Estimation of scour depth around cross-vane structures using a novel non-tuned high-accuracy machine learning approach


Due to the vital role of rivers and canals, the protection of their banks and beds is critically important. There are various methods for protecting beds and banks of rivers and canals in which “cross-vane structures” is one of them. In this paper, the scour hole depth at the downstream of cross-vane structures with different shapes (i.e., J, I, U, and W) is simulated utilizing a modern artificial intelligence method entitled “Outlier Robust Extreme Learning Machine (ORELM)”. The observational data are divided into two groups: training (70%) and test (30%). After that, the most optimal activation function for simulating the scour depth at the downstream of cross-vane structures is selected. Then, using the input parameters including the ratio of the structure length to the channel width (b/B), the densimetric Froude number (Fd), the ratio of the difference between the downstream and upstream depths to the structure height (Δy/hst) and the structure shape factor \( \left( \phi \right) \), eleven different ORELM models are developed for estimating the scour depth. Subsequently, the suitable model and also the most effective input parameters are identified through the conduction of an uncertainty analysis. The suitable model simulates the scour values by the dimensionless parameters b/B, Fd, Δy/hst. For this model, the values of the correlation coefficient (R), Variance accounted for (VAF) and the Nash-Sutcliffe efficiency (NSC) for the suitable model in the test mode are obtained 0.956, 91.378 and 0.908, respectively. Also, the dimensionless parameters b/B, Δy/hst. are detected as the most effective input parameters. Furthermore, the results of the suitable model are compared with the extreme learning machine model and it is concluded that the ORELM model is more accurate. Moreover, an uncertainty analysis exhibits that the ORELM model has an overestimated performance. Besides, a partial derivative sensitivity analysis (PDSA) model is performed for the suitable model.

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  1. 1

    Leopold L B, Wolman M G and Miller J P 1964 Fluvial processes in geomorphology. San Francisco: WH Freeman and Co., p. 522

  2. 2

    Rosgen D L 2001 The cross-vane, w-weir and j-hook vane structures. their description, design and application for stream stabilization and river restoration. In Wetlands Engineering & River Restoration 2001 (pp. 1–22)

  3. 3

    Scurlock S M, Cox A L, Thornton C I and Baird D C 2012 Maximum velocity effects from vane-dike installations in channel bends. In: Proceedings of ASCE Congress World Environmental and Water Resources (pp. 2614–2626)

  4. 4

    Pagliara S, Kurdistani S M and Santucci I 2013a Scour downstream of J-Hook vanes in straight horizontal channels. Acta Geophys. 61(5): 1211–1228

    Article  Google Scholar 

  5. 5

    Pagliara S and Kurdistani S M 2013 Scour downstream of cross-vane structures. Hydro-environ. Res. 7(4): 236–242

    Article  Google Scholar 

  6. 6

    Pagliara S, Kurdistani S M and Cammarata L 2013b Scour of clear water rock W-weirs in straight rivers. Hydra. Eng. 140(4): 060140021-16

    Google Scholar 

  7. 7

    Pagliara S, Sagvand Hassanabadi L and Mahmoudi Kurdistani S 2015 Logvane scour in clear water condition. River Res. App. 31(9): 1176–1182

    Article  Google Scholar 

  8. 8

    Mahmoudi Kurdistani S and Pagliara S 2015 Scour characteristics downstream of grade-control structures: Log-vane and log-deflectors comparison. In: World Environmental and Water Resources Congress (pp. 1831–1840)

  9. 9

    Pagliara S, Hassanabadi L and Kurdistani S M 2015. Clear water scour downstream of log deflectors in horizontal channels. Irrig. Drain. Eng. 141(9): 040150071-13

    Article  Google Scholar 

  10. 10

    Pagliara S and Kurdistani S M 2017. Flume experiments on scour downstream of wood stream restoration structures. Geomorphology 279: 141–149

    Article  Google Scholar 

  11. 11

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

    Article  Google Scholar 

  12. 12

    Azimi H, Bonakdari H, Ebtehaj I, Talesh S H A, Michelson D G and Jamali A 2017 Evolutionary Pareto optimization of an ANFIS network for modeling scour at pile groups in clear water condition. Fuzzy Sets Syst. 319: 50–69

    MathSciNet  Article  Google Scholar 

  13. 13

    Najafzadeh M, Barani G A and Kermani M R H 2013 Abutment scour in clear-water and live-bed conditions by GMDH network. Water Sci. Technol. 67(5): 1121–1128

    Article  Google Scholar 

  14. 14

    Moradi F, Bonakdari H, Kisi O, Ebtehaj I, Shiri J and Gharabaghi B 2019 Abutment scour depth modeling using neuro-fuzzy-embedded techniques. Mar. Georesour. Geotechnol. 37(2): 190–200

    Article  Google Scholar 

  15. 15

    Azimi H, Bonakdari H, Ebtehaj I, Shabanlou S, Talesh S H A and Jamali A 2019 A pareto design of evolutionary hybrid optimization of ANFIS model in prediction abutment scour depth. Sādhanā 44(7): 169

    MathSciNet  Article  Google Scholar 

  16. 16

    Wuppukondur A and Chandra V 2018. Control of bed erosion at 60 river confluence using vanes and piles. Int. J. Civ. Eng. 16(6): 619–627

    Article  Google Scholar 

  17. 17

    Shabanlou S, Azimi H, Ebtehaj I and Bonakdari H 2018. Determining the scour dimensions around submerged vanes in a 180 bend with the gene expression programming technique. J. Mar. Sci. Appl. 17(2): 233–240

    Article  Google Scholar 

  18. 18

    Riahi-Madvar H, Dehghani M, Seifi A, Salwana E, Shamshirband S, Mosavi A and Chau K W 2019 Comparative analysis of soft computing techniquesRBF, MLP, and ANFIS with MLR and MNLR for predicting grade-control scour hole geometry. Eng. Appl. Comput. Fluid Mech. 13(1): 529–550

    Google Scholar 

  19. 19

    Huang G B, Zhu Q Y and Siew C K 2004 Extreme learning machine: a new learning scheme of feedforward neural networks. Neural Netw. 2: 985–990

    Google Scholar 

  20. 20

    Huang G B, Zhu Q Y and Siew C K 2006 Extreme learning machine: theory and applications. Neurocomputing 70(1–3): 489–501

    Article  Google Scholar 

  21. 21

    Rao C R and Mitra S K 1971 Generalized inverse of matrices and its applications. Wiley, New York

    Google Scholar 

  22. 22

    Zhang, K and Luo M 2015 Outlier-robust extreme learning machine for regression problems. Neurocomputing 151: 1519–1527

    Article  Google Scholar 

  23. 23

    Yang J and Zhang Y 2011 Alternating direction algorithms for \ell_1-problems in compressive sensing. SIAM J. Sci. Comput. 33(1): 250–278

    MathSciNet  Article  Google Scholar 

  24. 24

    Azimi H, Bonakdari H, Ebtehaj I, Gharabaghi B and Khoshbin, F 2018 Evolutionary design of generalized group method of data handling-type neural network for estimating the hydraulic jump roller length. Acta. Mecha, 229(3): 1197–1214

    Article  Google Scholar 

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Correspondence to Saeid Shabanlou.

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Azimi, A.H., Shabanlou, S., Yosefvand, F. et al. Estimation of scour depth around cross-vane structures using a novel non-tuned high-accuracy machine learning approach. Sādhanā 45, 152 (2020).

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  • Cross-vane structures
  • scour
  • outlier robust extreme learning machine
  • uncertainty analysis
  • partial derivative sensitivity analysis