Application of genetic algorithms in the optimization of empirical relations to estimate of geometrical characteristics of the scour hole downstream of grade control structures

Grade-control structures are aimed at preventing excessive channel-bed degradation in
alluvial channels and at the outlet of a grassed waterway to stabilize the waterway outlet. The
erosive action of the weir overflow may, however, cause significant local scour downstream
and may endanger the stability of these structures. The scour process can be split up into
different time phases. In the beginning the development of scour is very fast, and eventually
an equilibrium situation is reached depending on clear water or live bed flow condition.
Appropriate design of grade-control structures requires estimate geometric characteristics
of the downstream scour. The local scour downstream of a grade-control structure located on
an alluvial bed is a very complex and dynamic phenomenon which is influenced by many
parameters. Most of these parameters are related to each other and determination of them is
difficult. The estimation of maximum scour depth is very important in planning, design and
management of hydraulic structures. Therefore, there is a great need to develop good prediction methods for geometric
characteristics of scour hole downstream of grade control structures. Some of researchers
studied scour downstream of grade-control structures and presented different empirical
equations for estimation of maximum scour depth based on experimental data. The results of
literatures show that the equation of D'Agostino and Ferro (2004) can be used as one of the
most important empirical equations to estimate the maximum scour depth.
In this study, coefficients of D'Agostino and Ferro (2004) equation to estimate of the
maximum scour depth, horizontal distance between the weir crest and the maximum scour
depth position, horizontal distance between the weir crest and sand deposition and maximum
height of sediment deposition, were optimized by applying genetic algorithm.
For this purpose, the field and laboratory data of Veronese (1937), Bormann and Julien
(1991), D’Agostino(1994), Mossa (1998), Lenzi et al. (2000), Missiaga stream (2004),
Falciai and Giacomin (1978), Some large-scale data ((Veronese 1937), Scimemi (1939),
Whittaker and Schleiss (1984)) and shahabi (2010) were used for training and validation of
the equations.
The efficiency and accuracy of each equations were examined based on statistical
Analyses such as percent error, root mean square error, mean bias error and correlation
coefficient using independent data sets of training data and were compared with the results
obtained from the equations proposed by D'Agostino and Ferro (2004).
The results show that the value of percent error, root mean square error, mean bias error
and correlation coefficient for maximum scour depth, horizontal distance between the weir
crest and the maximum scour depth position, horizontal distance between the weir crest and
sand deposition and maximum height of sediment deposition were 46.09, 11.78, 10.28 and
118.05, respectively. The corresponding values are 128.1, 27.73, 15.23 and 194.46 by using
D'Agostino and Ferro relation. The results showed that the root mean square error and mean bias error are decreased by
using proposed equations and the accuracy of obtained results by presented equations is
higher than D'Agostino and Ferro (2004) equations. So it is recommended to use the proposed
relations for assessing the characteristics of scour hole downstream of grade control
structures.