WIAS Preprint No. 2537, (2018)

A Bayesian approach to parameter identification in gas networks



Authors

  • Hajian, Soheil
  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Schillings, Claudia
  • Strogies, Nikolai

2010 Mathematics Subject Classification

  • 35L40 65C50 65M32

Keywords

  • Bayesian inversion, distributed friction coefficient, gas network/pipeline, hyperbolic PDE system

DOI

10.20347/WIAS.PREPRINT.2537

Abstract

The inverse problem of identifying the friction coefficient in an isothermal semilinear Euler system is considered. Adopting a Bayesian approach, the goal is to identify the distribution of the quantity of interest based on a finite number of noisy measurements of the pressure at the boundaries of the domain. First well-posedness of the underlying non-linear PDE system is shown using semigroup theory, and then Lipschitz continuity of the solution operator with respect to the friction coefficient is established. Based on the Lipschitz property, well-posedness of the resulting Bayesian inverse problem for the identification of the friction coefficient is inferred. Numerical tests for scalar and distributed parameters are performed to validate the theoretical results.

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