Abstract
Longitudinal dispersion in pipelines leads to changes in the characteristics of contaminants. It is critical to quantify these changes because the contaminants travel through water networks or through chemical reactors. The essential characteristics of longitudinal dispersion in pipes can be described by the longitudinal dispersion coefficient. This paper presents the application of the adaptive Neuro fuzzy group method of data handling to develop new empirical formulae for the prediction of longitudinal dispersion coefficients in pipe flow using 233 experimental case studies of dispersion coefficient with a R e range of 900 to 500,000 spanning laminar, transitional and turbulent pipe flow. The NF-GMDH network was improved using particle swarm optimization based evolutionary algorithm. The group method data handling is used to develop empirical relations between the longitudinal dispersion coefficient and various control variables, including the Reynolds number, the average velocity, the pipe friction coefficient and the pipe diameter. GMDH holds advantage in the case of small data samples due to the optimal choice of the model complexity with automatic adaptation to an unknown level of the data uncertainties. Sensitivity analysis is performed on the developed model and the weight and importance of each control variable is presented. The results indicate that the proposed relations are simpler than previous numerical solutions and can effectively evaluate the longitudinal dispersion coefficients in pipe flow.
Similar content being viewed by others
References
Amanifard N, Nariman-Zadeh N, Farahani MH, Khalkhali A (2008) Modeling of multiple short-length-scale stall cells in an axial compressor using evolved GMDH neural networks. J Energ Convers Manage 49(10):2588–2594
Austin RG, van Bloemen WB, McKenna S, Choi CY (2008) Mixing at cross junctions in water distribution systems–part II, an experimental study. J Water Resour Plan Manag ASCE 134:295–302
Buchberger SG, Lee YH, Bloom G, Rolf B (1999) Dispersion of mass in intermittent laminar flow through pipe. In: Savic D, Walters G (eds) Water industry systems: modeling and optimization applications, 1st edn. Research Studies Press, Baldock, pp 89–101
Buyukyildiz M, Tezel G, Yilmaz V (2014) Estimation of the change in lake water level by artificial intelligence methods. Water Resour Manag 28(13):4747–4763
Chang J, Bai T, Huang Q, Yang D (2013) Optimization of water resources utilization by PSO-GA. Water Resour Manag 27(10):3525–3540
Chikwendu SC (1986) Calculation of Longitudinal Shear Dispersivity using an N-zone Model as Nàinfinity. J Fluid Mech 167:19–30.
Cutter MR (2004) Dispersion in Steady Pipe Flow with Reynolds Number Under 10,000. Master of Science Thesis Submitted to University of Cincinnati, August 18, 2004
Ekambara K, Joshi JB (2003) Axial mixing in pipe flows: turbulent and transitional regions. Chem Eng Sci 58:2715–2724
Flint LF, Eisenklam P (1969) Longitudinal gas dispersion in transitional and turbulent flow through a straight tube. Can J Chem Eng 47:101–106
Fowler FC, Brown GG (1943) Contamination by successive flow in pipe lines. Am Inst Chem Eng 39:491–516
Hart J, Guymer I, Jones A, Stovin V (2013) Longitudinal dispersion coefficients within turbulent and transitional pipe flow. Experimental and Computational Solutions of Hydraulic Problems GeoPlanet: Earth and Planetary Sciences, pp. 133–145
Hwang HS (2006) Fuzzy GMDH-type neural network model and its application to forecasting of mobile communication. Comput Ind Eng 50:450–457
Iba H, De Garis H (1996) Extending genetic programming with recombi-native guidance, in: P. Angeline, K. Kinnear (Eds.). Advances in Genetic Programming 2 MIT Press Cambridge
Kennedy J, Eberhart RC (1995) Particle swarm optimization. Proc. the fourth IEEE Int. Conf. on Neural Networks 1942–1948
Keyes JJ (1955) Diffusional film characteristics in turbulent flow: dynamic response method. Am Inst Chem Eng J 1:305–311
Li Y, Qian F (2002) Neuro fuzzy GMDH network and its application to the soft-Ensor for ethene distillation process. Intell Control Autom Proc 4th World Congr 3:2478–2482
Mohapatra S, Sargonkar A, Labhasetwar PK (2014) Distribution network assessment using EPANET for intermittent and continuous water supply. Water Resour Manag 28(11):3745–3759
Nagasaka K, Ichihashi H, Leonard R (1995) Neuro-fuzzy GMDH and its application to modeling grinding characteristics. Int J Prod Res 33(5):1229–1240
Najafzadeh M, Azamathulla HM (2013) Group method of data handling to predict scour depth around bridge piers. Neural Comput 23(7–8):2107–2112
Najafzadeh M, Lim SY (2014) Application of improved neuro-fuzzy GMDH to predict scour downstream of sluice gates. Earth Sci Inform. doi:10.1007/s12145-014-0144-8
Najafzadeh M, Barani GA, Hessami Kermani MR (2013) Abutment scour in live-bed and clear-water using GMDH. Netw Water Sci Technol 67(5):1121–1128
Ohtani T, Ichihashi H, Miyoshi T, Tani N (1998) A Pointing Device Using Coordinate Transformation of Neurofuzzy GMDH. Second International Conference on Knowledge-Based Intelligent Electronic Systems 21–23 April 1998 Adelaide Australia
Onwubolu GC (2008) Design of hybrid differential evolution and group method in data handling networks for modeling and prediction. Inf Sci 178:3618–3634
Rachid FBF, Araujo JH, Baptista RM (2002) Predicting mixing volumes in serial transport in pipelines. J Fluids Eng 124:528–534
Rossman LA, Clark RM, Grayman WM (1994) Modeling chlorine residuals in drinking water distribution system. J Environ Eng ASCE 120(4):803–820
Salajegheh E, Gholizadeh S, Khatibinia M (2008) Optimal design of structures for earthquake loads by a hybrid RBF-BPSO method. Earthq Eng Eng Vib 7(1):14–24
Sanikhani H, Kisi O, Kiafar H, Ghavidel S (2015) Comparison of different data-driven approaches for modeling lake level fluctuations: the case of Manyas and Tuz lakes. Water Resources Management Jan 2015
Sattar AM (2014a) Gene Expression models for the prediction of longitudinal dispersion coefficient in transitional and turbulent pipe flow. J Pipeline Syst Eng Pract ASCE 5(1):04013011
Sattar AM (2014b) Gene expression models for prediction of dam breach parameters. J Hydroinf 16(3):550–571
Shi Y, Eberhart RC (1998) A modified swarm optimizer in: Proc. of the IEEE Int. Conf. on Evolutionary Computation, Anchorage 69–73
Sittel CN, Threadgill WD, Schnelle KB (1968) Longitudinal dispersion for turbulent flow in pipes. Ind Eng Chem Fundam 7:39–43
Takashi O, Hidetomo I, Tetsuya M, Kazunori N (1998) Orthogonal and successive projection methods for the learning of neurofuzzy GMDH. Inf Sci 110:5–24
Taylor GI (1954) The dispersion of matter in turbulent flow through a pipe. Proc R Soc A223:446–468
Taylor JR (1994) Risk Analysis for process plant, pipelines and transport. Taylor and Francis, Abingdon Oxon, RN
Tichacek LJ, Barkelew CH, Baron T (1957) Axial mixing in pipes. Am Inst Chem Eng 3(4):439–442
Trench CJ (2001) How pipelines make the oil market work - Their networks, operation and regulation. Allegro Energy Group, New York
Tzatchkov VG, Aldama AA, Arreguin FI (2002) Advection-dispersion-reaction modeling in water distribution networks. ASCE J Water Resour Plan Manag 128(5):334–342
Xiao-mei Z, Zhi-huan S, LI Ping (2002) The Improved GMDH-type Neural Network and Its Application to Forecasting Chaotic Time Series. J Circuits Syst 2002–01.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Najafzadeh, M., Sattar, A.M.A. Neuro-Fuzzy GMDH Approach to Predict Longitudinal Dispersion in Water Networks. Water Resour Manage 29, 2205–2219 (2015). https://doi.org/10.1007/s11269-015-0936-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-015-0936-8