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<p>Piano key weir is a type of non-linear weir that excels at rehabilitation of dams. Therefore, precise control of its discharge capacity is of prime importance for water management and flood control, which is governed by its coefficient of discharge (<i>C</i><sub>PKW</sub>). Traditional empirical equations for estimating <i>C</i><sub>PKW</sub> often struggle to capture the complex nonlinear relationships governing <i>C</i><sub>PKW</sub>. The current study addresses this limitation through the application of machine learning techniques to predict <i>C</i><sub>PKW</sub> for Type-A Piano Key Weirs (PKWs). To overcome the complexity of the traditional method, machine learning techniques, Support Vector Regression (SVR), Extreme Gradient Boosting (XGBoost), Random Forest (RF), and a Hybrid SVR–RF model were developed and tested on an extensive experimental dataset of Type-A PKW. The performance of the proposed model was evaluated by using statistical indicators, such as coefficient of determination (<i>R</i>²), root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (<i>R</i>). Among the tested models, SVR achieved the highest accuracy (<i>R</i><sup>2</sup> = 0.9916, RMSE = 0.0427, MAE = 0.0279, <i>R</i> = 0.9962), followed by hybrid SVR–RF and XGBoost models, while RF model performed moderately. Sensitivity analysis using Shapely Additive Explanations (SHAP) revealed that relative crest length (<i>L/W</i>) is the most influential parameter for <i>C</i><sub>PKW</sub>, followed by the relative upstream head (<i>H/P</i>) and relative weir height (<i>P/W</i><sub>u</sub>), whereas inlet-to-outlet key width ratio (<i>W</i><sub>i</sub><i>/W</i><sub>o</sub>) shows minimal effect on <i>C</i><sub>PKW</sub>. A user-friendly graphical user interface (GUI) was also developed to enable real-time prediction of <i>C</i><sub>PKW</sub>, enhancing the practical applicability of the models.</p>

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Application of machine learning models for predicting the coefficient of discharge of Type-A Piano Key Weirs

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Md Saddam Quamar,
  • Zulfequar Ahmad

摘要

Piano key weir is a type of non-linear weir that excels at rehabilitation of dams. Therefore, precise control of its discharge capacity is of prime importance for water management and flood control, which is governed by its coefficient of discharge (CPKW). Traditional empirical equations for estimating CPKW often struggle to capture the complex nonlinear relationships governing CPKW. The current study addresses this limitation through the application of machine learning techniques to predict CPKW for Type-A Piano Key Weirs (PKWs). To overcome the complexity of the traditional method, machine learning techniques, Support Vector Regression (SVR), Extreme Gradient Boosting (XGBoost), Random Forest (RF), and a Hybrid SVR–RF model were developed and tested on an extensive experimental dataset of Type-A PKW. The performance of the proposed model was evaluated by using statistical indicators, such as coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R). Among the tested models, SVR achieved the highest accuracy (R2 = 0.9916, RMSE = 0.0427, MAE = 0.0279, R = 0.9962), followed by hybrid SVR–RF and XGBoost models, while RF model performed moderately. Sensitivity analysis using Shapely Additive Explanations (SHAP) revealed that relative crest length (L/W) is the most influential parameter for CPKW, followed by the relative upstream head (H/P) and relative weir height (P/Wu), whereas inlet-to-outlet key width ratio (Wi/Wo) shows minimal effect on CPKW. A user-friendly graphical user interface (GUI) was also developed to enable real-time prediction of CPKW, enhancing the practical applicability of the models.