H2 optimal and frequency limited approximation methods for large-scale LTI dynamical systems

Abstract

Model order reduction over a bounded frequency range is more adapted than the standard H 2 approximation whenever the entire frequential behaviour of the large-scale model is not needed or not accurately known. However most of the methods that enable to reduce a model on a limited frequency range are based on the use of weights. Yet their determination is often an issue for engineers. That is why, in this paper, two weight-free model approximation algorithms are proposed. They are based on recent algorithms that achieve local H 2 optimal model reduction (see Gugercin (2007), Van Dooren et al. (2008) and Gugercin et al. (2008)). The proposed algorithms efficiency are validated both on a standard benchmark and on an industrial use case.

A‐priori pole selection for reduced models in vibro‐acoustics

“…If we choose only the mirror images of eigenvalues lying in a specific frequency region as new expansion points, the reduced model is valid in this frequency region. This choice is only possible due to the second order structure, so the strategy differs from the use of frequency-limited Gramians for first order systems proposed in [3,4].…”

Model reduction using a frequency-limited -cost

“…Recently two variants of these methods have been published. The first one is a frequency-weighted version that is applicable on siso systems, see Anić et al (2013), and the second one is a frequency-limited version with the same goal as the method presented in this article, but using a different technique, see Vuillemin et al (2013).…”

“…• wbt-weighted balanced truncation, an implementation of the method in Enns (1984) • flbt-frequency limited balanced truncation, an implementation of the method in Gawronski and Juang (1990) • mflbt-modified frequency limited balanced truncation, an implementation of the method in Gugercin and Antoulas (2004) • flistia-frequency limited iterative tangential interpolation algorithm (see Vuillemin et al (2013)), the implementation in the more-toolbox is used…”

Frequency-limited pseudo-optimal rational Krylov algorithm for power system reduction

“…The algorithm requires the solution of Lyapunov equations and linear matrix inequalities (LMIs) to find the optimal ROM, which is not feasible in a large-scale setting. In [22], the problem is described as bitangential Hermite interpolation, which can be solved in a computationally efficient way. However, the original system is required to be converted into pole-residue form, which is again computationally not feasible in a large-scale setting.…”

“…However, the original system is required to be converted into pole-residue form, which is again computationally not feasible in a large-scale setting. Moreover, both the algorithm [21] and [22] are iterative algorithms with no guarantee on the convergence, and they do not have a modal preservation property. In this paper, we consider the same problem of [20] and propose a computationally efficient MOR algorithm that ensures a good accuracy in the specified frequency region with explicit modal preservation.…”