Log in

A novel ensemble model using artificial neural network for predicting wave-induced forces on coastal bridge decks

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

Due to the effects of climate change, coastal engineering structures are more vulnerable to the wave forces caused by natural hazards, especially for low-lying bridges. To facilitate the structural design and risk assessment of coastal bridges under extreme events, it is imperative to efficiently predict the wave-induced forces with high accuracy. In this study, a novel predictive model for wave-induced forces is established using the ensemble learning technique. Specifically, four state-of-the-art surrogate models, namely the support vector regression (SVR), Kriging (KRG), polynomial chaos expansion (PCE), and decision tree (DT) are employed to construct a weighted predictive model, where the weights of individual models are implicitly determined by the artificial neural network (ANN). Depending on the architecture of the ANN model, e.g., with or without a hidden layer, these four surrogate models can be ensembled nonlinearly (ANN1) or linearly (ANN2). Four benchmark functions and two ocean engineering cases are utilized to validate the performance of the established ensemble models. The coefficient of determination R2, maximum absolute error (MAE), and root mean square error (RMSE) are used as the error metrics. The results show that the proposed ANN-based ensemble strategy is capable of providing robust and accurate approximation for different force components; it can effectively reduce the adverse effect of poorly behaved candidate surrogates by wisely assigning weights to the individual models, which is beneficial to protect against the use of the worst surrogate model. It is envisioned that the proposed ensemble models can be extended to predict wave forces of unstable wave conditions, thus facilitating the associated risk assessment and structural design of ocean infrastructure assets.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

References

  1. Acar E (2010) Various approaches for constructing an ensemble of metamodels using local measures. Struct Multidiscip Optim 42:879–896

    Google Scholar 

  2. Acar E, Rais-Rohani M (2009) Ensemble of metamodels with optimized weight factors. Struct Multidiscip Optim 37:279–294

    Google Scholar 

  3. Ataei N, Padgett JE (2015) Fragility surrogate models for coastal bridges in hurricane prone zones. Eng Struct 103:203–213

    Google Scholar 

  4. Bishop CM (1995) Neural networks for pattern recognition. Oxford University Press, Oxford

    MATH  Google Scholar 

  5. Breiman L, Friedman JH, Olshen RA, Stone CJ (1984) Classification and regression trees. Chapman & Hall/CRC, Boca Raton

    MATH  Google Scholar 

  6. Brunton SL, Noack BR, Koumoutsakos P (2020) Machine learning for fluid mechanics. Annu Rev Fluid Mech 52:477–508

    MathSciNet  MATH  Google Scholar 

  7. Cha YJ, Choi W, Büyüköztürk O (2017) Deep learning-based crack damage detection using convolutional neural networks. Comput Aided Civ Infrastruct Eng 32:361–378

    Google Scholar 

  8. Chen X, Chen Z, Xu G, Zhuo X, Deng Q (2021) Review of wave forces on bridge decks with experimental and numerical methods. Adv Bridge Eng 2:1

    Google Scholar 

  9. Davis SE, Cremaschi S, Eden MR (2018) Efficient surrogate model development: impact of sample size and underlying model dimensions. Comput Aided Chem Eng 44:979–984

    Google Scholar 

  10. De’ath G, Fabricius KE (2000) Classification and regression trees: a powerful yet simple technique for ecological data analysis. Ecology 81:3178–3192

    Google Scholar 

  11. Douglass SL, Hughes SA, Rogers S, Chen Q (2004) The impact of Hurricane Ivan on the coastal roads of Florida and Alabama: a preliminary report. Rep. to Coastal Transportation Engineering Research and Education Center, Univ. of South Alabama, Mobile, Ala, pp 1–19

  12. Géron A (2019) Hands-on machine learning with Scikit-Learn, Keras, and TensorFlow: concepts, tools, and techniques to build intelligent systems. O’Reilly Media, Newton

    Google Scholar 

  13. Goel T, Haftka RT, Shyy W, Queipo NV (2007) Ensemble of surrogates. Struct Multidiscip Optim 33:199–216

    Google Scholar 

  14. Huang B, Duan L, Yang Z, Zhang J, Kang A, Zhu B (2019) Tsunami forces on a coastal bridge deck with a box girder. J Bridge Eng 24:04019091

    Google Scholar 

  15. Huang B, Yang Z, Zhu B, Zhang J, Kang A, Pan L (2019) Vulnerability assessment of coastal bridge superstructure with box girder under solitary wave forces through experimental study. Ocean Eng 189:106337

    Google Scholar 

  16. Hu X, Zhang H, Mei H, ** using the stacking ensemble machine learning method in Lushui, Southwest China. Appl Sci 10(11):4016

    Google Scholar 

  17. ** J, Meng B (2011) Computation of wave loads on the superstructures of coastal highway bridges. Ocean Eng 38:2185–2200

    Google Scholar 

  18. Jörges C, Berkenbrink C, Stumpe B (2021) Prediction and reconstruction of ocean wave heights based on bathymetric data using LSTM neural networks. Ocean Eng 232:109046

    Google Scholar 

  19. Jamei M, Karbasi M, Olumegbon IA, Mosharaf-Dehkordi M, Ahmadianfar I, Asadi A (2021) Specific heat capacity of molten salt-based nanofluids in solar thermal applications: a paradigm of two modern ensemble machine learning methods. J Mol Liq 335:116434

    Google Scholar 

  20. Lataniotis C, Wicaksono D, Marelli S, Sudret B (2021) UQLab user manual–Kriging (Gaussian process modelling). In: Report UQLab-V14-105. Chair of Risk, Safety and Uncertainty Quantification, ETH Zurich, Zurich

  21. Lay T, Kanamori H, Ammon Charles J, Nettles M, Ward Steven N, Aster Richard C, Beck Susan L, Bilek Susan L, Brudzinski Michael R, Butler R et al (2005) The Great Sumatra–Andaman earthquake of 26 December 2004. Science 308:1127–1133

    Google Scholar 

  22. Liu H, Xu S, Wang X, Meng J, Yang S (2016) Optimal weighted pointwise ensemble of radial basis functions with different basis functions. AIAA J 54:3117–3133

    Google Scholar 

  23. Marelli S, Sudret B (2015) UQLab: a framework for uncertainty quantification in MATLAB. ETH-Zürich, Zürich

    Google Scholar 

  24. Marelli S, Sudret B (2021) UQLab user manual–Polynomial chaos expansions. In: Report UQLab-V14-104. Chair of Risk, Safety and Uncertainty Quantification, ETH Zurich, Zurich

  25. Mazinani I, Ismail Z, Shamshirband S, Hashim A, Mansourvar M, Zalnezhad E (2016) Estimation of tsunami bore forces on a coastal bridge using an extreme learning machine. Entropy 18(5):167

    Google Scholar 

  26. McConnell K, Allsop W, Allsop NWH, Cruickshank I (2004) Piers, jetties and related structures exposed to waves: guidelines for hydraulic loadings. Thomas Telford, London

    Google Scholar 

  27. McPherson RL (2010) Hurricane induced wave and surge forces on bridge decks. Texas A&M University, College Station

    Google Scholar 

  28. Morgan JN, Sonquist JA (1963) Problems in the analysis of survey data, and a proposal. J Am Stat Assoc 58:415–434

    MATH  Google Scholar 

  29. Moustapha M, Lataniotis C, Marelli S, Sudret B (2021) UQLab user manual—support vector machines for regression. In: Report UQLab-V14-111. Chair of Risk, Safety and Uncertainty Quantification, ETH Zurich, Zurich

  30. Okeil Ayman M, Cai CS (2008) Survey of short- and medium-span bridge damage induced by Hurricane Katrina. J Bridge Eng 13:377–387

    Google Scholar 

  31. Padgett J, DesRoches R, Nielson B, Yashinsky M, Kwon O-S, Burdette N, Tavera E (2008) Bridge damage and repair costs from Hurricane Katrina. J Bridge Eng 13:6–14

    Google Scholar 

  32. Pena B, Huang L (2021) Wave-GAN: a deep learning approach for the prediction of nonlinear regular wave loads and run-up on a fixed cylinder. Coast Eng 167:103902

    Google Scholar 

  33. Perrone MP, Cooper LN (1992) When networks disagree: ensemble methods for hybrid neural networks. Institute for Brain and Neural Systems, Brown University, Providence

    Google Scholar 

  34. Pourzangbar A, Brocchini M, Saber A, Mahjoobi J, Mirzaaghasi M, Barzegar M (2017) Prediction of scour depth at breakwaters due to non-breaking waves using machine learning approaches. Appl Ocean Res 63:120–128

    Google Scholar 

  35. Qu K, Wen BH, Ren XY, Kraatz S, Sun WY, Deng B, Jiang CB (2020) Numerical investigation on hydrodynamic load of coastal bridge deck under joint action of solitary wave and wind. Ocean Eng 217:108037

    Google Scholar 

  36. Quinlan JR (1986) Induction of decision trees. Mach Learn 1:81–106

    Google Scholar 

  37. Quinlan JR (1993) C 4.5: programs for machine learning. The Morgan Kaufmann Series in Machine Learning, San Mateo

    Google Scholar 

  38. Robertson Ian N, Riggs HR, Yim Solomon C, Young Yin L (2007) Lessons from Hurricane Katrina storm surge on bridges and buildings. J Waterw Port Coast Ocean Eng 133:463–483

    Google Scholar 

  39. Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4:409–423

    MathSciNet  MATH  Google Scholar 

  40. Saeidpour A, Chorzepa MG, Christian J, Durham S (2018) Parameterized fragility assessment of bridges subjected to hurricane events using metamodels and multiple environmental parameters. J Infrastruct Syst 24(4):04018031

    Google Scholar 

  41. Vapnik V, Golowich S, Smola A (1997) Support vector method for function approximation, regression estimation, and signal processing. Adv Neural Inf Process Sys 9:281–287

    Google Scholar 

  42. Viana FAC, Haftka RT, Steffen V (2009) Multiple surrogates: how cross-validation errors can help us to obtain the best predictor. Struct Multidiscip Optim 39:439–457

    Google Scholar 

  43. Wang J, Li C, Xu G, Li Y, Kareem A (2021) Efficient structural reliability analysis based on adaptive Bayesian support vector regression. Comput Methods Appl Mech Eng 387:114172

    MathSciNet  MATH  Google Scholar 

  44. Wang J, Xu G, Li Y, Kareem A (2022) AKSE: a novel adaptive Kriging method combining sampling region scheme and error-based stop** criterion for structural reliability analysis. Reliab Eng Syst Saf 219:108214

    Google Scholar 

  45. Wang J, Xue S, Xu G (2021) A hybrid surrogate model for the prediction of solitary wave forces on the coastal bridge decks. Infrastructures 6(12):170

    Google Scholar 

  46. **u D, Karniadakis GE (2002) The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24:619–644

    MathSciNet  MATH  Google Scholar 

  47. Xu G, Cai C, Deng L (2016) Numerical prediction of solitary wave forces on a typical coastal bridge deck with girders. Struct Infrastruct Eng 13:254–272

    Google Scholar 

  48. Xu G, Cai CS, Chen Q (2017) Countermeasure of air venting holes in the bridge deck–wave interaction under solitary waves. J Perform Constr Facil 31:04016071

    Google Scholar 

  49. Xu G, Cai CS, Han Y (2016) Investigating the characteristics of the solitary wave-induced forces on coastal twin bridge decks. J Perform of Constr Fac 30(4):04015076

    Google Scholar 

  50. Xu G, Cai CS, Han Y, Wu C, Xue F (2017) Numerical assessment of the wave loads on coastal twin bridge decks under stokes waves. J Coast Res 34:628–639

    Google Scholar 

  51. Xu G, Cai CS, Hu P, Dong Z (2016) Component level-based assessment of the solitary wave forces on a typical coastal bridge deck and the countermeasure of air venting holes. Pract Period Struct Des Constr 21

  52. Xu G, Chen Q, Chen J (2018) Prediction of solitary wave forces on coastal bridge decks using artificial neural networks. J Bridge Eng 23

  53. Xu G, Kareem A, Shen L (2020) Surrogate modeling with sequential updating: applications to bridge deck–wave and bridge deck–wind interactions. J Comput Civ Eng 34(4):04020023

    Google Scholar 

  54. Xu G, ** Y, Xue S, Yuan P, Wang J (2022) Hydrodynamic shape optimization of an auxiliary structure proposed for circular bridge pier based on a developed adaptive surrogate model. Ocean Eng 259:111869

    Google Scholar 

  55. Zerpa LE, Queipo NV, Pintos S, Salager J-L (2005) An optimization methodology of alkaline–surfactant–polymer flooding processes using field scale numerical simulation and multiple surrogates. J Petrol Sci Eng 47:197–208

    Google Scholar 

Download references

Acknowledgements

The financial support from NSFC (Grant no. 52078425) is highly appreciated. All the opinions presented here are those of the writers, not necessarily representing those of the sponsors.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to **sheng Wang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, G., Ji, C., Wei, H. et al. A novel ensemble model using artificial neural network for predicting wave-induced forces on coastal bridge decks. Engineering with Computers 39, 3269–3292 (2023). https://doi.org/10.1007/s00366-022-01745-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-022-01745-z

Keywords

Navigation