Document Type : Article

**Authors**

Department of Civil Engineering, Razi University, Kermanshah, Iran

**Abstract**

This study show the combination of computational fluid dynamics (CFD) and soft computing techniques to make viewpoint for two-phase flow modelling and accuracy evaluation of soft computing methods in the three-dimensional flow variables prediction in curved channels. Therefore, artificial neural network (ANN) and support vectors machines (SVM) models with CFD is designed to estimate velocity and flow depth variable in 60° sharp bend. Experimental results in 6 different flow discharges of 5, 7.8, 13.6, 19.1, 25.3 and 30.8 l/s to train and test, ANN and SVM models is used. The results of numerical models with experimental values are compared and the models accuracy is confirmed. The results evaluation show that all three models ANN, SVM and CFD perform well in flow velocity prediction, with correlation coefficient (*R*) of 0.952, o.806, and 0.680, and flow depth (*R*) of 0.999, 0.696, and 0.614 respectively. ANN model to predict both velocity and flow depth variables with mean absolute relative error (*MARE*) of 0.055 and 0.004 is the best model. Then SVM and CFD models with *MARE* of 0.069 and 0.089 in velocity prediction and in flow depth prediction CFD and SVM models with *MARE* of 0.007 and 0.011 are the best models, respectively.

**Keywords**

**Main Subjects**

References:

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26. Najafzadeh, M. and Sattar, A.M. "Neuro-fuzzy GMDH approach to predict longitudinal dispersion in water networks", Water Resources Management, 29(7), pp. 2205-2219 (2015).

27. Gholami, A., Bonakdari, H., Ebtehaj, I., and Akhtari, A.A. "Design of an adaptive neuro-fuzzy computing technique for predicting flow variables in a 90 sharp bend", Journal of Hydroinformatics, 19(4), jh2017200 (2017).

28. Gholami, A., Bonakdari, H., Zaji, A.H., Fenjan, S.A., and Akhtari, A.A. "New radial basis function network method based on decision trees to predict flow variables in a curved channel", Neural Computing and Applications, 30(9), pp. 2771-2785 (2018).

29. Gholami, A., Bonakdari, H., Zaji, A.H., Ajeel Fenjan, S., and Akhtari, A.A. "Design of modified structure multi-layer perceptron networks based on decision trees for the prediction of flow parameters in 90 openchannel bends", Engineering Applications of Computational Fluid Mechanics, 10(1), pp. 193-08 (2016).

30. Gholami, A., Bonakdari, H., Ebtehaj, I., Shaghaghi, S., and Khoshbin, F. "Developing an expert group method of data handling system for predicting the geometry of a stable channel with a gravel bed", Earth Surface Processes and Landforms, 42(10), pp. 1460- 1471 (2017). DOI: 10.1002/esp.4104.

31. Shaghaghi, S., Bonakdari, H., Gholami, A., Ebtehaj, I., and Zeinolabedini, M. "Comparative analysis of GMDH neural network based on genetic algorithm and particle swarm optimization in stable channel design", Applied Mathematics and Computation, 313, pp. 271- 286 (2017).

32. Kaveh, A. and Nasrollahi, A. "Charged system search and particle swarm optimization hybridized for optimal design of engineering structures", Scientia Iranica, Transactions A: Civil Engineering, 21, pp. 295-305 (2014).

33. Ebtehaj, I., Bonakdari, H., Zaji, A.H., Azimi H., and Sharifi, A. "Gene expression programming to predict the discharge coefficient in rectangular side weirs", Applied Soft Computing, 35, pp. 618-628 (2015).

34. Karimi, S., Bonakdari, H., and Gholami, A. "Determination discharge capacity of triangular labyrinth side weir using multi-layer neural network (ANN-MLP)", Current World Environment, 10(Special issue 1), pp. 111-119 (2015).

35. Zarif Sanayei, H.R., Talebbeydokhti, N., and Moradkhani, H. "3D estimation of metal elements in sediments of the Caspian Sea with moving least square and radial basis function interpolation methods", Scientia Iranica, Transactions A: Civil Engineering, 22, pp. 1661-1673 (2015).

36. Bonakdari, H., Baghalian, S., Nazari, F., and Fazli, M. "Numerical analysis and prediction of the velocity field in curved open channel using artificial neural network and genetic algorithm", Engineering Applications of Computational Fluid Mechanics, 5(3), pp. 384-396 (2011).

37. Sahu, M., Jana, S., Agarwal, S., and Khatua, K.K. "Point form velocity prediction in meandering open channel using artificial neural network", 2nd International Conference on Environmental Science and Technology, 6, pp. 209-212, Singapore: IACSIT Press (2011).

38. Gholami, A., Bonakdari, H., Zaji, A.H., and Akhtari, A.A. "Simulation of open channel bend characteristics using computational fluid dynamics and artificial neural networks", Engineering Applications of Computational Fluid Mechanics, 9(1), pp. 355-361 (2015).

39. Fenjan, S.A., Bonakdari, H., Gholami, A., and Akhtari, A.A. "Flow variables prediction using experimental, computational fluid dynamic and artificial neural network models in a sharp bend", International Journal of Engineering-Transactions A: Basics, 29(1), pp. 14-21 (2016).

40. Gholami, A., Bonakdari, H., Zaji, A.H., Akhtari, A.A., and Khodashenas, S.R. "Predicting the velocity field in a 90 open channel bend using a gene expression programming model", Flow Measurement and Instrumentation, 46, pp. 189-192 (2015).

41. Gholami, A., Bonakdari, H., Zaji, A.H., Michelson, D.G., and Akhtari, A.A. "Improving the performance of multi-layer perceptron and radial basis function models with a decision tree model to predict flow variables in a sharp 90 bend", Applied Soft Computing, 48, pp. 563-583 (2016).

42. Akhtari, A.A., Abrishami, J., and Sharifi, M.B. Experimental investigations water surface characteristics in strongly-curved open channels", Journal of Applied Sciences, 9(20), pp. 3699-3706 (2009).

43. Armfield Limited, Co., Instruction Manual of Miniature Propeller Velocity Meter Type H33 (1995).

44. Fluent Manual, Manual and User Guide of Fluent Software, Fluent Inc (2005).

45. Rezaeian Zadeh, M., Amin, S., Khalili, D., and Singh, V.P. "Daily out flow prediction by multilayer perception with logistic sigmoid and tangent sigmoid activation functions", Journal of Water Resources Management, 24(11), pp. 2673-2688 (2010).

46. Ebtehaj, I. and Bonakdari, H. "Evaluation of sediment transport in sewer using artificial neural network", Engineering Applications of Computational Fluid Mechanics, 7(3), pp. 382-392 (2013).

47. Levenberg, K. "A method for the solution of certain non-linear problems in least-squares", The Quarterly of Applied Mathematics, 2, pp. 164-168 (1944).

48. Zaji, A.H. and Bonakdari, H. "Application of artificial neural network and genetic programming models for estimating the longitudinal velocity field in open channel junctions", Flow Measurement and Instrumentation, 41, pp. 81-89 (2015).

49. Vapnik, V., The Nature of Statistical Learning Theory, Springer Verlag, New York, USA (1995).

50. Vapnik, V.N. and Vapnik, V., Statistical Learning Theory, 1, Wiley, New York (1998).

51. Adarsh, S. "Prediction of longitudinal dispersion coefficient in natural channels using soft computing techniques", Scientia Iranica. Transaction A, Civil Engineering, 17(5), pp. 363-371 (2010).

52. Wang, R., Zhan, Y., and Zhou, H. "Application of transform in fault diagnosis of power electronics circuits", Scientia Iranica, 19(3), pp. 721-726 (2012).

53. Ebtehaj, I., Bonakdari, H., Shamshirband, S., and Mohammadi, K. "A combined support vector machinewavelet transform model for prediction of sediment transport in sewer", Flow Measurement and Instrumentation, 47, pp. 19-27 (2016).

54. Ebtehaj, I. and Bonakdari, H. "A support vector regression-fire y algorithm-based model for limiting velocity prediction in sewer pipes", Water Science & Technology, 73(9), pp. 2244-2250 (2016).

55. Bowden, G.J., Maier, H.R., and Dandy, G.C. "Optimal division of data for neural network models in water resources applications", Water Resources Research, 38(2), pp. 1-11 (2002).

2. Shukry, A. "Flow around bends in an open flume", Transactions, ASCE, 115, pp. 751-788 (1950).

3. Rozovskii, I.L. "Flow of water in bends of open channels", Israel Program for Science Translation, Jerusalem, pp. 1-233 (1961).

4. DeVriend, H.J. and Geoldof, H.J. "Main flow velocity in short river bends", Journal of Hydraulics Engineering, 109(7), pp. 991-1011 (1983).

5. Bergs, M.A. "Flow processes in a curved alluvial channel", Ph.D. Thesis, The University of Iowa (1990).

6. Ye, J. and McCorquodale, J.A. "Simulation of curved open channel flows by 3D hydrodynamic model", Journal of Hydraulic Engineering- ASCE, 124(7), pp. 687-698 (1998).

7. Blanckaert, K. and Graf, W.H. "Mean flow and turbulence in open channel bend", Journal of Hydraulic Engineering, 127(10), pp. 835-847 (2001).

8. Barbhuiya, A.K. and Talukdar, S. "Scour and three dimensional turbulent flow fields measured by ADV at a 90 horizontal forced bend in a rectangular channel", Flow Measurement and Instrumentation, 21, pp. 312-321 (2010).

9. Ramamurthy, A., Han, S., and Biron, P. "Threedimensional simulation parameters for 90 open channel bend flows", Journal of Computing in Civil Engineering. ASCA, 27(3), pp. 282-291 (2013).

10. Gholami, A., Akhtari, A.A., Minatour, Y., Bonakdari, H., and Javadi, A.A. "Experimental and numerical study on velocity fields and water surface profile in a strongly-curved 90 open channel bend", Engineering Applications of Computational Fluid Mechanics, 8(3), pp. 447-461 (2014).

11. Leschziner, M.A. and Rodi, W. "Calculation of strongly curved open channel flow", Journal of the Hydraulics Division, 105(10), pp. 1297-1314 (1979).

12. Naji, M.A., Ghodsian, M., Vaghefi, M., and Panahpur, N. "Experimental and numerical simulation of flow in a 90 bend", Flow Measurement and Instrumentation, 21(3), pp. 292-298 (2010).

13. DeMarchis, M. and Napoli, E. "3D numerical simulation of curved open channel flows", Proceedings of 6th International Conference on Water Resources, Hydraulics & Hydrology, pp. 86-91, Chalkida, Evia Island, Greece, May 11-13 (2006).

14. Bodnar, T., Prihoda, J. "Numerical simulation of turbulent free-surface flow in curved channel", Flow, Turbulence and Combustion, 76, pp. 429-442 (2006).

15. Gholami, A., Bonakdari, H., and Akhtari, A.A. "Assessment of water depth change patterns in 120 sharp bend using numerical model", Water Science and Engineering, 4(9), pp. 336-344 (2016).

16. Bonakdari, H., Larrarte, F., and Joannis, C. "Effect of a bend on the velocity field in a circular sewer with free surface flow", Proceeding of 6th International Conference on Sustainable Techniques and Strategies in Urban Water Management, pp. 1401-1408, Lyon, France, June 24-28 (2007).

17. Zeng, J., Constantinescu, G., Blanckaert, K., and Weber, L. "Flow and bathymetry in sharp openchannel bends: Experiments and predictions", Water Resources Research, 44(9), w09401, pp. 1-22 (2008).

18. Gholami, A., Bonakdari, H., and Akhtari, A.A. "Developing finite volume method (FVM) in numerical simulation of flow pattern in 60 open channel bend", Journal of Applied Research in Water and Wastewater, 3(1), pp. 193-200 (2016).

19. Kisi, O. and Cigizoglu, H.K. "Comparison of different ANN techniques in river flow prediction", Civil Engineering Environment System, 14, pp. 211-231 (2007).

20. Najafzadeh, M. and Azamathulla, H.M. "Neuro-fuzzy GMDH to predict the scour pile groups due to waves", Journal of Computing in Civil Engineering, 29(5), 04014068 (2013).

21. Najafzadeh, M., Barani, G.A., and Hessami Kermani, M.R. "Estimation of pipeline scour due to waves by GMDH", Journal of Pipeline Systems Engineering and Practice, 5(3), 06014002 (2014).

22. Najafzadeh, M. and Zahiri, A. "Neuro-fuzzy GMDHbased evolutionary algorithms to predict flow discharge in straight compound channels", Journal of Hydrologic Engineering, 20(12), 04015035 (2015).

23. Najafzadeh, M., Barani, G.A., and Hessami-Kermani, M.R. "Evaluation of GMDH networks for prediction of local scour depth at bridge abutments in coarse sediments with thinly armored beds", Ocean Engineering, 104, pp. 387-396 (2015).

24. Najafzadeh, M., Etemad-Shahidi, A., and Lim, S.Y. "Scour prediction in long contractions using ANFIS and SVM", Ocean Engineering, 111, pp. 128-135 (2016).

25. Najafzadeh, M., Balf, M.R., and Rashedi, E. "Prediction of maximum scour depth around piers with debris accumulation using EPR, MT, and GEP models", Journal of Hydroinformatics, 18(5), pp. 867-884 (2016).

26. Najafzadeh, M. and Sattar, A.M. "Neuro-fuzzy GMDH approach to predict longitudinal dispersion in water networks", Water Resources Management, 29(7), pp. 2205-2219 (2015).

27. Gholami, A., Bonakdari, H., Ebtehaj, I., and Akhtari, A.A. "Design of an adaptive neuro-fuzzy computing technique for predicting flow variables in a 90 sharp bend", Journal of Hydroinformatics, 19(4), jh2017200 (2017).

28. Gholami, A., Bonakdari, H., Zaji, A.H., Fenjan, S.A., and Akhtari, A.A. "New radial basis function network method based on decision trees to predict flow variables in a curved channel", Neural Computing and Applications, 30(9), pp. 2771-2785 (2018).

29. Gholami, A., Bonakdari, H., Zaji, A.H., Ajeel Fenjan, S., and Akhtari, A.A. "Design of modified structure multi-layer perceptron networks based on decision trees for the prediction of flow parameters in 90 openchannel bends", Engineering Applications of Computational Fluid Mechanics, 10(1), pp. 193-08 (2016).

30. Gholami, A., Bonakdari, H., Ebtehaj, I., Shaghaghi, S., and Khoshbin, F. "Developing an expert group method of data handling system for predicting the geometry of a stable channel with a gravel bed", Earth Surface Processes and Landforms, 42(10), pp. 1460- 1471 (2017). DOI: 10.1002/esp.4104.

31. Shaghaghi, S., Bonakdari, H., Gholami, A., Ebtehaj, I., and Zeinolabedini, M. "Comparative analysis of GMDH neural network based on genetic algorithm and particle swarm optimization in stable channel design", Applied Mathematics and Computation, 313, pp. 271- 286 (2017).

32. Kaveh, A. and Nasrollahi, A. "Charged system search and particle swarm optimization hybridized for optimal design of engineering structures", Scientia Iranica, Transactions A: Civil Engineering, 21, pp. 295-305 (2014).

33. Ebtehaj, I., Bonakdari, H., Zaji, A.H., Azimi H., and Sharifi, A. "Gene expression programming to predict the discharge coefficient in rectangular side weirs", Applied Soft Computing, 35, pp. 618-628 (2015).

34. Karimi, S., Bonakdari, H., and Gholami, A. "Determination discharge capacity of triangular labyrinth side weir using multi-layer neural network (ANN-MLP)", Current World Environment, 10(Special issue 1), pp. 111-119 (2015).

35. Zarif Sanayei, H.R., Talebbeydokhti, N., and Moradkhani, H. "3D estimation of metal elements in sediments of the Caspian Sea with moving least square and radial basis function interpolation methods", Scientia Iranica, Transactions A: Civil Engineering, 22, pp. 1661-1673 (2015).

36. Bonakdari, H., Baghalian, S., Nazari, F., and Fazli, M. "Numerical analysis and prediction of the velocity field in curved open channel using artificial neural network and genetic algorithm", Engineering Applications of Computational Fluid Mechanics, 5(3), pp. 384-396 (2011).

37. Sahu, M., Jana, S., Agarwal, S., and Khatua, K.K. "Point form velocity prediction in meandering open channel using artificial neural network", 2nd International Conference on Environmental Science and Technology, 6, pp. 209-212, Singapore: IACSIT Press (2011).

38. Gholami, A., Bonakdari, H., Zaji, A.H., and Akhtari, A.A. "Simulation of open channel bend characteristics using computational fluid dynamics and artificial neural networks", Engineering Applications of Computational Fluid Mechanics, 9(1), pp. 355-361 (2015).

39. Fenjan, S.A., Bonakdari, H., Gholami, A., and Akhtari, A.A. "Flow variables prediction using experimental, computational fluid dynamic and artificial neural network models in a sharp bend", International Journal of Engineering-Transactions A: Basics, 29(1), pp. 14-21 (2016).

40. Gholami, A., Bonakdari, H., Zaji, A.H., Akhtari, A.A., and Khodashenas, S.R. "Predicting the velocity field in a 90 open channel bend using a gene expression programming model", Flow Measurement and Instrumentation, 46, pp. 189-192 (2015).

41. Gholami, A., Bonakdari, H., Zaji, A.H., Michelson, D.G., and Akhtari, A.A. "Improving the performance of multi-layer perceptron and radial basis function models with a decision tree model to predict flow variables in a sharp 90 bend", Applied Soft Computing, 48, pp. 563-583 (2016).

42. Akhtari, A.A., Abrishami, J., and Sharifi, M.B. Experimental investigations water surface characteristics in strongly-curved open channels", Journal of Applied Sciences, 9(20), pp. 3699-3706 (2009).

43. Armfield Limited, Co., Instruction Manual of Miniature Propeller Velocity Meter Type H33 (1995).

44. Fluent Manual, Manual and User Guide of Fluent Software, Fluent Inc (2005).

45. Rezaeian Zadeh, M., Amin, S., Khalili, D., and Singh, V.P. "Daily out flow prediction by multilayer perception with logistic sigmoid and tangent sigmoid activation functions", Journal of Water Resources Management, 24(11), pp. 2673-2688 (2010).

46. Ebtehaj, I. and Bonakdari, H. "Evaluation of sediment transport in sewer using artificial neural network", Engineering Applications of Computational Fluid Mechanics, 7(3), pp. 382-392 (2013).

47. Levenberg, K. "A method for the solution of certain non-linear problems in least-squares", The Quarterly of Applied Mathematics, 2, pp. 164-168 (1944).

48. Zaji, A.H. and Bonakdari, H. "Application of artificial neural network and genetic programming models for estimating the longitudinal velocity field in open channel junctions", Flow Measurement and Instrumentation, 41, pp. 81-89 (2015).

49. Vapnik, V., The Nature of Statistical Learning Theory, Springer Verlag, New York, USA (1995).

50. Vapnik, V.N. and Vapnik, V., Statistical Learning Theory, 1, Wiley, New York (1998).

51. Adarsh, S. "Prediction of longitudinal dispersion coefficient in natural channels using soft computing techniques", Scientia Iranica. Transaction A, Civil Engineering, 17(5), pp. 363-371 (2010).

52. Wang, R., Zhan, Y., and Zhou, H. "Application of transform in fault diagnosis of power electronics circuits", Scientia Iranica, 19(3), pp. 721-726 (2012).

53. Ebtehaj, I., Bonakdari, H., Shamshirband, S., and Mohammadi, K. "A combined support vector machinewavelet transform model for prediction of sediment transport in sewer", Flow Measurement and Instrumentation, 47, pp. 19-27 (2016).

54. Ebtehaj, I. and Bonakdari, H. "A support vector regression-fire y algorithm-based model for limiting velocity prediction in sewer pipes", Water Science & Technology, 73(9), pp. 2244-2250 (2016).

55. Bowden, G.J., Maier, H.R., and Dandy, G.C. "Optimal division of data for neural network models in water resources applications", Water Resources Research, 38(2), pp. 1-11 (2002).

Transactions on Civil Engineering (A)

March and April 2019Pages 726-741