A new framework for H2-optimal model reduction

Abstract

In this contribution, a new framework for H 2 -optimal reduction of multiple-input, multipleoutput linear dynamical systems by tangential interpolation is presented. The framework is motivated by the local nature of both tangential interpolation and H 2 -optimal approximations. The main advantage is given by a decoupling of the cost of optimization from the cost of reduction, resulting in a significant speedup in H 2 -optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producing H 2 -optimal reduced models at a far lower cost than conventional algorithms. The paper ends with a brief discussion on how the idea behind the framework can be extended to approximate further system classes, thus showing that this truly is a general framework for interpolatory H 2 reduction rather than just an additional reduction algorithm.

Predicting near optimal interpolation points for parametric model order reduction using regression models

“…For the case of generally structured systems as considered in this paper, no solution to this problem for projection-based model reduction is known yet. Another idea for future investigations is the reduction of the computational costs of StrAIKA by considering an additional layer of approximation as it has been done for IRKA-like methods in [6,18].…”

“…While SPTF-IRKA employs a complete run of TF-IRKA to construct an order-r unstructured approximation of the structured reduced-order model Σ, in SPTF-IRKA the transfer function Ĥ is sampled in the frequency range of interest Ω to reveal all essential system dynamics. Similar to the methods discussed in [6,18] the intermediate models Σ and Σ L are used to leverage the computational costs of different tasks.…”

“…In this situation, the outer loop of SPTF-IRKA (Algorithm 2) can also be seen as a prereduction step that reduces the computational costs of TF-IRKA. Similar ideas to reduce the computational costs of iterative model-order reduction methods have been used, for example, in [6,14,18].…”

Automatic model order reduction for vibro‐acoustic problems

“…In the iterative algorithm, r linear systems of order n have to be solved each iteration, making the method rather expensive. Instead of performing the iterative optimization step on the full order model, CIRKA creates an intermediate reduced model, which is used for the optimization [5]. Using [6], CIRKA can be modified to find a local optimum for the expansion points in a certain frequency range, making the reduced model valid in this region.…”