The Effect of Hydraulic Partitioning on Prediction the Rate of Bed Load Transport in Gravel-bed Rivers using Support Vector Machine

Evaluation and prediction of sediment transport and associated processes have been one of the main issues of hydraulic and river engineers. There are some variables which affect the amount of bed load of a stream or river which may carry such as hydraulic, hydrological and sediment parameters caused the complexity of sediment transport phenomenon. Furthermore, gravel-bed rivers have features that distinguish them from sand-bed rivers and caused problems and challenges in their analysis. Considering the influential parameters to predict bed load transport rate in 20 gravel-bed rivers, in this study, the accuracy of support vector machine was investigated in different intervals of hydraulic and sediment parameters. The obtained results confirm the superiority of the model with input parameters of Froude number, the ratio of average velocity to shear velocity (), the ratio of hydraulic radius to the median grain diameter () and shields number () with Nash-Sutcliffe efficiency (NSE) of 0.806. In a second step, the data in different intervals are categorized according to the hydraulic and sediment characteristics using trial and error. Obtained results show that prediction of bed load transport with the median diameters of sediment particles (D₅₀) ranging from 1 to 1.4 mm led to significant outcomes of NSE= 0.952, as well as flow condition in the intervals of 0.65 and 0.75 of Froude number generate better predictive ability with NSE= 0.925. Besides, it is found that hydraulic conditions govern the rivers flow in specific intervals of Shear Reynolds number and bed slope of channel led to better predictive ability of bed load transport rate in gravel-bed rivers.
Extended Abstract
1-Introduction
Evaluation and prediction of sediment transport and associated processes have been one of the main issues of hydraulic and river engineers. Determination of the bed load transport rate in natural rivers is depended on different factors such as hydraulic, hydrological and sediment parameters. Prediction ability of bed load transport is variable due to complexities that governs fluvial sediment transport in different flow conditions. In recent years, intelligent methods have been introduced as a reliable alternative of classic formulas and have been widely used to predict sediment transport rate in rivers. Since intelligent methods are applied for various rivers with different flow conditions, it is necessary to evaluate the accuracy of these methods in quantification of bed load under varied hydraulic conditions. According to this, Support vector machine (SVM) was used as a common kernel based approach to determine influential parameters to predict bed load transport in gravel-bed rivers. In a second step, the applicability of SVM with best input combination is investigated in intervals of different parameters based on hydraulic and sediment properties.
2-Materials and Methods
In this study, 966 data points from 20 gravel-bed rivers located in USA were used to predict the bed load transport rate. This dataset covers a diverse set of streams and rivers with different topographic, morphologic, hydraulic and sedimentological characteristics. 75 percent of each river data were selected for training the models and remaining 25 percent of data were used to validate models. The RBF kernel function was used as core tool of support vector machine for all proposed models. After optimization of parameters for kernel function, the bed load transport rate was predicted and obtained results from different models were investigated in terms of correlation coefficient (R), Root mean square error (RMSE) and Nash-Sutcliffe (NSE). in order to assess the capability of SVM in quantification of bed load under varied hydraulic conditions, Froude number (Fr) and bed slope of channel (S₀) were selected as a parameters describing the hydraulic conditions and median diameter of the sediment particles (D₅₀) and shear Reynolds number (Re_*) were considered as a representative of sediment characteristic. Bed load transport rate was predicted in various intervals of mentioned parameters and obtained results were studied.
3-Results and Discussion
The comparison of developed models confirmed the superiority of model (4) in quantification of bed load transport rate. Model including parameters Froude number, ratio of average velocity to shear velocity (V/U_*), the ratio of bed hydraulic radius to median diameter (R/D₅₀) and Shields number (θ) with the highest level of R (0.898), NSE (0.806) and lowest value of RMSE (0.029) for test series showed more precise results. Performing the sensitivity analysis demonstrated the remarkable impact of parameter V/U_* in modeling process. Furthermore, obtained results showed that prediction of bed load transport with the median diameters of sediment particles (D₅₀) ranging from 1 to 1.4 mm led to significant outcomes of NSE= 0.952, as well as flow condition in the intervals of 0.65 and 0.75 of Froude number generated better predictive ability with NSE= 0.925. According to prediction results of bed load transport in proposed intervals of Froude number, it can be seen that small variations in values of Froude number led to notable effects on accuracy of prediction process. Additionally, stable conditions in transportation of bed loaded with finer particles (median diameter of particles less than 2 mm) caused better predictive capability in compare of transportation of bed load with coarse material. Prediction of bed load with shear Reynolds number between 100-300 yielded better accuracy while changes in river tendency for transportation of bed load with coarser material in shear Reynolds number from 300 to 450 decreased modelling accuracy dramatically.  Despite the fact that sediment transport predictions in steep channels are further complicated, the obtained results of SVM approach demonstrated a good performance in prediction of bed load of rivers with relatively high bed slope ranging from 0.0048 to 0.0174.
4-Conclusion
In this paper, it was attempted to depict the influence of various hydraulic conditions on prediction process of bed load transport rate in gravel-bed rivers. Results revealed that complicated nature of sediment transport under different flow characteristic such as different Froude number and bed slope of channel can even reduce the accuracy of intelligent methods in predicting tasks. Differences between the characteristic of rivers cause different effective parameter in bed load transport at various flow conditions. Therefore, further researches may be carried out to investigate the effective parameters for predicting bed load in different hydraulic conditions using intelligent methods.