Weirs are a commonly used system to adjust water surface level and to control the flow in canals and hydraulic structures. Labyrinth weirs are a type of weirs that can pass through a certain amount of flow which has a lower upstream water level than the linear weirs, by increasing the effective length. In the present study, the performance of multilayer perceptron (MLP) networks, radial basis function networks and support vector machines with different kernel functions were investigated in order to estimate the discharge coefficient (C_d) of labyrinth weirs with quarter-round crests. For this purpose, 454 laboratory data were used. The non-dimensional parameters of L/W, a, W/P, and H_t/P were considered as the input, and the non-dimensional parameter of C_d was regarded as the output in the models. In comparison with the other models, the performance of the MLP model with RMSE, R, and DC of 0.019, 0.985, and 0.971, respectively, was more acceptable and closer to the experimental data. Also, the data density plot and the violin plot showed that the dispersion and distribution of the probability of the estimated data to the MLP model with the data obtained from the laboratory have a very close and similar adaptation.

Gates in dams and irrigation canals have been used for the purpose of controlling discharge or water surface regulation. To compute the discharge under a gate, discharge coefficient (C_d) should be first determined precisely. From a novel point of view, this study investigates the effect of sill shape under the vertical sluice gate on C_d using four artificial intelligence methods, which are used to estimate C_d, (i) random forest (RF), (ii) deep learning (DL), (iii) gradient boosting machine (GBM), and (iv) generalized linear model (GLM). A sluice gate along with twelve different forms of sills was fabricated and tested in the University of Tabriz, Iran. Different flow rates were considered in the hydraulic laboratory with four gate openings. As a result, a total of 180 runs could be tested. The results showed that the installation of sill under the vertical gate has a positive effect on flow discharge. Sill shapes can be characterized by their hydraulic radius (R_s). Sensitivity analysis among the dimensionless parameters proved that R_s/G (the ratio of the hydraulic radius of the sills with respect to the gate opening) has a significant role in the determination of C_d. A semi-circular sill shape has a more positive effect on the increase of C_d than the other shapes.

This study investigates experimentally and numerically the effects of sills with different geometric specifications at various positions on the hydraulic characteristics of flow through sluice gates. The simulation results showed that the RNG turbulence model’s statistical indicators yield high accuracy compared to the k-ε, k-ω, and LES turbulence models. The discharge coefficient (C_d) has an inverse relationship with gate opening. Regarding sill state, the discharge coefficient is higher than no-sill state. In the case of non-suppressed sills, the C_d decreases compared to the smaller openings as the opening of the gate changes. The results showed that the C_d with a sill in the tangent position upstream of the gate is higher than the downstream tangent and below situations. Increasing the sill length leads to an increase in flow shear stress and consequently a decrease in C_d. The C_d of gates with different sill thicknesses is always higher than the no-sill state, but due to the constant ratio of the fluid depth above the sill to the gate opening, the C_d increases to a certain extent and then decreases with increasing sill thickness.

In the present study, the performance of the support vector machine for estimating vertical drop hydraulic parameters in the presence of dual horizontal screens has been investigated. For this purpose, 120 different laboratory data were used to estimate three parameters of the drop: the relative length, the downstream relative depth, and the residual relative energy in the support vector machine. For each parameter, 12 models were analyzed by using a support vector machine. The performance of the models was evaluated with statistical criteria (R2, DC, and RMSE) and the best model was introduced for each of the parameters. The evaluation criteria for the relative length of the vertical drop equipped with dual horizontal screens for the testing stage are R2 = 0.992, DC = 0.981 and RMSE = 0.050. Also, the values of the downstream relative depth evaluation indicators for the testing stage are R2 = 0.9866, DC = 0.980 and, RMSE = 0.0064. For the residual relative energy parameter, the values of the residual relative energy evaluation indicators are R2 = 0.9949, DC = 0.9853 and RMSE = 0.0056. The results showed the capacity for this approach to predict the hydraulic performance of these systems with accuracy.