Stability-Preserving Interpolation Strategy for Parametric MOR of Gas Pipeline-Networks
Optimization and control of large transient gas networks require the fast simulation of the underlying parametric partial differential algebraic systems. Surrogate modeling techniques based on linearization around specific stationary states, spatial semi-discretization and model order reduction allow for the set-up of parametric reduced order models that can act as basis sample to cover a wide parameter range by means of matrix interpolations. However, the interpolated models are often not stable. In this paper, we develop a stability-preserving interpolation method.
The German CRC TRR 154 Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks is acknowledged.
- 1.Amsallem, D., Farhat, C.: An online method for interpolating linear parametric reduced-order models. SIAM J. Sci. Comput. 33(5), 2169–2198 (2011)Google Scholar
- 2.Geuss, M., Panzer, K., Lohmann, B.: On parametric model order reduction by matrix interpolation. In: European Control Conference (2013)Google Scholar
- 3.Kailath, T.: Linear Systems. Prentice Hall, Englewood Cliffs (1980)Google Scholar
- 4.Lu, Y.: Gramian projection-based interpolation strategy for parametric MOR of gas pipeline-networks. Ph.D. thesis, FAU Erlangen-Nürnberg (2017)Google Scholar
- 5.Lu, Y., Marheineke, N., Mohring, J.: Interpolation strategy for BT-based parametric MOR for gas pipeline-networks. In: MS&A – Modeling, Simulation and Application. Springer, Heidelberg (2017)Google Scholar