Generalizations of data-driven balancing: What to sample for different balancing-based reduced models
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911119891759104 |
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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 |