Erratum for “Genetic Programming to Predict Bridge Pier Scour” by H. Md. Azamathulla, Aminuddin Ab Ghani, Nor Azazi Zakaria, and Aytac Guven

Azamathulla, H. Md.; Ab Ghani, Aminuddin; Zakaria, Nor Azazi; Guven, Aytac

doi:10.1061/(ASCE)HY.1943-7900.0000683

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Aug 15, 2013

Erratum for “Genetic Programming to Predict Bridge Pier Scour” by H. Md. Azamathulla, Aminuddin Ab Ghani, Nor Azazi Zakaria, and Aytac Guven

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Authors: H. Md. Azamathulla [email protected], Aminuddin Ab Ghani [email protected], Nor Azazi Zakaria [email protected], and Aytac Guven [email protected]Author Affiliations

Publication: Journal of Hydraulic Engineering

Volume 139, Issue 9

https://doi.org/10.1061/(ASCE)HY.1943-7900.0000683

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The following corrections should be noted for the original paper, and the authors apologize for the typographical errors and other mistakes in the extraction of genetic programming (GP) equations from the trained model.

The authors have been informed by the readers of the Journal that Eqs. (4) and (5) in the original paper predicted very high values of the scour depth. Using the same database for training and testing as before, the authors have developed new equations based on GP formulation.

The equations on p. 167 should be as follows:

\frac{d_{s}}{y} = {(\frac{2^{2^{T_{1}} - 1} - d_{50} / b - 1}{y / b})}^{0.5}

(4)

where

T_{1} = {[\frac{1 - T_{2} (F_{r} - 0.224)}{- 0.682 σ (y / b)}]}^{2} \frac{- 1}{\frac{T_{2}^{2}}{y / b} + T_{3} + \frac{1}{L / b {(y / b)}^{2}}} + T_{2} (F_{r} - 0.224)

(5a)

T_{2} = 2 {[\frac{\frac{(F_{r} - 0.224)}{L / b} + F_{r} - d_{50} / b - 0.736}{y / b} + (F_{r} - 0.224)]}^{2}

(5b)

T_{3} = {[\frac{2 T_{2}}{(y / b) (F_{r} - 0.224)} - 0.73]}^{2} {[\frac{2 (d_{50} / b)}{T_{2} (F_{r} - 0.224)}]}^{2}

(5c)

\frac{d_{s}}{y} = 1.82 {(\frac{d_{50}}{y})}^{0.042} {(\frac{b}{y})}^{0.28} {(\frac{L}{y})}^{0.37} {F r}^{0.42} σ^{- 0.03159}

(10)

These equations will replace those in the original paper. In fact, the GP was described in the original paper such that it would be introduced as an extension of the familiar genetic algorithm in the simplest terms, although the code used might have applied GP in a different manner.

With these new Eqs. (4) and (5), the details in Table 4 of the original paper will be modified as shown.

Table 4. Comparison of Predicted and Observed Scour Depths for the Testing Set

Method	Coefficient of determination ( $R^{2}$ )	Root-mean square error (RMSE)	Average error (AE %)	Average absolute deviation ( $δ$ )
Predictions to observed $d_{s} / y$ for testing set
GP	0.845	0.037	$- 11.450$	23.345
RBF	0.691	0.105	$- 59.450$	43.513
Eq. 10 (authors)	0.745	0.345	$- 15.673$	29.567
Eq. 11 (HEC-18)	0.425	0.271	$- 174.055$	113.497
Predictions to observed $d_{s} / y > 0.2$ for testing set
GP	0.789	0.076	8.567	17.453
RBF	0.467	0.167	14.781	27.987
Eq. 10 (authors)	0.534	0.105	12.56	23.786
Eq. 11 (HEC-18)	0.119	0.380	$- 97.060$	81.874

Note: RBF = radial basis function; HEC-18 = pier scour equation recommended by the Federal Highway Administration’s Hydraulic Engineering Circular.

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Journal of Hydraulic Engineering

Volume 139 • Issue 9 • September 2013

Pages: 1020

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Received: Jul 26, 2012

Accepted: Sep 27, 2012

Published online: Aug 15, 2013

Published in print: Sep 1, 2013

Discussion open until: Jan 15, 2014

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H. Md. Azamathulla [email protected]

M.ASCE

Associate Professor, River Engineering and Urban Drainage Research Centre (REDAC), Universiti Sains Malaysia, Engineering Campus, Nibong Tebal, Pulau Pinang 14300, Malaysia (corresponding author). E-mail: [email protected]

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Aminuddin Ab Ghani [email protected]

Professor and Deputy Director, REDAC, Universiti Sains Malaysia, Engineering Campus, Nibong Tebal, Pulau Pinang 14300, Malaysia. E-mail: [email protected]

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Nor Azazi Zakaria [email protected]

Professor and Director, REDAC, Universiti Sains Malaysia, Engineering Campus, Nibong Tebal, Pulau Pinang 14300, Malaysia. E-mail: [email protected]

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Aytac Guven [email protected]

Associate Professor, Dept. of Civil Engineering, Univ. of Gaziantep, Gaziantep 27310, Turkey. E-mail: [email protected]

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