Prediction Of Discharge Coefficient Research Articles

Estimating Discharge Coefficient of PK-Weir Under Subcritical Conditions Based on High-Accuracy Machine Learning Approaches

This article adopts four high-accuracy machine learning-based approaches for the prediction of discharge coefficient of a Piano Key Weir (PK-weir) under subcritical condition located on the straight open-channel flume. These approaches consist of least-square support vector machine (LS-SVM), extreme learning machine (ELM), Bayesian ELM (BELM), and logistic regression (LR). For this purpose, 70 laboratory test results are used for determining discharge coefficient of PK-weir for a wide range of discharge values. Root-mean-squared error (RMSE), Nash–Sutcliffe model efficiency coefficient (NSE), the coefficient of correlation (R), threshold statistics (TS), and scatter index (SI) are used for comparing the performance of the models. The simulation results indicate that an improvement in predictive accuracy could be achieved by the ELM approach in comparison with LS-SVM and LR (RMSE of 0.016 and NSE of 0.986), while the BELM model’s generalization capacity enhanced, with RMSE of 0.011 and NSE of 0.989 in validation dataset. The results show that BELM is a simple and efficient algorithm which exhibits good performance; hence, it can be recommended for estimating discharge coefficient.

CFD Based Prediction of Discharge Coefficient of Sonic Nozzle with Surface Roughness

Due to its simplicity and accuracy, sonic nozzle is widely used in gas flow measurement, gas flow meter calibration standard, and flow control. The nozzle obtains mass flow rate by measuring temperature and pressure in the inlet during choked flow condition and calculate the flow rate using the one-dimensional isentropic flow equation multiplied by a discharge coefficient, which takes into account multiple non-isentropic effects, which causes the reduction in mass flow. Proper determination of discharge coefficient is crucial to ensure the accuracy of mass flow measurement by the nozzle. Available analytical solution for the prediction of discharge coefficient assumes that the nozzle wall is hydraulically smooth which causes disagreement with experimental results. In this paper, the discharge coefficient of sonic nozzle is determined using computational fluid dynamics method by taking into account the roughness of the wall. It is found that the result shows better agreement with the experiment data compared to the analytical result.

Discussion of “Combination of Computational Fluid Dynamics, Adaptive Neuro-Fuzzy Inference System, and Genetic Algorithm for Predicting Discharge Coefficient of Rectangular Side Orifices” by Hamed Azimi, Saeid Shabanlou, Isa Ebtehaj, Hossein Bonakdari, and Saeid Kardar

Discussion of “Combination of Computational Fluid Dynamics, Adaptive Neuro-Fuzzy Inference System, and Genetic Algorithm for Predicting Discharge Coefficient of Rectangular Side Orifices” by Hamed Azimi, Saeid Shabanlou, Isa Ebtehaj, Hossein Bonakdari, and Saeid Kardar

Closure to “Combination of Computational Fluid Dynamics, Adaptive Neuro-Fuzzy Inference System, and Genetic Algorithm for Predicting Discharge Coefficient of Rectangular Side Orifices” by Hamed Azimi, Saeid Shabanlou, Isa Ebtehaj, Hossein Bonakdari, and Saeid Kardar

Closure to “Combination of Computational Fluid Dynamics, Adaptive Neuro-Fuzzy Inference System, and Genetic Algorithm for Predicting Discharge Coefficient of Rectangular Side Orifices” by Hamed Azimi, Saeid Shabanlou, Isa Ebtehaj, Hossein Bonakdari, and Saeid Kardar

Development of more accurate discharge coefficient prediction equations for rectangular side weirs using adaptive neuro-fuzzy inference system and generalized group method of data handling

A rectangular side weir is a hydraulic structure commonly utilized all around the world in urban stormwater and wastewater sewer networks and in irrigation drainage systems to deviate excessive flow passing through the main channel. In this study, a genetic algorithm (GA) is employed to identify the best selection of adaptive neuro-fuzzy inference system (ANFIS) membership functions and the evolutionary design of a generalized group method of data handling (GMDH) structure for prediction of the side weir discharge coefficient. Moreover, the Singular Value Decomposition (SVD) method is applied to calculate the linear parameters of the ANFIS results and linear coefficient vectors in GMDH (ANFIS-GA/SVD and GMDH-GA/SVD). The side weir dimensionless length, Froude number, the ratio of weir height to upstream flow depth, and the ratio of weir length to upstream flow depth serve as inputs to the ANFIS-GA/SVD and GMDH-GA/SVD models to forecast the discharge coefficient. We compared the results of these multi-objective methods with the single-objective methods and found that the multi-objective methods are superior regarding accuracy. Sensitivity analysis is also carried out to determine the impact of each parameter on discharge coefficient estimation. ANFIS-GA/SVD outperformed ANFIS-GA, GMDH-GA/SVD, GMDH-GA and existing regression-based and machine learning-based equations. The uncertainty analysis is also carried out to assess the quantitative performance of all models. The results indicate that the uncertainty width for the best model (ANFIS-GA/SVD) is ±0.0067.

Modeling discharge coefficient of normal and inverted orientation labyrinth weirs using machine learning techniques

A labyrinth weir is a polygonal overflow weir that is characterized by its hydraulic performance and distinct geometric shape (triangular, trapezoidal or rectangular cycles). The present study provides new knowledge and design information on the performance and operation of adaptive neuro-fuzzy inference system (ANFIS) and gene expression programming (GEP) techniques for predicting discharge coefficient of labyrinth weirs in a flume. Discharge coefficient, Cd, was considered as a function of headwater ratio, upstream Froude number, magnification ratio, sidewall angle, apex ratio, and cycle width ratio (dimensionless parameters). The records obtained through 300 laboratory data sets were used to determine the Cd of labyrinth weirs. The results showed that the best GEP model determined the Cd values of the normal and inverted orientation labyrinth weir with a RMSE of 0.0139, 0.590, DC of 0.977, 0.852 and R of 0.996, 0.923, respectively by using the four dimensionless parameters of Fr, HT/P, Lc/W and A/w as input variables. The best ANFIS model determined the Cd value of the normal orientation labyrinth weir by using all six dimensionless parameters (RMSE = 0.0110, DC = 0.964, R = 0.987) and inverted orientation labyrinth weir by using three dimensionless parameters of HT/P, α, and w/p as input variables (RMSE = 0.0290, DC = 0.952, R = 0.987). The results of sensitivity analysis showed that Fr in the GEP model and Fr and HT/P in the ANFIS model are the most effective variables for determining Cd for normal and inverted orientation labyrinth weirs, respectively. It was found that when low headwater ratios were eliminated from analysis, performance accuracy of the models was improved.

Predication of discharge coefficient of cylindrical weir-gate using adaptive neuro fuzzy inference systems (ANFIS)

Settlement of sediments behind weirs and accumulation of materials floating on water behind gates decreases the performance of these structures. Weir-gate is a combination of weir and gate structures which solves them Infirmities. Proposing a circular shape for crest of weirs to improve their performance, investigators have proposed cylindrical shape to improve the performance of weir-gate structure and call it cylindrical weir-gate. In this research, discharge coefficient of weir-gate was predicated using adaptive neuro fuzzy inference systems (ANFIS). To compare the performance of ANFIS with other types of soft computing techniques, multilayer perceptron neural network (MLP) was prepared as well. Results of MLP and ANFIS showed that both models have high ability for modeling and predicting discharge coefficient; however, ANFIS is a bit more accurate. The sensitivity analysis of MLP and ANFIS showed that Froude number of flow at upstream of weir and ratio of gate opening height to the diameter of weir are the most effective parameters on discharge coefficient.

Predicting discharge coefficient of triangular labyrinth weir using Support Vector Regression, Support Vector Regression-firefly, Response Surface Methodology and Principal Component Analysis

Weirs are hydraulic structures which conduct the most powerful flow with large overflow. Discharge flow predication is based on capacity discharge designation by designer. In this paper, the discharge capacity in triangular labyrinth side-weirs is computed by using new techniques with high precision. The four employed techniques for computation of discharge capacity are: Support Vector Regression (SVR), Support Vector Regression–Firefly (SVR- Firefly), Response Surface Methodology (RSM) and Principal Component Analysis (PCA). A comparison between the computed discharge capacity and empirical results is considered in this paper. Determination coefficient (R2), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), SI and δ are five statistical indicators which help us to measure the precision of the designed models. The statistical indices indicated that the SVR-Firefly model has the highest ability among the models for simulation, with average MAPE=0.49%, R2=0.991 and RMSE=0.0035. Like the results achieved by the SVR-Firefly, comparatively good results were obtained by both PCA and SVR models. The SVR model suggested the average MAPE value near 1.073 in the training mode under the most unfavorable conditions. The MAPE value equal to 1.23 was also obtained in the test mode. This proves that the value of error rate is tolerable.

Predicting discharge coefficient of triangular labyrinth weir using extreme learning machine, artificial neural network and genetic programming

Weirs are a type of hydraulic structure used to direct and transfer water flows in the canals and overflows in the dams. The important index in computing flow discharge over the weir is discharge coefficient (Cd). The aim of this study is accurate determination of the Cd in triangular labyrinth side weirs by applying three intelligence models [i.e., artificial neural network (ANN), genetic programming (GP) and extreme learning machine (ELM)]. The calculated discharge coefficients were then compared with some experimental results. In order to examine the accuracy of Cd predictions by ANN, GP and ELM methods, five statistical indices including coefficient of determination (R2), root-mean-square error (RMSE), mean absolute percentage error (MAPE), SI and δ have been used. Results showed that R2 values in the ELM, ANN and GP methods were 0.993, 0.886 and 0.884, respectively, at training stage and 0.971, 0.965 and 0.963, respectively, at test stage. The ELM method, having MAPE, RMSE, SI and δ values of 0.81, 0.0059, 0.0082 and 0.81, respectively, at the training stage and 0.89, 0.0063, 0.0089 and 0.88, respectively, at the test stage, was superior to ANN and GP methods. The ANN model ranked next to the ELM model.

Prediction of discharge coefficient of side weir using adaptive neuro-fuzzy inference system

Predicting the discharge coefficient of the hydraulic structures is one of the main subjects related to the hydro-system management. Weirs are the common hydraulic structure widely used in the water engineering projects. Side weir is the common type of hydraulic structure used in water engineering projects. Principal component analysis of the affective parameters on the side weir discharge coefficient leads to develop optimal structure for the empirical formulas and artificial intelligent models. In this paper, the principal component analysis (PCA) technique was used to define the most important affective parameters on the discharge coefficient of side weir (\({\text{Cd}}_{\text{sw}}\)). The result of the PCA showed that the Froude number and ratio of the weir height to the upstream flow depth (P/h1) are the most influential parameters affecting the \({\text{Cd}}_{\text{sw}}\). Developing the adaptive neuro-fuzzy inference system (ANFIS) based on the PCA result showed that the optimal ANFIS structure is related to consider the five and four Gaussian membership function for the Froude number and P/h1 parameters, respectively. The correlation coefficient of the ANFIS model during the training and testing stage was found to be 0.96 and 0.86 correspondingly.

Predictive modeling the side weir discharge coefficient using neural network

Weirs are common structures that are widely used in the almost water engineering projects such as hydropower systems, irrigation and drainage networks along with sewage networks. A side weir has many possible uses in hydraulic engineering and has been investigated as an important structure in hydro systems, as well. In this paper, predicting the discharge coefficient of side weirs ( $$Cd_{sw}$$ ) was considered using the empirical formulas, multilayer perceptron (MLP) and radial basis function (RBF) neural network as delegate of artificial neural network models. The results indicate that Emiroglu formula by correlation coefficient of (R2 = 0.65) and root mean square error of (RMSE = 0.03) is the accurate one among the empirical formulas. Evaluating the performance of the RBF model with ten neurons in the hidden layer involving error indices of (R2 = 0.71 and RMSE = 0.08) showed that this model was a bit better than Emiroglu formula. The structure of MLP model was considered as similar to RBF model whereas the tangent sigmoid was used instead to the radial basis function. The results of MLP model showed that this model with R2 = 0.89 and RMSE = 0.067 had suitable performance for predicting discharge coefficient. Performance of MLP was more accurate compared to RBF model.

Improved side weir discharge coefficient modeling by adaptive neuro-fuzzy methodology

In this article, the accuracy of a soft computing technique is evaluated in terms of discharge coefficient prediction of an improved triangular side weir. The process includes simulating the discharge coefficient with the Adaptive Neuro-Fuzzy Inference System (ANFIS). Matlab software is used for ANFIS modeling. To identify the most appropriate input variables, eight different input combinations with various numbers of inputs are examined. The performance of the proposed system is confirmed by comparing the ANFIS and experimental results for the testing dataset. The performance evaluation demonstrates that the ANFIS model with five inputs (Root Mean Square Error (RMSE) of 0.014) is more accurate than the ANFIS model with one input (RMSE = 0.088). The ANFIS model results are also compared with the results obtained from previous regression and soft computing studies.

Prediction of side weir discharge coefficient by support vector machine technique

Side weirs have many possible applications in the field of hydraulic engineering. They are also considered an important structure in hydro systems. In this study, the support vector machine (SVM) technique was employed to predict the side weir discharge coefficient. The performance of SVM was compared with other types of soft computing techniques such as artificial neural networks (ANN) and adaptive neuro fuzzy inference systems (ANFIS). While ANN and ANFIS models provided a good prediction performance, the SVM model with a radial basis function kernel function outperforms them. The best SVM model was developed with a gamma coefficient and epsilon of 15 and 0.3, respectively. The SVM yielded a coefficient of determination (R2) equal to 0.96 and 0.93 for the training and testing data. Sensitivity analyses of the ANN, ANFIS and SVM models showed that the Froude number and ratio of weir length to the flow depth upstream of the weir are the most effective parameters for the prediction of the discharge coefficient.

Adaptive neuro-fuzzy inference system multi-objective optimization using the genetic algorithm/singular value decomposition method for modelling the discharge coefficient in rectangular sharp-crested side weirs

In the present article, the adaptive neuro-fuzzy inference system (ANFIS) is employed to model the discharge coefficient in rectangular sharp-crested side weirs. The genetic algorithm (GA) is used for the optimum selection of membership functions, while the singular value decomposition (SVD) method helps in computing the linear parameters of the ANFIS results section (GA/SVD-ANFIS). The effect of each dimensionless parameter on discharge coefficient prediction is examined in five different models to conduct sensitivity analysis by applying the above-mentioned dimensionless parameters. Two different sets of experimental data are utilized to examine the models and obtain the best model. The study results indicate that the model designed through GA/SVD-ANFIS predicts the discharge coefficient with a good level of accuracy (mean absolute percentage error = 3.362 and root mean square error = 0.027). Moreover, comparing this method with existing equations and the multi-layer perceptron–artificial neural network (MLP-ANN) indicates that the GA/SVD-ANFIS method has superior performance in simulating the discharge coefficient of side weirs.

The Effect of Predicting Discharge Coefficient by Neural Network on Increasing the Numerical Modeling Accuracy of Flow Over Side Weir

Prediction and modeling of hydraulic phenomenon is an important part of hydraulic engineering activities. One of the applications of prediction and modeling is estimating the discharge coefficient for hydraulic structures. Side weirs are widely used for allocating and removing excess flow in water engineering projects. The governing equation on side weir hydraulic characteristics is spatially varied flow (SVF). Computer modeling of hydraulic characteristics this structure includes the calculation of water surface profiles and estimating the discharge coefficient (Cdsw). The numerical method was used to calculate the water surface profile and there are several ways to estimate the Cdsw, such as experimental formulas and computational intelligence techniques. In this paper, the Fourth Runge Kutta method is used for numerical solution of SVF and firstly to estimate Cdsw, some famous empirical equations are assessed. Among the empirical formulas, the Borghei is the most accurate one. To increase the accuracy of computer modeling, the Multilayer Neural network (MLP) is developed to estimate Cdsw. The result shows that using neural network to estimate Cdswincreases the accuracy of the final model about 16 %.

Performance evaluation of two different neural network and particle swarm optimization methods for prediction of discharge capacity of modified triangular side weirs

Technical design of side weirs needs high accuracy in predicting discharge coefficient. In this study, discharge coefficient prediction performance of multi-layer perceptron neural network (MLPNN) and radial basis neural network (RBNN) were compared with linear and nonlinear particle swarm optimization (PSO) based equations. Performance evaluation of the model was done by using root mean squared error (RMSE), coefficient of determination (R2), mean absolute error (MAE), average absolute deviation (δ) and mean absolute relative error (MARE). Comparison of the results showed that both neural networks and PSO based equations could determine discharge coefficient of modified triangular side weirs with high accuracy. The RBNN with RMSE of 0.037 in test data was found to be better than MLPNN with RMSE of 0.044 and multiple linear and nonlinear PSO based equations (ML-PSO and MNL-PSO) with RMSE of 0.043 and 0.041, respectively. However, due to their simplicity, PSO based equations can be sufficient for use in practical cases.

Discharge coefficient of a broad crested side weir in an earthen channel

Side weirs are widely used to divert flows from rivers and channels. However, the hydraulic behavior of this type of weir is complex and difficult to predict accurately. Previous studies on side weirs have generally focused on side weirs in rectangular channels with a smooth bed. However, one of the applications of side weirs is in irrigation systems which have trapezoidal cross sections and significant bed roughness. The present study investigates the hydraulic behavior of a broad crested side weir in an earthen channel with a rough bed under subcritical flow. These investigations showed that the side weir discharge coefficient is influenced by four main parameters which are upstream Froude number, ratio of the main channel width to the upstream flow depth, ratio of the length of the side weir to the main channel width and ratio of side weir height to the upstream flow depth. The results showed that the discharge coefficient of the side weir gives a lower coefficient value compared to other researchers’ equations. Nearly 90 experimental tests were carried out and finally new equations are proposed for prediction of discharge coefficient of a broad crested side weir in an earthen channel under subcritical conditions which can be mainly used in common irrigation systems.

Predicting discharge coefficient of compound broad-crested weir by using genetic programming (GP) and artificial neural network (ANN) techniques

Compound broad-crested weir is a typical hydraulic structure that provides flow control and measurements at different flow depths. Compound broad-crested weir mainly consists of two sections; first, relatively small inner rectangular section for measuring low flows, and a wide rectangular section at higher flow depths. In this paper, series of laboratory experiments was performed to investigate the potential effects of length of crest in flow direction, and step height of broad-crested weir of rectangular compound cross-section on the discharge coefficient. For this purpose, 15 different physical models of broad-crested weirs with rectangular compound cross-sections were tested for a wide range of discharge values. The results of examination for computing discharge coefficient were yielded by using multiple regression equations based on the dimensional analysis. Then, the results obtained were also compared with genetic programming (GP) and artificial neural network (ANN) techniques to investigate the applicability, ability, and accuracy of these procedures. Comparison of results from the GP and ANN procedures clearly indicates that the ANN technique is less efficient in comparison with the GP algorithm, for the determination of discharge coefficient. To examine the accuracy of the results yielded from the GP and ANN procedures, two performance indicators (determination coefficient (R 2) and root mean square error (RMSE)) were used. The comparison test of results clearly shows that the implementation of GP technique sound satisfactory regarding the performance indicators (R 2 = 0.952 and RMSE = 0.065) with less deviation from the numerical values.

Discharge coefficient performance of Venturi, standard concentric orifice plate, V-cone and wedge flow meters at low Reynolds numbers

The relation between the Reynolds number and differential producer discharge coefficient was obtained through solutions to the steady, Reynolds-averaged Navier–Stokes equations. Discharge coefficients were also obtained experimentally for the purpose of validating the numerical results. The focus of the study was directed toward low Reynolds numbers commonly associated with pipeline transportation of viscous fluids, however high Reynolds number were also considered. The study indicates that, at low Reynolds numbers, the discharge coefficients decrease rapidly with decreasing Reynolds number for Venturi, V-cone, and wedge flow meters. The orifice plate meter did not follow the general trends of the other meters, but rather as the Reynolds number decreased, the discharge coefficient increased to a maximum before sharply dropping off with further decrease in the Reynolds number. The results presented herein provide an improved understanding of differential flow meters operating at low Reynolds numbers, and demonstrate the usefulness of computational fluid dynamics in predicting discharge coefficient trends at very low Reynolds numbers.

Use of artificial neural networks for prediction of discharge coefficient of triangular labyrinth side weir in curved channels

Side weirs have been extensively used in hydraulic and environmental engineering applications. The discharge coefficient of the triangular labyrinth side weirs is 1.5-4.5 times higher than that of rectangular side weirs. This study aims to estimate the discharge coefficient (Cd) of triangular labyrinth side weir in curved channel by using artificial neural networks (ANN). In this study, 7963 laboratory test results are used for determining the Cd. The performance of the ANN model is compared with multiple nonlinear and linear regression models. Root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics are used as comparing criteria for the evaluation of the models' performances. Based on the comparisons, it was found that the neural computing technique could be employed successfully in modeling discharge coefficient from the available experimental data. There were good agreements between the measured values and the values obtained using the ANN model. It was found that the ANN model with RMSE of 0.1658 in validation stage is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0.2054 and 0.2926, respectively.