Estimation of scour depth at bridges with complex pier foundations using support vector regression integrated with feature selection

  • Nhat-Duc Hoang
  • Kuo-Wei Liao
  • Xuan-Linh TranEmail author
Original Paper


This study aims at establishing machine learning models based on the support vector regression (SVR) for estimating local scour around complex piers under steady clear-water condition. A data set consisting of scour depth measurement cases has been collected to construct the prediction models. The data set includes eight influencing factors that consider aspects of pier geometry, flow property, and river bed material. Moreover, to enhance the performance of the SVR model, filter and wrapper feature selection strategies are used. The research finding is that all feature selection approaches can help to improve the prediction accuracy compared with the SVR model that uses all available features. Notably, the feature selection method based on the variable neighborhood search (VNS) algorithm achieves the best performance (MAPE = 21.65%, R2 = 0.85). Accordingly, the prediction model produced by SVR and VNS can be useful for assisting decision makers in the task of structural health monitoring as well as the design phase of bridges.


Scour depth prediction Bridge Scour Complex pier foundations Support vector regression Feature selection Variable neighborhood search 


Supplementary material

13349_2018_287_MOESM1_ESM.xlsx (17 kb)
Supplementary material 1 (XLSX 16 kb)


  1. 1.
    Mueller DS, Wagner CR (2005) Field observations and evaluations of streambed scour at bridges. Office of Engineering Research and Development Federal Highway Administration, McLeanGoogle Scholar
  2. 2.
    Kallias AN, Imam B (2016) Probabilistic assessment of local scour in bridge piers under changing environmental conditions. Struct Infrastruct Eng 12:1228–1241. CrossRefGoogle Scholar
  3. 3.
    Warren LP (2011) Scour at Bridges: stream stability and scour assessment at bridges in Massachusetts US Geological SurveyGoogle Scholar
  4. 4.
    Deng L, Cai CS (2010) Bridge scour: prediction, modeling, monitoring, and countermeasures. Pract Period Struct Des Constr 15:125–134. CrossRefGoogle Scholar
  5. 5.
    Landers MN (1992) Bridge Scour Sata Management. Published in Hydraulic Engineering: saving a threatened resource—in search of solutions. In: Proceedings of the Hydraulic Engineering sessions at Water Forum’92 Baltimore, Maryland, August 2–6, 1992 Published by American Society of Civil EngineersGoogle Scholar
  6. 6.
    Richardson EV, Davis SR (2001) Evaluating scour at bridges (HEC-18) Technical Rep No NHI 01-001. FHWA, Washington, DCGoogle Scholar
  7. 7.
    Hong J-H, Chiew Y-M, Lu J-Y, Lai J-S, Lin Y-B (2012) Houfeng bridge failure in Taiwan. J Hydraul Eng 138:186–198. CrossRefGoogle Scholar
  8. 8.
    Raikar RV, Dey S (2005) Scour of gravel beds at bridge piers and abutments. Proc Inst Civ Eng Water Manag 158:157–162. CrossRefGoogle Scholar
  9. 9.
    Toth E (2015) Asymmetric error functions for reducing the underestimation of local scour around bridge piers: application to neural networks models. J Hydraul Eng 141:04015011. CrossRefGoogle Scholar
  10. 10.
    Liao K-W, Hoang N-D, Gitomarsono J (2018) A probabilistic safety evaluation framework for multi-hazard assessment in a bridge using SO-MARS learning model. KSCE J Civ Eng 22:903–915. CrossRefGoogle Scholar
  11. 11.
    Prendergast LJ, Hester D, Gavin K (2016) Determining the Presence of scour around bridge foundations using vehicle-induced vibrations. J Bridge Eng 21:04016065. CrossRefGoogle Scholar
  12. 12.
    Wang C, Yu X, Liang F (2017) A review of bridge scour: mechanism, estimation, monitoring and countermeasures. Nat Hazards 87:1881–1906. CrossRefGoogle Scholar
  13. 13.
    Zarafshan A, Iranmanesh A, Ansari F (2012) Vibration-based method and sensor for monitoring of bridge scour. J Bridge Eng 17:829–838. CrossRefGoogle Scholar
  14. 14.
    Park C-W, Park HI, Cho Y-K (2017) Evaluation of the applicability of pier local scour formulae using laboratory and field data. Mar Georesour Geotechnol 35:1–7. CrossRefGoogle Scholar
  15. 15.
    Melville B (2008) The physics of local scour at bridge piers. In: Proceedings of the Fourth International Conference on Scour and Erosion, Tokyo, JapanGoogle Scholar
  16. 16.
    Azimi H, Bonakdari H, Ebtehaj I, Ashraf Talesh SH, Michelson DG, 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. MathSciNetCrossRefGoogle Scholar
  17. 17.
    Arneson LA, Zevenbergen LW, Lagasse PF, Clopper PE (2012) Evaluating scour at bridges Publication No FHWA HIF 12-003. Federal Highway Administration, Washington, DCGoogle Scholar
  18. 18.
    Ataie-Ashtiani B, Baratian-Ghorghi Z, Beheshti AA (2010) Experimental investigation of clear-water local scour of compound piers. J Hydraul Eng 136:343–351. CrossRefGoogle Scholar
  19. 19.
    Melville BW, Coleman SE (2000) Bridge scour. Water Resources Publications, Littleton, ColoGoogle Scholar
  20. 20.
    Etemad-Shahidi A, Rohani MS (2014) Prediction of scour at abutments using piecewise regression. Proc Inst Civ Eng Water Manag 167:79–87. CrossRefGoogle Scholar
  21. 21.
    Muzzammil M (2010) ANFIS approach to the scour depth prediction at a bridge abutment. J Hydroinform 12:474–485. CrossRefGoogle Scholar
  22. 22.
    Cheng M-Y, Cao M-T (2014) Hybrid intelligent inference model for enhancing prediction accuracy of scour depth around bridge piers. Struct Infrastruct. Google Scholar
  23. 23.
    Choi S-U, Choi B, Lee S (2017) Prediction of local scour around bridge piers using the ANFIS method. Neural Comput Appl 28:335–344. CrossRefGoogle Scholar
  24. 24.
    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
  25. 25.
    Hosseini R, Amini A (2015) Scour depth estimation methods around pile groups KSCE J. Civ Eng 19:2144–2156. Google Scholar
  26. 26.
    Zounemat-Kermani M, Beheshti A-A, Ataie-Ashtiani B, Sabbagh-Yazdi S-R (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. CrossRefGoogle Scholar
  27. 27.
    Najafzadeh M, Barani G-A, Hessami-Kermani M-R (2014) Group method of data handling to predict scour at downstream of a ski-jump bucket spillway. Earth Sci Inf 7:231–248. CrossRefGoogle Scholar
  28. 28.
    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
  29. 29.
    Azamathulla HM, Ghani AA, Zakaria NA, Guven A (2010) Genetic programming to predict bridge pier scour. J Hydraul Eng 136:165–169. CrossRefGoogle Scholar
  30. 30.
    Azamathulla HM (2012) Gene expression programming for prediction of scour depth downstream of sills. J Hydrol 460:156–159. CrossRefGoogle Scholar
  31. 31.
    Kang F, Li J (2016) Artificial bee colony algorithm optimized support vector regression for system reliability analysis of slopes. J Comput Civ Eng 30:04015040. CrossRefGoogle Scholar
  32. 32.
    Prayogo D, Susanto YTT (2018) Optimizing the prediction accuracy of friction capacity of driven piles in cohesive soil using a novel self-tuning least squares support vector machine. Adv Civ Eng 2018:9. Google Scholar
  33. 33.
    Guyon I, Elisseeff A (2003) An introduction to variable and feature selection. J Mach Learn Res 3:1157–1182zbMATHGoogle Scholar
  34. 34.
    Imamoto H, Ohtoshi K (1987) Local Scour around a non-uniform circular pier. In: Proceedings of IAHR Congress, Lausanne, Switzerland, pp 304–309Google Scholar
  35. 35.
    Melville BW, Raudkivi AJ (1996) Effects of foundation geometry on bridge pier scour. J Hydraul Eng 122:203–209. CrossRefGoogle Scholar
  36. 36.
    Raudkivi AJ, Ettema R (1983) Clear water scour at cylindrical piers. J Hydraul Eng 109:338–350. CrossRefGoogle Scholar
  37. 37.
    Liao K-W, Muto Y, Lin J-Y (2017) Scour depth evaluation of a bridge with a complex pier foundation. KSCE J Civ Eng. Google Scholar
  38. 38.
    Coleman SE (2005) Clearwater local scour at complex piers. J Hydraul Eng 131:330–334. CrossRefGoogle Scholar
  39. 39.
    Sheppard DM, Renna R (2005) Florida bridge scour manual Florida DOT. Tallahassee, FloridaGoogle Scholar
  40. 40.
    Vapnik VN (1998) Statistical learning theory. Wiley, New YorkzbMATHGoogle Scholar
  41. 41.
    Kazem A, Sharifi E, Hussain FK, Saberi M, Hussain OK (2013) Support vector regression with chaos-based firefly algorithm for stock market price forecasting. Appl Soft Comput 13:947–958. CrossRefGoogle Scholar
  42. 42.
    Salcedo-Sanz S, Rojo-Álvarez JL, Martínez-Ramón M, Camps-Valls G (2014) Support vector machines in engineering: an overview Wiley interdisciplinary reviews. Data Min Knowl Disc 4:234–267. CrossRefGoogle Scholar
  43. 43.
    Vu DT, Hoang N-D (2016) Punching Shear capacity estimation of FRP-reinforced concrete slabs using a hybrid machine learning approach. Struct Infrastruct Eng 12:1153–1161CrossRefGoogle Scholar
  44. 44.
    Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14:199–222. MathSciNetCrossRefGoogle Scholar
  45. 45.
    Cheng M-Y, Hoang N-D (2017) Estimating construction duration of diaphragm wall using firefly-tuned least squares support vector machine. Neural Comput. Google Scholar
  46. 46.
    Tien Bui D, Tuan TA, Hoang N-D, Thanh NQ, Nguyen DB, Van Liem N, Pradhan B (2016) Spatial prediction of rainfall-induced landslides for the Lao Cai area (Vietnam) using a hybrid intelligent approach of least squares support vector machines inference model and artificial bee colony optimization. Landslides. Google Scholar
  47. 47.
    Unler A, Murat A (2010) A discrete particle swarm optimization method for feature selection in binary classification problems. Eur J Oper Res 206:528–539. CrossRefzbMATHGoogle Scholar
  48. 48.
    Robnik-Šikonja M, Kononenko I (2003) Theoretical and empirical analysis of ReliefF and RReliefF. Mach Learn 53:23–69. CrossRefzbMATHGoogle Scholar
  49. 49.
    Robnik-Šikonja M, Kononenko I (1997) An adaptation of relief for attribute estimation in regression machine learning. In: Proceedings of the Fourteenth International Conference (ICML’97), Morgan Kaufmann, pp 296–304Google Scholar
  50. 50.
    Hoang N-D, Tien Bui D, Liao K-W (2016) Groutability estimation of grouting processes with cement grouts using differential flower pollination optimized support vector machine. Appl Soft Comput 45:173–186. CrossRefGoogle Scholar
  51. 51.
    Liu H, Motoda H (2007) Computational methods of feature selection. CRC Press, Taylor & Francis Group, Boca RatonzbMATHGoogle Scholar
  52. 52.
    Kohavi R, John GH (1997) Wrappers for feature subset selection. Artif Intell 97:273–324. CrossRefzbMATHGoogle Scholar
  53. 53.
    Reunanen J (2003) Overfitting in making comparisons between variable selection methods. J Mach Learn Res 3:1371–1382zbMATHGoogle Scholar
  54. 54.
    Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24:1097–1100. MathSciNetCrossRefzbMATHGoogle Scholar
  55. 55.
    Hoos HH, Stützle T (2004) Stochastic local search foundations and applications. Morgan Kaufmann/Elsevier, AmsterdamzbMATHGoogle Scholar
  56. 56.
    Cheng M-Y, Prayogo D, Wu Y-W (2018) Prediction of permanent deformation in asphalt pavements using a novel symbiotic organisms search–least squares support vector regression. Neural Comput Appl. Google Scholar
  57. 57.
    Wang J, Zhong D, Wu B, Shi M (2018) Evaluation of compaction quality based on SVR with CFA: case study on compaction quality of earth-rock dam. J Comput Civil Eng 32:05018001. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Civil Engineering, Institute of Research and DevelopmentDuy Tan UniversityDa NangVietnam
  2. 2.Department of Bioenvironmental Systems EngineeringNational Taiwan UniversityTaipeiTaiwan

Personalised recommendations