Frequency domain analysis of transient flow in pipelines; application of the genetic programming to reduce the linearization errors

Document Type: Research Paper

Authors

1 Department of Civil Engineering, Faculty of Engineering,Shahid Chamran University of Ahvaz, Ahvaz, Iran.

2 Department of Hydraulic Structure, Faculty of Water Science Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

3 Department of Civil Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

Abstract

The transient flow analyzing by the frequency domain method (FDM) is computationally much faster than the method of characteristic (MOC) in the time domain. FDM needs no discretization in time and space, but requires the linearization of governing equations and boundary conditions. Hence, the FDM is only valid for small perturbations in which the system’s hydraulics is almost linear. In this study, the linearization errors of the FDM applied to a reservoir-pipe-valve system (RPV) are discussed and by using the Genetic Programming (GP), some correction coefficients are defined to reduce them. By applying the correction coefficient at the opening size of the valve, the first frequency of the frequency domain method is modified. Moreover, the responses at higher-order frequencies are evaluated by some new correction factors obtained by the GP. Solving an illustrative example shows that the error of the system can be significantly reduced by using the applied correction factors.

Keywords


  1. Izquierdo J, Iglesias P, (2002). Mathematical modelling of hydraulic transients in simple systems. Mathematical and Computer Modelling, pp: 801-812.
  2. Wood D.J, et al., (2005). Numerical methods for modeling transient flow in distribution systems. Journal (American Water Works Association), pp: 104-115.
  3. Zhao M, Ghidaoui MS, (2004). Godunov-type solutions for water hammer flows. Journal of Hydraulic Engineering, pp: 341-348.
  4. Chaudhry, M.H., Applied Hydraulic Transients, Springer New York, 2013.
  5. Wylie E.B., Streeter V.L., and Suo L., Fluid transients in systems. Prentice Hall Englewood Cliffs, NJ, Vol. 1. 1993.
  6. Lee P.J, et al., (2013). Frequency domain analysis of pipe fluid transient behaviour. Journal of hydraulic research, pp: 609-622.
  7. Kim S.-H., (2010). Design of surge tank for water supply systems using the impulse response method with the GA algorithm. Journal of Mechanical Science and Technology, pp: 629-636.
  8. Ranginkaman MH, Haghighi A, and Samani H.M.V, (2017). Application of the Frequency Response Method for Transient Flow Analysis of Looped Pipe Networks. International Journal of Civil Engineering, pp: 677-687.
  9. Riasi A, Nourbakhsh A, and Raisee M, (2010). Numerical modeling for hydraulic resonance in hydropower systems using impulse response. Journal of Hydraulic Engineering, pp. 929-934.
  10. Capponi C, et al., (2017). Leak Detection in a Branched System by Inverse Transient Analysis with the Admittance Matrix Method. Water Resources Management, pp: 1-15.
  11. Ferrante M, et al., (2016). Numerical transient analysis of random leakage in time and frequency domains. Civil Engineering and Environmental Systems, pp: 70-84.
  12. Ranginkaman M, Haghighi A, and Vali Samani H, (2016). Inverse frequency response analysis for pipelines leak detection using the particle swarm optimization. Iran University of Science & Technology, pp: 1-12.
  13. Duan H, et al., (2014). Transient wave-blockage interaction and extended blockage detection in elastic water pipelines. Journal of fluids and structures, pp: 2-16.
  14. Duan H.-F., et al., (2013). Extended blockage detection in pipes using the system frequency response: analytical analysis and experimental verification. Journal of Hydraulic Engineering, pp: 763-771.
  15. Bergant A, et al., (2013). Waterhammer tests in a long PVC pipeline with short steel end sections. Journal of Hydraulic Structures, pp: 24-36.
  16. Lee PJ, et al., (2003). Leak detection in pipes by frequency response method using a step excitation: By WITNESS MPESHA, M. HANIF CHAUDHRY, and SARAH L. GASSMAN, Journal of Hydraulic Research, pp: 55-62.
  17. Lee PJ, and Vítkovský JP, (2010). Quantifying linearization error when modeling fluid pipeline transients using the frequency response method. Journal of Hydraulic Engineering, pp: 831-836.
  18. Lee, PJ, (2013). Energy analysis for the illustration of inaccuracies in the linear modelling of pipe fluid transients. Journal of Hydraulic Research, pp: 133-144.
  19. Riyahi M.M, Haghighi A, (2018). Investigation of error resources in the transient flow simulation of pipelines in the frequency domain using the transfer matrix method, Modares Mechanical Engineering, pp: 10-18 (in Persian).
  20. Ghidaoui M.S, et al., (2005).A review of water hammer theory and practice. Applied Mechanics Reviews, pp: 49.
  21. Bozorg-Haddad O, Soleimani S, and Loáiciga HA, (2017). Modeling Water-Quality Parameters Using Genetic Algorithm–Least Squares Support Vector Regression and Genetic Programming. Journal of Environmental Engineering, pp: 04017021.
  22. Pourzangbar A, et al., (2017). Predicting scour depth at seawalls using GP and ANNs. Journal of Hydroinformatics, pp: 349-363.
  23. Gandomi A.H., Alavi A.H., and Ryan C., Handbook of genetic programming applications. Springer, 2015.
  24. Flood I, (2008). Towards the next generation of artificial neural networks for civil engineering. Advanced Engineering Informatics, pp: 4-14.
  25. Giustolisi O, et al., (2007). A multi-model approach to analysis of environmental phenomena. Environmental Modelling & Software, pp: 674-682.
  26. Poli R, Langdon W, and McPhee N, (2008). A field guide to genetic programming (With contributions by JR Koza). Published via http://lulu.com .
  27. Cramer N.L., A representation for the adaptive generation of simple sequential programs. in Proceedings of the first international conference on genetic algorithms. 1985.
  28. Koza J.R., Genetic programming: on the programming of computers by means of natural selection, MIT press, 1992.
  29. Searson D.P., Leahy D.E. Willis M.J. (2010). GPTIPS: an open source genetic programming toolbox for multigene symbolic regression. in Proceedings of the International multiconference of engineers and computer scientists.
  30. Searson D.P., Leahy D.E., Willis M.J. (2011). Predicting the toxicity of chemical compounds using GPTIPS: a free genetic programming toolbox for MATLAB, in Intelligent Control and Computer Engineering. Springer.