Black box stability preserving reduction techniques in the Loewner framework for the efficient time domain simulation of dynamical systems with damping treatments

Abstract

New applications, such as material characterization, auralization and virtual sensing, have renewed the need and interest in efficient transient time-domain simulations of dynamical systems. However, the typical required numerical simulations for these applications are cumbersome to compute due to the high computational burden involved in the calculation of mechanical systems. Model order reduction techniques are important enablers to reduce this computation time. However, many reduction techniques fail when viscous or thermal damping is present in the system. This work elaborates on two non-intrusive reduction techniques using the Loewner framework which can serve as a tool for the efficient time domain simulation of second order dynamical systems with damping treatments. The reduced models are constructed using frequency domain data, however, for time domain simulations, the reduced models need to be real-valued and stable. One methodology exploits the well-known inverse fast Fourier transform, while the second methodology employs a reduced order model which serves as an input for a time marching technique. Although the Loewner reduction technique does not preserve the stability of the original system, both proposed methodologies show to be able to return an accurate and sufficiently stable time domain response.