long-time numerical simulations of large-scale mechanistic models of complex systems (e.g., molecular dynamics, computational fluid dynamics, structural finite element, or multi-body dynamics models) are still problematic, either due to numerical instabilities or the excessive necessary computational resources. Therefore, reduced models that can be simulated for long-time and provide truthful approximations to the actual long-time dynamics, are needed. A new framework — based on new concepts of dynamical consistency and subspace robustness — for identifying subspaces suitable for reduced-order model development is presented. Model reductions based on proper and smooth orthogonal decompositions (POD and SOD, respectively) are considered and tested using a nonlinear four-degree-of-freedom model. It is shown that the new framework identifies subspaces that provide accurate model reductions for a range of forcing parameters, and that only four and higher dimensional models could be dynamically consistent. In addition, for reduced-order models based on randomly driven data, a four-dimensional SOD-based model outperformed a five-dimensional POD-based model. Finally, randomly driven data-based models generally outperformed harmonically driven data-based models when tested for a wide range of forcing amplitudes.

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