Tracing of large branched pipeline hydraulic networks of high optimality rank with graph presentation

M.B. Abazokov, V.Ch. Kudaev

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Abstract: The paper deals with a tracing technique for large branched pipeline hydraulic networks of the high optimality rank. The novelty of the method is that while increasing the optimization rank of the designed networks, the redundant graph of possible connections between nodes is dynamically reduced. In this case, the redundant graph of the follow-up rank is formed from previous networks rank. The method provides a computer solution to the problem of tracing of large networks containing more than one hundred nodes of the seventh optimality rank. The system is developed for large pipeline networks design of regional and interregional pipe distribution network (PDN) for irrigation purpose.

Keywords: pipeline flow network, computer design, tracing, dynamic graph of possible connections of network nodes, dimension reduction, optimality rank increase

For citation. Abazokov M.B., Kudaev V.Ch. Tracing of large branched pipeline hydraulic networks of high optimality rank with graph presentation. News of the Kabardino-Balkarian Scientific Center of RAS. 2023. No. 4(114). Pp. 39–54. DOI: 10.35330/1991-6639-2023-4-114-39-54

References

1. Bulatov V.P., Kassinskaya L.I. Some methods for minimizing a concave function on a convex polyhedron. Metody optimizatsii i ikh prilozheniya [Optimization Methods and Applications]. Irkutsk: SEI SO AN USSR, 1987. Pp. 151–172. (In Russian)
2. Antsiferov E.G., Ashchepkov L.T., Bulatov V.P. Metody optimizatsii i ikh prilozheniya. CH. 1. Matematicheskoye programmirovaniye [Methods of optimization and their applications. Part 1. Mathematical programming]. Novosibirsk: Nauka, 1990. 158 p. ISBN 5-02-029658-9. (In Russian)
3. Trubin V.A., Mikhalevich V.S., Shor N.Z. Optimizatsionnyye zadachi proizvodstvennotransportnogo planirovaniya [Optimization problems of production and transport planning]. Moscow: Nauka, 1986. 260 p. (In Russian)
4. Merenkov A.P., Sennova E.V., Sumarokov S.V. et al. Matematicheskoye modelirovaniye i optimizatsiya sistem teplo-, vodo-, nefte- i gazosnabzheniya [Mathematical modeling and optimization of heat, water, oil and gas supply systems]. Novosibirsk: Nauka, 1992. 407 p. (In Russian)
5. Tui H. Concave programming under linear constraints. Doklady AN SSSR. 1964. Vol. 159. No. 1. Pp. 32–35. (In Russian)
6. Kudaev V.Ch., Abazokov M.B. Rank optimization of streaming networks. Vestnik KRAUNC. Phys.-Math. Sciences. 2018. No. 4(24). Pp. 178–185. DOI: 10.18454/2079-6641-2018-24-4-178-185. (In Russian)
7. Kudaev V.Ch., Abazokov M.B. Computer design of flow networks of P-th rank of optimality. News of the Kabardino-Balkarian Scientific Center of RAS. 2019. No. 6(92). Pp. 122–131. DOI:10.35330/1991-6639-2019-6-92-122-131. (In Russian)
8. Kudaev V.Ch., Abazokov M.B. Cluster optimization of high-rank optimality of flow networks. Vestnik KRAUNC. Phys.-Math. Sciences. 2021. Vol. 37. No. 4. Pp. 104–118. DOI: 10.26117/2079-6641-2021-37-4-104-118. (In Russian)
9. Kudaev V.Ch. Ranks of extremums and structural optimization of large network systems. News of the Kabardino-Balkarian Scientific Center of RAS. 2016. No. 4(72). Pp. 15–24. (In Russian)
10. Nekrasova O.A., Khasilev V.Ya. Optimal tree of a pipeline system. Ekonomika i matematicheskiye metody [Economics and Mathematical Methods]. 1970. Vol. 4. No. 3. Pp. 427–432. (In Russian)
11. Abramov N.N., Pospelova M.M., Somov M.A. et al. Raschet vodoprovodnykh setey [Calculation of water supply networks]. Moskow: Stroyizdat, 1983. 278 p. (In Russian)
12. Abazokov M.B., Bagov M.A., Kudaev V.Ch. Computer design of large pipeline networks of high optimality rank. Doklady AMAN. 2022. No. 4. Vol. 22. Pp. 39–56. DOI: https://doi.org/10.47928/1726-9946-2022-22-4-39-56. (In Russian)

Information about the authors

Abazokov Mukhammed Borisovich, junior researcher, Institute of Applied Mathematics and Automation – branch of Kabardino-Balkarian Scientific Center of the RAS;
360000, Russia, Nalchik, 89 A Shortanov street;
Abazokov.Mukhammed@yandex.ru, ORCID: https://orcid.org/0000-0002-6847-403X
Kudaev Valery Cherimovich, Ph.D., leading researcher, Institute of Applied Mathematics and Automation – branch of Kabardino-Balkarian Scientific Center of the RAS;
360000, Russia, Nalchik, 89 A Shortanov street;
vchkudaev@mail.ru, ORCID: https://orcid.org/0000-0002-8313-4199