Discharge Coefficient Of Side Weir Research Articles

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.

Firefly optimization algorithm effect on support vector regression prediction improvement of a modified labyrinth side weir's discharge coefficient

A principal step in designing dividing hydraulic structures entails determining the side weir discharge coefficient. In this study, Firefly optimization-based Support Vector Regression (SVR-FF) is introduced and examined in terms of predicting the discharge coefficient of a modified labyrinth side weir. Ten non-dimensional parameters of various geometrical and hydraulic conditions are defined as the input parameters for the SVR-FF and the side weir discharge coefficient is defined as the output. Improvements in SVR prediction accuracy are determined by comparing SVR-FF with the traditional SVR model. The results indicate that the SVR-FF model with RMSE of 0.035 is about 10% more accurate than SVR with RMSE of 0.039. Thus, combining the Firefly optimization algorithm with SVR increases the prediction model performance.

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 Effectiveness of Overflow Improvement of Broad-Crested Side Weirs according to Installing a Hydraulic Structure

In this study, the effectiveness of overflow improvement of weir was tested by conducting hydraulic experiments at the designated spot for installment of side weir under the condition of installment of hydraulic structures such as small reservoir in mainstream. The height of the reservoir was set up as a third of that of the weir, accordingly the rate of the height of the weir and the distance of the reservoir from the weir() were 0.05, 0.025, 0.0167 each. As a result, overflows per unit width increased by 8.1%, 5.4% and 3.9% perspectively. A new discharge coefficient that adds as parameter to the existing discharge coefficient of trapezoidal broad crested side weir was suggested and the application of the new formula of discharge coefficient by comparing measured overflow with calculated overflow was identified.

Gene expression programming to predict the discharge coefficient in rectangular side weirs

In this study, gene expression programming (GEP) is employed as a new method for estimating the side weir discharge coefficient. The accuracy of existing equations in evaluating the side weir discharge coefficient is first examined. Afterward, taking into consideration the dimensionless parameters that affect the estimation of this parameter and sensitivity analysis, five different models are presented. Coefficient determination (R2), root mean square error (RMSE), mean absolute relative error (MARE), scatter index (SI) and BIAS are used for measuring the models’ performance. Two sets of experimental data are applied to evaluate the models. According to the results obtained indicate that the model with Froude number (F1), dimensionless weir length (b/B), ratio of weir length to depth of upstream flow (b/y1), and ratio of weir height to its length (p/y1) parameters of R2=0.947, MARE=0.05, RMSE=0.037, BIAS=0.01 and SI=0.067, performed the best. Accordingly, this new equation proposed through GEP can be utilized for estimating the discharge coefficient in rectangular sharp-crested side weirs.

Determination Discharge Capacity of Triangular Labyrinth Side Weir Using Multi-Layer Neural Network (ANN-MLP)

statistic indexes have been used to assess the accuracy of the results. The results of the examinations indicate that using MLP model along with simultaneous use of dimensionless parameters for the purposes of estimating discharge coefficient: the ratio of water behind the weir to the channel width (h/b), ratio of weir crest length to weir height (L/W), relative Froude number (F=V/√(2Side weirs are used in open channels to control flood and the flow passing through it. Discharge capacity is one of the crucial hydraulic parameters of side weirs. The aim of this study is to determine the effect of the intended dimensionless parameters on predicting the discharge coefficient of triangular labyrinth side weir. MAPE, RMSE, and Rgy)) and vertex angle (ϴ), offered the best results (MAPE= 0.67, R2= 0.99, RMSE = 0.009) in comparison with other models.

Discharge coefficient of compound triangular–rectangular sharp-crested side weirs in subcritical flow conditions

Side weirs are among the important hydraulic structures for flow diversion in flood schemes or sewer networks. Side weirs are generally rectangular or triangular in shape and have a limitation for precise measurement of low and high flow. Therefore compound side weirs are suggested for accurate flow measurement in a wide range of discharges. In this study, the discharge coefficient of compound sharp-crested side weir consisting of rectangular and triangular part was studied experimentally. The results are in agree with previous study which show the discharge coefficient of a compound side weir is a function of the upstream Froude number ((Fr1), the ratio of weighted crest height of the weir to upstream water depth (w¯/y1) and the ratio of weir length to upstream water depth (L/y1). Based on the experimental data and regression modeling, a dimensionless equation has been developed for estimation of the discharge coefficient and two equations have been proposed for estimation of flow discharge in compound triangular–rectangular sharp-crested side weirs. The results also show that there is a good agreement between estimated and measured data.

GMDH-type neural network approach for modeling the discharge coefficient of rectangular sharp-crested side weirs

Estimating the discharge coefficient using hydraulic and geometrical specifications is one of the influential factors in predicting the discharge passing over a side weir. Taking into account the fact that existing equations are incapable of estimating the discharge coefficient well, artificial intelligence methods are used to predict it. In this study, Group Method of Data Handling (GMDH) was used for the purpose of predicting the discharge coefficient in a side weir. The Froude number (F1), weir dimensionless length (b/B), ratios of weir length to depth of upstream flow (b/y1) and weir height to its length (p/y1) were taken as input parameters to express a new model for predicting the discharge coefficient. Two different sets of laboratory data were used to train the artificial network and test the new model. Different statistical indexes were used to evaluate the performance of the GMDH model presented for two states, training and testing. The results indicate that the proposed model predicts the discharge coefficient precisely (MAPE = 5.263 & RMSE = 0.038) and this model is more accurate in predicting than the feed-forward neural network model and existing nonlinear regression equations.

Sensitivity analysis of the discharge coefficient of a modified triangular side weir by adaptive neuro-fuzzy methodology

The discharge coefficient of a modified triangular side weir is analyzed regarding various non-dimensional input sets. It is desirable to select and analyze factors or parameters that are truly relevant or the most influential to triangular side weir discharge coefficient estimation and prediction. The Adaptive Neuro-Fuzzy Inference System (ANFIS) is applied for the selection of the most prominent triangular side weir discharge coefficient parameters based on ten input parameters. The input variables were searched using the ANFIS network to specify the input parameters’ effects on the discharge coefficients. According to the obtained results, the side weir included angle has the most effect on modeling the discharge coefficient. Then by using the selected input variables, the discharge coefficient was modeled with ANFIS, artificial neural network, support vector machine and multi non linear regression methods. The results show that ANFIS could predict the discharge coefficient significantly better than the other investigated models.

Flow characteristics at trapezoidal broad-crested side weir

Abstract Broad-crested side weirs have been the subject of numerous hydraulic studies; however, the flow field at the weir crest and in front of the weir in the approach channel still has not been fully described. Also, the discharge coefficient of broad-crested side weirs, whether slightly inclined towards the stream or lateral, still has yet to be clearly determined. Experimental research was carried out to describe the flow characteristics at low Froude numbers in the approach flow channel for various combinations of in- and overflow discharges. Three side weir types with different oblique angles were studied. Their flow characteristics and discharge coefficients were analyzed and assessed based on the results obtained from extensive measurements performed on a hydraulic model. The empirical relation between the angle of side weir obliqueness, Froude numbers in the up- and downstream channels, and the coefficient of obliqueness was derived.

Rectangular side weirs discharge coefficient estimation in circular channels using linear genetic programming approach

Side weirs are diversion structures extensively used in irrigation, flood protection and combined sewer systems. Accurate estimation of the discharge coefficient (Cd) of side weirs is essential to compute the water surface profile over the weirs and to determine the lateral outflow rate from the system. In this paper, we have utilized a linear genetic programming (LGP) technique to develop new empirical formulas for the estimation of Cd of sharp-edged rectangular side weirs located in circular channels. For this aim, we have employed a total of 1,686 laboratory experimental observations in both sub- and supercritical flow regimes in order to train and validate the proposed models. The performance of the LGP-based models was also compared with those of different multilinear and nonlinear regression models in terms of root mean squared errors, mean absolute errors, and determination coefficient. The results indicated that an explicit LGP-based model using only mathematical functions could be employed successfully in Cd estimation in both sub- and supercritical flow conditions. Genetic-based sensitivity analysis among the input parameters demonstrated that Froude number at upstream of the weir has the most impact on the Cd estimation.

Determining side-weir discharge coefficient using Anfis

The effects of parameters such as weir length, height of weir, water depth at weir entrance and bed slope on the discharge coefficient of a rectangular sharp-crested side weir were analysed using standard linear regression and the adaptive neuro-fuzzy inference system (Anfis). The results showed that the Anfis model performed better than the regression model in all different scenarios defined in this study. Anfis can simulate the discharge coefficient better than the regression model and always works better. Without considering the channel slope, both models represent satisfactory results, but the Anfis model shows more sensitivity to channel slope than does the regression model. Based on the results of this study, the Anfis model is suggested for estimation of side weir discharge coefficient.

Predicting the side weir discharge coefficient using the optimized neural network by genetic algorithm

Side weir is one of the structures which are widely used in water engineering projects So study on the flow characteristics especially discharge coefficient ( ) of this type of weir is important. Several Empirical formulas proposed to calculate the that they usually associated with significant errors. Thus, using mathematical methods based on artificial intelligence is inevitable. Artificial neural network (ANN) is a very useful data-modeling tool that is able to capture and represent complex input and outputs relationships. In this study, accuracy the some famous empirical formula was assessed and Borghei and Parvaneh was most accuracy formula with ( ). To increase the accuracy of production the multi-layer neural network (MLP) has developed. This model, in the first, trained by a back propagation method such as levenberg_marquardt and its performance was determined. the error indexes in the train and testing process are equal to ( and ). To increase the accuracy of MLP model, instead of increasing the size of the network (increase in the number of neurons and layers), Genetic Algorithm was used to train this model (GANN)and obtained an optimized value for Bias and weights. The final results show that using the GA to training the MLP model cased to increase in accuracy .The performance of the optimized neural network (GANN) in training and testing is equal to ( and ). Normal 0 false false false EN-US X-NONE AR-SA

Discharge Characteristics of a Trapezoidal Labyrinth Side Weir with One and Two Cycles in Subcritical Flow

AbstractA labyrinth weir provides an effective way to increase weir crest length without an associated increase in structure width. Labyrinth side weirs have important advantages compared to conventional side weirs in term of discharge capacity, length of the channel opening, and nappe height over the weir. A different equation is needed for each number of cycles to determine the discharge coefficient of labyrinth side weir. Unlike labyrinth spillways, one or two cycles are mostly sufficient for the labyrinth side weirs to accommodate the required discharge. This study examines the hydraulic characteristics of trapezoidal labyrinth side weirs with two cycles in a subcritical situation and the effect on discharge capacity of using single or multiple cycles in side weirs with the same length openings and crest lengths. The results show that a side weir with one cycle has slightly greater discharge coefficient. In addition, the variation of the discharge capacity was investigated for both one-cycle and two-c...

Discharge coefficient of rectangular sharp-crested side weirs, Part I: Traditional weir equation

A comprehensive study was performed to examine the flow characteristics over rectangular sharp-crested side weirs based on the traditional weir equation. To obtain a generally convenient discharge coefficient relationship, series of experiments were conducted according to manipulation of different prevailing parameters. The flow regime was consistently subcritical for upstream Froude numbers ranging from 0.08 to 0.91. Furthermore, experimental data sets of the former investigators were also applied. In order to identify the most important parameters affecting the discharge coefficient of rectangular sharp-crested side weirs, a sensitivity analysis was carried out based upon an artificial neural network modeling. Results of the sensitivity analysis indicated the Froude number to be the most influential parameter on discharge coefficient. Accordingly, a power equation is derived for estimating the discharge coefficient, which is applicable for both sub- and supercritical flow conditions simultaneously. Moreover, considering all the influential parameters, a nonlinear correlation was obtained with the highest precision to determine the discharge coefficient of sharp-crested rectangular side weirs.

Anfis to estimate discharge capacity of rectangular side weir

The adaptive neuro-fuzzy inference system (Anfis) is considered for flow over rectangular side weirs located on a straight channel as a substantial part of distribution channels in irrigation systems and treatment units. To estimate the outflow over a rectangular sharp-crested side weir, the discharge coefficient in the side weir equation needs to be determined in accordance with the effective dimensionless parameters F1 (Froude number), L/b (weir length/channel width), L/h1 (weir length/flow depth), and p/h1 (weir height/flow depth). The discharge coefficient of rectangular side weirs was determined using 843 laboratory test results. The performance of the Anfis model is compared with multilinear and nonlinear regression models. The criteria used for the evaluation of the performance of models are root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics. Comparison results indicated that the Anfis technique could be successfully employed in modelling discharge coefficients. It is found that the Anfis model with RMSE of 0·043 in the test period is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0·054 and 0·106, respectively.

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.