Sensitivity Analysis and Discharge Coefficient Estimation in Semicircular Weirs Using Machine Learning Methods

Document Type : Original Article

Authors

1 Department of Hydraulic Structures, Faculty of Water Engineering and Environmental Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 Department of Hydraulic Structures, Faculty of Water Engineering and Environmental Science , Shahid Chamran University of Ahvaz, Ahvaz, Iran

3 Department of Hydraulic Structures , Faculty of Water Engineering and Environmental Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

Objective This study aims to develop and evaluate two machine learning models, namely Extreme Learning Machine (ELM) and eXtreme Gradient Boosting (XGBoost), incorporating Bayesian Optimization and cross-validation techniques, for the prediction of the discharge coefficient (Cd) of semicircular side weirs.
 
Method: The modeling process is based on a dataset comprising 233 experimental observations sourced from two independent studies, encompassing both geometric and hydraulic parameters. Bayesian Optimization was implemented using five-fold cross-validation on the training set. For each parameter combination, the root mean square error (RMSE) was computed, and once the objective function (RMSE) reached a satisfactory threshold, the corresponding parameter set was selected as the final model structure. The optimized model was subsequently validated using the test dataset, and its predictive performance was compared against baseline models.
 
Results: The results indicated that the XGBoost model achieved higher predictive accuracy with a coefficient of determination (R²) of 0.99 for the training set and 0.92 for the test set, outperforming the ELM model, which yielded R² values of 0.91 and 0.879 for the respective datasets. Sensitivity analysis using Sobol, Morris, Entropy-based, and SHAP methods consistently identified the HT/P ratio (hydraulic head to weir height) as the most influential input parameter in predicting Cd. Specifically, Sobol analysis revealed that nearly the entire variance in the model output could be attributed to this single parameter, with negligible interaction effects from other variables.
 
Conclusions: All sensitivity analysis techniques confirmed the robustness and reliability of the developed models. The integration of machine learning algorithms with Bayesian Optimization proves to be an effective and powerful framework for flow modeling in hydraulic systems.

Keywords

Main Subjects

References

Arham Namazi, F. S., & Mozaffari, J. (2023). Investigation of labyrinth weirs discharge coefficient with the same length. Flow Measurement and Instrumentation, 94, 102468. https://doi.org/10.1016/j.flowmeasinst.2023.102468
Azimi, H., & Shiri, H. (2021). Assessment of ice-seabed interaction process in clay using extreme learning machine. International Journal of Offshore and Polar Engineering, 31(04), 411–420. https://doi.org/10.17736/ijope.2021.mt31
Bilhan, O., Emiroglu, M. E., Miller, C. J., & Ulas, M. (2018). The evaluation of the effect of nappe breakers on the discharge capacity of trapezoidal labyrinth weirs by ELM and SVR approaches. Flow Measurement and Instrumentation, 64, 71–82. https://doi.org/10.1016/j.flowmeasinst.2018.10.009
Bonakdari, H., Gholami, A., Mosavi, A., Kazemian-Kale-Kale, A., Ebtehaj, I., & Azimi, A. H. (2020). A novel comprehensive evaluation method for estimating the bank profile shape and dimensions of stable channels using the maximum entropy principle. Entropy, 22(11), 1218. https://doi.org/10.3390/e22111218
Borghei, S. M., & Parvaneh, A. (2011). Discharge characteristics of a modified oblique side weir in subcritical flow. Flow Measurement and Instrumentation, 22(5), 370–376. https://doi.org/10.1016/j.flowmeasinst.2011.04.009
Borisova, N. M., & Belikov, V. V. (2023). Optimization of Spillway Design of Reconstructed Shavan Dam Using Numerical 2D-Modeling. Power Technology and Engineering, 57(1), 67–74. Scopus. https://doi.org/10.1007/s10749-023-01624-7
Chen, T., & Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785–794. https://doi.org/10.1145/2939672.2939785
Dutta, D., Mandal, A., & Afzal, M. S. (2020). Discharge performance of plan view of multi-cycle W-form and circular arc labyrinth weir using machine learning. Flow Measurement and Instrumentation, 73, 101740. https://doi.org/10.1016/j.flowmeasinst.2020.101740
Emami, S., Parsa, J., Emami, H., & Abbaspour, A. (2021). Investigation of Discharge Coefficient of Triangular Duckbill Labyrinth Weirs Using Fluent Software and Gray Wolf and Elections Algorithms. Civil Infrastructure Researches, 6(2), 107–121. https://doi.org/10.22091/cer.2021.6942.1250
Ghaderi, D., Ebrahimnezhadian, H., & Mollazadeh, M. (2024). Three-dimensional analysis of the performance of circular stepped spillways in the skimming flow regime. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 46(7). https://doi.org/10.1007/s40430-024-05004-8
Haghiabi, A. H., Parsaie, A., & Ememgholizadeh, S. (2018). Prediction of discharge coefficient of triangular labyrinth weirs using Adaptive Neuro Fuzzy Inference System. Alexandria Engineering Journal, 57(3), 1773–1782. https://doi.org/10.1016/j.aej.2017.05.005
Hussein, B. S., & Jalil, S. A. (2024). Influence of Labyrinth Side Weir Shape Modification on the Hydrodynamic Performance: Experimental and Numerical Study. Arabian Journal for Science and Engineering, 50, 12881-12902. https://doi.org/10.1007/s13369-024-09563-9
Ikinciogullari, E. (2024). Energy dissipation performance of labyrinth and harmonic stepped spillways. Journal of Hydroinformatics, 26(10), 2668–2682. https://doi.org/10.2166/hydro.2024.221
Koc, K., Ekmekcioğlu, Ö., & Gurgun, A. P. (2021). Integrating feature engineering, genetic algorithm and tree-based machine learning methods to predict the post-accident disability status of construction workers. Automation in Construction, 131, 103896. https://doi.org/10.1016/j.autcon.2021.103896
Kisi, O., Emin Emiroglu, M., Bilhan, O., & Guven, A. (2012). Prediction of lateral outflow over triangular labyrinth side weirs under subcritical conditions using soft computing approaches. Expert Systems with Applications, 39(3), 3454–3460. https://doi.org/10.1016/j.eswa.2011.09.035
Li, J., Duan, Q. Y., Gong, W., Ye, A., Dai, Y., Miao, C., Di, Z., Tong, C., & Sun, Y. (2013). Assessing parameter importance of the Common Land Model based on qualitative and quantitative sensitivity analysis. Hydrology and Earth System Sciences, 17(8), 3279–3293.
Li, S., Shen, G., Parsaie, A., Li, G., & Cao, D. (2024). Discharge modeling and characteristic analysis of semi-circular side weir based on the soft computing method. Journal of Hydroinformatics, 26(1), 175–188. https://doi.org/10.5194/hessd-10-2243-2013
Lundberg, S. M., & Lee, S.-I. (2017). A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems, 30. https://proceedings.neurips.cc/paper/2017/hash/8a20a8621978632d76c43dfd28b67767-Abstract.html
Mishra, S., & Knowlton, R. G. (2003). Testing for input-output dependence in performance assessment models. Proceedings of the 10th International High-Level Radioactive Waste Management Conference (IHLRW), March 30-April 2, 2003, Las Vegas, Nevada, 882–887. https://doi.org/10.1023/a:1007058325258
Morris, M. D. (1991). Factorial Sampling Plans for Preliminary Computational Experiments. Technometrics, 33(2), 161–174. https://doi.org/10.1080/00401706.1991.10484804
King, D. M., & Perera, B. J. C. (2013). Morris method of sensitivity analysis applied to assess the importance of input variables on urban water supply yield–A case study. Journal of hydrology, 477, 17-32. https://www.sciencedirect.com/science/article/pii/S0022169412008918
Petrovic, A., Strumberger, I., Antonijevic, M., Jovanovic, D., Mladenovic, D., & Chabbra, A. (2022). Firefly-xgboost approach for pedestrian detection. 2022 IEEE Zooming Innovation in Consumer Technologies Conference (ZINC), 197–202. https://ieeexplore.ieee.org/abstract/document/9840700/
Piraei, R., Afzali, S. H., & Niazkar, M. (2023). Assessment of XGBoost to Estimate Total Sediment Loads in Rivers. Water Resources Management, 37(13), 5289–5306. https://doi.org/10.1007/s11269-023-03606-w
Rao, S. S., & Shukla, M. K. (1971). Characteristics of flow over weirs of finite crest width. Journal of the Hydraulics Division, 97(11), 1807–1816. https://doi.org/10.1061/JYCEAJ.0003138
Safarrazavi Zadeh, M., Esmaeili Varaki, M., & Biabani, R. (2021). Experimental study on flow over sinusoidal and semicircular labyrinth weirs. ISH Journal of Hydraulic Engineering, 27(sup1), 304–313. https://doi.org/10.1080/09715010.2019.1644679
Sangsefidi, Y., & Ghodsian, M. (2018). Investigation of effects of entrance channel walls on the hydraulic performance of arced labyrinth weirs. https://www.sid.ir/paper/256636/en
Savaedi, A., Zayeri, M., Ghomeshi, M., & Daryaee, M. (2024b). Application of Artificial Intelligence in Predicting the Discharge Coefficient of Labyrinth Weirs with Harmonic Plans. Irrigation and Drainage Structures Engineering Research, 25(96), 82–61. https://doi.org/10.22092/idser.2025.368037.1602
Shafiei, S., Najarchi, M., & Shabanlou, S. (2020). Simulation of labyrinth weir discharge coefficient by modern artificial intelligence models. Modares Civil Engineering Journal, 20(1), 204–218. https://mcej.modares.ac.ir/browse.php?a_id=35509&sid=16&slc_lang=en
Simsek, O., Gumus, V., & Ozluk, A. (2023). Prediction of discharge coefficient of the trapezoidal broad-crested weir flow using soft computing techniques. Neural Computing and Applications, 35(24), 17485–17499. https://doi.org/10.1007/s00521-023-08615-9
Sobol, I. M. (1993). Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Exp., 1(4), 407–414. https://www.scirp.org/reference/referencespapers?referenceid=2692473
Suleimany, J. M. F. S., Aurahman, T. H., & Mamand, B. S. (2022). Flow simulation over semicircular labyrinth weir using ANSYS-fluent. Tikrit Journal of Engineering Sciences, 29(1), 83–98. https://doi.org/10.25130/tjes.29.1.7
Wu, J., Ma, D., & Wang, W. (2022). Leakage Identification in Water Distribution Networks Based on XGBoost Algorithm. Journal of Water Resources Planning and Management, 148(3), 04021107. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001523
Yıldız, A., Marti, A. İ., & Göğüş, M. (2024). The hydraulic investigation of harmonic plan weirs. Flow Measurement and Instrumentation, 95, 102512. https://doi.org/10.1016/j.flowmeasinst.2023.102512
Zare, H., Vaghefi, M., Mahmoudi, A., & Behroozi, A. M. (2023). Experimental Exploration of Flow Hydraulics and Discharge Coefficient for an Inclined Circular Labyrinth Weir. Water Resources Management, 37(11), 4521–4536. https://doi.org/10.1007/s11269-023-03577-y
Zeng, X., Wang, D., & Wu, J. (2012). Sensitivity analysis of the probability distribution of groundwater level series based on information entropy. Stochastic Environmental Research and Risk Assessment, 26, 345–356. https://doi.org/10.1007/s00477-012-0556-2
Advanced Technologies in Water Efficiency
Volume 6, Issue 2
July 2026
Pages 1-23

Files

History

  • Receive Date: 05 June 2025
  • Revise Date: 09 October 2025
  • Accept Date: 16 December 2025

Share

How to cite

Statistics