Gramian Projection-based Interpolation Strategy for Parametric Model Order Reduction of Gas Pipeline-Networks

Document Type
Doctoral Thesis
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Issue Year
Lu, Yi

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-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.

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