Gramian Projection-based Interpolation Strategy for Parametric Model Order Reduction of Gas Pipeline-Networks
Gramsche Projektion-basierte Interpolationsstrategie für parametrische Modellreduktion von Gasrohrnetzwerken
Please always quote using this URN: urn:nbn:de:bvb:29-opus4-86490
- This thesis aims to investigate the applicability of model order reduction for
gas transport in pipeline-networks. For this purpose, we consider two different
MOR techniques, one for linear systems and the other for nonlinear systems.
A new framework is developed for the linear case, which is composed of lin-
earizing the nonlinear model, performing the spatial discretization based on stag-
gered grids, transforming the linear, time-invariant system in descriptor form into
standard state-space form based on the reduction of the differentiation-index by
applying the singular value decomposition of the system matrices and reducing
the full order model via Gramian projection-basedThis thesis aims to investigate the applicability of model order reduction for
gas transport in pipeline-networks. For this purpose, we consider two different
MOR techniques, one for linear systems and the other for nonlinear systems.
A new framework is developed for the linear case, which is composed of lin-
earizing the nonlinear model, performing the spatial discretization based on stag-
gered grids, transforming the linear, time-invariant system in descriptor form into
standard state-space form based on the reduction of the differentiation-index by
applying the singular value decomposition of the system matrices and reducing
the full order model via Gramian projection-based methods, e.g. the balanced
truncation, balancing-free method, singular perturbation approximation and the
optimal Hankel-norm approximation.
The reason for this framework is the development of a stability-preserving
matrix interpolation strategy for parametric reduced order models. In comparison
to the existing matrix interpolation method, new steps include transforming the
reduced order model into modal form, reordering the parametric eigenmodes
according to the correlation and instead of the matrix pencil only interpolating
the eigvenvalues with positive weighting coefficients.
For the nonlinear case, the standard quadratic-bilinearization model order re-
duction method for systems with a single input is extended to systems with multi-
ple inputs by using the properties of the Kronecker product. The method consists
of the quadratic-bilinearization of the nonlinear full order model by employing
new variables for the nonlinear terms, approximating the resulting quadratic-
bilinear system by its homogeneous subsystems of degree k, k ∈ N, and reducing
the subsystems by using moment-matching.
Nonzero initial values may lead to worse error-behavior for the model order
reduction. A method tackling the latter issue is proposed and discussed. Ad-
ditionally, we show that the parametric quadratic-bilinear reduced order models
can be evaluated over a wide parameter range by using matrix interpolation.…
Author: | Yi Lu |
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Persistent identifiers - URN: | urn:nbn:de:bvb:29-opus4-86490 |
Referee: | Nicole Marheineke |
Document Type: | Doctoral Thesis |
Language: | English |
Year of publication: | 2017 |
Date of online publication (Embargo Date): | 2017/07/28 |
Publishing Institution: | Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) |
Granting institution: | Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Naturwissenschaftliche Fakultät |
Acceptance date of the thesis: | 2017/06/29 |
Release Date: | 2017/08/07 |
SWD-Keyword: | model order reduction; gas transport in pipeline-networks; stability-preserving matrix interpolation |
Institutes: | Naturwissenschaftliche Fakultät / Department Mathematik |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 519 Wahrscheinlichkeiten, angewandte Mathematik |
open_access (DINI-Set): | open_access |
Licence (German): |