Anfis to estimate discharge capacity of rectangular side weir

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.

Discharge coefficient of a semi-elliptical side weir in subcritical flow

Introduction: Side weir structures are extensively used in hydraulic engineering, irrigation and environmental engineering, and it usually consists of a main weir and a lateral channel. Side weirs are also used as an emergency structure. This structure is installed on one side or both sides of the main channel to divert the flow from the main channel to the side channel. Lateral outflow takes place when the water surface in the main channel rises above the weir sill. Flow over a side weir is a typical case of spatially varied flow with decreasing discharge. There have been extensive studies on side weir overflows. Most of the previous theoretical analysis and experimental research works are related to the flow over rectangular side weirs in rectangular main channels. In the current study, the flow conditions over a trapezoidal side weir located in a rectangular main channel in subcritical flow regime is considered. Materials and Methods: The experiments were performed in a rectangular open channel having provisions for a side weir at one side of the channel. The main channel was horizontal with 12 m length, 0.25 m width, and 0.5 m height, and it was installed on a frame; lateral channel that has a length of 6 m, width of 0.25 m, and height of 1 m. It was set up parallel to the main channel; walls and its bed were made up of Plexiglas plates. The side weir was positioned at a distance of 6 m from the channel’s entrance. A total of 121 experiments on trapezoidal side weirs were carried out. Results and Discussion: For trapezoidal side weir, effective non-dimensionnal parameters were identified using dimensional analysis and Buckingham's Pi-Theorem. Finally, the following non-dimensional parameters were considered as the most effective ones on the discharge coefficient of the trapezoidal side weir flow. in which Fr1= upstream Froude number, P= hight of the trapezoidal side weir, y1= upstream water depth, z=side slope of the trapezoidal side weir and T=top flow width of the trapezoidal side weir. Water surface profiles were measured along the weir crest, the main channel centerline, and far from the weir section. Different elevations in water surface profile depend on the upstream Froude number in the main channel; depth differences in low Froude numbers are at minimum values, and in high Froude numbers are at maximum amounts. The water surface level along the crest drops at the entrance of the side weir to the first half of the side weir; and it has been attributed to the side weir entrance effect at the upstream. Afterwards, the water level rises towards the downstream of the weir. According to the experimental results, measurements of the water in the centerline of the main channel are reliable and water surface drop is negligible. According to the parameters affecting the discharge coefficient for each value of z, discharge coefficient equations were developed with acceptable accuracy such that the effects of this parameter were shown separately. Finally, the general equation was proposed. The general functional form for discharge coefficient is presented as follows where the effect of the side slope parameter, z, is also considered. The mean and maximum percentage errors of the discharge coefficient computed using the proposed equation are as 2.6% and 11.5% , respectively. Conclusion: In this study, the characteristics of trapezoidal side weir overflows in subcritical flow regime were discussed. For this purpose, experimental data related to the water surface profile of the side weir and discharge coefficient were collected and analyzed. The results showed that the most efficient section for measuring water surface profile is located at the center line of the main channel. It was found that for trapezoidal side weir, the discharge coefficient depends on the Froude number, the ratio of crest height to initial depth, the overflow length to initial depth, and the side slope of the weir. In this study, conventional trapezoidal weir theory has been used in order to evaluate the discharge coefficient and provide side weir discharge equation. For this purpose, three reference depths were considered for conventional weir, and for each depth an equation was developed for the discharge coefficient. Comparison between predicted values and experimental data showed that average flow depth results in accurate outcomes for assessing the discharge coefficient. The average value of error for discharge coefficient estimation by the proposed equation is 2.6%. Thus this equation is proposed for use in practice by water engineers. Keywords: Control structure, Conventional weir, Discharge coefficient, Spatially varied flow, Trapezoidal side weir, Water surface profile

Study of flow at side weir in narrow flume using visualization techniques

Side weirs are widely used to measure and control flows passing through main canals. In this study, a hybrid model is developed to approximate the discharge coefficient of side weirs located on converging canals for the first time, meaning that the adaptive neuro‐fuzzy inference system (ANFIS) network is optimized by means of the firefly algorithm. After that, six ANFIS and adaptive neuro‐fuzzy inference system‐firefly algorithm (ANFIS‐FA) models are introduced using input parameters. In addition, in this study, Monte Carlo simulation is employed to study the modelling accuracy. Furthermore, the k‐fold cross‐validation approach is implemented to validate the modelling results. Analysing the modelled results demonstrates that the hybrid models are more accurate than the ANFIS ones. The superior model simulates the discharge coefficient values with reasonable accuracy. For example, the values of the determination coefficient (R2), the mean absolute error (MAE) and the root mean square error (RMSE) for the superior model are calculated as 0.993, 0.011 and 0.015, respectively. Also, about 98% of the superior model results have errors less than 12%. According to the uncertainty analysis results, the superior model has an overestimated performance. A sensitivity analysis indicates that the flow Froude number at the side weir downstream is the most effective input parameter. © 2020 John Wiley & Sons, Ltd.

A piano key side weir (PKSW) is a non-linear weir that discharge exceeds linear weirs by increasing the length in width. PKSW can be used in side weirs with space limitation. As side weirs are extensively used in flood control, water level control in rivers, and water supply channels, it is necessary to use PKSW as side weirs. This research discusses the discharge coefficient of a PKSW by assessing a C-type PKSW at 30° and 120° sections of a channel with a longitudinal curve. Dimensional analysis was used for identifying the parameters effective in the discharge coefficient. The effects of these parameters are examined by analysing the effective parameters. Finally, an empirical relationship has been proposed for determining the discharge coefficient based on the dimensionless parameters for calculating the discharge coefficient with the correlation coefficient of 0.88 and the mean error of 0.091. The influence of the parameter on the PKSW is more than that of the remaining parameters: With an increase in the value of this parameter, considering decreases in the length of the deviation and a lack of submerged inlet keys, the coefficient of discharge increases.

Side weirs are flow diversion devices that are widely used in irrigation, drainage and urban sewage systems. The present study focuses on the investigation of the effect of oblique side weirs on the discharge coefficient of a side weir under subcritical flow condition in rectangular channels. In this study 106 laboratory tests were conducted and the results were analyzed to find out the influence of non-dimensional parameters on the discharge coefficient of the weirs. The angles of side weirs varied from 0 to 17.5 degrees in six steps, three heights (5, 10 and 15 centimeters) and three lengths (100, 80 and 40 centimeters). Two descriptions of the discharge coefficient (traditional side weir coefficients, Cd, and De-Marchi, CM), along with different discharges and related parameters were used. According to the results, Cd is more sensitive to b1/b2 (ratio of channel bottom widths), whereby CM is sensitive to L/b1 (ratio of side weir length to bottom width). The correction formula for estimating the oblique side weir discharge coefficient with a traditional shape shows that a 17.5 degree angle with side wall causes 40 percent change in the discharge coefficient.

The effect of increasing the number of cycles on the performance of labyrinth side weir

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 coefficient for an inclined side weir crest using a constant energy approach

Bottom-hinged flap gates on side weirs are often used for the regulation of flow diversion in case of water abstraction for a variety of needs. In this study, a new equation for the discharge coefficient of a bottom-hinged flap gate on a side weir was proposed on the basis of discharge measurements. The equation was divided into two parts. The first part covers the impact of the sharp-crested side weir and the second the influence of the position and the width of the flap gate. In this manner, the discharge coefficient can be calculated with other authors’ equations for a sharp-crested side weir, which then must be multiplied by the new proposed coefficient. Very good agreement was found between the obtained discharge coefficients and the one calculated with the proposed equation. Furthermore, the results were compared with the equations of other authors for the discharge coefficients of sharp- and broad crested side weirs. The agreement was found to be very good. Additionally, measurements of water levels along the edge of the flap gate and measurements of the velocity field were carried out with a computer-aided visualization method. From these measurements, it was possible to show that the contraction of the water jet varies with the gate-opening angle. It was also found that the side weir with a flap gate has the most favorable hydrodynamic shape around the gate-opening angle of 33°, where the discharge coefficient reaches its maximum.

Globally, wind energy if properly harnessed, could serve as a source of energy generation in Africa. This study compared the performance of two Machine Learning (ML) algorithms (Linear regression and Random Forest) in predicting wind speed in five major cities in Africa (Yaoundé, Pretoria, Nairobi, Cairo and Abuja). Wind data were collected between January 1, 2000, and December 31, 2022, using the Solar Radiation Data Archive. The data preprocessing was carried out with 80% of the data used for training and 20% for validation. The performance of these ML algorithms was evaluated using Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and coefficient of determination (R2). The result shows that Nairobi (3.814795 m/s) closely followed by Cairo (3.606453 m/s) has the highest mean wind speed while Yaoundé (1.090512 m/s) has the lowest. Based on the performance metrics used, the two Machine Learning algorithms were competitive. Still, the Linear Regression (LR) algorithm outperformed the Random Forest Algorithm in predicting wind speed in all the selected major African cities. In Yaoundé (RMSE = 0.3892, MAE= 0.3001, MAPE =0.5030), Pretoria (RMSE=1.2339, MAE=0.9480, MAPE=0.7450) Nairobi (RMSE= 0.4223, MAE =0.6499, MAPE =0.1872), Nairobi (RMSE=0.6499, MAE=0.5171, MAPE =0.1872), Cairo (RMSE =1.0909, MAE =0.8544, MAPE =0.3541) and Abuja (RMSE = 0.70245, MAE =0.5441, MAPE= 0.4515) the Linear regression algorithms was found to outperformed Random Forest Regression. Therefore, the Linear regression algorithm is more reliable in predicting wind speed compared with the Random Forest regression.

A novel approach for estimation of discharge coefficient in broad-crested weirs based on Harris Hawks Optimization algorithm

Determination of discharge capacity of rectangular side weirs using Schmidt approach

Slips and falls are leading causes of injury-related incidents, and one of the most effective ways to prevent slips is to use slip-resistant footwear. To evaluate footwear slip resistance, two main experiments are conducted: (1) human-centered tests, and (2) mechanical tests. Human-centered slip resistance tests better capture real-world locomotion dynamics than mechanical tests, but they are costly and time-consuming. This study aimed to develop a predictive model that estimates human-centered slipperiness score called Maximum Achievable Angle (MAA) outcomes using mechanical slip resistance measurements, enabling accessible footwear evaluation. Thirty-seven winter footwear samples were tested using both human-centered MAA testing and the SATRA STM 603 mechanical slip resistance tester on wet and dry ice surfaces. Ten linear and non-linear regression models were trained using a nested 5-fold cross-validation approach with unseen footwear in each fold to support generalizability. Model performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), coefficient of determination (R2), and Bland-Altman analysis. Across all models, the Ridge model produced the most conservative and consistent results, achieving an RMSE of 2.73° and MAE of 2.27° on wet ice, and an RMSE of 1.58° and MAE of 1.33° on dry ice. Although the results are close to the ± 1° acceptable range of MAA, slight deviations in some cases highlight opportunities for future model improvement. Mechanical slip resistance metrics can be used to reasonably predict human-centered MAA outcomes. While prediction accuracy is promising, further refinement is needed to fully meet the precision requirements for footwear slip resistance certification.