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Machine Learning Based Prediction of Hydraulic Jump Lengths in Stilling Basins for Barrages and Low-Head Hydraulic Structures

Authors

  • Abdul Rehman

    Civil Engineering Department, University of Engineering and Technology, Lahore, Pakistan
    Author

  • Habib ur Rehman

    Civil Engineering Department, University of Engineering and Technology, Lahore, Pakistan
    Author

  • Noor Muhammad Khan

    Civil Engineering Department, University of Engineering and Technology, Lahore, Pakistan
    Author

DOI:

https://doi.org/10.22581/0320

Keywords:

Appurtenances, Hydraulic Jump, Machine Learning, Stilling Basins, Low Froude Number

Abstract

A hydraulic-jump-type stilling basin is a popular choice for energy dissipation, where the high-velocity, supercritical flow from a dam spillway transitions into a low-velocity, subcritical flow. Stilling basins are designed such that the hydraulic jump forms within the basin, ensuring the safety of the downstream natural streambed. Thus, prediction of length of hydraulic jump is critical in deciding the basins dimensions. Experimental data on hydraulic jump type stilling basins under low inflow Froude number were collected from the literature. Six machine learning (ML) models were trained and tested using experimental data related to low inflow Froude number stilling basins. For each model, the feature importance score was calculated using a permutation-based method, which showed that the inflow Froude number (F1) and the sequent depth ratio (Y) were most significant features for prediction of the length of the hydraulic jump across all ML models. The evaluation of the models' performance indicated that the artificial neural network based model and CatBoost performed better, with higher coefficients of determination (from 0.85 to 0.93), lower error metrics, and a balanced distribution of errors during training, testing, and validation. Whereas Random Forest and AdaBoost based models showed least coefficient of determination (both having 0.84) at the model training stage. Support vector machine based model performed least at the testing stage with coefficient of determination of 0.54.

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Author Biography

  • Habib ur Rehman, Civil Engineering Department, University of Engineering and Technology, Lahore, Pakistan

    Professor Emeritus, Civil Engineering Department, UET, Lahore

    Dean, Faculty of Engineering and Technology, The University of Lahore, Lahore, Pakistan

References

A. J. Peterka, “Hydraulic Design of Stilling Basins and Energy Dissipators,” Denver, 1984.

R. Steinke et al., “Low Froude Number Stilling Basins-Hydrodynamic Characterization,” Journal of Hydraulic Engineering, vol. 147, no. 4, Apr. 2021, doi: 10.1061/(asce)hy.1943-7900.0001867.

R. L. George, “Low Froude Number Stilling Basin Design,” 1978, United States Department of the Interior, Bureau of Reclamation, Denver, Colorado.

N. G. Bhowmik, “Hydraulic Jump Type Stilling Basins for Froude Number 2.5 to 4.5,” Urbana, 1971.

N. Hassanpour, A. H. Dalir, D. Farsadizadeh, and C. Gualtieri, “An experimental study of hydraulic jump in a gradually expanding rectangular stilling basin with roughened bed,” Water (Switzerland), vol. 9, no. 12, Dec. 2017, doi: 10.3390/w9120945.

M. W. Zaffar and I. Hassan, “Hydraulic investigation of stilling basins of the barrage before and after remodelling using FLOW-3D,” Water Supply, vol. 23, no. 2, pp. 796–820, Feb. 2023, doi: 10.2166/ws.2023.032.

Z. Xu, Z. Liu, and Y. Peng, “Performance comparison of prediction of hydraulic jump length under Multiple neural network models,” IEEE Access, 2024, doi: 10.1109/ACCESS.2024.3430075.

K. C. Shikhar, K. P. Bhattarai, T. De Shan, S. Mishra, I. Joshi, and A. K. Singh, “Comprehensive performance analysis of training functions in flow prediction modeusing artificial neural network,” Water SA, vol. 50, no. 2, pp. 190–200, Apr. 2024, doi: 10.17159/wsa/2024.v50.i2.4099.

P. Samui, S. N. Yesilyurt, H. Y. Dalkilic, Z. M. Yaseen, S. S. Roy, and S. Kumar, “Comparison of different optimized machine learning algorithms for daily river flow forecasting,” Earth Sci Inform, vol. 16, no. 1, pp. 533–548, Mar. 2023, doi: 10.1007/s12145-022-00896-3.

Y. Uzun and S. Y. Kumcu, “Estimation of Equilibrium Scour Depth Around Abutments Using Artificial Intelligence,” Water (Basel), vol. 17, no. 7, p. 1010, Mar. 2025, doi: 10.3390/w17071010.

M. Nda, M. S. Adnan, M. A. B. M. Yusoff, and R. M. Nda, “An Overview of Machine Learning Techniques for Sediment Prediction †,” Engineering Proceedings, vol. 56, no. 1, 2023, doi: 10.3390/ASEC2023-16599.

S. Q. Nguyen, L. C. Nguyen, T. Ngo-Duc, and S. Ouillon, “Applying a machine learning-based method for the prediction of suspended sediment concentration in the Red river basin,” Model Earth Syst Environ, vol. 10, no. 2, pp. 2675–2692, Apr. 2024, doi: 10.1007/s40808-023-01915-y.

S. N. Mousavi, D. Farsadizadeh, F. Salmasi, and A. Hosseinzadeh Dalir, “Evaluation of pressure fluctuations coefficient along the USBR Type II stilling basin using experimental results and AI models,” ISH Journal of Hydraulic Engineering, vol. 28, no. S1, pp. 207–214, 2022, doi: 10.1080/09715010.2020.1743208.

P. Sihag, O. F. Dursun, S. S. Sammen, A. Malik, and A. Chauhan, “Prediction of aeration efficiency of Parshall and Modified Venturi flumes: application of soft computing versus regression models,” Water Supply, vol. 21, no. 8, pp. 4068–4085, Dec. 2021, doi: 10.2166/ws.2021.161.

R. Daneshfaraz et al., “Estimating the effect of sand-roughened bed on hydraulic jump characteristics using heuristic models,” Results in Engineering, vol. 23, Sep. 2024, doi: 10.1016/j.rineng.2024.102724.

M. Zarei, O. Bozorg-Haddad, S. Baghban, M. Delpasand, E. Goharian, and H. A. Loáiciga, “Machine-learning algorithms for forecast-informed reservoir operation (FIRO) to reduce flood damages,” Sci Rep, vol. 11, no. 1, Dec. 2021, doi: 10.1038/s41598-021-03699-6.

R. Gonzalez Perea, R. Ballesteros, J. F. Ortega, and M. Á. Moreno, “Water and energy demand forecasting in large-scale water distribution networks for irrigation using open data and machine learning algorithms,” Comput Electron Agric, vol. 188, Sep. 2021, doi: 10.1016/j.compag.2021.106327.

K. Roushangar and R. Ghasempour, “Explicit prediction of expanding channels hydraulic jump characteristics using gene expression programming approach,” Hydrology Research, vol. 49, no. 3, pp. 815–830, Jun. 2018, doi: 10.2166/nh.2017.262.

M. F. Sauida, “Prediction of hydraulic jump length downstream of multi-vent regulators using Artificial Neural Networks,” Ain Shams Engineering Journal, vol. 7, no. 2, pp. 819–826, Jun. 2016, doi: 10.1016/J.ASEJ.2015.12.005.

H. V. Ho, “Determination of the surface roller length of hydraulic jumps in horizontal rectangular channels using the machine learning method,” Stochastic Environmental Research and Risk Assessment, vol. 38, no. 7, pp. 2539–2562, Jul. 2024, doi: 10.1007/s00477-024-02697-0.

E. Gul, O. F. Dursun, and A. Mohammadian, “Experimental study and modeling of hydraulic jump for a suddenly expanding stilling basin using different hybrid algorithms,” Water Supply, vol. 21, no. 7, pp. 3752–3771, Nov. 2021, doi: 10.2166/ws.2021.139.

H. Azimi, H. Bonakdari, and I. Ebtehaj, “Gene expression programming-based approach for predicting the roller length of a hydraulic jump on a rough bed,” ISH Journal of Hydraulic Engineering, vol. 27, no. S1, pp. 77–87, 2021, doi: 10.1080/09715010.2019.1579058.

M. Karbasi and H. M. Azamathulla, “GEP to predict characteristics of a hydraulic jump over a rough bed,” KSCE Journal of Civil Engineering, vol. 20, no. 7, pp. 3006–3011, Nov. 2016, doi: 10.1007/s12205-016-0821-x.

M. Heydari, S. Shabanlou, and B. Sanahmadi, “Self-adaptive extreme learning machine-based prediction of roller length of hydraulic jump on rough bed,” ISH Journal of Hydraulic Engineering, vol. 28, no. 2, pp. 152–162, 2022, doi: 10.1080/09715010.2020.1852978.

S. Baharvand, A. Jozaghi, R. Fatahi-Alkouhi, S. Karimzadeh, R. Nasiri, and B. Lashkar-Ara, “Comparative Study on the Machine Learning and Regression-Based Approaches to Predict the Hydraulic Jump Sequent Depth Ratio,” Iranian Journal of Science and Technology - Transactions of Civil Engineering, vol. 45, no. 4, pp. 2719–2732, Dec. 2021, doi: 10.1007/s40996-020-00526-2.

J. Demšar et al., “Orange: Data Mining Toolbox in Python Tomaž Curk Matija Polajnar Laň Zagar,” 2013.

J. Saputra, C. Lawrencya, J. M. Saini, and S. Suharjito, “Hyperparameter optimization for cardiovascular disease data-driven prognostic system,” Vis Comput Ind Biomed Art, vol. 6, no. 1, Dec. 2023, doi: 10.1186/s42492-023-00143-6.

A. M. M. Abdalmajeed, M. Mahmoud, A. E. R. A. El-Fikky, H. A. Fayed, and M. H. Aly, “Improved indoor visible light positioning system using machine learning,” Opt Quantum Electron, vol. 55, no. 3, Mar. 2023, doi: 10.1007/s11082-022-04482-1.

M. S. Berkani, S. Giurgea, C. Espanet, J. L. Coulomb, and C. Kieffer, “Study on optimal design based on direct coupling between a FEM simulation model and L-BFGS-B algorithm,” IEEE Trans Magn, vol. 49, no. 5, pp. 2149–2152, 2013, doi: 10.1109/TMAG.2013.2245871.

R. Parhi and R. D. Nowak, “The Role of Neural Network Activation Functions,” IEEE Signal Process Lett, vol. 27, pp. 1779–1783, 2020, doi: 10.1109/LSP.2020.3027517.

A. R. Lubis, M. Lubis, and Al-Khowarizmi, “Optimization of distance formula in k-nearest neighbor method,” Bulletin of Electrical Engineering and Informatics, vol. 9, no. 1, pp. 326–338, Feb. 2020, doi: 10.11591/eei.v9i1.1464.

C. J. C. Burges, “A Tutorial on Support Vector Machines for Pattern Recognition,” 1998.

V. Piccialli and M. Sciandrone, “Nonlinear optimization and support vector machines,” Ann Oper Res, vol. 314, no. 1, pp. 15–47, Jul. 2022, doi: 10.1007/s10479-022-04655-x.

J. C. M. Sánchez, H. G. A. Mesa, A. T. Espinosa, S. R. Castilla, and F. G. Lamont, “Improving wheat yield prediction through variable selection using Support Vector Regression, Random Forest, and Extreme Gradient Boosting,” Smart Agricultural Technology, vol. 10, p. 100791, Mar. 2025, doi: 10.1016/J.ATECH.2025.100791.

L. Breiman, “Random forests,” Mach Learn, vol. 45, no. 1, pp. 5–32, Oct. 2001, doi: 10.1023/A:1010933404324/METRICS.

C. Bentéjac, A. Csörgő, and G. Martínez-Muñoz, “A comparative analysis of gradient boosting algorithms,” Artif Intell Rev, vol. 54, no. 3, pp. 1937–1967, Mar. 2021, doi: 10.1007/s10462-020-09896-5.

M. K. Elshaarawy, “Metaheuristic-driven CatBoost model for accurate seepage loss prediction in lined canals,” Multiscale and Multidisciplinary Modeling, Experiments and Design, vol. 8, no. 5, May 2025, doi: 10.1007/s41939-025-00800-8.

Y. Huang, Z. He, Y. Qin, Y. Lu, and K. Chen, “Optimizing office building performance in the HSWW region of China using simulation with Hyperopt CatBoost and SPEA2,” Sci Rep, vol. 15, no. 1, Dec. 2025, doi: 10.1038/s41598-025-85267-w.

Y. Freund and R. E. Schapire, “A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting,” J Comput Syst Sci, vol. 55, no. 1, pp. 119–139, Aug. 1997, doi: 10.1006/JCSS.1997.1504.

T. T. Wong, “Performance evaluation of classification algorithms by k-fold and leave-one-out cross validation,” Pattern Recognit, vol. 48, no. 9, pp. 2839–2846, Sep. 2015, doi: 10.1016/j.patcog.2015.03.009.

V. A. Huynh-Thu and P. Geurts, “Optimizing model-agnostic random subspace ensembles,” Mach Learn, vol. 113, no. 2, pp. 993–1042, Feb. 2024, doi: 10.1007/s10994-023-06427-5.

Published

2026-01-01

Issue

Vol. 45 No. 1 (2026): January Issue

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Articles

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Copyright (c) 2026 Mehran University Research Journal of Engineering and Technology

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How to Cite

Machine Learning Based Prediction of Hydraulic Jump Lengths in Stilling Basins for Barrages and Low-Head Hydraulic Structures. (2026). Mehran University Research Journal of Engineering and Technology, 45(1), 47-61. https://doi.org/10.22581/0320

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