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The results of SVM models for relative energy dissipation ratio are given in Table 7. According to Table 7 it can be seen that for the three cases of basins, without appurtenances, with negative step, and with central sill, the model E(II) with input parameters F1 and h1/B represented higher performance in comparison with the other models. The results of developed models for the basin with negative step and central sill revealed that using relative height of sill or step as input variables caused an increment in model efficiency. Comparison between the obtained results from the developed models for basins without appurtenances and with negative step indicated that for symmetric channels, the basin without any appurtenances presented higher accuracy. For asymmetric channels, the superior performance was obtained for the basin with negative step. However, according to Table 7, the basin with central sill, in predicting relative energy dissipation, performed more successfully than the other cases. Figure 8 shows the verification between measured and estimated values for the best SVM models for expanding channels.
Table 7

Statistical parameters of the SVM models for relative energy dissipation

ConditionSVM modelsOptimal parameters
Performance criteria
Train
Test
cɛγRDCRMSERDCRMSE
Basin without appurtenances 
 Sym channel E(I) 8.0 0.120 0.957 0.909 0.046 0.950 0.898 0.047 
E(II) 10 0.100 4 0.984 0.982 0.030 0.989 0.978 0.034 
 Asym channel E(I) 8.0 0.001 0.873 0.756 0.072 0.867 0.741 0.100 
E(II) 10 0.001 0.959 0.917 0.042 0.935 0.848 0.077 
Basin with negative step 
 Sym channel E(I) 10 0.100 0.890 0.790 0.069 0.869 0.710 0.081 
E(II) 8.0 0.001 3 0.982 0.982 0.031 0.957 0.908 0.045 
E(III) 8.0 0.001 0.974 0.972 0.035 0.945 0.945 0.049 
 Asym channel E(I) 10 0.001 0.961 0.924 0.052 0.959 0.918 0.054 
E(II) 10 0.120 8 0.989 0.984 0.027 0.976 0.981 0.032 
E(III) 5.0 0.100 0.799 0.977 0.029 0.956 0.908 0.055 
Basin with central sill 
 Sym channel E(I) 8.0 0.100 0.980 0.961 0.045 0.976 0.953 0.047 
E(II) 10 0.100 4 0.993 0.985 0.027 0.992 0.984 0.030 
E(III) 10 0.001 0.981 0.965 0.042 0.980 0.964 0.044 
ConditionSVM modelsOptimal parameters
Performance criteria
Train
Test
cɛγRDCRMSERDCRMSE
Basin without appurtenances 
 Sym channel E(I) 8.0 0.120 0.957 0.909 0.046 0.950 0.898 0.047 
E(II) 10 0.100 4 0.984 0.982 0.030 0.989 0.978 0.034 
 Asym channel E(I) 8.0 0.001 0.873 0.756 0.072 0.867 0.741 0.100 
E(II) 10 0.001 0.959 0.917 0.042 0.935 0.848 0.077 
Basin with negative step 
 Sym channel E(I) 10 0.100 0.890 0.790 0.069 0.869 0.710 0.081 
E(II) 8.0 0.001 3 0.982 0.982 0.031 0.957 0.908 0.045 
E(III) 8.0 0.001 0.974 0.972 0.035 0.945 0.945 0.049 
 Asym channel E(I) 10 0.001 0.961 0.924 0.052 0.959 0.918 0.054 
E(II) 10 0.120 8 0.989 0.984 0.027 0.976 0.981 0.032 
E(III) 5.0 0.100 0.799 0.977 0.029 0.956 0.908 0.055 
Basin with central sill 
 Sym channel E(I) 8.0 0.100 0.980 0.961 0.045 0.976 0.953 0.047 
E(II) 10 0.100 4 0.993 0.985 0.027 0.992 0.984 0.030 
E(III) 10 0.001 0.981 0.965 0.042 0.980 0.964 0.044 

Bold values correspond to the superior model for each condition.

Figure 8

Comparison of observed and predicted relative energy dissipation 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 8

Comparison of observed and predicted relative energy dissipation 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.

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