Skip to Main Content
The obtained results from SVM models for predicting the length of hydraulic jump in three different sudden diverging stilling basins are indicated in Table 6 and Figure 7. The superior performance was obtained for the model L(II) in which the basin with a central sill was used and input parameters were F1, (h₂h₁)/h₁. Based on the results of the symmetric basin with negative step demonstrated in Table 6, the model L(IV) with input parameters F1, S/h1 was more accurate than the other models, while for the case of the asymmetric basin the model L(II) was superior. According to the obtained results from the models L(I), L(III) and L(IV), it could be inferred that for modeling the length of hydraulic jump in diverging basins, adding parameters h2/h1 and S/h1 as an input parameter caused an increment in model efficiency. However, the results of the model L(II), as the superior model, indicated that parameter (h₂h₁)/h₁ was more effective than parameters h2/h1 and S/h1 in improving the model accuracy. It can be stated that the developed models for a basin with central sill, in predicting of hydraulic jump length, performed more successfully than the two other cases. The scatter plots of observed and predicted relative length of hydraulic jump for the superior model of each case are shown in Figure 7.
Table 6

Statistical parameters of the SVM models for relative length of hydraulic jump

ConditionSVM modelsOptimal parameters
Performance criteria
Train
Test
cɛγRDCRMSERDCRMSE
Basin without appurtenances 
 Sym channel L(I) 10 0.100 0.903 0.812 0.072 0.855 0.720 0.090 
L(II) 10 0.010 5 0.908 0.819 0.069 0.856 0.722 0.088 
L(III) 10 0.010 0.907 0.818 0.071 0.855 0.721 0.089 
Basin with negative step 
 Sym channel L(I) 10 0.001 0.895 0.798 0.079 0.884 0.763 0.091 
L(II) 10 0.001 0.929 0.857 0.069 0.912 0.827 0.077 
L(III) 8.0 0.001 0.925 0.850 0.070 0.910 0.827 0.077 
L(IV) 10 0.100 6 0.935 0.877 0.065 0.930 0.848 0.065 
 Asym channel L(I) 8.0 0.100 0.930 0.861 0.057 0.920 0.845 0.066 
L(II) 10 0.100 4 0.956 0.912 0.048 0.921 0.846 0.061 
L(III) 8.0 0.001 0.922 0.849 0.065 0.892 0.820 0.078 
L(IV) 10 0.001 0.930 0.859 0.058 0.920 0.845 0.065 
L(V) 8.0 0.100 0.907 0.820 0.067 0.857 0.734 0.091 
Basin with central sill 
 Sym channel L(I) 10 0.100 0.935 0.872 0.055 0.898 0.804 0.083 
L(II) 10 0.001 2 0.958 0.915 0.035 0.930 0.860 0.048 
L(III) 10 0.100 0.936 0.879 0.052 0.921 0.833 0.073 
L(IV) 10 0.001 0.932 0.867 0.056 0.923 0.848 0.064 
L(V) 10 0.100 0.921 0.840 0.061 0.882 0.763 0.089 
ConditionSVM modelsOptimal parameters
Performance criteria
Train
Test
cɛγRDCRMSERDCRMSE
Basin without appurtenances 
 Sym channel L(I) 10 0.100 0.903 0.812 0.072 0.855 0.720 0.090 
L(II) 10 0.010 5 0.908 0.819 0.069 0.856 0.722 0.088 
L(III) 10 0.010 0.907 0.818 0.071 0.855 0.721 0.089 
Basin with negative step 
 Sym channel L(I) 10 0.001 0.895 0.798 0.079 0.884 0.763 0.091 
L(II) 10 0.001 0.929 0.857 0.069 0.912 0.827 0.077 
L(III) 8.0 0.001 0.925 0.850 0.070 0.910 0.827 0.077 
L(IV) 10 0.100 6 0.935 0.877 0.065 0.930 0.848 0.065 
 Asym channel L(I) 8.0 0.100 0.930 0.861 0.057 0.920 0.845 0.066 
L(II) 10 0.100 4 0.956 0.912 0.048 0.921 0.846 0.061 
L(III) 8.0 0.001 0.922 0.849 0.065 0.892 0.820 0.078 
L(IV) 10 0.001 0.930 0.859 0.058 0.920 0.845 0.065 
L(V) 8.0 0.100 0.907 0.820 0.067 0.857 0.734 0.091 
Basin with central sill 
 Sym channel L(I) 10 0.100 0.935 0.872 0.055 0.898 0.804 0.083 
L(II) 10 0.001 2 0.958 0.915 0.035 0.930 0.860 0.048 
L(III) 10 0.100 0.936 0.879 0.052 0.921 0.833 0.073 
L(IV) 10 0.001 0.932 0.867 0.056 0.923 0.848 0.064 
L(V) 10 0.100 0.921 0.840 0.061 0.882 0.763 0.089 

Bold values correspond to the superior model for each condition.

Figure 7

Comparison of observed and predicted relative length of hydraulic jump for superior model; (a) symmetric basin without appurtenances, (b) symmetric basin with negative step, (c) asymmetric basin with negative step, (d) symmetric basin with central sill.

Figure 7

Comparison of observed and predicted relative length of hydraulic jump for superior model; (a) symmetric basin without appurtenances, (b) symmetric basin with negative step, (c) asymmetric basin with negative step, (d) symmetric basin with central sill.

Close Modal

or Create an Account

Close Modal
Close Modal