Numerical Issues and Approximated Models for the Diagnosis of Transmission Pipelines - Publication - Bridge of Knowledge

Your account

login

Search

Numerical Issues and Approximated Models for the Diagnosis of Transmission Pipelines

Abstract

The chapter concerns numerical issues encountered when the pipeline flow process is modeled as a discrete-time state-space model. In particular, issues related to computational complexity and computability are discussed, i.e., simulation feasibility which is connected to the notions of singularity and stability of the model. These properties are critical if a diagnostic system is based on a discrete mathematical model of the flow process. The starting point of the study is determined by the partial differential equations obtained from the momentum and mass conservation laws by using physical principles. A realizable computational model is developed by approximation of the principal equations using the finite difference method. This model is expressed in terms of the recombination matrix A which is the key of the analysis by taking into account its possible singularity and stability. The nonsingularity of the matrix A for nonzero and finite, time and spatial steps is proven by the Lower–Upper decomposition. A feature of the discrete model allows the derivation of a nonsingular aggregated model, whose stability can be analyzed. By considering the Courant–Friedrichs–Lewy condition and data from experimental studies, numerical stability conditions are derived and limitations for the feasible discretized grid are obtained. Moreover, the optimal relationship between the time and space steps which ensures a maximum stability margin is derived. Because the inverse of matrix A, composed of four tridiagonal matrices, is required for the main diagnosis methods, two analytical methods for the inversion are discussed which reduce the system’s initialization time and allow designing an accurate and fast diagnosis algorithm. By considering that each inversion method generates its particular structure, two different flow models are generated: one based on auxiliary variables and the other suitable if the stability condition of A is satisfied. The applicability of the two models is shown by considering the norm of the difference between their behaviors for a finer discretization grid . A similarity measure is proposed which considers the number of pipeline segments as well as the ratio between the time and spatial steps . Thus, the system’s computational efficiency is improved and satisfactory results are shown with respect to the base model, if a highly dimensional model with the approximated diagonal matrix is considered.

Citations

  • 3

    CrossRef

  • 0

    Web of Science

  • 3

    Scopus

Authors (2)

Cite as

Full text

download paper
downloaded 42 times
Publication version
Accepted or Published Version
License
Copyright (Springer International Publishing AG 2017)

Keywords

Details

Category:
Monographic publication
Type:
rozdział, artykuł w książce - dziele zbiorowym /podręczniku w języku o zasięgu międzynarodowym
Title of issue:
Modeling and Monitoring of Pipelines and Networks strony 39 - 62
Language:
English
Publication year:
2017
Bibliographic description:
Kowalczuk Z., Tatara M. S.: Numerical Issues and Approximated Models for the Diagnosis of Transmission Pipelines// Modeling and Monitoring of Pipelines and Networks/ ed. Cristina Verde, Lizeth Torres Cham, Switzerland: Springer, 2017, s.39-62
DOI:
Digital Object Identifier (open in new tab) 10.1007/978-3-319-55944-5_3
Bibliography: test
  1. Belsito, S., Lombardi, P., Andreussi, P., & Banerjee, S. (1998). Leak detection in liquefied gas pipelines by artificial neural networks. AIChE, 44(12), 2675-2688. open in new tab
  2. Billmann, L. & Isermann, R. (1987). Leak detection methods for pipelines. Auto- matica, 23(3), 381-385. open in new tab
  3. Brogan, W. (1991). Modern control theory. Boston: Prentice Hall.
  4. Da Fonseca, C. & Petronilho, J. (2001). Explicit inverses of some tridiagonal ma- trices. Linear Algebra and its Applications, 325, 7-21. open in new tab
  5. Dick, M. (2012). Stabilization of the gas flow in networks: Boundary feedback sta- bilization of quasilinear hyperbolic systems on networks. Ph.D. thesis. Erlangen- Nürnberg: Friedrich-Alexander-Universität. open in new tab
  6. Gunawickrama, K. (2001). Leak detection methods for transmission pipelines. Ph.D. thesis. Gdask: Gdask Univeristy of Technology.
  7. Hooke, R., & Jeeves, T. A. (1961). "Direct search" solution of numerical and statistical problems Journal of the Association for Computing Machinery (ACM). 8 (2): 212229. open in new tab
  8. Kowalczuk, Z., & Gunawickrama, K. (1998). Detection of leakages in industry pipelines using a cross-correlation approach. Pomiary Automatyka Kontrola, 44(4), 140-146.
  9. Kowalczuk, Z., & Gunawickrama, K. (2004). Detection and localisation of leaks in transmission pipelines, chapter 21, (pp. 821-864). New York: Springer. open in new tab
  10. Kowalczuk, Z., & Tatara, M. (2013)p Analytical modeling of flow processes: Anal- ysis of computability of a state-space model. In XI International Conference on Diagnostics of Processes and Systems (pp. 74.1-12). Lagów, Lubuski. open in new tab
  11. Kowalczuk, Z. & Tatara, M. (2016). Approximate models and parameter analysis of the flow process in transmission pipelines (pp. 239-252). Springer. open in new tab
  12. Kreyszig, E. (2006). Advanced engineering mathematics. (Vol. 9). Columbus: John Wiley and Sons Inc.
  13. Reddy, H., Narasimhan, S., Bhallamudi, S.M., & Bairagi, S. (2011). Leak detection in gas pipeline networks using an efficient state estimator. Part-I: Theory and simulations. Computers and Chemical Engineering, 35(4), 651-661. open in new tab
  14. Strikwerda, J. (2007). Finite difference schemes and partial differential equations. SIAM. open in new tab
  15. MathWorks. (2012). MATLAB and Curve Fitting Toolbox release 2012b Natick, Massachusetts, United States: Technical Report.
  16. Torres, L., Besançon, G., & Verde, C. (2012). Leak detection using parameter iden- tification. In 8th IFAC symposium SAFEPROCESS-2012. Mexico City, Mexico. open in new tab
  17. Verde, C. and Torres, L. (2015). Referenced model based observers for locating leaks in a branched pipeline. In The 9th international federation of automatic control (IFAC) symposium SAFEPROCESS, (pp. 1066-1071). Paris: IFAC. open in new tab
  18. Walpole, R., Myers, R., Myers, S., & Ye, K. (2012). Probability and statistics for engineers and scientists. (9th ed.). Boston: Prentice Hall.
Verified by:
Gdańsk University of Technology

seen 107 times

Recommended for you

Modeling of medium flow processes in transportation pipelines - the synthesis of their state-space models and the analysis of the mathematical properties of the models for leak detection purposes

2019

Analytical ‘Steady-State’-Based Derivation and Clarification of the Courant-Friedrichs-Lewy Condition for Pipe Flow

2021

Flow Process Models for Pipeline Diagnosis

2021

FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations

2023
Meta Tags