Skip to main content

Advertisement

SpringerLink
Log in

Evolutionary design of generalized group method of data handling-type neural network for estimating the hydraulic jump roller length

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Hydraulic jumps generally occur subsequent to structures such as ogee spillways, control gates, and weirs. The jump roller length is considered one of the main hydraulic jump parameters. In this study, the roller length of a hydraulic jump on a rough channel bed is predicted using a novel, evolutionary, generalized structure design of a group method of data handling (GS-GMDH)-type neural network. The topology of GMDH is designed with a genetic algorithm . Initially, the three most important non-dimensional parameters affecting hydraulic jump roller length, including the Froude number upstream of a hydraulic jump \(\left( {Fr} \right) \), the ratio of sequent depths \(\left( {{h_2 }/{h_1 }} \right) \), and the relative roughness \(\left( {{ks}/{h_1 }} \right) \) were used to generate four different GS-GMDH models, and the most accurate model is identified. The best new GS-GMDH model prediction statistics, including RMSE, MARE, and correlation coefficient are 1.816, 0.081, and 0.966, respectively, while the scatter index and BIAS values are 0.084 and 1.45, respectively. A partial derivative sensitivity analysis of the input parameters for the new model is also performed. The new model predictions are then compared with predictions of a number of other models. The superior performance of the new GS-GMDH over these existing models is illustrated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bradley, J.N., Peterka, A.J.: The hydraulic design of stilling basins: hydraulic jumps on a horizontal apron (Basin I). J. Hydraul. Div. 83, 1–24 (1957)

    Google Scholar 

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

    Google Scholar 

  3. Leutheusser, H.J., Schiller, E.J.: Hydraulic jump in a rough channel. Water Power Dam Constr. 27, 186–191 (1975)

    Google Scholar 

  4. Hughes, W., Flack, J.: Hydraulic jump properties over a rough bed. J. Hydraul. Eng. 110, 1755–1771 (1984)

    Article  Google Scholar 

  5. Hager, W.H., Bremen, R., Kawagoshi, N.: Classical hydraulic jump: length of roller. J. Hydraul. Res. 28, 591–608 (1990)

    Article  Google Scholar 

  6. Ead, S., Rajaratnam, N.: Hydraulic jumps on corrugated beds. J. Hydraul. Eng. 128, 656–663 (2002)

    Article  Google Scholar 

  7. Carollo, F., Ferro, V., Pampalone, V.: Hydraulic jumps on rough beds. J. Hydraul. Eng. 133, 989–999 (2007)

    Article  Google Scholar 

  8. Pagliara, S., Lotti, I., Palermo, M.: Hydraulic jump on rough bed of stream rehabilitation structures. J. Hydro-Environ. Res. 2, 29–38 (2008)

    Article  Google Scholar 

  9. Bejestan, M.S., Neisi, K.: A new roughened bed hydraulic jump stilling basin. Asian J. Appl. Sci. 2, 436–445 (2009)

    Article  Google Scholar 

  10. Carollo, F., Ferro, V., Pampalone, V.: New solution of classical hydraulic jump. J. Hydraul. Eng. 135, 527–531 (2009)

    Article  Google Scholar 

  11. Afzal, N., Bushra, A., Seena, A.: Analysis of turbulent hydraulic jump over a transitional rough bed of a rectangular channel: universal relations. J. Eng. Mech. 137, 835–845 (2011)

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Carollo, F., Ferro, V., Pampalone, V.: New expression of the hydraulic jump roller length. J. Hydraul. Eng. 138, 995–999 (2012)

    Article  Google Scholar 

  14. Carollo, F., Ferro, V., Pampalone, V.: Sequent depth ratio of B-jumps on smooth and rough beds. J. Agric. Eng. 44, 82–86 (2013)

    Google Scholar 

  15. Ahmed, H.M.A., El Gendy, M., Mirdan, A.M.H., Ali, A.A.M., Abdel Haleem, F.S.S.: Effect of corrugated beds on characteristics of submerged hydraulic jump. Ain. Shams. Eng. J. 5, 1033–1042 (2014)

    Article  Google Scholar 

  16. Velioglu, D., Tokyay, N., Dincer, A.I.: A numerical and experimental study on the characteristics of hydraulic jumps on rough beds. In: E-proceedings of the 36th IAHR World Congress, Hague, Netherlands, pp. 1–9 (2015)

  17. Talatahari, S., Kaveh, A.: A general model for meta-heuristic algorithms using the concept of fields of forces. Acta Mech. 221, 99–118 (2011)

    Article  MATH  Google Scholar 

  18. Talatahari, S., Kaveh, A., Sheikholeslam, R.: Engineering design optimization using chaotic enhanced charged system search algorithms. Acta Mech. 223, 2269–2285 (2012)

    Article  MATH  Google Scholar 

  19. Li, J., Pan, Q., Mao, K.: A discrete teaching-learning-based optimization algorithm for realistic flowshop rescheduling problems. Eng. Appl. Artif. Intell. 37, 279–292 (2015)

    Article  Google Scholar 

  20. Bonakdari, H., Ebtehaj, I.: Verification of equation for non-deposition sediment transport in flood water canals. In: 7th International Conference on Fluvial Hydraulics, RIVER FLOW 2014; Lausanne; Switzerland; 3–5 September, pp. 1527–1533 (2014)

  21. Ebtehaj, I., Bonakdari, H.: Evaluation of sediment transport in sewer using artificial neural network. Eng. Appl. Comput. Fluid Mech. 7, 382–392 (2013)

    Google Scholar 

  22. Ebtehaj, I., Bonakdari, H.: Performance evaluation of adaptive neural fuzzy inference system for sediment transport in sewers. Water Resour. Manag. 28, 4765–4779 (2014)

    Article  Google Scholar 

  23. Najafzadeh, M., Barani, G.A., Hessami Kermani, M.R.: Estimation of pipeline scour due to waves by GMDH. J. Pipeline Syst. Eng. Pract. 5, 06014002 (2014)

    Article  Google Scholar 

  24. Ebtehaj, I., Bonakdari, H., Zaji, A.H., Azimi, H., Sharifi, A.: Gene expression programming to predict the discharge coefficient in rectangular side weirs. Appl. Soft. Comput. 5, 618–628 (2015)

    Article  Google Scholar 

  25. Toth, E.: Asymmetric error functions for reducing the underestimation of local scour around bridge piers: application to neural networks models. J. Hydraul. Eng. 141, 04015011 (2015)

    Article  Google Scholar 

  26. Khoshbin, F., Bonakdari, H., Ashraf Talesh, S.H., Ebtehaj, I., Zaji, A.H., Azimi, H.: 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, 1–16 (2016)

    Article  MathSciNet  Google Scholar 

  27. Omid, M.H., Omid, M., Esmaeeli, V.M.: Modelling hydraulic jumps with artificial neural networks. Proc. Inst. Civ. Eng. Water Manag. 158, 65–70 (2005)

    Article  Google Scholar 

  28. Naseri, M., Othman, F.: Determination of the length of hydraulic jumps using artificial neural networks. Adv. Eng. Softw. 48, 27–31 (2012)

    Article  Google Scholar 

  29. Abbaspour, A., Farsadizadeh, D., Ghorbani, M.A.: Estimation of hydraulic jump on corrugated bed using artificial neural networks and genetic programming. Water Sci. Eng. 6, 189–198 (2013)

    Google Scholar 

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

    Article  Google Scholar 

  31. Karbasi, M., Azamathulla, H.M.: GEP to predict characteristics of a hydraulic jump over a rough bed. KSCE J. Civ. Eng. 20, 1–6 (2015)

    Google Scholar 

  32. Mahtabi, G., Satari, M.T.: Investigation of hydraulic jump characteristics in rough beds using M5 model tree. Jordan J. Agric. Sci. 12, 631–648 (2016)

    Google Scholar 

  33. Azimi, H., Bonakdari, H., Ebtehaj, I., Michelson, D.G.: 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. Appl. (2016). https://doi.org/10.1007/00521-016-2560-9

  34. Najafzadeh, M., Lim, S.Y.: Application of improved neuro-fuzzy GMDH to predict scour depth at sluice gates. Earth. Sci. Inf. 8, 187–196 (2015)

    Article  Google Scholar 

  35. Najafzadeh, M.: Neurofuzzy-based GMDH-PSO to predict maximum scour depth at equilibrium at culvert outlets. J. Pipeline Syst. Eng. Pract. 5, 06015001 (2015)

    Google Scholar 

  36. Ebtehaj, I., Bonakdari, H., Zaji, A.H., Azimi, H., Khoshbin, F.: GMDH-type neural network approach for modeling the discharge coefficient of rectangular sharp-crested side weirs. Eng. Sci. Technol. Int. J. 18, 746–757 (2015)

    Article  Google Scholar 

  37. Ebtehaj, I., Bonakdari, H., Khoshbin, F., Azimi, H.: Pareto genetic design of group method of data handling type neural network for prediction discharge coefficient in rectangular side orifices. Flow. Meas. Instrum. 41, 67–74 (2015)

    Article  Google Scholar 

  38. Ebtehaj, I., Bonakdari, H., Khoshbin, F.: Evolutionary design of a generalized polynomial neural network for modelling sediment transport in clean pipes. Eng. Optim. 48, 1793–1807 (2016)

    Article  Google Scholar 

  39. Garg, V.: Inductive group method of data handling neural network approach to model basin sediment yield. J. Hydraul. Eng. 20, C6014002 (2014)

    Google Scholar 

  40. Shaghaghi, S., Bonakdari, H., Gholami, A., Ebtehaj, I., Zeinolabedini, M.: Comparative analysis of GMDH neural network based on genetic algorithm and particle swarm optimization in stable channel design. Appl. Math. Comput. 313, 271–286 (2017)

    Google Scholar 

  41. Gholami, A., Bonakdari, H., Ebtehaj, I., Shaghaghi, S., Khoshbin, F.: Developing an expert group method of data handling system for predicting the geometry of a stable channel with a gravel bed: New model for predicting stable channel geometry with a gravel bed. Earth Surf. Proc. Landf. (2017). https://doi.org/10.1002/esp.4104

  42. Badyalina, B., Shabri, A.: Flood frequency analysis at ungauged site using group method of data handling and canonical correlation analysis. Mod. Appl. Sci. 9(6), 48 (2015)

    Article  Google Scholar 

  43. Besarati, S.M., Myers, P.D., Covey, D.C., Jamali, A.: Modeling friction factor in pipeline flow using a GMDH-type neural network. Cogent. Eng. 2, 1056929 (2015)

    Article  Google Scholar 

  44. Ivakhnenko, A.G.: Polynomial theory of complex systems. IEEE Trans. Syst. Man Cybern. 4, 364–378 (1971)

    Article  MathSciNet  Google Scholar 

  45. Farlow, S.J.: Self-Organizing Method in Modelling: GMDH Type Algorithm. Marcel Dekker, New York (1984)

    MATH  Google Scholar 

  46. Muller, J.A., Lemke, F.: Self-Organizing Data Mining. Libri, Hamburg (2000)

    Google Scholar 

  47. Nariman-Zadeh, N., Darvizeh, A., Felezi, M.E., Gharababei, H.: Polynomial modelling of explosive compaction process of metallic powders using GMDH-type neural networks and singular value decomposition. Model. Simul. Mater. Sci. Eng. 10, 727–744 (2002)

  48. Jamali, A., Nariman-Zadeh, N., Darvizeh, A., Masoumi, A., Hamrang, S.: Multi-objective evolutionary optimization of polynomial neural networks for modelling and prediction of explosive cutting process. Eng. Appl. Artif. Intell. 22, 676–687 (2009)

    Article  Google Scholar 

  49. Nariman-Zadeh, N., Jamali, A.: Pareto genetic design of GMDH-type neural networks for nonlinear systems. In: Drchal, J., Koutnik, J. (eds.) Proceedings of the International Workshop on Inductive Modelling, pp. 96–103. Czech Technical University, Prague, Czech Republic (2007)

  50. Ebtehaj, I., Bonakdari, H.: Comparison of genetic algorithm and imperialist competitive algorithms in predicting bed load transport in clean pipe. Water Sci. Tech. 70, 1695–1701 (2014)

    Article  Google Scholar 

  51. Nariman-Zadeh, N., Darvizeh, A., Jamali, A., Moeini, A.: Evolutionary design of generalized polynomial neural networks for modelling and prediction of explosive forming process. J. Mater. Process. Tech. 164, 1561–1571 (2005)

    Article  Google Scholar 

  52. Kondo, T., Ueno, J.: Revised gmdh-type neural network algorithm with a feedback loop identifying sigmoid function neural network. Inter. J. Innov. Comput. Inf. Control 2, 985–996 (2006)

    MATH  Google Scholar 

  53. Ebtehaj, I., Bonakdari, H.: Bed load sediment transport estimation in a clean pipe using multilayer perceptron with different training algorithms. KSCE J. Civ. Eng. 20, 581–589 (2016)

    Article  Google Scholar 

  54. Ebtehaj, I., Bonakdari, H.: Assessment of evolutionary algorithms in predicting non-deposition sediment transport. Urban Water J. 13, 499–510 (2016)

    Article  Google Scholar 

  55. Ebtehaj, I., Bonakdari, H., Zaji, A.H.: A nonlinear simulation method based on a combination of multilayer perceptron and decision trees for predicting non-deposition sediment transport. Water Sci. Tech: Water Supply 16, 1198–1206 (2016)

    Google Scholar 

  56. Kumar, M., Lodhi, A.S.: Hydraulic jump over sloping rough floors. ISH J. Hydraul. Eng. 22, 127–134 (2016)

    Article  Google Scholar 

  57. Gazendam, E., Gharabaghi, B., Ackerman, J., Whiteley, H.: Integrative neural networks models for stream assessment in restoration projects. J. Hydrol. 536, 339–350 (2016)

    Article  Google Scholar 

  58. Atieh, M., Mehltretter, S., Gharabaghi, B., Rudra, R.: Integrated neural networks model for prediction of sediment rating curve parameters for ungauged basins. J. Hydrol. 531(3), 1095–1107 (2015)

    Article  Google Scholar 

  59. Sattar, A.M., Gharabaghi, B.: Gene expression models for prediction of longitudinal dispersion coefficient in streams. J. Hydrol. 524, 587–596 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Environmental Research Center, Razi University, Kermanshah, Iran

    Hamed Azimi, Hossein Bonakdari, Isa Ebtehaj & Fatemeh Khoshbin

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

    Hossein Bonakdari & Isa Ebtehaj

  3. School of Engineering, University of Guelph, Guelph, ON, NIG 2W1, Canada

    Bahram Gharabaghi

Authors
  1. Hamed Azimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hossein Bonakdari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Isa Ebtehaj
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bahram Gharabaghi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fatemeh Khoshbin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hossein Bonakdari.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Azimi, H., Bonakdari, H., Ebtehaj, I. et al. Evolutionary design of generalized group method of data handling-type neural network for estimating the hydraulic jump roller length. Acta Mech 229, 1197–1214 (2018). https://doi.org/10.1007/s00707-017-2043-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-017-2043-9

Search

Navigation