# Scouring Depth Assessment Downstream of Weirs Using Hybrid Intelligence Models
## 4 Conclusions  
In the current study, several algorithms consist of standalone ANFIS as well as four hybrid models, namely ANFIS-Cultural, ANFIS -BBO, ANFIS-IWO and ANFIS-TLBO are used to predict the maximum depth of scouring. Three input parameters consist of \(\frac{d_{0}}{\hbar_{t}}\), \(\frac{2}{\hbar_{t}}\) and \(\frac{U_{0}}{U_{C}}\), extracted from [PERSON] (1937), [PERSON] (1978) and [PERSON] (1994) experimental studies are employed to established three corresponding combinations which are noted as \(M1\) (all input parameters included), \(M2\) (all input parameters without \(\frac{2}{\hbar_{t}}\)) and \(M3\) (only \(\frac{U_{0}}{U_{C}}\) as input parameters). Several statistical indices (namely \begin{table}
\begin{tabular}{c c c} \hline \hline
**Technique** & _RMSE_ & _MAE_ \\ \hline ANFIS-IWO (testing phase) & 0.14755 & 0.107 \\ [PERSON] et al. (2016). & 0.4465 & 0.3951 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison between the prediction performance achieved by the best predictive model in the present study and empirical formulas proposed by [PERSON] et al. [1]. MAE_, _RMSE_, _CC_ and _WI_) along with graphical performance evaluators (namely scatterplot, heat map, Taylor diagram and boxplot) are utilized to measure the models' prediction accuracy in both the training and testing phase. Overall, prediction outcomes show the high prediction performance of the _ANFIS_ - _IWO_\(-\)_M1_ model in both training (\(RMSE=0.111\), \(CC=0.917\)) and testing (\(RMSE=0.147\), \(CC=0.932\)) phases compared to other models. The _ANFIS_\(-\)_M1_ results (\(RMSE_{testing}=0.192\), \(CC_{testing}=0.883\)) correspond to the second rank of accuracy. The _M1_ input combination which involves all parameters is considered as the best combination, while _M3_ shows the poorest prediction performance. All graphical performance assessments also confirm the adequacy of _ANFIS_ - _IWO_\(-\)_M1_ to predict the scouring depth downstream of weirs. Additionally, the uncertainty analysis shows that the selection of input parameters with _R_\(-\)_factor_ index of 1.72 has a higher impact on predicted results than choosing of the predictive model with _R_\(-\)_factor_ of 1.15. In conclusion, the proposed ANFIS model hybrid with _IWO_ optimization algorithms demonstrates a strong predictive model to measure the maximum scour depth. To conduct the further investigations for scouring depth downstream of weirs, the authors propose the following insights: (i) it is possible to compare the results of optimized ANFIS models with either classic AI algorithms such as Artificial Neural Networks and Support vector Machines or novel hybrid models. (ii) The other predictive variables such as geometric standard deviation of sediment grain size (\(\sigma_{g}\)), Reynolds number (_Re_) and densimetric Froude number (_Frd_) can be included to predict the scouring depth downstream of weirs. (iii) The improvement of modelling strategy could be obtained using information theory to determine mostly correlated input variables. (iv) Assessing the scouring depth downstream of weirs in compound channels is more complicated than simple rectangular channels. The complexity is raised due to site-specific geometry, and hydraulic characteristics in compound channels. In future, similar studies can be conducted to estimate the scouring depth downstream of weirs in compound channels using artifice intelligence models.