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The Application of Soft Computing Models and Empirical Formulations for Hydraulic Structure Scouring Depth Simulation: A Comprehensive Review, Assessment and Possible Future Research Direction

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Abstract

Prediction of scouring characteristics is one of the major issues in hydraulic and hydrology engineering. Over the past five decades, numerous empirical formulations (EFs), based on the regression of scouring data observed from laboratory experiments in the field, have been developed to predict scouring characteristics (typically, the equilibrium scour depth); yet, these EFs are sensitive to uncertainty of effective parameters and in some cases could not comprehend the actual internal mechanism between variables. In the last 20 years, Soft Computing (SC) approaches have been increasingly adopted as an alternative for modeling scouring depth surrounding hydraulic structures. In this respect, several SC algorithms are examined as new era of modeling methodologies for extracting scouring depth equations. Lately, these algorithms have been vastly adopted for scouring simulation with various advanced version of SC such as hybrid intelligence models. The motivation of the current research is to exhibit all the established researches on the implementation of EF and SC models for multiple scouring depth modeling such as around pipeline, bridges abutment, piles and grade-control structures. A comprehensive review of the up-to-date researches on the scouring depth phenomena is presented, placing special emphasis on the recent applications of SC models and also recalling all the performed experimental laboratory studies. The review is included an informative evaluation and assessment of the surveyed researches. The improvement in prediction performance provided by the SC models when compared to empirical formulations is discussed and based on the current state-of-the-art, several research gaps are recognized, and possible future research directions are proposed.

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Authors and Affiliations

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

    Ahmad Sharafati & Masoud Haghbin

  2. Department of Mechanical and Construction Engineering, Northumbria University, Wynne Jones Building, Newcastle upon Tyne, NE1 8ST, UK

    Davide Motta

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Zaher Mundher Yaseen

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Appendix: Notations

Appendix: Notations

RBNN:

Radial Basis Neural Network

MLR:

Multiple Linear Regression

ERBFNN:

Hybrid of (RBFNN + Fuzzy Logic (FL) + Artificial Bee Colony)

FFBP:

Feed Forward Back Propagation

RBF:

Radial Basis Function

MNLR:

Multiple Non Linear Regression

GEP:

Genetic Expression Programming

GP:

Genetic Programing

SVM:

Support Vector Machine

SVR:

Support Vector Regression

GRNN:

General Regression Neural Network

MT:

Model Tree

ANFIS:

Adaptive Neuro Fuzzy Inference System

GA:

Genetic Algorithm

FE:

Finite Elements

GMDH:

Group Method of Data Handling

FFCC:

Feed Forward Computational Complexity Normalized

NRMSE:

Root Mean Square Error

E:

Efficiency

R 2 :

Coefficient of Determination

MAPE:

Mean Absolute Percent Error

RMSE:

Root-Mean-Square Error

AE:

Average Error

δ:

Average Absolute Deviation)

AAE:

Average Absolute Error

MAD:

Mean Absolute Deviation

R:

Correlation Coefficient

MPE:

Mean Percentage Error

RAE:

Relative Absolute Error

RSE:

Relative Squared Error

MAE:

Mean Absolute Error

SSE:

Sum of Squared Error

MSE:

Mean Squared Error

BIAS:

Mean Signed Error

POUE:

Percentages of Overall Under Estimation Error

ENS:

Nash–Sutcliffe Efficiency

SI:

Scatter Index

D & Ia:

Index of Agreement

MSRE:

Mean Squared Relative Error

MARE:

Mean Absolute Relative Error

NMB:

Normalized Mean Bias

SE:

Standard Error

CF:

Correlation Factor

AMRE:

Absolute Mean Relative Error

DR:

Discrepancy Ratio

Notation for empirical formulations:

  • Bridge

Ds: equilibrium scouring depth, b: diameter of bridge pier, Frcr: critical Froude number, y and y: flow depth, U: velocity, \(\alpha\): opening ration, \(\rho_{\text{g}}\): gravitational density, Fd: densiometric particle Froude number, T: dimensionless time, \(\sigma\): sediment non-uniformity, N: shape number, l: transverse length of abutment, q: discharge, KS: shape factor, Fr: Froude number, Re: Reynolds number.

  • G.C.S:

\({\varphi } = {\text{Submerged angle of repose of bed sediment}}\), \(\upgamma_{\text{s}} = {\text{Specific Weight of Sediment}}\) \(\upgamma = {\text{Specific Weight of water}}\) \({\text{Cd}} = {\text{Jet diffusion coefficient }}\) \({\text{y}}_{0}\) = Jet thickness entering in tail water \(\upbeta = {\text{jet angle}}\) \({\text{D}}_{\text{p}} = {\text{drop height of structures}}\) \({\text{h}} = {\text{tail water depth}}\), KC = The Keulegan–Carpenter q = discharge, Ucr = Critical velocity Re = Reynolds Number, Fr = Froude number, GS = Sediment specific gravity, Ucr = Critical velocity. d50 = median particle size

  • Pipelines:

e: gap between the pipes; D: pipe diameter, h = water depth, Fr = Froude number, GS = Sediment specific gravity, Ucr = Critical velocity. \(\theta_{cr}\) = critical shields number, KC = The Keulegan–Carpenter number \(\tau_{0}\) = shields number, d50 = median particle size q = discharge; Re: Reynolds Number

  • Piles:

H: water depth; Fr: Froude number, GS: Sediment specific gravity; Ucr: Critical velocity;\(\theta_{cr}\) = critical shields number; KC: The Keulegan–Carpenter number;\(\tau_{0}\): shields number; d50: median particle size, q: discharge.

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Sharafati, A., Haghbin, M., Motta, D. et al. The Application of Soft Computing Models and Empirical Formulations for Hydraulic Structure Scouring Depth Simulation: A Comprehensive Review, Assessment and Possible Future Research Direction. Arch Computat Methods Eng 28, 423–447 (2021). https://doi.org/10.1007/s11831-019-09382-4

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  • DOI: https://doi.org/10.1007/s11831-019-09382-4

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