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A combined adaptive neuro-fuzzy inference system–firefly algorithm model for predicting the roller length of a hydraulic jump on a rough channel bed

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Abstract

Hydraulic jumps can occur downstream of hydraulic structures, such as normal weirs, gates and ogee spillways. The roller length is one of the most important parameters of hydraulic jumps in open channels. In this study, the roller length of a hydraulic jump on a rough bed is predicted using a hybrid of adaptive neuro-fuzzy inference systems and the firefly algorithm (ANFIS–FA). First, the effect of parameters including the Froude number (Fr), sequent depth (h 2/h 1) and relative roughness (ks/h 1) upstream of a hydraulic jump is studied. Following the modeling result analysis, ANFIS–FA is introduced as the superior model for estimating the roller length of a hydraulic jump on a rough bed according to Fr, h 2/h 1 and ks/h 1. The calculated MAPE, RMSE and correlation coefficient values for the superior model are 7.606, 1.771 and 0.970, respectively. ANFIS–FA predicted approximately 40 % of the results with less than 5 % error, and only 36 % of data had more than 10 % error.

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References

  1. Rajaratnam N (1968) Hydraulic jumps on rough beds. Trans Eng Inst Can 11(A-2):1–8

    Google Scholar 

  2. Leutheusser HJ, Schiller EJ (1975) Hydraulic jump in a rough channel. Water Power Dam Constr 27(5):186–191

    Google Scholar 

  3. Hughes W, Flack J (1984) Hydraulic jump properties over a rough bed. J Hydraul Eng 110(12):1755–1771. doi:10.1061/(ASCE)0733-9429(1984)110:12(1755)

    Article  Google Scholar 

  4. Hager WH, Bremen R, Kawagoshi N (1990) Classical hydraulic jump: length of roller. J Hydraul Res 28(5):591–608. doi:10.1080/00221689009499048

    Article  Google Scholar 

  5. Ead S, Rajaratnam N (2002) Hydraulic jumps on corrugated beds. J Hydraul Eng 128(7):656–663. doi:10.1061/(ASCE)0733-9429(2002)128:7(656)

    Article  Google Scholar 

  6. Carollo F, Ferro V, Pampalone V (2007) Hydraulic jumps on rough beds. J Hydraul Eng 133(9):989–999. doi:10.1061/(ASCE)0733-9429(2007)133:9(989)

    Article  Google Scholar 

  7. Pagliara S, Lotti I, Palermo M (2008) Hydraulic jump on rough bed of stream rehabilitation structures. J Hydro Environ Res 2(1):29–38. doi:10.1016/j.jher.2008.06.001

    Article  Google Scholar 

  8. Carollo F, Ferro V, Pampalone V (2009) New solution of classical hydraulic jump. J Hydraul Eng 135(6):527–531. doi:10.1061/(ASCE)HY.1943-7900.0000036

    Article  Google Scholar 

  9. Afzal N, Bushra A, Seena A (2011) Analysis of turbulent hydraulic jump over a transitional rough bed of a rectangular channel: universal relations. J Eng Mech 137(12):835–845. doi:10.1061/(ASCE)EM.1943-7889.0000294

    Article  Google Scholar 

  10. Ezizah G, Yousif N, Mostafa S (2012) Hydraulic jumps in new roughened beds. Asian J Appl Sci 5(2):96–106

    Article  Google Scholar 

  11. Mok KM, Yuen KV, Cheong KH, Hoi KI (2013) A search of the dominant free surface fluctuation frequency downstream of the oscillating hydraulic jump with the Bayesian spectral density approach. Phys Scr T 155:014007. doi:10.1088/0031-8949/2013/T155/014007

    Article  Google Scholar 

  12. Ahmed HMA, El Gendy M, Mirdan AMH, Ali AAM, Abdel Haleem FSS (2014) Effect of corrugated beds on characteristics of submerged hydraulic jump. Ain Shams Eng J 5:1033–1042. doi:10.1016/j.asej.2014.06.006

    Article  Google Scholar 

  13. Velioglu D, Tokyay ND, Dincer AI (2015) A numerical and experimental study on the characteristics of hydraulic jumps on rough beds. In: E-proceedings of the 36th IAHR World Congress 28 June–3 July, The Hague, the Netherlands. pp 1–9

  14. Ghani AA, Azamathulla HM (2014) Development of GEP-based functional relationship for sediment transport in tropical rivers. Neural Comput Appl 24(2):271–276. doi:10.1007/s00521-012-1222-9

    Article  Google Scholar 

  15. Dash NB, Panda SN, Remesan R, Sahoo N (2010) Hybrid neural modeling for groundwater level prediction. Neural Comput Appl 19(8):1251–1263. doi:10.1007/s00521-010-0360-1

    Article  Google Scholar 

  16. Rezaeianzadeh M, Tabari H, Yazdi AA, Isik S, Kalin L (2014) Flood flow forecasting using ANN, ANFIS and regression models. Neural Comput Appl 25(1):25–37. doi:10.1007/s00521-013-1443-6

    Article  Google Scholar 

  17. Sattar AM (2014) Gene expression models for the prediction of longitudinal dispersion coefficients in transitional and turbulent pipe flow. J Pipeline Syst Eng Pract 5(1):04013011. doi:10.1061/(ASCE)PS.1949-1204.0000153

    Article  Google Scholar 

  18. Sattar AM, Gharabaghi B (2015) Gene expression models for prediction of longitudinal dispersion coefficient in streams. J Hydrol 524:587–596. doi:10.1016/j.jhydrol.2015.03.016

    Article  Google Scholar 

  19. Sattar AM (2014) Gene expression models for prediction of dam breach parameters. J Hydroinform 16(3):550–571. doi:10.2166/hydro.2013.084

    Article  MathSciNet  Google Scholar 

  20. Ebtehaj I, Bonakdari H (2016) Assessment of evolutionary algorithms in predicting non-deposition sediment transport. Urban Water J 13(5):499–510. doi:10.1080/1573062X.2014.994003

    Article  Google Scholar 

  21. Thompson J, Sattar AM, Gharabaghi B, Warner RC (2016) Event-based total suspended sediment particle size distribution model. J Hydrol 536:236–246. doi:10.1016/j.jhydrol.2016.02.056

    Article  Google Scholar 

  22. Ebtehaj I, Bonakdari H, Shamshirband S, Mohammadi K (2016) A combined support vector machine-wavelet transform model for prediction of sediment transport in sewer. Flow Meas Instrum 47:19–27. doi:10.1016/j.flowmeasinst.2015.11.002

    Article  Google Scholar 

  23. Yuen KV, Lam HF (2006) On the complexity of artificial neural networks for smart structures monitoring. Eng Struct 28(7):977–984. doi:10.1016/j.engstruct.2005.11.002

    Article  Google Scholar 

  24. Zounemat-Kermani M, Beheshti AS, Ataie-Ashtiani B, Sabbagh-Yazdi SR (2009) Estimation of current-induced scour depth around pile groups using neural network and adaptive neuro-fuzzy inference system. Appl Soft Comput 9:746–755. doi:10.1016/j.asoc.2008.09.006

    Article  Google Scholar 

  25. Ebtehaj I, Bonakdari H (2013) Evaluation of sediment transport in sewer using artificial neural network. Eng. Appl Com Fluid Mech 7(3):382–392. doi:10.1080/19942060.2013.11015479

    Google Scholar 

  26. Khoshbin F, Bonakdari H, Ashraf Talesh SH, Ebtehaj I, Zaji AH, Azimi H (2015) Adaptive neuro-fuzzy inference system multi-objective optimization using the genetic algorithm/singular value decomposition method for modelling the discharge coefficient in rectangular sharp-crested side weirs. Eng Optim 48(6):933–948. doi:10.1080/0305215X.2015.1071807

    Article  Google Scholar 

  27. Omid MH, Omid M, Esmaeeli VM (2005) Modelling hydraulic jumps with artificial neural networks. Proc Inst Civ Eng Water Manage 158(2):65–70. doi:10.1680/wama.2005.158.2.65

    Article  Google Scholar 

  28. Naseri M, Othman F (2012) Determination of the length of hydraulic jumps using artificial neural networks. Adv Eng Soft 48:27–31. doi:10.1016/j.advengsoft.2012.01.003

    Article  Google Scholar 

  29. Abbaspour A, Farsadizadeh D, Ghorbani MA (2013) Estimation of hydraulic jump on corrugated bed using artificial neural networks and genetic programming. Water Sci Eng 6(2):189–198. doi:10.3882/j.issn.1674-2370.2013.02.007

    Google Scholar 

  30. Houichi L, Dechemi N, Heddam S, Achour B (2013) An evaluation of ANN methods for lengths of hydraulic jumps in U-shaped channel. J Hydroinform 15(1):147–154. doi:10.2166/hydro.2012.138

    Article  Google Scholar 

  31. Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. Syst Man Cybern IEEE Trans 23(3):665–685. doi:10.1109/21.256541

    Article  Google Scholar 

  32. Jang JS, Sun CT, Mizutani E (1997) Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence. Prentice-Hall, Inc, New Jersey, USA

  33. Yang XS (2010) Firefly algorithm, stochastic test functions and design optimization. Int J Bio Inspir Comput 2(2):78–84. doi:10.1504/IJBIC.2010.032124

    Article  Google Scholar 

  34. Ch S, Sohani SK, Kumar D, Malik A, Chahar BR, Nema AK, Panigrahi BK, Dhiman RC (2014) A support vector machine-firefly algorithm based forecasting model to determine malaria transmission. Neurocomputing 129:279–288. doi:10.1016/j.neucom.2013.09.030

    Article  Google Scholar 

  35. Pearson K (1895) Notes on regression and inheritance in the case of two parents. Proc R Soc A 58:240–242

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Razi University, Kermanshah, Iran

    Hamed Azimi, Hossein Bonakdari & Isa Ebtehaj

  2. Department of Electrical and Computer Engineering, University of British Colombia, Vancouver, BC, Canada

    Hossein Bonakdari & David G. Michelson

Authors
  1. Hamed Azimi
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  2. Hossein Bonakdari
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  3. Isa Ebtehaj
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  4. David G. Michelson
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Correspondence to Hossein Bonakdari.

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Azimi, H., Bonakdari, H., Ebtehaj, I. et al. A combined adaptive neuro-fuzzy inference system–firefly algorithm model for predicting the roller length of a hydraulic jump on a rough channel bed. Neural Comput & Applic 29, 249–258 (2018). https://doi.org/10.1007/s00521-016-2560-9

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