Robust and Dynamically Consistent Model Order Reduction for Nonlinear Dynamic Systems

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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.