Robust and dynamically consistent reduced order models

Document Type

Conference Proceeding

Date of Original Version



The need for reduced order models (ROMs) has be- come considerable higher with the increasing technological advances that allows one to model complex dynamical sys- Tems. When using ROMs, the following two questions al- ways arise: 1) "What is the lowest dimensiona- ROM?" and 2) "How well does the ROM capture the dynamics of the full scale system mode-?" This paper considers the newly developed concepts the authors refer to as subspace robustness- The ROM is valid over a range of initial conditions, forcing functions, and system parameters-and dynamical con- sistency-the ROM embeds the nonlinear manifold{which quanitatively answers each question. An eighteen degree- of-freedom pinned-pinned beam which is supported by two nonlinear springs is forced periodically and stochastically for building ROMs. Smooth and proper orthogonal decom- positions (SOD and POD, respectively) based ROMs are dynamically consistent in four or greater dimensions. In the strictest sense POD-based ROMs are not considered coherent whereas, SOD-based ROMs are coherent in roughly five dimesions and greater. Is is shown that in the periodically forced case, the full scale dynamics are captured in a five- dimensional POD and SOD-based ROM. For the randomly forced case, POD and SOD-based ROMs need three dimensions but SOD captures the dynamics better in a lower- dimensional space. When the ROM is developed from a different set of initial conditions and forcing values, SOD outperforms POD in periodic forcing case and are equal in the random forcing case. Copyright © 2013 by ASME.

Publication Title

ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)


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