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Receiving More Accurate Predictions for Longitudinal Dispersion Coefficients in Water Pipelines: Training Group Method of Data Handling Using Extreme Learning Machine Conceptions

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Abstract

Longitudinal dispersion coefficient (LDC) is known as the most remarkable environmental variables which plays a key role in evaluation of pollution profiles in water pipelines. Even though, there is a wide range of numerical models to estimate coefficient of longitudinal dispersion, these mathematical techniques may often come in quite few inaccuracies due to complex mechanism of convection-diffusion processes in pollutant transition in water pipelines. In this research work, to obtain more accurate prediction of LDC, general structure of group method of data handling (GMDH) is modified by means of extreme learning machine (ELM) conceptions. In fact, with getting inspiration from ELM, a novel GMDH method, called GMDH network based on using extreme learning machine (GMDH-ELM), is proposed in which weighting coefficients of quadratic polynomials applied in conventional GMDH are no longer required to be updated either using back propagation technique or other evolutionary algorithms through training stage. In fact, an intermediate parameter is employed to establish a relationship between the input and output in each neuron of the GMDH model. In this way, a well-known and reliable dataset (233 experimental data) related to LDC in water network pipelines, as output vector, is applied to conduct training and testing phases. Through datasets, the Re number, the average longitudinal flow velocity, the friction factor of pipeline and the diameter of pipe are considered as inputs of the proposed approach. The results of GMDH-ELM model indicate a highly satisfying level of precision in both training and testing phases. Furthermore, feed forward structure of GMDH model was improved by particle swarm optimization (PSO) and gravitational search algorithm (GSA) to predict LDC. Through a sound judgment, a comparison is drawn between the performance of GMDH-ELM and other developed GMDH models. Moreover, several empirical equations existing in literature have been applied for comparisons. Overall, results of GMDH-ELM have permissible superiority over the other soft computing tools and conventional predictive models.

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References

  • Alizamir M, Kisi O, Zounemat-Kermani M (2018) Modelling long-term groundwater fluctuations by extreme learning machine using hydro-climatic data. Hydrol Sci J 63(1):63–73

    Article  Google Scholar 

  • Anastasakis L, Mort N (2009) Exchange rate forecasting using a combined parametric and nonparametric self-organising modelling approach. Expert Syst Appl 36(10):12001–12011

    Article  Google Scholar 

  • Bandapalli C, Sutaria B, Bhatt D, Singh K (2017) Experimental investigation and estimation of surface roughness using ANN, GMDH & MRA models in high speed micro end milling of Titanium Alloy (grade-5). Mater Today Proc 4(2):1019–1028

    Article  Google Scholar 

  • Chen G, Liu L, Zhang Z, Huang S (2017) Optimal reactive power dispatch by improved GSA-based algorithm with the novel strategies to handle constraints. Appl Soft Comput 50:58–70

    Article  Google Scholar 

  • Chikwendu S (1986) Calculation of longitudinal shear dispersivity using an N-zone model as \({N}\rightarrow \infty \). J Fluid Mech 167:19–30

    Article  Google Scholar 

  • Chon K, Lu S (2001) A new algorithm for autoregression moving average model parameter estimation using group method of data handling. Ann Biomed Eng 29(1):92–98

    Article  Google Scholar 

  • Cutter MR (2004) Dispersion in steady pipe flow with reynolds number under 10,000. Ph.D. thesis, University of Cincinnati

  • Davidson J, Farquharson D, Picken J, Taylor D (1955) Gas mixing in long pipelines. Chem Eng Sci 4(5):201–205

    Article  Google Scholar 

  • Deissler R (1950) Analytical and experimental investigation of adiabatic turbulent flow in smooth tubes. Technical report, National Advisory Committee for Aeronautics

  • Dorn M, Braga A, Llanos C, Coelho L (2012) A GMDH polynomial neural network-based method to predict approximate three-dimensional structures of polypeptides. Expert Syst Appl 39(15):12268–12279

    Article  Google Scholar 

  • Ebtehaj I, Bonakdari H, Gharabaghi B (2018a) Development of more accurate discharge coefficient prediction equations for rectangular side weirs using adaptive neuro-fuzzy inference system and generalized group method of data handling. Measurement 116:473–482

    Article  Google Scholar 

  • Ebtehaj I, Bonakdari H, Moradi F, Gharabaghi B, Sheikh-Khozani Z (2018b) An integrated framework of extreme learning machines for predicting scour at pile groups in clear water condition. Coast Eng 135:1–15

    Article  Google Scholar 

  • Ekambara K, Joshi J (2003) Axial mixing in pipe flows: turbulent and transition regions. Chem Eng Sci 58(12):2715–2724

    Article  Google Scholar 

  • Flint L (1967) On the velocity profile for turbulent flow in a straight pipe. Chem Eng Sci 22(8):1127–1131

    Article  Google Scholar 

  • Flint L, Eisenklam P (1969) Longitudinal gas dispersion in transitional and turbulent flow through a straight tube. Can J Chem Eng 47(2):101–106

    Article  Google Scholar 

  • Fowler FC, Brown GG (1943) Contamination by successive flow in pipe lines. American Institute of chemical engineers

  • Giorgi M, Malvoni M, Congedo P (2016) Comparison of strategies for multi-step ahead photovoltaic power forecasting models based on hybrid group method of data handling networks and least square support vector machine. Energy 107:360–373

    Article  Google Scholar 

  • Hart J, Guymer I, Jones A, Stovin V (2013) Longitudinal dispersion coefficients within turbulent and transitional pipe flow. In: Experimental and computational solutions of hydraulic problems. Springer, pp 133–145

  • He P, Tao T, Xin K, Li S, Yan H (2016) Modelling water distribution systems with deficient pressure: an improved iterative methodology. Water Resour Manag 30 (2):593–606

    Article  Google Scholar 

  • Heddam S, Kisi O (2017) Extreme learning machines: a new approach for modeling dissolved oxygen (DO) concentration with and without water quality variables as predictors. Environ Sci Pollut Res 24(20):16702–16724

    Article  Google Scholar 

  • Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1-3):489–501

    Article  Google Scholar 

  • Huang G, Chen L (2007) Convex incremental extreme learning machine. Neurocomputing 70(16):3056–3062

    Article  Google Scholar 

  • Huang G, Chen L (2008) Enhanced random search based incremental extreme learning machine. Neurocomputing 71(16):3460–3468

    Article  Google Scholar 

  • Huang GB, Wang DH, Lan Y (2011) Extreme learning machines: a survey. Int J Mach Learn Cybern 2(2):107–122

    Article  Google Scholar 

  • Ivakhnenko A (1971) Polynomial theory of complex systems. IEEE Trans Syst Man Cybern SMC-1(4):364–378

    Article  Google Scholar 

  • Ivakhnenko A (1978) The group method of data handling in long-range forecasting. Technol Forecast Soc Chang 12(2):213–227

    Article  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization (pso). In: Proceedings of IEEE international conference on neural networks, perth, Australia, pp 1942–1948

  • Keyes JJ (1955) Diffusional film characteristics in turbulent flow: Dynamic response method. AIChE J 1(3):305–311

    Article  Google Scholar 

  • Levenspiel O (1958) Longitudinal mixing of fluids flowing in circular pipes. Ind Eng Chem 50(3):343–346

    Article  Google Scholar 

  • Madala H, Ivakhnenko A (1994) Inductive learning algorithms for complex systems modeling, vol 368. CRC Press, Boca Raton

  • Malm A, Moberg F, Rosén L, Pettersson TJ (2015) Cost-benefit analysis and uncertainty analysis of water loss reduction measures: case study of the gothenburg drinking water distribution system. Water Resour Manag 29(15):5451–5468

    Article  Google Scholar 

  • Meyer C (2000) Matrix analysis and applied linear algebra, vol 71. SIAM

  • Najafzadeh M, Sattar A (2015a) Neuro-fuzzy GMDH approach to predict longitudinal dispersion in water networks. Water Resour Manag 29(7):2205–2219

    Article  Google Scholar 

  • Najafzadeh M (2015b) Neuro-fuzzy GMDH systems based evolutionary algorithms to predict scour pile groups in clear water conditions. Ocean Eng 99:85–94

    Article  Google Scholar 

  • Najafzadeh M, Saberi-Movahed F (2019) GMDH-GEP to predict free span expansion rates below pipelines under waves. Marine Georesources & Geotechnology 37 (3):375–392

    Article  Google Scholar 

  • Naserbegi A, Aghaie M, Minuchehr A, Alahyarizadeh G (2018) A novel exergy optimization of bushehr nuclear power plant by gravitational search algorithm (GSA). Energy 148:373–385

    Article  Google Scholar 

  • Nazif S, Karamouz M, Yousefi M, Zahmatkesh Z (2013) Increasing water security: an algorithm to improve water distribution performance. Water Resour Manag 27(8):2903–2921

    Article  Google Scholar 

  • Puri V, Chauhan Y, Singh N (2017) A comparative design study and analysis of inner and outer rotor permanent magnet synchronous machine for power generation in vertical axis wind turbine using GSA and GSA-PSO. Sustain Energy Technol Assess 23:136–148

    Google Scholar 

  • Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    Article  Google Scholar 

  • Rashedi E, Nezamabadi-Pour H, Saryazdi S (2011) Filter modeling using gravitational search algorithm. Eng Appl Artif Intell 24(1):117–122

    Article  Google Scholar 

  • Rezaie-Balf M, Kisi O (2018) New formulation for forecasting streamflow: evolutionary polynomial regression vs. extreme learning machine. Hydrol Res 49 (3):939–953

    Article  Google Scholar 

  • Sattar A (2013) Gene expression models for the prediction of longitudinal dispersion coefficients in transitional and turbulent pipe flow. J Pipeline Syst Eng Pract 5 (1):04013011

    Article  Google Scholar 

  • Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE International conference on evolutionary computation proceedings. IEEE world congress on computational intelligence (cat. no. 98TH8360). IEEE, pp 69–73

  • Sittel Jr, C, Threadgill W, Schnelle Jr K (1968) Longitudinal dispersion for turbulent flow in pipes. Ind Eng Chem Fund 7(1):39–43

    Article  Google Scholar 

  • Smith SS, Schulze RK (1948) Interfacial mixing characteristics of products in products pipe line-Part 1. The Petroleum Engineer 20(8):330–337

    Google Scholar 

  • Taylor G (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proc R Soc Lond Ser Math Phys Sci 219(1137):186–203

    Google Scholar 

  • Taylor G (1954) The dispersion of matter in turbulent flow through a pipe. Proc R Soc Lond Ser Math Phys Sci 223(1155):446–468

    Google Scholar 

  • Tichacek L, Barkelew C, Baron T (1957) Axial mixing in pipes. AIChE J 3(4):439–442

    Article  Google Scholar 

  • Witczak M, Korbicz J, Mrugalski M, Patton R (2006) A GMDH neural network-based approach to robust fault diagnosis: Application to the DAMADICS benchmark problem. Control Eng Pract 14(6):671–683

    Article  Google Scholar 

  • Yuan X, Chen C, Yuan Y, Huang Y, Tan Q (2015) Short-term wind power prediction based on LSSVM–GSA model. Energy Convers Manag 101:393–401

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Sciences and Modern Technologies, Graduate University of Advanced Technology, Kerman, Iran

    Farid Saberi-Movahed

  2. Department of Water Engineering, Faculty of Civil and Surveying Engineering, Graduate University of Advanced Technology, Kerman, Iran

    Mohammad Najafzadeh

  3. Department of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Adel Mehrpooya

Authors
  1. Farid Saberi-Movahed
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  2. Mohammad Najafzadeh
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  3. Adel Mehrpooya
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Correspondence to Mohammad Najafzadeh.

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Saberi-Movahed, F., Najafzadeh, M. & Mehrpooya, A. Receiving More Accurate Predictions for Longitudinal Dispersion Coefficients in Water Pipelines: Training Group Method of Data Handling Using Extreme Learning Machine Conceptions. Water Resour Manage 34, 529–561 (2020). https://doi.org/10.1007/s11269-019-02463-w

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