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A novel boosting ensemble committee-based model for local scour depth around non-uniformly spaced pile groups

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Abstract

Prediction of the scour depth around non-uniformly spaced pile groups (PGs) is one of the most complex problems is hydraulic engineering. Different types of empirical methods have been developed for estimating the scour depth around the PGs. However, the majority of the existing methods are based on simple regression methods and have serious limitations in modelling the highly nonlinear and complex relationships between the scour depth and its influential variables, especially for the non-uniformly spaced pile. Hence, this study combines prediction powers of tree popular machine learning (ML) methods, namely, Gaussian process regression (GPR), random forest (RF), and M5 model tree (M5Tree) using novel Least Least-squares (LS) Boosting Ensemble committee-based data intelligent technique to more accurately estimate local scour depth around non-uniformly spaced pile groups. A total of 353 laboratory experiments data were compiled from published papers. non-dimensional results obtained demonstrated that the ensemble model can more accurately estimate the scour depth than the individual predictions of the GPR, RF, and M5Tree models. The proposed Ensemble model with correlation coefficient (R), root mean square error (RMSE) and mean absolute percentage of error (MAPE) of 0.972, 0.0153 m, and 10.89%, respectively, significantly outperformed all existing empirical models. Furthermore, the sensitivity analysis demonstrated that the pile diameter is the most influential variable in estimating the scour depth.

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Abbreviations

CLe:

Confidence limits of prediction errors

\(d_{50}\) :

Average size of bed sediment (mm)

\(D_{p}\) :

Diameter of piles (m)

D Proj :

Sum of the non-overlapping projected widths of piles (m)

\(E_{L,M}\) :

Legate and McCabe’s Index

\(E_{r}\) :

Relative deviation

G :

Spacing typical distance between piles in the group

I A :

Index of agreement

\(K_{Smn}\) :

Correction factor for pile spacing

m :

Piles number in parallel to the flow

MAPE:

Mean absolute percentage error

n :

Piles number normal to the flow

P c :

Pearson correlation coefficient

PI:

Performance index

R :

Correlation coefficient

RAE:

Relative absolute error

RMSE:

Root mean square error

\(S_{A}\) :

Magnitude degree of dependency

SDR:

Standard deviation reduction

\({\text{SDev}}\) :

Standard deviation

S m :

Longitudinal spacing between piles in the flow direction (m)

S n :

Transverse spacing between piles perpendicular to flow direction (m)

\(SI\) :

Scatter Index

\(U_{{}}\) :

Average flow velocity (m/s)

\(U_{c}\) :

Critical flow velocity (m/s)

\(W\) :

Projected width of pile (m)

\(y\) :

Approach depth flow (m

\(\mu\) :

Dynamic viscosity of fluid (Pa. s)

\(\nu^{*}\) :

Learning rate coefficient

\(\rho\) :

Fluid density, Kg/m3

CAM:

Cosine amplitude method

GPR:

Gaussian process regression

RF:

Random forest

PGs:

Pile groups

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Authors and Affiliations

  1. Department of Civil Engineering, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran

    Iman Ahmadianfar

  2. Faculty of Engineering, Shohadaye Hoveizeh University of Technology, Dasht-e Azadegan, Susangerd, Iran

    Mehdi Jamei

  3. Water Engineering Department, Faculty of Agriculture, University of Zanjan, Zanjan, Iran

    Masoud Karbasi

  4. Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Ahmad Sharafati

  5. School of Engineering, University of Guelph, Guelph, ON, N1G 2W1, Canada

    Bahram Gharabaghi

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  1. Iman Ahmadianfar
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Ahmadianfar, I., Jamei, M., Karbasi, M. et al. A novel boosting ensemble committee-based model for local scour depth around non-uniformly spaced pile groups. Engineering with Computers 38, 3439–3461 (2022). https://doi.org/10.1007/s00366-021-01370-2

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