<p>This paper presents a stacked machine learning model to enhance the accuracy of time-dependent scour depth estimation around cylindrical piers. Traditional empirical methods often fall short due to the complex interactions between sediment, flow, and structural parameters. By integrating advanced machine learning techniques, including categorical boosting (CatBoost), extra trees regression (ETR), extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM), gradient boosting regression (GBR), random forest regression (RFR), decision tree regression (DTR), adaptive boosting (AdaBoost), and linear regression (LR), the proposed model not only improves predictive performance but also prevents overfitting and offers interpretability regarding the influence of various input parameters. The model utilizes a comprehensive dataset encompassing critical variables such as flow velocity, sediment characteristics, and pier geometry, achieving a coefficient of determination, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7856_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="95" /> </InlineMediaObject> <EquationSource Format="TEX">\(R^2= 0.99936\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0.99936</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7856_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="118" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {MSE}=0.000004\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>MSE</mtext> <mo>=</mo> <mn>0.000004</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7856_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="122" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {RMSE}=0.00192\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>RMSE</mtext> <mo>=</mo> <mn>0.00192</mn> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_7856_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="114" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {MAE}= 0.00149\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>MAE</mtext> <mo>=</mo> <mn>0.00149</mn> </mrow> </math></EquationSource> </InlineEquation> on the testing dataset. Furthermore, feature analyses on the input dataset reveal that the features including time, flow velocity, and pier and sediment dimensions are the most important factors in scour depth prediction.</p>

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An efficient ensemble learning model for time-dependent scour depth estimation

  • Hojjat Emami,
  • Babak Azarnavid,
  • Ali Raeisi Isa-Abadi,
  • Mojtaba Fardi

摘要

This paper presents a stacked machine learning model to enhance the accuracy of time-dependent scour depth estimation around cylindrical piers. Traditional empirical methods often fall short due to the complex interactions between sediment, flow, and structural parameters. By integrating advanced machine learning techniques, including categorical boosting (CatBoost), extra trees regression (ETR), extreme gradient boosting (XGBoost), light gradient boosting machine (LightGBM), gradient boosting regression (GBR), random forest regression (RFR), decision tree regression (DTR), adaptive boosting (AdaBoost), and linear regression (LR), the proposed model not only improves predictive performance but also prevents overfitting and offers interpretability regarding the influence of various input parameters. The model utilizes a comprehensive dataset encompassing critical variables such as flow velocity, sediment characteristics, and pier geometry, achieving a coefficient of determination, \(R^2= 0.99936\) R 2 = 0.99936 , \(\text {MSE}=0.000004\) MSE = 0.000004 , \(\text {RMSE}=0.00192\) RMSE = 0.00192 , and \(\text {MAE}= 0.00149\) MAE = 0.00149 on the testing dataset. Furthermore, feature analyses on the input dataset reveal that the features including time, flow velocity, and pier and sediment dimensions are the most important factors in scour depth prediction.