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The results of dimensionless mean bed shear stress modeling are shown is Table 2.

Different flumes with rectangular cross sections and several aspect ratios (B/h) were employed in their experiments to estimate the mean bed shear stress and wall shear stress.

Also for mean bed shear stress MAE as fitness function and F4 as mathematical function showed the best results with RMSE of 0.0185 than other GP models.

Table 5 The output program of the GP model for (a) modeling the mean wall shear stress and (b) modeling the mean bed shear stress Open image in new window.

The output program for modeling mean bed shear stress in the GP model with aspect ratios as input data, MAE as fitness function and F4 as mathematical function set is presented in Table 5.

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Two soft computing methods were extended in order to predict the mean wall and bed shear stress in open channels.

In this study, two different soft computing methods GP and GAA were extended in order to estimate mean wall and bed shear stresses in smooth rectangular channels.

The performance of the GAA and GP models in predicting mean wall and bed shear stress were evaluated using statistical comparisons of the predicted and observed outputs.

Considering the aspect ratio as input data, two different fitness functions were investigated to select the best one for modeling the mean wall and bed shear stress.

The root mean square error can be calculated by: {text{RMSE}} = sqrt {frac{{sumlimits_{i = 1}^{n} {left( {x_{ip} - x_{im} } right)^{2} } }}{n}}, (20 where x ip is the mean wall or bed shear stress predicted by the models, x im is the value of wall or bed shear stress obtained from the experimental results, and n is the number of observations.

In order to predict the mean bed and wall shear stress in smooth rectangular channels, the experimental results of Cruff (1965), Ghosh and Roy (1970), Kartha and Leutheusser (1970), Myers (1978), Knight and Macdonald (1979), Knight (1981), Noutsopoulos and Hadjipanos (1982), Knight et al. (1984) and Seckin et al. (2006) were used.

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