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Numerical Issues and Approximated Models for the Diagnosis of Transmission Pipelines

Abstrakt

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.

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Copyright (Springer International Publishing AG 2017)

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Kategoria:
Publikacja monograficzna
Typ:
rozdział, artykuł w książce - dziele zbiorowym /podręczniku w języku o zasięgu międzynarodowym
Tytuł wydania:
Modeling and Monitoring of Pipelines and Networks strony 39 - 62
Język:
angielski
Rok wydania:
2017
Opis bibliograficzny:
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:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1007/978-3-319-55944-5_3
Bibliografia: 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. otwiera się w nowej karcie
  2. Billmann, L. & Isermann, R. (1987). Leak detection methods for pipelines. Auto- matica, 23(3), 381-385. otwiera się w nowej karcie
  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. otwiera się w nowej karcie
  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. otwiera się w nowej karcie
  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. otwiera się w nowej karcie
  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. otwiera się w nowej karcie
  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. otwiera się w nowej karcie
  11. Kowalczuk, Z. & Tatara, M. (2016). Approximate models and parameter analysis of the flow process in transmission pipelines (pp. 239-252). Springer. otwiera się w nowej karcie
  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. otwiera się w nowej karcie
  14. Strikwerda, J. (2007). Finite difference schemes and partial differential equations. SIAM. otwiera się w nowej karcie
  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. otwiera się w nowej karcie
  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. otwiera się w nowej karcie
  18. Walpole, R., Myers, R., Myers, S., & Ye, K. (2012). Probability and statistics for engineers and scientists. (9th ed.). Boston: Prentice Hall.
Weryfikacja:
Politechnika Gdańska

wyświetlono 107 razy

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