Neural Computing and Applications

, Volume 31, Issue 12, pp 9145–9156 | Cite as

Sensitivity analysis of parameters affecting scour depth around bridge piers based on the non-tuned, rapid extreme learning machine method

  • Isa Ebtehaj
  • Hossein BonakdariEmail author
  • Amir Hossein Zaji
  • Hassan Sharafi
Original Article


The extreme learning machine (ELM) is a new, non-tuned and fast training algorithm for feedforward neural networks (FFNN). It is highly precise and randomly produces the input weights of single-layer FFNN. In the current study, the scour depth around bridge piers is predicted by ELM as a powerful method of nonlinear system modeling. To predict scour depth, the effective dimensionless parameters are determined through dimensional analysis. Due to the complexity of scour mechanisms around bridges, different models with diverse input numbers are presented. In 5 categories, 31 different models were obtained for modeling and ELM analysis. Following the training and validation of each model presented, the optimum model was selected from each of the 5 categories and its relationship to the respective category was identified to help determine scour depth in practical engineering. For the best models presented in the different input modes, new explicit expressions were deduced. The results show that the most important parameters affecting relative scour depth (ds/y) include ratio of pier width to flow depth (D/y) and ratio of pier length to flow depth (L/y) (RMSE = 0.08; MARE = 0.0.35). The ELM performance was compared for a range of pier geometries with regression-based equations. The results confirm that ELM outperforms other methods.


Artificial intelligence Bridge pier Extreme learning machine (ELM) Sensitivity analysis Scour depth 

List of symbols


Pier width


Local scour depth


Median diameter of particles


Froude number


Gravitational acceleration


Activation function (Eq. 5)


Pier length


Neurons in the hidden layer


Number of input samples (Eq. 5)


Average velocity of approaching flow


Input-hidden layer


Connecting weight between the ith input neuron and the jth hidden neuron (Eq. 3)


Flow depth


Hidden-output layer weight


Connecting weight between the jth hidden neuron and the kth output neuron (Eq. 3)


Standard deviation related to bed grain size


Compliance with ethical standards

Conflict of interest

The authors declare there is no conflict of interest.


  1. 1.
    Lyn DA, Neseem E, Ramachandra Rao A, Altschaeffl AG (2000) A laboratory sensitivity study of hydraulic parameters important in the deployment of fixed-in-place scour-monitoring devices. Joint Transportation Research Program. Report No. FHWA/IN/JTRP-2000/12. Purdue University, Indiana, USAGoogle Scholar
  2. 2.
    Firat M, Gungor M (2009) Generalized regression neural networks and feed forward neural networks for prediction of scour depth around bridge piers. Adv Eng Softw 40:731–737. CrossRefzbMATHGoogle Scholar
  3. 3.
    Laursen EM, Toch A (1956) Scour around bridge piers and abutments. Iowa Highway Research Board, WashingtonGoogle Scholar
  4. 4.
    Breusers HNC, Nicollet G, Shen HW (1977) Local scour around cylindrical piers. J Hydraul Res 15:211–252CrossRefGoogle Scholar
  5. 5.
    Richardson EV, Harrison LJ, Richardson JR, Davis SR (1993) Evaluating scour at bridges, 2nd edn. Federal Highway Administration, US Department of Transportation, McLeanGoogle Scholar
  6. 6.
    Melville B, Chiew Y (1999) Time scale for local scour at bridge piers. J Hydraul Eng 125:59–65. CrossRefGoogle Scholar
  7. 7.
    Azamathulla HM, Yusoff MAM (2013) Soft computing for prediction of river pipeline scour depth. Neural Comput Appl 23(7–8):2465–2469. CrossRefGoogle Scholar
  8. 8.
    Samadi M, Jabbari E, Azamathulla HM (2014) Assessment of M5′ model tree and classification and regression trees for prediction of scour depth below free overfall spillways. Neural Comput Appl 24(2):357–366. CrossRefGoogle Scholar
  9. 9.
    Azimi H, Bonakdari H, Ebtehaj I, Michelson DG (2016) 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. CrossRefGoogle Scholar
  10. 10.
    Ebtehaj I, Bonakdari H, Shamshirband S, Mohammadi K (2015) A combined support vector machine-wavelet transform model for prediction of sediment transport in sewer. Flow Meas Instrum 47:19–27. CrossRefGoogle Scholar
  11. 11.
    Sattar AM (2014) Gene Expression models for the prediction of longitudinal dispersion coefficients in transitional and turbulent pipe flow. J Pipeline Syst Eng Pract 5:04013011. CrossRefGoogle Scholar
  12. 12.
    Khoshbin F, Bonakdari H, Ashraf Talesh SH, Ebtehaj I, Zaji AH, Azimi H (2016) 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. CrossRefGoogle Scholar
  13. 13.
    Sattar AM, Gharabaghi B (2015) Gene expression models for prediction of longitudinal dispersion coefficient in streams. J Hydrol 524:587–596. CrossRefGoogle Scholar
  14. 14.
    Najafzadeh M, Barani GA, Azamathulla HM (2014) Prediction of pipeline scour depth in clear-water and live-bed conditions using group method of data handling. Neural Comput Appl 24:629–635. CrossRefGoogle Scholar
  15. 15.
    Guven A, Gunal M (2008) Genetic programming approach for prediction of local scour downstream of hydraulic structures. J Irrig Drain Eng 134:241–249. CrossRefGoogle Scholar
  16. 16.
    Guven A, Azamathulla HM, Zakaria NA (2009) Linear genetic programming for prediction of circular pile scour. Ocean Eng 36:985–991. CrossRefGoogle Scholar
  17. 17.
    Azamathulla HM, Ab Ghani A, Zakaria NA, Guven A (2009) Genetic programming to predict bridge pier scour. J Hydraul Eng 136:165–169. CrossRefGoogle Scholar
  18. 18.
    Khan M, Azamathulla HM, Tufail M (2012) Gene-expression programming to predict pier scour depth using laboratory data. J Hydroinform 1:628–645. CrossRefGoogle Scholar
  19. 19.
    Pal M, Singh NK, Tiwari NK (2011) Support vector regression based modeling of pier scour using field data. Eng Appl Artif Intell 24:911–916. CrossRefGoogle Scholar
  20. 20.
    Hong J, Goyal M, Chiew Y, Chua L (2012) Predicting time-dependent pier scour depth with support vector regression. J Hydrol 468:241–248. CrossRefGoogle Scholar
  21. 21.
    Kaya A (2010) Artificial neural network study of observed pattern of scour depth around bridge piers. Comput Geotech 37:413–418. CrossRefGoogle Scholar
  22. 22.
    Balouchi B, Nikoo MR, Adamowski J (2015) Development of expert systems for the prediction of scour depth under live-bed conditions at river confluences: application of ANNs and the M5P model tree. Appl Soft Comput 34:51–59. CrossRefGoogle Scholar
  23. 23.
    Najafzadeh M, Barani GA, Hessami-Kermani MR (2013) GMDH based back propagation algorithm to predict abutment scour in cohesive soils. Ocean Eng 59:100–106. CrossRefGoogle Scholar
  24. 24.
    Najafzadeh M, Barani GA, Hessami-Kermani MR (2013) Group method of data handling to predict scour depth around vertical piles under regular waves. Sci Iran 20:406–413. CrossRefGoogle Scholar
  25. 25.
    Najafzadeh M, Lim SY (2014) Application of improved neuro-fuzzy GMDH to predict scour depth at sluice gates. Earth Sci Inform 8:187–196. CrossRefGoogle Scholar
  26. 26.
    Najafzadeh M (2015) Neuro-fuzzy GMDH systems based evolutionary algorithms to predict scour pile groups in clear water conditions. Ocean Eng 99:85–94. CrossRefGoogle Scholar
  27. 27.
    Najafzadeh M (2015) Neuro-fuzzy GMDH based particle swarm optimization for prediction of scour depth at downstream of grade control structures. Eng Sci Technol Int J 18:42–51. CrossRefGoogle Scholar
  28. 28.
    Olatunji SO, Selamat A, Raheem A, Azeez A (2013) Extreme learning machines based model for predicting permeability of carbonate reservoir. Int J Digit Content Technol Appl 7:450–459CrossRefGoogle Scholar
  29. 29.
    Li B, Cheng C (2014) Monthly discharge forecasting using wavelet neural networks with extreme learning machine. Sci China Technol Sci 57:2441–2452. CrossRefGoogle Scholar
  30. 30.
    Deo R, Şahin M (2015) Application of the extreme learning machine algorithm for the prediction of monthly Effective Drought Index in eastern Australia. Atmos Res 153(512):525. CrossRefGoogle Scholar
  31. 31.
    Cao J, Yang J, Wang Y (2015) Extreme learning machine for reservoir parameter estimation in heterogeneous reservoir. In: Proceedings of the ELM-2014. Springer, vol 2, pp 199–208Google Scholar
  32. 32.
    Khan M, Azamathulla HM, Tufail M, Ab Ghani A (2012) Bridge pier scour prediction by gene expression programming. Proc ICE Water Manag 165:481–493. CrossRefGoogle Scholar
  33. 33.
    Azamathulla HM, Deo MC, Deolalikar PB (2005) Neural networks for estimation of scour downstream of a ski-jump bucket. J Hydraul Eng 131:898–908. CrossRefGoogle Scholar
  34. 34.
    Guven A, Gunal M (2008) Prediction of scour downstream of grade-control structures using neural networks. J Hydraul Eng 134:1656–1660. CrossRefGoogle Scholar
  35. 35.
    Najafzadeh M, Barani GA (2011) Comparison of group method of data handling based genetic programming and back propagation systems to predict scour depth around bridge piers. Sci Iran 18:1207–1213. CrossRefGoogle Scholar
  36. 36.
    Mohammed TH, Noor MJMM, Ghazali AH, Huat BBK (2005) Validation of some bridge pier scour formulate using field and laboratory data. Am J Environ Sci 1:119–125. CrossRefGoogle Scholar
  37. 37.
    Landers MN, Mueller DS (1999) U.S. Geological survey field measurements of pier scour. In: Proceedings of the compendium of papers on ASCE water resources engineering conference 1991 to 1998, pp 585–607Google Scholar
  38. 38.
    Richardson EV, Davis SR (2001) Evaluating scour at bridge, hydraulic engineering circular No. 18 (HEC-18). US Department of Transportation, Federal HighwayGoogle Scholar
  39. 39.
    Johnson PA (1992) Reliability-basd pier scour engineering. J Hydraul Eng 118:1344–1357. CrossRefGoogle Scholar
  40. 40.
    Shen HW, Schneider VR, Karaki S (1969) Local scour around bridge piers. J Hydraul Div 95:1919–1940Google Scholar
  41. 41.
    Huang GB, Zhou H, Ding X, Zhang R (2012) Extreme learning machine for regression and multiclass classification. IEEE Trans Syst Man Cybern Part B 42:513–529. CrossRefGoogle Scholar
  42. 42.
    Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489–501. CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringRazi UniversityKermanshahIran
  2. 2.Environmental Research CenterRazi UniversityKermanshahIran

Personalised recommendations