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In the testing stage, it can be seen that coefficient correlation obtained by Equations (16)–(20) (R = 0.944) demonstrated relatively better prediction than those yielded by EPR (R = 0.909) and GEP (R = 0.925). Also, the MT approach provided more accurate results with RMSE = 0.241, MAE = 0.178, and RAE = 0.089 compared with EPR (RMSE = 0.310, MAE = 0.243, and RAE = 0.167) and GEP (RMSE = 0.286, MAE = 0.232, and RAE = 0.105) techniques. In accordance with quantitative comparisons of performances in Table 5, it can be generally said that the proposed equations given by the MT approach are the most efficient model to provide the scour depth around bridge piers with debris accumulations. The scatter plots between the predicted and observed scour depths for the testing of the proposed models are presented in Figure 7.
Table 5

Results of performances for proposed models and empirical equations

ModelTraining stage
RRMSERSEMAERAE
EPR 0.959 0.318 0.0789 0.253 0.405 
MT 0.898 0.533 0.477 0.295 0.477 
GEP 0.86 0.578 0.295 0.336 0.512 
 Testing stage
RRMSERSEMAERAE
EPR 0.909 0.310 0.289 0.243 0.167 
MT 0.944 0.241 0.137 0.178 0.089 
GEP 0.925 0.286 0.136 0.232 0.105 
Equation (9) 0.832 0.513 0.516 0.446 1.43 
Equation (10) 0.832 0.554 0.602 0.489 3.12 
Equation (11) 0.738 0.713 0.995 0.605 1.32 
Equation (12) 0.650 0.669 0.878 0.579 1.74 
ModelTraining stage
RRMSERSEMAERAE
EPR 0.959 0.318 0.0789 0.253 0.405 
MT 0.898 0.533 0.477 0.295 0.477 
GEP 0.86 0.578 0.295 0.336 0.512 
 Testing stage
RRMSERSEMAERAE
EPR 0.909 0.310 0.289 0.243 0.167 
MT 0.944 0.241 0.137 0.178 0.089 
GEP 0.925 0.286 0.136 0.232 0.105 
Equation (9) 0.832 0.513 0.516 0.446 1.43 
Equation (10) 0.832 0.554 0.602 0.489 3.12 
Equation (11) 0.738 0.713 0.995 0.605 1.32 
Equation (12) 0.650 0.669 0.878 0.579 1.74 
Figure 7

Scatter plot of observed and predicted scour depth in live-bed condition for testing of the proposed models.

Figure 7

Scatter plot of observed and predicted scour depth in live-bed condition for testing of the proposed models.

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