Journal of Hydraulic Structures

Journal of Hydraulic Structures

Multi-level multi-model data-driven ensemble approach for river bedload formulation

Articles in Press

Document Type : Research Paper

Authors
Hossien Riahi-Madvar
Akram Seifi
Department of Water Engineering, Faculty of Agriculture, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
10.22055/jhs.2026.51608.1375
Abstract
Estimation of bedload transport in rivers is a complex process and needs substantial efforts in pre-processing and ensemble modeling to derive desired level of prediction accuracy. This paper aims to develop a framework for the formulation of bedload transport in rivers using multi-level Multi-Model Ensemble (MME) approach to derive improved explicit formulations hybridized with multiple pre-processed-based models. Three pre-processing techniques of feature selection by Gamma Test (GT), dimension reduction by principal component analysis (PCA), and data clustering by subset selection of maximum dissimilarity (SSMD) are utilized at level 0. The multi-linear regression (MLR), MLR-PCA, artificial neural network (ANN), ANN-PCA, Gene expression programming (GEP), GEP-PCA, Group method of data handling (GMDH) and GMDH-PCA are used to develop individual explicit formulations at level 1, and the inferred formulas are hybridized with the MME approach at level 2 by Pareto optimality. A newly revised discrepancy ratio (RDR) for error distributions in conjunction with several statistical and graphical indicators were used to evaluate the strategy's performance. Results of MME showed that the proposed framework acted as an efficient tool in explicit equation induction for bedload transport (i.e., 33–96% reduction of RMSE; 2-29% increase of R2, 2-138% increase of NSE and 38-98% reduction of RAE in testing step in comparison with the best individual model) and clearly outperformed estimations made by other models. The current study highlights the importance of pre-processing and multi-modelling techniques in deep learning models to encounter the challenges of function finding for complex bedload transport estimations in multiple observed datasets.
Keywords
Multi-model ensembles approach
bedload transport
function finding
equation optimization
machine learning
Subjects
  1. Abbaszadeh H, Daneshfaraz R, Sume V, Abraham J. Experimental investigation and application of soft computing models for predicting flow energy loss in arc-shaped constrictions. AQUA—Water Infrastructure, Ecosystems and Society. 2024 Mar 1;73(3):637-61.
  2. Abbaszadeh H, Tarinejad R, Roushangar K, Daneshfaraz R. Investigation of the Effects of Internal Structure and Material Properties on the Hydraulic Performance of Rectangular Gabion Weirs: Experimental and Numerical Study. Water Resources Management. 2026 Jun;40(8):376.
  3. Abbaszadeh H, Tarinejad R. Soft Computing and Predicting Labyrinth Gates Discharge Coefficient. Water Resources. 2025 Aug;52(4):701-14.
  4. Afan HA, El-shafie A, Mohtar WHMW, Yaseen ZM. Past, present and prospect of an artificial intelligence (AI) based model for sediment transport prediction. Journal of Hydrology. 2016;541:902-913.
  5. Ahmadianfar I, Kheyrandish A, Jamei M, Gharabaghi B. Optimizing operating rules for multi-reservoir hydropower generation systems: an adaptive hybrid differential evolution algorithm. Renewable Energy. 2021;167:774-790.
  6. Barry JJ. Bed load transport in gravel-bed rivers [dissertation]. Boise (ID): University of Idaho; 2007. 164 p.
  7. Bhattacharya B, Price RK, Solomatine DP. Machine learning approach to modeling sediment transport. Journal of Hydraulic Engineering. 2007 Apr;133(4):440-50.
  8. Bhattacharya B, Price RK, Solomatine DP. Machine learning approach to modeling sediment transport. Journal of Hydraulic Engineering. 2007;133(4):440-450.
  9. Cao Z. Turbulent bursting-based sediment entrainment fluctuation. Journal of Hydraulic Engineering. 1997;123(3):233-236.
  10. Dey S. Fluvial hydrodynamics: hydrodynamic and sediment transport phenomena. Berlin: Springer-Verlag; 2014.
  11. Dietterich TG. Ensemble methods in machine learning. InInternational workshop on multiple classifier systems 2000 Jun 21 (pp. 1-15). Berlin, Heidelberg: Springer Berlin Heidelberg.
  12. Ebadzadeh P, Abbaszadeh H, Daneshfaraz R, Abraham J. Enhancing energy dissipation in stepped weirs: numerical analysis and machine learning of ANN, SVM and non-linear regression predictions. Multiscale and Multidisciplinary Modeling, Experiments and Design. 2025 Aug;8(8):345.
  13. Ebtehaj I, Bonakdari H, Safari MJ, Gharabaghi B, Zaji AH, Madavar HR, Khozani ZS, Es-haghi MS, Shishegaran A, Mehr AD. Combination of sensitivity and uncertainty analyses for sediment transport modeling in sewer pipes. International Journal of Sediment Research. 2020 Apr 1;35(2):157-70.
  14. Ebtehaj I, Bonakdari H, Zaji AH, Gharabaghi B. Evolutionary optimization of neural network to predict sediment transport without sedimentation. Complex & Intelligent Systems. 2021;7(1):401-416.
  15. Gao P. An equation for bed-load transport capacities in gravel-bed rivers. Journal of Hydrology. 2011;402(3-4):297-305.
  16. Ghani AA, Azamathulla HM. Development of GEP-based functional relationship for sediment transport in tropical rivers. Neural Computing and Applications. 2014;24(2):271-276.
  17. Gupta D, Hazarika BB, Berlin M, Sharma UM, Mishra K. Artificial intelligence for suspended sediment load prediction: a review. Environmental earth sciences. 2021 May;80(9):346.
  18. Hassanzadeh Y, Abbaszadeh H, Abedi A, Abraham J. Numerical simulation of the effect of downstream material on scouring-sediment profile of combined spillway-gate. AQUA—Water Infrastructure, Ecosystems and Society. 2024 Dec 1;73(12):2322-43.
  19. in Computer Science. Vol. 1857. Berlin: Springer; 2000. p. 1–15.
  20. Khatibi R, Ghorbani MA, Naghshara S, Aydin HARU, Karimi V. A framework for ‘inclusive multiple modelling’ with critical views on modelling practices – applications to modelling water levels of Caspian Sea and lakes Urmia and Van. Journal of Hydrology. 2020;587:124923.
  21. Khosravi K, Cooper JR, Daggupati P, Pham BT, Bui DT. Bedload transport rate prediction: Application of novel hybrid data mining techniques. Journal of Hydrology. 2020 Jun 1;585:124774.
  22. Kitsikoudis V, Sidiropoulos E, Hrissanthou V. Machine learning utilization for bed load transport in gravel-bed rivers. Water resources management. 2014 Sep;28(11):3727-43.
  23. Kitsikoudis V, Sidiropoulos E, Hrissanthou V. Machine learning utilization for bed load transport in gravel-bed rivers. Water Resources Management. 2014;28(11):3727-3743.
  24. Liu MY, Huai WX, Yang ZH, Zeng YH. A genetic programming-based model for drag coefficient of emergent vegetation in open channel flows. Advances in Water Resources. 2020;140:103582.
  25. Lu C, Zhang T, Zhang R, Zhang C. Adaptive robust kernel PCA algorithm. In: 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’03). Vol 6. IEEE; 2003. p. VI-621.
  26. Meyer-Peter E, Müller R. Formulas for bed-load transport. In: IAHSR 2nd meeting, Stockholm, appendix 2. International Association for Hydraulic Research; 1948.
  27. Mir AA, Patel M, Albalawi F, Bajaj M, Tuka MB. A comparative ensemble approach to bedload prediction using metaheuristic machine learning. Scientific Reports. 2024 Oct 28;14(1):25725.
  28. Montes C, Kapelan Z, Saldarriaga J. Predicting non-deposition sediment transport in sewer pipes using random forest. Water Research. 2021;189:116639.
  29. Mosavi A, Ozturk P, Chau KW. Flood prediction using machine learning models: Literature review. Water. 2018 Oct 27;10(11):1536.
  30. Najafpour N, Emamgholizadeh S, Torabi Podeh H, Haghiabi AH. Estimation of sediment transport rate of Karun River (Iran). Journal of Hydraulic Structures. 2016;2(2):74-84. 10.22055/jhs.2016.12874
  31. Noori R, Karbassi A, Sabahi MS. Evaluation of PCA and gamma test techniques on ANN operation for weekly solid waste prediction. Journal of Environmental Management. 2010;91(3):767-771.
  32. Noori R, Karbassi AR, Moghaddamnia A, Han D, Zokaei-Ashtiani MH, Farokhnia A, Gousheh MG. Assessment of input variables determination on the SVM model performance using PCA, gamma test, and forward selection techniques for monthly stream flow prediction. Journal of Hydrology. 2011;401(3-4):177-189.
  33. Qasem SN, Ebtehaj I, Riahi Madavar H. Optimizing ANFIS for sediment transport in open channels using different evolutionary algorithms. Journal of Applied Research in Water and Wastewater. 2017;4(1):290-298.
  34. Ramachandran P, Zoph B, Le QV. Searching for activation functions. arXiv preprint arXiv:1710.05941. 2017.
  35. Recking A, Boucinha V, Frey P. Experimental study of bed-load grain size sorting near incipient motion on steep slopes. In: River flow 2004, Naples; 2004. p. 253-258.
  36. Riahi-Madvar H, Dehghani M, Parmar KS, Nabipour N, Shamshirband S. Improvements in the explicit estimation of pollutant dispersion coefficient in rivers by subset selection of maximum dissimilarity hybridized with ANFIS firefly algorithm (FFA). IEEE Access. 2020;8:60314-60337.
  37. Riahi-Madvar H, Dehghani M, Seifi A, Singh VP. Pareto optimal multigene genetic programming for prediction of longitudinal dispersion coefficient. Water Resources Management. 2019;33(3):905-921.
  38. Riahi-Madvar H, Seifi A. Uncertainty analysis in bed load transport prediction of gravel bed rivers by ANN and ANFIS. Arabian Journal of Geosciences. 2018 Nov;11(21):688.
  39. Riahi-Madvar H, Seifi A. Uncertainty analysis in bedload transport prediction of gravel bed rivers by ANN and ANFIS. Arabian Journal of Geosciences. 2018;11(21):1-20.
  40. Roshangar, K., Joulazadeh, S. Evaluation the Performance of Artificial Neural Network Method and Deep Learning Method for Prediction of Bed Load in Gravel-Bed Rivers. Journal of Water and Soil Conservation, 2022; 29(1): 75-94. doi: 10.22069/jwsc.2022.19695.3515
  41. Roushangar K, Mehrabani FV, Shiri J. Modeling river total bed material load discharge using artificial intelligence approaches (based on conceptual inputs). Journal of Hydrology. 2014;514:114-122.
  42. Roushangar K, Shahnazi S. Prediction of sediment transport rates in gravel-bed rivers using Gaussian process regression. Journal of Hydroinformatics. 2020;22(2):249-262.
  43. Safari MJS, Mohammadi B, Kargar K. Invasive weed optimization-based adaptive neuro-fuzzy inference system hybrid model for sediment transport with a bed deposit. Journal of Cleaner Production. 2020;276:124267.
  44. Sahraei S, Alizadeh MR, Talebbeydokhti N, Dehghani M. Bed material load estimation in channels using machine learning and meta-heuristic methods. Journal of Hydroinformatics. 2017;20:100-116.
  45. Samantaray S, Sahoo A, Paul S, Ghose DK. Prediction of bed-load sediment using newly developed support-vector machine techniques. Journal of Irrigation and Drainage Engineering. 2022 Oct 1;148(10):04022034.
  46. Seifi A, Riahi H. Estimating daily reference evapotranspiration using hybrid gamma test least square support vector machine, gamma test ANN, and gamma test ANFIS models in an arid area of Iran. Journal of Water and Climate Change. (Accepted).
  47. Seifi A, Soroush F. Pan evaporation estimation and derivation of explicit optimized equations by novel hybrid meta-heuristic ANN based methods in different climates of Iran. Computers and Electronics in Agriculture. 2020;173:105418.
  48. Shaghaghi S, Bonakdari H, Gholami A, Kisi O, Shiri J, Binns AD, Gharabaghi B. Stable alluvial channel design using evolutionary neural networks. Journal of Hydrology. 2018;566:770-782.
  49. Teimourey, R., Dehghani, A. A. Comparison of Different Methods for Estimating Bed Load using developed software of STE (case study: Babolroud River). Journal of Water and Soil Conservation, 2020; 27(1): 229-236. doi: 10.22069/jwsc.2019.16553.3184.
  50. Zhang Z, Wang K, Zhu L, Wang Y. A Pareto improved artificial fish swarm algorithm for solving a multi-objective fuzzy disassembly line balancing problem. Expert Systems with Applications. 2017;86:165-176.
  51. Zhou ZH. Ensemble methods: foundations and algorithms. CRC press; 2025 Feb 15.
  52. Zounemat-Kermani M, Mahdavi-Meymand A, Alizamir M, Adarsh S, Yaseen ZM. On the complexities of sediment load modeling using integrative machine learning: application of the great river of Loíza in Puerto Rico. Journal of Hydrology. 2020;585:124759
Journal of Hydraulic Structures

Articles in Press, Accepted Manuscript
Available Online from 22 September 2026