Speaker
Description
Modal truncation has long been a fundamental approach of model order reduction: to systematically eliminate eigenmodes of a dynamical system that contribute little to the modeling behavior over a given time/frequency range. Typically, this procedure requires the ability to access and utilize intrusive state-space information about the underlying full-order system, which can be infeasible for larger state dimensions or impossible if the full-order system is not known in closed form. Data-driven approaches like proper orthogonal decomposition address these concerns by identifying empirical modes of the system derived from multiple time-domain trajectories of the full-order model, whereafter model reduction can proceed as in the state-space formulation. In this work, we show how one can truncate empirical eigenmodes with only frequency-domain samples of a system's transfer function by utilizing contour integral methods.
After reviewing the necessary theoretical foundations, we will discuss how contour integration and the pole-residue decomposition of an underlying system can be combined to identify all eigenvalues within an arbitrary domain in the complex plane. This tool allows us to perform modal truncation, or identify a stable-unstable decomposition of the underlying system. Through the use of a key result of Keldysh, contour integral methods can also identify eigenvalues of analytic nonlinear matrix-valued functions. We will show numerical experiments illustrating how our data-driven modal truncation method performs on application problems and compare with other state-of-the-art methods.