a. parsaei

In the present study, the flow rate in flues containing lateral semi-cylinders (SMBF) was simulated and estimated under free and submerged conditions using back vector machine models (SVM), spin multivariate adaptive regression (MARS), and multilayer artificial neural network (MLPNN) model. In free flow mode, the dimensionless parameters extracted from the dimensional analysis include the ratio of upstream flow to throat width and contraction ratio (throat width to channel width), and in the submerged state, in addition to these two parameters, the depth-to-throat width, and bottom-depth parameters upstream depth were used as input and the two-dimensional form of flow rate was used as the output of the models. The results showed that in free flow mode in the validation stage, the MARS model with statistical indices of R2 = 0.985, RMSE = 0.008, MAPE = 0.87%, and the SVM model with statistical indices of  R2 = 0.971, RMSE = 0.0012, MAPE =1.376%, and MLPNN model with statistical indices of R2 = 0.973,  RMSE = 0.011, MAPE = 1.304% have modeled and predicted the flow rate. In the submerged state, the statistical indices of the developed MARS model were R2 = 0.978, RMSE = 0.018, MAPE = 3.6%, and the statistical indices of the SVM model were R2 = 0.988, RMSE = 0.014, 2%. MAPE = 4, and the statistical indicators of the MLPNN model were R2 = 0.966, RMSE = 0.022, and MAPE = 5.7%. In the development of SVM and MLPNN models, radial kernel and hyperbolic tangent functions were used, respectively.

In this research, soft computational models including multiple adaptive spline regression model (MARS) and data group classification model (GMDH) were used to estimate the geometric dimensions of stable alluvial channels including channel surface width (w), flow depth (h), and longitudinal slope (S) and the results of the developed models were compared with the multilayer neural network (MLP) model. To develop the models, the flow rate parameters (Q), the average particle size in the floor and body (d50) as well as the shear stress (t) as input and the parameters of water surface width (w), flow depth (h), and longitudinal slope (S) were used as output parameters. Soft computing models were developed in two scenarios based on raw parameters and dimensionless form independent and dependent parameters. The results showed that the statistical characteristics in estimating w, the best performance is related to the MARS model, whose statistical indicators of accuracy in the training stage are R2 = 0.902, RMSE=1.666 and in the test phase is R2 = 0.844, RMSE=2.317. In estimating the channel depth, the performance of both GMDH and MARS models is approximately equal, both of which were developed based on the dimensionless form of flow rate as the input variable. The statistical indicators of both models in the training stage are R2 » 0.90, RMSE » 8.15 and in the test phase is R2 » 0.90, RMSE = 7.40. The best performance of the developed models in estimating the longitudinal slope of the channel was related to both MARS and GMDH models, although, in part, the accuracy of the GMDH model with statistical indicators R2 = 0.942, RMSE = 0.0011 in the training phase and R2 = 0.925, RMSE = 0.0014 in the experimental stage is more than the MARS model.