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External Validation Criteria and Uncertainty Analysis of Maximum Scour Depth at Downstream of Stilling Basins Based on EPR and MT Approaches

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Iranian Journal of Science and Technology, Transactions of Civil Engineering Aims and scope Submit manuscript

Abstract

In the present research, external validation criteria and uncertainty analysis are conducted to predict maximum scour depth at downstream of the stilling basins using evolutionary polynomial regression (EPR) and model tree (MT) and nonlinear regression (NLR). Data sets used to develop models were collected from experimental models of stilling basins. Effective parameters on the scour depth were included those of discharge, approaching flow depth, mean flow velocity, geometric characteristics of stilling basins and physical properties of bed sediments at downstream of stilling basins. At first, MT and EPR models are implemented based on input–output data sets and result of performances for training and testing stages are evaluated. In addition, external validations and uncertainty analyses on the formulations given by EPR and MT are carried out using statistical errors functions and have absolute mean prediction errors less than that NLR technique. Finally, results of uncertainty and the prediction errors are compared with the GEP, MT, EPR and NLR models to select GEP model as a reliable model with the highest accuracy and smaller errors than other models.

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Abbreviations

\(q\) :

Unit discharge of spillway

\(g\) :

Acceleration due to gravity

\(d_{50}\) :

Median sediment size

\(\sigma_{\text{g}}\) :

Geometric standard deviation of sediment size distribution

\(d_{\text{w}}\) :

Tail water depth

\(h_{d}\) :

Spillway height

\(L\) :

Length of stilling basin

\(\rho_{\text{s}}\) :

Density of sediment

\(\rho_{\text{w}}\) :

Density of water

\(d_{\text{s}}\) :

Maximum scour depth

\(l_{\text{h}}\) :

Length of the scour hole

\(l_{\text{s}}\) :

Length of the deepest point of the scour hole

m :

Maximum number of additive terms

X i :

Model input variables

Ŷ :

Model output variables

ES(j,i):

Exponents of variables

\(O\) :

Measured outputs

\(\overline{O}\) :

Mean of measured output

\(P\) :

Predicted outputs

\(\overline{P}\) :

Average of predicted outputs

\(M\) :

Number of data sets

\(j\) :

Counter for sample of data sets

R:

Correlation coefficient

RMSE:

Root mean squared error

MAPE:

Mean absolute percentage error

k, k ′ :

Gradients of the regression line

m, n :

Coefficients of determination for the regression line

R m :

Cross-validation

e j :

Prediction error

S e :

Standard deviation

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Authors and Affiliations

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

    Masoud Mesbahi & Seyed-Abbas Hosseini

  2. Department of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran

    Nasser Talebbeydokhti & Seied Hosein Afzali

Authors
  1. Masoud Mesbahi
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  2. Nasser Talebbeydokhti
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  3. Seyed-Abbas Hosseini
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  4. Seied Hosein Afzali
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Correspondence to Masoud Mesbahi.

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Mesbahi, M., Talebbeydokhti, N., Hosseini, SA. et al. External Validation Criteria and Uncertainty Analysis of Maximum Scour Depth at Downstream of Stilling Basins Based on EPR and MT Approaches. Iran J Sci Technol Trans Civ Eng 41, 87–99 (2017). https://doi.org/10.1007/s40996-016-0025-0

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