Generalizations of data-driven balancing: What to sample for different balancing-based reduced models

Fuente: arXiv
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Hauptverfasser: Reiter, Sean, Gosea, Ion Victor, Gugercin, Serkan
Format: Preprint
Veröffentlicht: 2023
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author Reiter, Sean
Gosea, Ion Victor
Gugercin, Serkan
author_facet Reiter, Sean
Gosea, Ion Victor
Gugercin, Serkan
contents The quadrature-based balanced truncation (QuadBT) framework of arXiv:2104.01006 is a non-intrusive reformulation of balanced truncation (BT), a classical projection-based model-order reduction technique for linear systems. QuadBT is non-intrusive in the sense that it builds approximate balanced truncation reduced-order models entirely from system response data, e.g., transfer function measurements, without the need to reference an explicit state-space realization of the underlying full-order model. In this work, we generalize the QuadBT framework to other types of balanced truncation model reduction. Namely, we show what transfer function data are required to compute data-driven reduced models by balanced stochastic truncation, positive-real balanced truncation, and bounded-real balanced truncation. In each case, these data are evaluations of particular spectral factors associated with the system of interest. These results lay the theoretical foundation for data-driven reformulations of the aforementioned BT variants. Although it is not yet clear how to compute or obtain these spectral factor data in a practical real-world setting, examples using synthetic (numerically evaluated) transfer function data are included to validate the data-based reduced models.
format Preprint
id arxiv_https___arxiv_org_abs_2312_12561
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Generalizations of data-driven balancing: What to sample for different balancing-based reduced models
Reiter, Sean
Gosea, Ion Victor
Gugercin, Serkan
Numerical Analysis
Systems and Control
Optimization and Control
93B15 (Primary) 93A15, 37M99, 65D30, 65K99, 15A24 (Secondary)
The quadrature-based balanced truncation (QuadBT) framework of arXiv:2104.01006 is a non-intrusive reformulation of balanced truncation (BT), a classical projection-based model-order reduction technique for linear systems. QuadBT is non-intrusive in the sense that it builds approximate balanced truncation reduced-order models entirely from system response data, e.g., transfer function measurements, without the need to reference an explicit state-space realization of the underlying full-order model. In this work, we generalize the QuadBT framework to other types of balanced truncation model reduction. Namely, we show what transfer function data are required to compute data-driven reduced models by balanced stochastic truncation, positive-real balanced truncation, and bounded-real balanced truncation. In each case, these data are evaluations of particular spectral factors associated with the system of interest. These results lay the theoretical foundation for data-driven reformulations of the aforementioned BT variants. Although it is not yet clear how to compute or obtain these spectral factor data in a practical real-world setting, examples using synthetic (numerically evaluated) transfer function data are included to validate the data-based reduced models.
title Generalizations of data-driven balancing: What to sample for different balancing-based reduced models
topic Numerical Analysis
Systems and Control
Optimization and Control
93B15 (Primary) 93A15, 37M99, 65D30, 65K99, 15A24 (Secondary)
url https://arxiv.org/abs/2312.12561