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<p>This study aims to accurately predict the energy dissipation rate (EDR) in modified semi-cylindrical weirs, which is essential for their efficient design. Three machine learning models—locally Weighted polynomial regression (LWPR), random forest (RF), and categorical boosting (CatBoost)—were applied individually to estimate the EDR. Additionally, four hybrid models combining these individual approaches were developed: LWPR-RF, RF-CatBoost, LWPR-CatBoost, and RF-CatBoost-LWPR. Sensitivity analysis using the Gamma Test and SHAP (Shapley Additive Explanations) was conducted to assess the influence of key dimensionless parameters on the EDR. The analysis revealed that the ratio of critical depth to the crest radius (<i>d</i><sub><i>C</i></sub>/<i>R</i>) and the downstream ramp angle (<i>θ</i>) significantly affected the EDR. Laboratory data reflecting diverse hydraulic conditions were split into a 75% training set and a 25% testing set for model development and validation. For model evaluation, mean absolute error, mean percentage error, root mean square error, correlation coefficient (<i>R</i><sup>2</sup>), mean absolute relative error, Scatter Index, Nash–Sutcliffe efficiency, and percent bias were used. To compare and rank the models, the Taylor diagram, regression error characteristic, and Performance Index (PI) were employed. The results showed that the hybrid models outperformed the individual models during training, with RF-CatBoost-LWPR achieving the highest PI = 4.64 and the lowest centered root mean square error (<i>E'</i> = 0.0091). The RF-CatBoost model followed closely with a PI of 4.6 and an <i>E'</i> of 0.0092. During the testing stage, all models performed similarly, with the single models slightly outperforming the hybrid models by a small margin. The LWPR model emerged as the top performer, achieving a PI of 0.44 and an <i>E'</i> of 0.0862. Closely following was the CatBoost model, ranking second with a PI of 0.43 and an <i>E'</i> of 0.0864. Despite these minor differences, all models demonstrated strong predictive capabilities during testing.</p>

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Enhanced energy dissipation prediction in modified semi-cylindrical weirs using machine learning techniques

  • 期刊论文

  • 发表日期：

    2025年2月13日

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  • Ehsan Afaridegan,
  • Reza Fatahi-Alkouhi,
  • Soudabeh Khalilian,
  • Abbas Moradi-Eshgafti,
  • Nosratollah Amanian

摘要

This study aims to accurately predict the energy dissipation rate (EDR) in modified semi-cylindrical weirs, which is essential for their efficient design. Three machine learning models—locally Weighted polynomial regression (LWPR), random forest (RF), and categorical boosting (CatBoost)—were applied individually to estimate the EDR. Additionally, four hybrid models combining these individual approaches were developed: LWPR-RF, RF-CatBoost, LWPR-CatBoost, and RF-CatBoost-LWPR. Sensitivity analysis using the Gamma Test and SHAP (Shapley Additive Explanations) was conducted to assess the influence of key dimensionless parameters on the EDR. The analysis revealed that the ratio of critical depth to the crest radius (dC/R) and the downstream ramp angle (θ) significantly affected the EDR. Laboratory data reflecting diverse hydraulic conditions were split into a 75% training set and a 25% testing set for model development and validation. For model evaluation, mean absolute error, mean percentage error, root mean square error, correlation coefficient (R2), mean absolute relative error, Scatter Index, Nash–Sutcliffe efficiency, and percent bias were used. To compare and rank the models, the Taylor diagram, regression error characteristic, and Performance Index (PI) were employed. The results showed that the hybrid models outperformed the individual models during training, with RF-CatBoost-LWPR achieving the highest PI = 4.64 and the lowest centered root mean square error (E' = 0.0091). The RF-CatBoost model followed closely with a PI of 4.6 and an E' of 0.0092. During the testing stage, all models performed similarly, with the single models slightly outperforming the hybrid models by a small margin. The LWPR model emerged as the top performer, achieving a PI of 0.44 and an E' of 0.0862. Closely following was the CatBoost model, ranking second with a PI of 0.43 and an E' of 0.0864. Despite these minor differences, all models demonstrated strong predictive capabilities during testing.