Discharge Coefficient Of Labyrinth Weirs Research Articles

A performance comparison of the meta model methods for discharge coefficient prediction of labyrinth weirs

Weirs are hydraulic structures with various applications, such as flow measurement, flow diverting, and/or flow control. Labyrinth weir as a nonlinear weir with a folded crest enhances the spillway system discharge capacity by increasing the crest length for a given channel width. As a remarkable parameter, the discharge coefficient plays an important role in determining weirs' passing capacity. So, it is important that the discharge coefficient be accurately represented to ensure an appropriate and economical design. This research evaluates the prediction accuracy of four soft computing techniques, such as support vector machines (SVM), gene expression programming (GEP), software (QNET), and artificial intelligence networks (ANN), to predict the discharge coefficient of labyrinth weirs using three different scenarios. The model's input parameters included the total water head ratio (HT/P), magnification (Lc/W), and cycle wall angle (α). On reviewing the outcomes of the developed models, it appeared that each of them demonstrated satisfactory performance in predicting the discharge coefficient. However, ANN and SVM reveal more accuracy compared to other techniques. The prediction results reveal that the ANN as a superior model has the following performance metrics: R2 = 0.998, DC coefficient = 0.996, and RMSE = 0.006. The sensitivity analysis results indicate that HT/P is the most effective factor in determining the labyrinth weir discharge coefficient in all methods. This suggests that the ratio of HT (total water head) to P (weir height) has a significant impact on the overall model performance. Upon comparing the results of this research with those of other researchers, it is evident that the evaluation indicators for all methods employed in this study are relatively superior.

Effect of Different Channels on Discharge Coefficient of Labyrinth Weirs

In this study, the effect of channel-bed slope and non-prismatic converging channel on the discharge coefficient of labyrinth weirs is numerically investigated utilizing FLOW-3D model. Numerical simulation results show that modifying the labyrinth weir channel through both methods improves the discharge coefficient. Among the selected bed slopes and converging channel wall, the slope of β=4% and angle of θ=10° yielded the highest discharge coefficient. For a ratio HT/P=0.1, (HT: flow height, P: weir height) the discharge coefficient and discharge rate for bed slope and convergence angle case were 19.22%, 23.9% and 22.28%, 25.91% higher than for a conventional labyrinth weir in prismatic channel, respectively. Simultaneous application of a bed slope and convergence angle significantly increases the discharge coefficient and discharge value case were 28.64% and 30.42% higher than compared to the conventional case. Therefore, changing the bed slope and wall angle of the weir channel increases the discharge coefficient and in this type of weir and these design alterations should be considered in weir design.

Prognostication of discharge coefficient of labyrinth weir using outlier robust extreme learning machine

In this paper, for the first time, a robust artificial intelligence (AI) technique called “outlier robust extreme learning machine (ORELM)” is used to estimate the discharge coefficient of labyrinth weirs. At the beginning, the number of the hidden layer neurons initials from 5 and continues to 45 and the most optimal number of the hidden layer neurons are taken into account equal to 5. Then, the numerical model is verified by the k-fold cross-validation approach in which k is considered equal to 5. After that, different activation functions are evaluated to detect the most accurate one for the numerical model. Subsequently, six different ORELM models are developed using the parameters affecting the discharge coefficient of labyrinth weirs. Also, the superior model and the most effective input parameters are identified through a sensitivity analysis. For example, the values of R2, RMSRE and NSC for the superior model are calculated 0.943, 5.224 and 0.940, respectively. Furthermore, the ratio of the head above the weir to the weir height (HT/P) and the ratio of the width of a single cycle to the weir height (w/P) are introduced as the most important input parameters. Also, the results of the ORELM superior model are compared with the artificial intelligence models including the extreme learning machine, artificial neural network and the support vector machine and it is concluded that ORELM has a better performance. Then, an uncertainty analysis is conducted for the ORELM, ELM, ANN and SVM models and it is proved that the ORELM has an overestimated performance. Eventually, a practical formula is presented to engineers without knowledge of artificial intelligence for approximating the discharge coefficient of labyrinth weirs. Additionally, a partial derivative sensitivity analysis is carried out for this equation.

A novel approach using CFD and neuro-fuzzy-firefly algorithm in predicting labyrinth weir discharge coefficient

In this paper, for the first time, to model the discharge coefficient of labyrinth weirs, the evolutionary firefly algorithm (FFA) is used for optimizing the membership functions of the adaptive neuro-fuzzy inference system (ANFIS). Also, to enhance the performance of the ANFIS and ANFIS-FFA models, the Monte Carlo simulations (MCs) are employed. Additionally, the k-fold cross-validation is utilized for training and testing the methods. Next, some input dimensionless parameters including the Froude number (Fr), the ratio of the head above the weir to the weir height (HT/P), cycle sidewall angle (α), the ratio of length of the weir crest to the channel width (Lc/W), the ratio of length of apex geometry to the width of a single cycle (A/w) and the ratio of the width of a single cycle to the weir height (w/P) are determined. After that, seven different models are developed for ANFIS and ANFIS-FFA. Then, by conducting a sensitivity analysis, the superior models (ANFIS-FFA 5 and ANFIS 5) and the most effective input parameter (Froude number) are identified. Moreover, the error distribution results exhibit that about 70% of the superior model results have errors less than 5%. Subsequently, the discharge coefficient is simulated by means of a computational fluid dynamics (CFD) model. Furthermore, a comparison of the CFD model with the ANFIS and ANFIS-FFA models reveals that the ANFIS-FFA model is significantly more accurate. Also, an uncertainty analysis is performed for the CFD, ANFIS and ANFIS-FFA models. Finally, a very simple code calculating the discharge coefficient of labyrinth wires is presented. This code can be easily employed without any knowledge on ANFIS, FFA and prior information about MATLAB.

Experimental study on flow over sinusoidal and semicircular labyrinth weirs

ABSTRACT For a given width, a labyrinth weir has a developed crest length, thereby increasing the flow capacity for a given upstream headwater. This paper experimentally studies the flow over labyrinth weirs with semicircular and sinusoidal configurations in a rectangular channel under a wide range of flow discharges. The effects of headwater ratio (HT/P), length of weir (L/P), arc radius ratio (R/P) and the number of cycles (N) on the discharge coefficient of semicircular and sinusoidal labyrinth weirs are investigated. Experimental results indicated the decreasing trend of Cd for HT/P>0.35 which is probably related to the progressive development of local submergence. Despite the effects of local submergence, the labyrinth weirs have nearly the same discharge coefficient as broad-crested weirs, and the flow discharge exceeded the linear weirs efficiency by ∼30. Additionally, reliable equations for estimating the discharge coefficient of labyrinth weirs with semicircular and sinusoidal configurations are presented.

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.