Modeling of Flow Friction Factor in Irrigation Pipes using Machine Learning Methods and Comparing with Empirical Equations

Document Type : Research Paper

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Abstract

The implicit Colebrook–White equation has been extensively used to estimate the friction factor of
turbulent flow in irrigation pipes. In the meantime, a practical and accurate solution for Colebrook–White
equation is, in particular, necessary for hydraulic computations of pressurized irrigation systems. In this
paper, the performance of some machine learning methods such as support vector regression (SVR), genetic
programming (GP) and M5 model trees have been evaluated and compared to the empirical equations in
friction factor estimation. The obtained results from statistical analysis of studied methods showed that
Buzzelli and Haaland empirical equations with root mean squared error (RMSE) of 0.00002 and 0.00015,
respectively and also genetic programming with RMSE of 0.00031, had better performances among the
others. Also, it was concluded that the M5 model trees and SVR with RMSE of 0.00204 and 0.00417,
respectively, had lower accuracy in comparison with the empirical equations and genetic programming
methods in estimating friction factor of irrigation pipes.

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References

منابع مورد استفاده
ستاری م ت و نهرین ف، 1392. پیش­بینی مقادیر حداکثر بارش روزانه با استفاده از سیستم­های هوشمند و مقایسه آن با مدل درختی M5، مطالعه موردی ایستگاه­های اهر و جلفا. فصلنامه علمی پژوهشی مهندسی آبیاری و آب. سال 4، شماره 14. صفحه­های 83 تا 98.
علیخانزاده ا، 1392. داده کاوی (Data mining) . نشر علوم رایانه، چاپ دوم، ساری، ایران.
فلاحی م ر، وروانی ه و گلیان س، 1390. پیش بینی بارش با استفاده از مدل رگرسیون درختی به منظور کنترل سیل. پنجمین کنفرانس سراسری آبخیزداری و مدیریت منابع آب و خاک کشور. 10 تا 11 اسفند. کرمان. ایران.
Barr DIH, 1981. Solutions of the Colebrook–White function for resistance to uniform turbulent flow. Proceedings - Institution of Civil Engineers 71 (2): 529–536.
Basak D, Pal S and Patranabis DC, 2007. Support vector regression. Neural Information Processing 11: 203-225.
Bralts VF, Kelly SF, Shayya WH and Segerlind LJ, 1993. Finite element analysis of microirrigation hydraulics using a virtual emitter system. Transactions of the American Society of Agricultural Engineers 36(3): 717-725.
Brkić D, 2011. Review of explicit approximations to the Colebrook relation for flow friction. Petroleum Science and Technology 77: 34-48.
Buzzelli D, 2008. Calculating friction in one step. Machine Design 80(12): 54–55.
Chen NH, 1979. An explicit equation for friction factor in pipes. Industrial and Engineering Chemistry Fundamentals 18(3): 296-297.
Churchill SW, 1977. Friction-factor equation spans all fluid flow regimes. Chemical Engineering Journal 84 (24): 91–92.
Colebrook CF and White CM, 1937. Experiments with fluid- friction in roughened pipes. Proceedings of the Royal Society of London 161: 367-381.
Eck B, 1973. Technische Stromungslehre. Springer, New York.
Finnemore EJ and Franzini JB, 2002. Fluid Mechanics with Engineering Applications. Mc- Graw-Hill.
Gerrish PJ, Bralts VF and Shayya WH, 1996a. An improved analysis of microirrigation hydraulics using a virtual emitter system. Transactions of the American Society of Agricultural Engineers 39(4): 1403-1410.
Gerrish PJ, Shayya WH and Bralts VF, 1996b. An improved method for incorporating pipe components into the analysis of hydraulic networks. Transactions of the American Society of Agricultural Engineers 39(4): 1337-1343.
Haaland SE, 1983. Simple and explicit formulas for friction factor in turbulent pipe flow. Journal of Fluids Engineering 105(1): 89-90.
Kisi O, Shiri J and Nikoofar B, 2012. Forecasting daily lake levels using artificial intelligence approaches. Computers & Geosciences 41: 169-180.
Koza JR, 1992. Genetic Programming, On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, ISBN 0-262-11170-5.
Lahiri SK and Ghanta KC, 2009. Support vector regression with parameter tuning assisted by differential evolution technique: Study on pressure drop of slurry flow in pipeline. Korean Journal of Chemical Engineering 26(5): 1175-1185.
Liu WC and Chen WB, 2012. Prediction of water temperature in a subtropical subalpine lake using an artificial neural network and three-dimensional circulation models. Computers &Geosciences 45: 13-25
Londhe SN and Dixit PR, 2011. Forecasting stream flow using model trees. International Journal of Earth Sciences and Engineering 4(6): 282-285.
Moody LF, 1947. An approximate formula for pipe friction factors. Transactions of the American Society of Mechanical Engineers 69(12): 1005-1011.
Pal M and Deswal S, 2009. M5 model tree based modelling of reference evapotranspiration. Hydrological Processes 23(10): 1437-1443.
Quinlan JR, 1992. Learning with continuous classes. In: Proc. AI’92 (Fifth Australian Joint Conference on Artificial Intelligence 343-348. World Scientific, Singapore.
Rao AR and Kumar B, 2007. Friction factor for turbulent pipe flow. Division of Mechanical Science, Civil Engineering. Indian Institute of Science, Bangalore, India. ID Code 9587.
Romeo E, Royo C and Monzon A, 2002. Improved explicit equation for estimation of the friction factor in rough and smooth pipes. Chemical Engineering Journal 86(3): 369-374.
Round GF, 1980. An explicit approximation for the friction factor-Reynolds number relation for rough and smooth pipes. Canadian Journal of Chemical Engineering 58 (1): 122–123.
Salmasi F, Khatibi R and Ghorbani MA, 2012. A study of friction factor formulation in pipes using artificial intelligence techniques and explicit equations. Turkish Journal of Engineering and Environmental Sciences 36: 121-138.
Samadianfard S, Delirhasannia R, Kisi O and Agirre-Basurko E, 2013. Comparative analysis of ozone level prediction models using gene expression programming and multiple linear regression. GEOFIZIKA 30: 43-74.
Samadianfard S, Sadraddini AA, Nazemi AH, Provenzano G and Kisi O, 2012. Estimating soil wetting patterns for drip irrigation using genetic programming. Spanish Journal of Agricultural Research 10(4): 1155-1166.
Sattari MT, Pal M, Apaydin H and Ozturk F, 2013. M5 Model Tree application in daily river flow forecasting in Sohu Stream, Turkey. Water Resources 40(3): 233-242.
Shirzad A, Tabesh M and Farmani R, 2014. A comparison between performance of support vector regression and artificial neural network in prediction of pipe burst rate in water distribution networks. KSCE Journal of Civil Engineering 18(4): 941-948.
Sonnad JR and Goudar CT, 2006. Turbulent flow friction factor calculation using a mathematically exact alternative to the Colebrook–White equation. Journal of Hydraulic Engineering ASCE 132(8): 863-867.
Vapnik VN, 1995. The Nature of Statistical Learning Theory, New York: Springer-Verlag.
Vapnik VN, 1998. Statistical Learning Theory, Wiley, New York.
Wood DJ, 1966. An explicit friction factor relationship. Civil Engineering 36(12): 60–61.
Yıldırım G, 2009. Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation. Advances in Engineering Software 40(11): 1183-1190.
Zigrang DJ and Sylvester ND, 1982. Explicit approximations to the solution of Colebrook friction factor equation. AIChE Journal 28(3): 514-515.
Water and Soil Science
Volume 26, 1-2
June 2016
Pages 45-57

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