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For evaluating hydraulic jump characteristics in sudden expanding channels with and without appurtenances, several models, according to the flow condition and geometry of the applied appurtenances, were developed. All of the SVM models were trained and tested to carry out the sequent depth ratio prediction in sudden diverging basins. The results of SVM models are shown in Table 5 and Figure 6. From the obtained results of statistical parameters (RMSE, R and DC) it can be stated that between the three types of basins, developed models for the case of the basin with a central sill in modeling of sequent depth ratio performed more successfully than the two other cases. In this state, the model S(II) with input parameters of F1 and h1/B led to more accurate outcome than the other models. This model also presented higher accuracy for basins without appurtenances and with negative step. A comparison between the results of the models S(I) and S(III) showed that for predicting the sequent depth ratio in diverging basins with appurtenances, using parameter S/h1 as input parameter improved the efficiency of the model. This parameter confirms the importance of the relative height of applied step and sill in sequent depth ratio estimating process in channels with appurtenances. Considering the results of the models S(I), S(II) and S(III), it could be inferred that the impact of parameter h1/B in increasing the accuracy of the model is more than that of parameter S/h1. Also, the model S(I) with only input parameter F1 showed desired accuracy. It could be stated that the applied method can successfully predict the sequence depth ratio using only the upstream flow characteristic as input data. Based on the results of Table 5, for basin with negative step, the models of the channel with asymmetric shape presented better results than symmetric basin, while for basin without appurtenances, the developed models for symmetric channel showed more accuracy. Figure 6 shows the verification between measured and estimated values for the best proposed model for all states.
Table 5

Statistical parameters of the SVM models for sequent depth ratio

Performance criteria
Optimal parameters
Train
Test
ConditionSVM modelscɛγRDCRMSERDCRMSE
Basin without appurtenances 
 Sym channel S(I) 5.0 0.10 0.958 0.916 0.044 0.955 0.911 0.043 
S(II) 6.0 0.10 4 0.977 0.952 0.034 0.945 0.882 0.049 
 Asym channel S(I) 5.0 0.10 0.880 0.771 0.068 0.874 0.754 0.097 
S(II) 5.0 0.10 5 0.959 0.918 0.041 0.933 0.854 0.075 
Basin with negative step 
 Sym channel S(I) 8.0 0.02 0.900 0.805 0.063 0.893 0.744 0.075 
S(II) 10 0.10 5 0.993 0.986 0.018 0.959 0.911 0.045 
S(III) 10 0.10 0.947 0.896 0.048 0.931 0.864 0.054 
 Asym channel S(I) 10 0.01 0.963 0.922 0.052 0.962 0.908 0.056 
S(II) 8.0 0.10 4 0.993 0.985 0.029 0.989 0.977 0.028 
S(III) 8.0 0.02 0.981 0.961 0.036 0.980 0.959 0.037 
S(IV) 10 0.01 0.960 0.920 0.054 0.951 0.910 0.056 
Basin with central sill 
 Sym channel S(I) 4.0 0.01 0.984 0.967 0.039 0.975 0.944 0.057 
S(II) 5.0 0.01 2 0.994 0.987 0.026 0.993 0.985 0.029 
S(III) 5.0 0.01 0.985 0.967 0.039 0.979 0.957 0.048 
S(IV) 2.0 0.01 0.983 0.965 0.041 0.975 0.940 0.058 
Performance criteria
Optimal parameters
Train
Test
ConditionSVM modelscɛγRDCRMSERDCRMSE
Basin without appurtenances 
 Sym channel S(I) 5.0 0.10 0.958 0.916 0.044 0.955 0.911 0.043 
S(II) 6.0 0.10 4 0.977 0.952 0.034 0.945 0.882 0.049 
 Asym channel S(I) 5.0 0.10 0.880 0.771 0.068 0.874 0.754 0.097 
S(II) 5.0 0.10 5 0.959 0.918 0.041 0.933 0.854 0.075 
Basin with negative step 
 Sym channel S(I) 8.0 0.02 0.900 0.805 0.063 0.893 0.744 0.075 
S(II) 10 0.10 5 0.993 0.986 0.018 0.959 0.911 0.045 
S(III) 10 0.10 0.947 0.896 0.048 0.931 0.864 0.054 
 Asym channel S(I) 10 0.01 0.963 0.922 0.052 0.962 0.908 0.056 
S(II) 8.0 0.10 4 0.993 0.985 0.029 0.989 0.977 0.028 
S(III) 8.0 0.02 0.981 0.961 0.036 0.980 0.959 0.037 
S(IV) 10 0.01 0.960 0.920 0.054 0.951 0.910 0.056 
Basin with central sill 
 Sym channel S(I) 4.0 0.01 0.984 0.967 0.039 0.975 0.944 0.057 
S(II) 5.0 0.01 2 0.994 0.987 0.026 0.993 0.985 0.029 
S(III) 5.0 0.01 0.985 0.967 0.039 0.979 0.957 0.048 
S(IV) 2.0 0.01 0.983 0.965 0.041 0.975 0.940 0.058 

Bold values correspond to the superior model for each condition.

Figure 6

Comparison of observed and predicted sequent depth ratio 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 6

Comparison of observed and predicted sequent depth ratio 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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