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<p>Estimation of pipe friction factor is essential for analyzing flow fields in engineering. Traditionally, the Darcy-Weisbach (D-W) friction factor is determined by iteratively solving the Colebrook-White (C-W) equation, although numerous empirical formulas have also been proposed. With advancements in Machine Learning (ML), this study aims to comprehensively evaluation performances of various ML models in predicting the D-W friction factor. The ML models include Random Forest Regression (RFR), Decision Tree Regression (DTR), Support Vector Regression (SVR), K-Nearest Neighbors, Artificial Neural Networks (ANN), Multiple Linear Regression (MLR), Adaptive Boosting (AdaBoost), Extreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost), and Histogram-based Gradient Boosting Regressor (HGBR). To the authors’ knowledge, while ANN, AdaBoost, DTR, XGBoost, and SVR have been used previously, applications of other ML models are novel in this context. A synthetic dataset of 2500 samples was generated using practical ranges of Reynolds number and relative roughness as inputs, with outputs derived from solving the C-W equation via the Newton-Raphson method. Model performance was assessed using a Ranking Index (RI) based on statistical metrics supplemented by reliability analysis. The results indicated that DTR, AdaBoost, RFR, CatBoost, and HGBR outperformed traditional empirical equations, achieving RI values above 0.93 and reliability exceeding 99%. Five empirical equations also demonstrated high accuracy. The findings suggest that while empirical equations remain valuable for simpler applications, ML models, particularly DTR, offer significant advantages for complex, non-linear datasets.</p>

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Estimating Pipe Friction Factors Using Machine Learning Approaches

  • 期刊论文

  • 发表日期：

    2025年9月23日

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  • Sanaz Roshan,
  • Nasser Taleb Beydokhti,
  • Seied Hosein Afzali,
  • Reza Piraei,
  • Majid Niazkar

摘要

Estimation of pipe friction factor is essential for analyzing flow fields in engineering. Traditionally, the Darcy-Weisbach (D-W) friction factor is determined by iteratively solving the Colebrook-White (C-W) equation, although numerous empirical formulas have also been proposed. With advancements in Machine Learning (ML), this study aims to comprehensively evaluation performances of various ML models in predicting the D-W friction factor. The ML models include Random Forest Regression (RFR), Decision Tree Regression (DTR), Support Vector Regression (SVR), K-Nearest Neighbors, Artificial Neural Networks (ANN), Multiple Linear Regression (MLR), Adaptive Boosting (AdaBoost), Extreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost), and Histogram-based Gradient Boosting Regressor (HGBR). To the authors’ knowledge, while ANN, AdaBoost, DTR, XGBoost, and SVR have been used previously, applications of other ML models are novel in this context. A synthetic dataset of 2500 samples was generated using practical ranges of Reynolds number and relative roughness as inputs, with outputs derived from solving the C-W equation via the Newton-Raphson method. Model performance was assessed using a Ranking Index (RI) based on statistical metrics supplemented by reliability analysis. The results indicated that DTR, AdaBoost, RFR, CatBoost, and HGBR outperformed traditional empirical equations, achieving RI values above 0.93 and reliability exceeding 99%. Five empirical equations also demonstrated high accuracy. The findings suggest that while empirical equations remain valuable for simpler applications, ML models, particularly DTR, offer significant advantages for complex, non-linear datasets.