Modeling bed-load discharge in sewer pipes with different boundary conditions using Gene Expression Programming (GEP)

Accurate prediction of the sediment load is one of the important issues to water engineering. Due to complexity of sedimentation phenomenon and influence of various parameters on estimation of sediment transport rate, determining the governing equations are difficult, and classical mathematical models are not sufficiently accurate in this regard. In the present study the applicability of Gene-Expression Programming (GEP) for modeling bed load discharge in sewer pipes with different boundary conditions was assessed (i.e. fixed and movable beds). Therefore different input models based on theoretical concepts were defined for each boundary condition. In order to develop the models, under two scenarios, different input combinations were considered, first scenario (Scenario1) which uses only hydraulic characteristics and second scenario (Scenario2) which uses both hydraulic and sediment characteristics as inputs for modeling bedload discharge. The sewer pipes experimental data available in the literature were applied for training and testing the employed GEP. For evaluating the efficiency of the models three statistical indexes which called: Determination Coefficient (DC), Correlation Coefficient (R) and Root Mean Square Errors (RSME) were used. Then the accuracy and capability of several available bed load formulas such as Ackers, Neilsen, May, Mayerle and Laursen were investigated and compared with GEP- best modes in each boundary. Also with considering this point that may there is no information about bed boundary condition and for evaluating the applicability of applied technique for a wide range of data; all data series of sediment transport were combined. Then, for predicting Cv, as the dependent variable, several models of Scenarioa 2 analyzed for the combined data. The obtained results confirmed the efficiency of Gene-Expression Programming method for estimation sediment discharge in sewage pipes, and proved this method superior to the semi- theoretical relationships. According to the results it was found that in scenario 1, for all of the cases, model (IV) with input parameters of Fr and y0/D presented better performance than the others models, however it was observed that Scenario 2, which took advantage of both hydraulic and sediment parameters as inputs for modeling sediment discharge in sewer pipes performed more successful than Scenario1 which used only combinations of hydraulic parameters as input variables for models. Comparison between the results of separate data sets and combined data set revealed that analyzing data sets separately led to more accurate outcome. According to the results from fixed beds, it was found that adding Frm and d50/y as an input parameter increased the accuracy of the models. For both smooth and rough beds, the model with input parameters λs, Frm, Dgr, d50/y presented better results from the RMSE, R, and DC viewpoints (i.e. highest R and DC and lowest RMSE). For movable beds condition in the two cases of separate dunes and continuous loos bedform, the model with input parameters of ys/D, Frm, Wb/y0 showed more accuracy. This model showed the influence of flow depth and width and depth of movable bed in estimating of bedload transport in sewer pipes. For loose beds Frm has dominant role than other parameters.