UDK 62.501
IDENTIFICATION OF HYDRAULIC RESISTANCE PARAMETERS IN HYDRAULIC NETWORK MODEL
N. R. Antropov1*, E. D. Agafonov2
1Siberian Federal University 79, Svobodny Av., Krasnoyarsk, 660041, Russian Federation 2Reshetnev Siberian State University of Science and Technology 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation *E-mail: agafonov@gmx.de
The work is devoted to the identification of hydraulic resistance coefficients in hydraulic network model. The problem raised in the paper is relevant for enterprises dealing with either pipeline transport of fluid hydrocarbons, or water supply and central heating. The proposed algorithm can be implemented for corresponding technological modes calculation and prediction. Complexity of real pipeline networks, uncertainty and instability of their parameters make parameters identification procedure indispensable. The network model under research is a system of nonlinear equations, drawn up in accordance with Kirchhoff’s laws for pipeline networks. Equations describe laws of flows conservation for nodes as well as pump heads and head drops along independent circuits of the network. To solve such system one traditionally implements Newton’s method or its modifications, for instance the successive approximation method. Mentioned methods have numerous disadvantages like instability and sensibility to initial approximation of the roots. The system of equations solving is accompanied with their parameters tuning usually with the Nonlinear Least Square Method. Again, the method can be instable due to overdefined and large-scale problem statement. In the paper we propose to substitute solution of the system with nonparametric estimation of the solution. We implement regression type estimate with respect to residuals of the equations calculated for measured data sample. Simultaneously parameters of the equations are identified. Modification of Kiefer–Wolfowitz procedure is used as an identification algorithm. Identification is performed with simultaneous evaluation of the solution of the system of equations. The use of appropriate algorithms is considered at three-loop pipeline network with a single active pressure. Numerical experiments with proposed algorithm demonstrate its applicability for practical identification problems solution.
Keywords: identification, parameter estimation, flow resistance
References

1. Lur’e M. V. Matematicheskoe modelirovanie protsessov truboprovodnogo transporta nefti, nefteproduktov i gaza [Mathematical Modeling of Oil, Fuels, and Gas Pipeline Transport Processes]. Moscow, Neft’ i gaz Publ., 2003, 335 p.

2. Basniev K. S., Dmitriev N. M., Rozenberg G. D. Neftegazovaya gidromekhanika [Hydrodynamics of Oil and Gas]. Moscow, Izhevsk, Institut komp’yuternykh issledovaniy Publ., 2005, 544 p.

3. Kassina N. V. Matematicheskoe modelirovanie dinamiki gidravlicheskikh sistem s ispol’zovaniem metodov analiticheskoy mekhaniki i teorii nelineynykh kolebaniy Dis. cand. tehn. nauk [Mathematical Modeling of the Dynamics of Hydraulic Systems Using Methods of Analytical Mechanics and the Theory of Nonlinear Oscillations. PhD diss]. Nizhny Novgorod, NNSU Publ., 2006, 118 p.

4. Trofimov V. V., Tarasenko V. P., Mashchenko V. I. Avtomatizirovannoe upravlenie magistral’nymi nefteprovodami [Automation Control of Trunk Pipelines]. Tomsk, TSU Publ., 1994, 247 p.

5. Eykhoff P. System Identification: Parameter and State Estimation. Chester, England: Wiley, 1974, 555 p.

6. Seleznev V. E., Aleshin V. V., Pryalov S. N. Matematicheskoe modelirovanie truboprovodnykh setey i sistem kanalov: metody, modeli i algoritmy [Mathematical Modeling of Pipeline Networks and Cannel Systems: Methods, Models, and Algorithms]. Moscow, Berlin, Direkt-Media Publ., 2014, 694 p.

7. Loginov K. V., Myznikov A. M., Fayzullin R. T. [Calculation, Optimization and Control Modes of Operation of Large-scale Hydraulic Networks]. Matematicheskoe modelirovanie. 2006, Vol. 18, No. 9, P. 92–106 (In Russ.).

8. Fayzullin R. T. [On the Solution of Nonlinear Algebraic Systems of Hydraulics]. Siberian Journal of Industrial Mathematics. 1999, Vol. 2, No. 2, P. 176–178 (In Russ.).

9. Myznikov A. M. [Solution of Large Systems of Nonlinear Equations Applied to Problems of Calculating Hydraulic, Thermal and Electrical Networks]. Matematicheskie struktury i modelirovanie. 2003, No. 11, P. 15–19 (In Russ.).

10. Myznikov A. M. Modelirovanie i identifikatsiya parametrov slozhnykh gidravlicheskikh setey: dis. kand. fiz.-mat. nauk [Modeling and Identification of Parameters of Complex Hydraulic Networks. PhD diss.]. Tyumen’, 2005, 116 p.

11. Myznikov A. M. [Specification of Drag Coefficients in Complex Hydraulic Networks Based on the Results of a Limited Number of Measurements]. Teplofizika i aeromekhanika. 2005, Vol. 12, No. 3, P. 513–516 (In Russ.).

12.Medvedev A. V. Osnovy teorii adaptivnykh system [Fundamentals of the Theory of Adaptive Systems]. Krasnoyarsk, SibSAU Publ., 2015, 526 p.

13. Kiefer J., Wolfowitz J. Stochastic evaluation of the maximum of a regression function. Ann. Math. Statist., 1952, Vol. 23, No. 3, P. 462–466.

14.Krasnoshtanov A. P. Kombinirovannye mnogosvyaznye sistemy [Combined Multiply Connected Systems]. Novosibirsk, Nauka Publ., 2001, 176 p.

15.Krasnoshtanov A. P. Metod generatsii resheniy na mnogosvyaznykh sistemakh v usloviyakh neopredelennosti: Dis. Doct. Tekhn. Nauk [The Method of Generating Solutions on Multiply Connected Systems Under Uncertainty. Dr. Tech. Sci. diss.]. Krasnoyarsk, 2001, 295 p.

16. Robbins H., Monro S. A stochastic Approximation Method. Ann. Math. Statist. 1951, Vol. 22, No. 3, P. 400–407.

17.Agafonov E. D., Antropov N. R. [On Estimation of Hydraulic Network Equation System]. Izvestiya Tul’skogo gosudarstvennogo universiteta. Tekhnicheskie nauki. 2014, No. 3, P. 110–117 (In Russ.).

 


Antropov Nikita Romanovich – postgraduate student, Department of Fuel Supply, Fuels and Lubricants, Siberian

Federal University, School of Petroleum and Natural Gas Engineering. Е-mail: underlag_sikrer@mail.ru.

Agafonov Evgeny Dmitrievich – Cand. Sc., Docent, Docent of Department of System Analysis and Operation

Research, Reshetnev Siberian State University of Science and Technology. Е-mail: agafonov@gmx.de.