There is a great importance for faithful reduced order models (ROMs) that are valid over a range of system parameters and initial conditions. In this paper, we demonstrate through two nonlinear dynamic models (pinned–pinned beam and thin plate) that are both randomly and periodically forced that smooth orthogonal decomposition (SOD)-based ROMs are valid over a wide operating range of system parameters and initial conditions when compared to proper orthogonal decomposition (POD)-based ROMs. Two new concepts of subspace robustness—the ROM is valid over a range of initial conditions, forcing functions, and system parameters—and dynamical consistency—the ROM embeds the nonlinear manifold—are used to show that SOD, as opposed to POD, can capture the low order dynamics of a particular system even if the system parameters or initial conditions are perturbed from the design case.
Robust and Dynamically Consistent Model Order Reduction for Nonlinear Dynamic Systems
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 30, 2014; final manuscript received August 24, 2014; published online September 24, 2014. Assoc. Editor: Prashant Mehta.
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Segala, D. B., and Chelidze, D. (September 24, 2014). "Robust and Dynamically Consistent Model Order Reduction for Nonlinear Dynamic Systems." ASME. J. Dyn. Sys., Meas., Control. February 2015; 137(2): 021011. https://doi.org/10.1115/1.4028470
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