An in-depth comparative analysis of data-driven and classic regression models for scour depth prediction around cylindrical bridge piers

Abstract

The study focuses on the critical concern of designing secure and resilient bridge piers, especially regarding scour phenomena. Traditional equations for estimating scour depth are limited, often leading to inaccuracies. To address these shortcomings, modern data-driven models (DDMs) have emerged. This research conducts a comprehensive comparison involving DDMs, including support vector machine (SVM), gene expression programming (GEP), multilayer perceptron (MLP), gradient boosting trees (GBT) and multivariate adaptive regression spline (MARS) models, against two regression equations for predicting scour depth around cylindrical bridge piers. Evaluation employs statistical indices, such as root-mean-square error (RMSE), coefficient of determination (R2), mean average error (MAE) and normalized discrepancy ratio (S(DDRmax)), to assess their predictive performance. A total of 455 datasets from previous research papers are employed for assessment. Dimensionless parameters Froude number Fr=Ugy\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left( {Fr = \\frac{U}{{\\sqrt {gy} }}} \\right)$$\\end{document}, Pier Froude number FrP=Ug′D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Fr_{P} = \\frac{U}{{\\sqrt {g^{\\prime } D} }}$$\\end{document}, and the ratio of scour depth to pier diameter (yD)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\frac{\ ext{y}}{{\ ext{D}}})$$\\end{document} are carefully selected as influential model inputs through dimensional analysis and the gamma test. The results highlight the superior performance of the SVM model. In the training phase, it exhibits an RMSE of 0.1009, MAE of 0.0726, R2 of 0.9401, and SDDR of 2.9237. During testing, the SVM model shows an RMSE of 0.023, MAE of 0.017, R2 of 0.984, and SDDR of 5.301. Additionally, it has an average error of − 0.065 and a total error of − 20.642 in the training set and an average error of − 0.005 and a total error of − 0.707 in the testing set. Conversely, the M5 model exhibits the lowest accuracy. The statistical metrics unequivocally establish the SVM model as significantly outperforming the experimental models, placing it in a higher echelon of predictive accuracy.