Model Reduction of Input-Output Dynamical Systems by Proper Orthogonal Decomposition

We performed a study based on an empirical-based model reduction technique known as balanced proper-orthogonal-decomposition (POD). The technique, applicable to nonlinear systems, yields a set of basis functions that spans a POD-based subspace capturing the essential input-output dynamics structure and projection of the original model on this subspace yields the balanced reduced-order model (BROM). In this study the performance of the BROM is compared to the original high-order linear model and the dependence on the sampling parameters is studied. Even with large number of snapshots, we show that at least 52 real states are needed for the BROM to produce good performance. The sampling frequency has to be high enough to cover twice of the high-frequency modes of interest. We develop a novel algorithm, which in linear systems is based on a direct decomposition of the discrete Hankel matrix. The algorithm serves as a generalized balanced POD scheme for input-output model reduction. The algorithm is especially e‐cient for reduced number of snapshots and it well-suits nonlinear systems since propagation of adjoint equation is not required. A single sample rate is found inadequate to cover both high and low-end frequencies. To reduce the number of snapshots signiflcantly, we show that multiple sampling rates improves performance dramatically.