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Flow Process Models for Pipeline Diagnosis

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Automatic Control, Robotics, and Information Processing

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 296))

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Abstract

This chapter examines the problem of modeling and parameterization of the transmission pipeline flow process. First, the base model for discrete time is presented, which is a reference for other developed models. Then, the diagonal approximation (AMDA) method is proposed, in which the tridiagonal sub-matrices of the recombination matrix are approximated by their diagonal counterparts, which allows for a simple determination of the explicit form of the inverse matrix. Another suggestion is the Thomas model (ATM), in which the basic model is reformulated to a form to which the Thomas algorithm applies, at which the computational complexity of the order \(\mathcal {O}(N)\) can be obtained. The fourth suggestion is a steady state analytical model (AMSS), characterizing the steady state after transient processes. In addition, the parameterization of the discrete models in space and time is analyzed, proposing a method ensuring the maximum margin of numerical stability. This model is verified by means of simulation tests. Finally, the developed model is compared with the basic model, taking into account the accuracy and time of calculations.

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Authors and Affiliations

  1. Department of Robotics and Decision Systems, Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233, Gdańsk, Poland

    Zdzisław Kowalczuk & Marek Sylwester Tatara

Authors
  1. Zdzisław Kowalczuk
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  2. Marek Sylwester Tatara
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Correspondence to Zdzisław Kowalczuk .

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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Piotr Kulczycki

  2. Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland

    Józef Korbicz

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Kowalczuk, Z., Tatara, M.S. (2021). Flow Process Models for Pipeline Diagnosis. In: Kulczycki, P., Korbicz, J., Kacprzyk, J. (eds) Automatic Control, Robotics, and Information Processing. Studies in Systems, Decision and Control, vol 296. Springer, Cham. https://doi.org/10.1007/978-3-030-48587-0_2

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