Errata
Erratum for “Genetic Programming to Predict Bridge Pier Scour” by H. Md. Azamathulla, Aminuddin Ab Ghani, Nor Azazi Zakaria, and Aytac Guven
1 − T 2 ðFr − 0.224Þ 2 T1 ¼ −0.682σðy=bÞ
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2
DOI: 10.1061/(ASCE)HY.1943-7900.0000133
T2 ¼ 2
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]
Professor and Deputy Director, REDAC, Universiti Sains Malaysia, Engineering Campus, Nibong Tebal, Pulau Pinang 14300, Malaysia. E-mail:
[email protected]
Professor and Director, REDAC, Universiti Sains Malaysia, Engineering Campus, Nibong Tebal, Pulau Pinang 14300, Malaysia. E-mail: redac01@ eng.usm.my
Aytac Guven Associate Professor, Dept. of Civil Engineering, Univ. of Gaziantep, Gaziantep 27310, Turkey. E-mail:
[email protected]
ðFr −0.224Þ 4 L=b
ð5aÞ
þ Fr − d50 =b − 0.736 y=b 2
32 þ ðFr − 0.224Þ5 ð5bÞ
2 2ðd50 =bÞ T 2 ðFr − 0.224Þ
ð5cÞ
0.042 0.28 0.37 ds d b L ¼ 1.82 50 Fr0.42 σ−0.03159 y y y y
ð10Þ
T3 ¼
Aminuddin Ab Ghani
Nor Azazi Zakaria
1 þ T 3 þ L=bðy=bÞ 2
þ T 2 ðFr − 0.224Þ
March 2010, Vol. 136, No. 3, pp. 165–169.
H. Md. Azamathulla, M.ASCE
−1 T 22 y=b
2T 2 − 0.73 ðy=bÞðFr − 0.224Þ
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
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: 2T 1 −1 ds 2 − d50 =b − 1 0.5 ¼ ð4Þ y y=b where
Method
Coefficient of Root-mean determination square error (RMSE) (R2 )
Average error (AE %)
Average absolute deviation (δ)
Predictions to observed ds =y for testing set GP 0.845 0.037 −11.450 RBF 0.691 0.105 −59.450 Eq. 10 (authors) 0.745 0.345 −15.673 Eq. 11 (HEC-18) 0.425 0.271 −174.055 Predictions GP RBF Eq. 10 (authors) Eq. 11 (HEC-18)
to observed ds =y > 0.2 for testing set 0.789 0.076 8.567 0.467 0.167 14.781 0.534 0.105 12.56 0.119 0.380 −97.060
23.345 43.513 29.567 113.497 17.453 27.987 23.786 81.874
Note: RBF = radial basis function; HEC-18 = pier scour equation recommended by the Federal Highway Administration’s Hydraulic Engineering Circular.
1020 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / SEPTEMBER 2013
J. Hydraul. Eng. 2013.139:1020-1020.
