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<p>The intensity of hydrodynamic pressure at the bottom of unlined plunge pools is the main cause of scouring and as a result a threat to dam foundations. This article aims to develop both statistical and machine learning models for estimating dynamic pressure coefficients at the Flat Bottom (FB) and Pre-Excavated or Scoured Bottom (PESB) of plunge pools. We developed a Predictive Statistical Model (PSM) based on an extensive experimental dataset to predict dynamic pressures at FB and PESB pools. The PSM incorporates two correction factors, <i>α</i> and <i>α’</i>, to relate respectively the mean pressure and fluctuations at PESB to those at FB pools. While <i>α’</i> is approximately unity, the <i>α</i> varies depending on the scour geometry: ranging from 0.35 to 0.61 for conical geometries and from 0.43 to 1.23 for cylindrical geometries. Lower values of <i>α</i> correspond to pools with minimal scour depths, whereas higher values are associated with deeper scour geometries. To evaluate the predictive performance of the models, various machine learning techniques, including Artificial Neural Networks (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Support Vector Regression (SVR), and Group Method of Data Handling (GMDH) were employed. The analysis of statistical error functions indicates that the SVR model achieves superior accuracy in predicting mean dynamic pressures in rocky plunge pools, outperforming other machine learning approaches. Furthermore, the PSM demonstrates higher predictive accuracy compared to existing empirical models. Although the SVR model exhibits the highest accuracy, the PSM offers a simplified structure that facilitates implementation without requiring specialized hardware or software, making it a practical and reliable tool for estimating hydrodynamic pressures in plunge pools.</p>

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Application of statistical and machine learning models for predicting hydrodynamic pressure characteristics at pre-excavated and scoured plunge pool bottoms

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Reza Fatahi-Alkouhi,
  • Ahmad Shanehsazzadeh,
  • Mahmoud Hashemi

摘要

The intensity of hydrodynamic pressure at the bottom of unlined plunge pools is the main cause of scouring and as a result a threat to dam foundations. This article aims to develop both statistical and machine learning models for estimating dynamic pressure coefficients at the Flat Bottom (FB) and Pre-Excavated or Scoured Bottom (PESB) of plunge pools. We developed a Predictive Statistical Model (PSM) based on an extensive experimental dataset to predict dynamic pressures at FB and PESB pools. The PSM incorporates two correction factors, α and α’, to relate respectively the mean pressure and fluctuations at PESB to those at FB pools. While α’ is approximately unity, the α varies depending on the scour geometry: ranging from 0.35 to 0.61 for conical geometries and from 0.43 to 1.23 for cylindrical geometries. Lower values of α correspond to pools with minimal scour depths, whereas higher values are associated with deeper scour geometries. To evaluate the predictive performance of the models, various machine learning techniques, including Artificial Neural Networks (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Support Vector Regression (SVR), and Group Method of Data Handling (GMDH) were employed. The analysis of statistical error functions indicates that the SVR model achieves superior accuracy in predicting mean dynamic pressures in rocky plunge pools, outperforming other machine learning approaches. Furthermore, the PSM demonstrates higher predictive accuracy compared to existing empirical models. Although the SVR model exhibits the highest accuracy, the PSM offers a simplified structure that facilitates implementation without requiring specialized hardware or software, making it a practical and reliable tool for estimating hydrodynamic pressures in plunge pools.