# Prediction of the Discharge Coefficient in Compound Broad-Crested-Weir Gate by Supervised Data Mining Techniques

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## Abstract

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_{dt}) using the computational fluid dynamics (CFD) modeling approach and soft computing models. First, CFD was applied to the experimental data and 61 compound BCW gates were numerically simulated by resolving the Reynolds-averaged Navier–Stokes equations and stress turbulence models. Then, six data-driven procedures, including M5P tree, random forest (RF), support vector machine (SVM), Gaussian process (GP), multimode ANN and multilinear regression (MLR) were used for estimating the coefficient of discharge (C

_{dt}) of the weir gates. The results showed the superlative accuracy of the SVM model compared to M5P, RF, GP and MLR in predicting the discharge coefficient. The sensitivity investigation revealed the h

_{1}/H as the most effective parameter in predicting the C

_{dt}, followed by the d/p, b/B

_{0}, B/B

_{0}and z/p. The multimode ANN model reduced the root mean square error (RMSE) of M5P, RF, GP, SVM and MLR by 37, 13, 6.9, 6.5 and 32%, respectively. The graphical inspection indicated the multimode ANN model as the most suitable for predicting the C

_{dt}of a BCW gate with minimum RMSE and maximum correlation.

## 1. Introduction

_{dt}in the compound BCW gate. All the effective parameters were changed to make different combinations of this structure. The BCW gate can be used as a flood control reservoir and a measuring device for minimizing the sediments and preventing their accumulation. An accurate prediction of the C

_{dt}in the compound BCW gate could significantly improve its operational management and, thus, water resources management.

## 2. Theoretical Background

_{1}< Z) (Figure 1b), the broad-crested weir performs like a basic weir, and there will be no flow over the compound section.

_{c}) will be lower than the central weir height (Z) and weir discharge (Q

_{w}) though the broad-crested weir can be as follows [60,61];

_{dw}denotes the weir discharge coefficient, C

_{v}denotes the weir velocity coefficient. Furthermore, h

_{1}, g, B and H

_{1}are the water height above the central weir, acceleration gravity, central weir width and head overall energy at the weir head assessment section, respectively.

_{1}) surpasses the central weir height (Z), and the weir acts as a compound weir (Figure 1c). Furthermore, the critical flow depth (y

_{c}) will be greater than the central weir height (Z). In this case, the BCW discharge (Q

_{w}) is obtained by Equation (4) [5,61]:

_{g}) can be obtained by utilizing the equation of energy, as below [62]:

_{dg}is the gate discharge coefficient and d, b and H are the gate opening height, gate breadth and level of upstream water, respectively. The investigation of the compound BCW and gate collectively for the two mentioned cases of compound BCW are elaborated below.

#### 2.1. Case 1

_{t}) is the sum of Equation (1) and Equation (7) and can be written as Equation (8). The discharge coefficient for the combined compound BCW gate (C

_{dt}) can be presented by Equation (9):

#### 2.2. Case 2

_{t}) (Figure 2c) is the sum of Equation (4) and Equation (7):

#### 2.3. Governing Equations and Numerical Method

_{x-z}, f

_{x-z}and b

_{x-z}denote body accelerations, viscous accelerations and flow losses in porous media, respectively. Furthermore, A

_{x}, A

_{y}and A

_{z}refer to the cross-sectional extent of the flow; ρ denotes the density of water, indicates the fractional volume open to flow in fractional area/volume obstacle representation (FAVOR), R

_{SOR}denotes the source term, p denotes the pressure, and the concluding terms constitute the inclusion of mass at a source signified by a geometry component. The term U

_{w}= (u

_{w}

_{,}u

_{w}, w

_{w}) is the velocity of the source component, and the term U

_{s}= (u

_{s}, v

_{s}, w

_{s}) is the velocity at the surface of the source relative to the source itself. R in Equation (12) is the coefficient that depends on the choice of coordination system.

_{e}normalization groups with the equation of stress), one equation model, large-eddy simulation (LES) and the Prandtl mixing-length model [69].

## 3. Methods

_{1}/L ≤ 0.35 (where h

_{1}and L refer to the hydraulic head on the weir’s central section and the compound weir’s length, respectively) to establish the physical and arithmetic design [70]. The flow separation was decreased by rounding with a radius of 0.065 m at the weir entrance to develop physical and numerical models of the weir [5]. Figure 3 shows the geometry of the experimental study conducted by Salmasi et al., [12].

_{K}and G

_{b}stand for the generation of turbulent kinetic energy arising because of average velocity gradients and buoyancy, separately, Y

_{M}is the fluctuating dilation in compressible turbulence, S

_{ε}and S

_{K}are the source terms set by the user, ${\alpha}_{k}$ and ${\alpha}_{\epsilon}$ are inverse effective Prandtl numbers for the turbulent kinetic energy and its dissipation, and ${c}_{1\epsilon}$, ${c}_{2\epsilon}$ and ${c}_{3\epsilon}$ are constants. Furthermore, the ${R}_{\epsilon}$ refers to the main difference between the numerical models used.

_{dw}.

_{dw}and can be used to simulate a combined compound BCW gate. The root mean square (RMSE) values were 0.2685 for k-w against 0.3122 for RNG, when the k-w model was used for the simulation of the combined compound BCW-gate structure by CFD code.

_{0}, L, P + Z), central weir height and width (Z and B) and gate opening height and width (d and b). For upstream water level (H), different values were considered and two types of compound weir performance (simple weir and compound weir (Figure 2) were studied. Considering the mentioned parameters, the results are presented using dimensionless parameters. The structure’s total section width (B

_{0}), the height of the structure (Z + P) and combined structure length (L) were considered as 0.25, 0.25 and 0.4, respectively. Table 2 shows the studied dimensionless parameters and values.

_{min}and X

_{max}boundary conditions. Y

_{min}, Y

_{max}and Z

_{min}were selected as boundary conditions. Furthermore, the symmetry was the Z

_{max}boundary condition. Figure 5 shows one of the used models and its boundary conditions.

_{dt}) were generated using the simulation results for the two mentioned cases. Using the generated C

_{dt}values, six soft computing-based models, including RF, M5P, SVM, GP, MLP and multimode ANN, were used to predict C

_{dt}. The mentioned dimensionless parameters were the inputs of the soft computing models.

#### 3.1. Soft Computing Models and Artificial Intelligence Techniques

#### 3.1.1. M5P Model

#### 3.1.2. Random Forest (RF)

#### 3.1.3. Gaussian Process (GP)

#### 3.1.4. Support Vector Machine (SVM)

#### 3.1.5. Multiple Linear Regression (MLR)

_{1}, x

_{2},…

_{,}x

_{n}stand for independent variables. MLR was developed in this study using XLSTAT software.

#### 3.1.6. Artificial Neural Networks (ANN)

## 4. Application of the Methods

_{0}, z/p, B/B

_{0}and h

_{1}/H whereas the C

_{dt}of the BCW gate was considered output.

## 5. Results and Discussion

_{dt}of the BCW gate using soft computing approaches are presented against the modeled (real) values in the figure to show their performance based on the best fit line (y = x).

_{dt}with CC of 0.9585, NSE of 0.8562, MAE of 0.0237, RMSE of 0.0276 and SI of 0.0337 during testing. The SVM reduced the RMSE of M5P, RF, GP and MLR by 32, 7.1, 0.4 and 27%, respectively. However, the difference between GP and SVM was minor. Figure 7 shows that the SVM-estimated C

_{dt}during training and testing was the closest to the best-fit line relative to other models. It confirmed the better performance of SVM compared to the other models. The outcomes of single-factor ANOVA presented in Table 6 show insignificant differences between theactual and predicted values for the different models.

#### 5.1. Sensitivity Investigation

_{1}/H is the most influencing parameter in predicting the C

_{dt}of BCW gate, followed by d/p, b/B

_{0}, B/B

_{0}and z/p.

#### 5.2. Results of Multimode ANN Model

_{dt}values were the output. The multimode ANN model was developed using a hit-and-miss process. Figure 8 indicates the structure of the novel multimode model in which five neurons in the input layer and four neurons in the latent layer were selected for predicting C

_{dt}of BCW gate.

_{dt}using novel multimode ANN models during the training and testing stages. The novel multimode ANN estimated C

_{dt}with CC = 0.9998 and 0.9618, RMSE of 0.0016 and 0.0258, MAE of 0.0013 and 0.0217, NSE as 0.9996 and 0.8746 and SI of 0.0020 and 0.0315 during training and testing, respectively. Overall, the performance of the novel multimode ANN was better than the RF, M5P, GP, SVM and MLR models in predicting C

_{dt}of BCW gate. Comparison with Table 5 revealed that the novel multimode ANN reduced the RMSE of M5P, RF, GP, SVM and MLR by 37, 13, 6.9, 6.5 and 32%, respectively.

_{dt}of a BCW gate.

_{dt}. Three statistical parameters involving RMSE, CC and standard deviation were used to evaluate the applied models’ accuracy in the Taylor diagram. Figure 11 indicates that the multimode ANN model attained a higher CC with minimal RMSE. The Taylor diagram also confirmed that the performance of the multimode ANN model surpassed the other applied models.

## 6. Conclusions

_{dt}) of a combined compound rectangular broad-crested weir (BCW) gate. For this purpose, the experimental results of a simple broad-crested weir were employed for the code’s calibration, and the k-w model was selected for numerical simulation. The effective parameters of the combined structure were changed for a comprehensive investigation. The studied dimensionless parameters were: b/Bo, d/P, B/Bo, Z/P and h

_{1}/H. A total of 61 compound BCW gates were numerically simulated using different values of the dimensionless parameters. Finally, the results of the calibrated CFD code were used to develop models for the prediction of a compound BCW-gate C

_{dt}. Six data-driven algorithms, including M5P tree, RF, Gaussian process, SVM, MLR and multimode ANN, were used.

_{1}/H as the most effective parameter, followed by d/p, b/B

_{0}, B/B

_{0}and z/p, in predicting C

_{dt}using SVM. The novel multimode ANN model outperformed all other models. It reduced the RMSE by 37, 13, 6.9, 6.5 and 32% of the M5P, RF, GP, SVM and MLR, respectively. The Taylor diagram and box plot also confirmed the novel multimode ANN model as the most suitable model in predicting the C

_{dt}of a BCW gate with minimum errors and maximum correlation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Salmasi, F.; Nouri, M.; Sihag, P.; Abraham, J. Application of SVM, ANN, GRNN, RF, GP and RT models for predicting discharge coefficients of oblique sluice gates using experimental data. Water Supply
**2020**, 21, 232–248. [Google Scholar] [CrossRef] - Salmasi, F.; Nouri, M.; Abraham, J. Laboratory Study of the Effect of Sills on Radial Gate Discharge Coefficient. KSCE J. Civ. Eng.
**2019**, 23, 2117–2125. [Google Scholar] [CrossRef] - Abbaspour, A.; Yasi, M. Flow over Truncated-Triangular Weirs. Master’s Thesis, University of Urmia, Urmia, Iran, 2001. (In Persian). [Google Scholar]
- Das, B.S.; Devi, K.; Khatua, K.K. Prediction of discharge in converging and diverging compound channel by gene expression programming. ISH J. Hydraul. Eng.
**2019**, 27, 385–395. [Google Scholar] [CrossRef] - Bos, M.G. Discharge Measurement Structures; International Institute for Land Reclamation and Improvement (ILRI): Wageningen, The Netherlands, 1986. [Google Scholar]
- Dayev, Z.; Kairakbaev, A.; Yetilmezsoy, K.; Bahramian, M.; Sihag, P.; Kıyan, E. Approximation of the discharge coefficient of differential pressure flowmeters using different soft computing strategies. Flow Meas. Instrum.
**2021**, 79, 101913. [Google Scholar] [CrossRef] - Al-Khatib, I.A.; Gogus, M. Prediction models for discharge estimation in rectangular compound broad-crested weirs. Flow Meas. Instrum.
**2014**, 36, 1–8. [Google Scholar] [CrossRef] - The United States Bureau of Reclamation (USBR). Water Measurement Manual, Chapter 7—Weirs,13, Special Weirs; Retrieved on 10 December 2013. Available online: http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/chap07_13.html (accessed on 10 December 2013).
- Cigno, E.; Magagnoli, C.; Pierce, M.; Iglesias, P. Lubricating ability of two phosphonium-based ionic liquids as additives of a bio-oil for use in wind turbines gearboxes. Wear
**2017**, 376–377, 756–765. [Google Scholar] [CrossRef] - Xu, T.; Jin, Y.-C. Numerical Study of the Flow over Broad-Crested Weirs by a Mesh-Free Method. J. Irrig. Drain. Eng.
**2017**, 143, 04017034. [Google Scholar] [CrossRef] - Göğüş, M.; Defne, Z.; Özkandemir, V. Broad-Crested Weirs with Rectangular Compound Cross Sections. J. Irrig. Drain. Eng.
**2006**, 132, 272–280. [Google Scholar] [CrossRef] - Salmasi, F.; Yıldırım, G.; Masoodi, A.; Parsamehr, P. Predicting discharge coefficient of compound broad-crested weir by using genetic programming (GP) and artificial neural network (ANN) techniques. Arab. J. Geosci.
**2012**, 6, 2709–2717. [Google Scholar] [CrossRef] - Haddadi, H.; Rahimpour, M. A discharge coefficient for a trapezoidal broad-crested side weir in subcritical flow. Flow Meas. Instrum.
**2012**, 26, 63–67. [Google Scholar] [CrossRef] - Altan-Sakarya, A.B.; Kökpınar, M.A. Computation of discharge for simultaneous flow over weirs and below gates (H-weirs). Flow Meas. Instrum.
**2013**, 29, 32–38. [Google Scholar] [CrossRef] - Negm, A.-A.M.; Al-Brahim, A.; Alhamid, A. Combined-free flow over weirs and below gates. J. Hydraul. Res.
**2002**, 40, 359–365. [Google Scholar] [CrossRef] - Alhamid, A.A. Analysis and formulation of flow through combined V-notch-gate-device. J. Hydraul. Res.
**1999**, 37, 697–705. [Google Scholar] [CrossRef] - Samani, J.M.; Mazaheri, M. Combined Flow over Weir and under Gate. J. Hydraul. Eng.
**2009**, 135, 224–227. [Google Scholar] [CrossRef] - Alhamid, A.A.; Husain, D.; Negm, A.A.M. Discharge equation for simultaneous flow over rectangular weirs and below inverted triangular weirs. Arab. Gulf J. Sci. Res.
**1996**, 14, 595–607. [Google Scholar] - Ferro, V. Simultaneous flow over and under a gate. J. Irrig. Drain. Eng.
**2000**, 126, 190–193. [Google Scholar] [CrossRef] - Kisi, O.; Shiri, J.; Karimi, S.; Adnan, R.M. Three Different Adaptive Neuro Fuzzy Computing Techniques for Forecasting Long-Period Daily Streamflows. In Big Data in Engineering Applications; Springer: Singapore, 2018; Volume 44, pp. 303–321. [Google Scholar] [CrossRef]
- Alizamir, M.; Kisi, O.; Adnan, R.M.; Kuriqi, A. Modelling reference evapotranspiration by combining neuro-fuzzy and evolu-tionary strategies. Acta Geophys.
**2020**, 68, 1113–1126. [Google Scholar] [CrossRef] - Roushangar, K.; Akhgar, S.; Salmasi, F. Estimating discharge coefficient of stepped spillways under nappe and skimming flow regime using data driven approaches. Flow Meas. Instrum.
**2018**, 59, 79–87. [Google Scholar] [CrossRef] - Adnan, R.; Jaafari, A.; Mohanavelu, A.; Kisi, O.; Elbeltagi, A. Novel Ensemble Forecasting of Streamflow Using Locally Weighted Learning Algorithm. Sustainability
**2021**, 13, 5877. [Google Scholar] [CrossRef] - Akbari, M.; Salmasi, F.; Arvanaghi, H.; Karbasi, M.; Farsadizadeh, D. Application of Gaussian Process Regression Model to Predict Discharge Coefficient of Gated Piano Key Weir. Water Resour. Manag.
**2019**, 33, 3929–3947. [Google Scholar] [CrossRef] - Seyedzadeh, A.; Maroufpoor, S.; Maroufpoor, E.; Shiri, J.; Bozorg-Haddad, O.; Gavazi, F. Artificial intelligence approach to estimate discharge of drip tape irrigation based on temperature and pressure. Agric. Water Manag.
**2019**, 228, 105905. [Google Scholar] [CrossRef] - Bahrami, B.; Mohsenpour, S.; Noghabi, H.R.S.; Hemmati, N.; Tabzar, A. Estimation of flow rates of individual phases in an oil-gas-water multiphase flow system using neural network approach and pressure signal analysis. Flow Meas. Instrum.
**2019**, 66, 28–36. [Google Scholar] [CrossRef] - Jahanpanah, E.; Khosravinia, P.; Sanikhani, H.; Kisi, O. Estimation of discharge with free overfall in rectangular channel using artificial intelligence models. Flow Meas. Instrum.
**2019**, 67, 118–130. [Google Scholar] [CrossRef] - Aghaee, A.; Aghaee, M.; Fathi, M.R.; Shoa’Bin, S.; Sobhani, S.M. A novel fuzzy hybrid multi-criteria decision-making approach for evaluating maintenance strategies in petrochemical industry. J. Qual. Maint. Eng.
**2020**, 27, 351–365. [Google Scholar] [CrossRef] - Safari, H.; Etezadi, S.; Moghadam, M.M.; Fathi, M.R. Maturity evaluation of supply chain procedures by combining SCOR and PST models. Int. J. Process Manag. Benchmarking
**2021**, 11, 707. [Google Scholar] [CrossRef] - Maroufpoor, S.; Maroufpoor, E.; Bozorg-Haddad, O.; Shiri, J.; Yaseen, Z.M. Soil moisture simulation using hybrid artificial intelligent model: Hybridization of adaptive neuro fuzzy inference system with grey wolf optimizer algorithm. J. Hydrol.
**2019**, 575, 544–556. [Google Scholar] [CrossRef] - Brandhorst, N.; Erdal, D.; Neuweiler, I. Soil moisture prediction with the ensemble Kalman filter: Handling uncertainty of soil hydraulic parameters. Adv. Water Resour.
**2017**, 110, 360–370. [Google Scholar] [CrossRef] - Salmasi, F.; Sattari, M.T. Predicting Discharge Coefficient of Rectangular Broad-Crested Gabion Weir Using M5 Tree Model. Iran. J. Sci. Technol. Trans. Civ. Eng.
**2017**, 41, 205–212. [Google Scholar] [CrossRef] - Salmasi, F.; Abraham, J. Discharge coefficients for ogee weirs including the effects of a sloping upstream face. Water Supply
**2020**, 20, 1493–1508. [Google Scholar] [CrossRef] - Wang, F.; Zheng, S.; Ren, Y.; Liu, W.; Wu, C. Application of hybrid neural network in discharge coefficient prediction of triangular labyrinth weir. Flow Meas. Instrum.
**2021**, 83, 102108. [Google Scholar] [CrossRef] - Haghiabi, A.H.; Parsaie, A.; Ememgholizadeh, S. Prediction of discharge coefficient of triangular labyrinth weirs using Adaptive Neuro Fuzzy Inference System. Alex. Eng. J.
**2018**, 57, 1773–1782. [Google Scholar] [CrossRef] - Karami, H.; Karimi, S.; Rahmanimanesh, M.; Farzin, S. Predicting discharge coefficient of triangular labyrinth weir using Support Vector Regression, Support Vector Regression-firefly, Response Surface Methodology and Principal Component Analysis. Flow Meas. Instrum.
**2017**, 55, 75–81. [Google Scholar] [CrossRef] - Zaji, A.H.; Bonakdari, H.; Shamshirband, S. Support vector regression for modified oblique side weirs discharge coefficient prediction. Flow Meas. Instrum.
**2016**, 51, 1–7. [Google Scholar] [CrossRef] - Kisi, O.; Emiroglu, M.E.; Bilhan, O.; Guven, A. Prediction of lateral outflow over triangular labyrinth side weirs under subcritical conditions using soft computing approaches. Expert Syst. Appl.
**2012**, 39, 3454–3460. [Google Scholar] [CrossRef] - Emiroglu, M.E.; Bilhan, O.; Kisi, O. Neural networks for estimation of discharge capacity of triangular labyrinth side-weir located on a straight channel. Expert Syst. Appl.
**2011**, 38, 867–874. [Google Scholar] [CrossRef] - Dursun, O.F.; Kaya, N.; Firat, M. Estimating discharge coefficient of semi-elliptical side weir using ANFIS. J. Hydrol.
**2012**, 426–427, 55–62. [Google Scholar] [CrossRef] - Kumar, M.; Sihag, P.; Tiwari, N.K.; Ranjan, S. Experimental study and modelling discharge coefficient of trapezoidal and rectangular piano key weirs. Appl. Water Sci.
**2020**, 10, 43. [Google Scholar] [CrossRef] [Green Version] - Azimi, H.; Bonakdari, H.; Ebtehaj, I. Design of radial basis function-based support vector regression in predicting the discharge coefficient of a side weir in a trapezoidal channel. Appl. Water Sci.
**2019**, 9, 78. [Google Scholar] [CrossRef] [Green Version] - Norouzi, R.; Daneshfaraz, R.; Ghaderi, A. Investigation of discharge coefficient of trapezoidal labyrinth weirs using artificial neural networks and support vector machines. Appl. Water Sci.
**2019**, 9, 1–10. [Google Scholar] [CrossRef] - Bilhan, O.; Emiroglu, M.E.; Miller, C.J.; Ulas, M. The evaluation of the effect of nappe breakers on the discharge capacity of trapezoidal labyrinth weirs by ELM and SVR approaches. Flow Meas. Instrum.
**2018**, 64, 71–82. [Google Scholar] [CrossRef] - Roushangar, K.; Khoshkanar, R.; Shiri, J. Predicting trapezoidal and rectangular side weirs discharge coefficient using machine learning methods. ISH J. Hydraul. Eng.
**2016**, 22, 254–261. [Google Scholar] [CrossRef] - Emiroglu, M.E.; Kisi, O. Prediction of Discharge Coefficient for Trapezoidal Labyrinth Side Weir Using a Neuro-Fuzzy Approach. Water Resour. Manag.
**2013**, 27, 1473–1488. [Google Scholar] [CrossRef] - Haghbin, M.; Sharafati, A. A review of studies on estimating the discharge coefficient of flow control structures based on the soft computing models. Flow Meas. Instrum.
**2022**, 83, 102119. [Google Scholar] [CrossRef] - Zarei, S.; Yosefvand, F.; Shabanlou, S. Discharge coefficient of side weirs on converging channels using extreme learning machine modeling method. Measurement
**2019**, 152, 107321. [Google Scholar] [CrossRef] - Bonakdari, H.; Zaji, A.H. New type side weir discharge coefficient simulation using three novel hybrid adaptive neuro-fuzzy inference systems. Appl. Water Sci.
**2018**, 8, 10. [Google Scholar] [CrossRef] [Green Version] - Ebtehaj, I.; Bonakdari, H.; Gharabaghi, B. 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. Measurement
**2018**, 116, 473–482. [Google Scholar] [CrossRef] - Khoshbin, F.; Bonakdari, H.; Ashraf Talesh, S.H.; Ebtehaj, I.; Zaji, A.H.; Azimi, H. Adaptive neuro-fuzzy inference system multi-objective optimization using the genetic algorithm/singular value decomposition method for modelling the dis-charge coefficient in rectangular sharp-crested side weirs. Eng. Optim.
**2016**, 48, 933–948. [Google Scholar] [CrossRef] - Ebtehaj, I.; Bonakdari, H.; Zaji, A.H.; Azimi, H.; Sharifi, A. Gene expression programming to predict the discharge coefficient in rectangular side weirs. Appl. Soft Comput.
**2015**, 35, 618–628. [Google Scholar] [CrossRef] - Aydin, M.C.; Emiroglu, M.E. Determination of capacity of labyrinth side weir by CFD. Flow Meas. Instrum.
**2013**, 29, 1–8. [Google Scholar] [CrossRef] - Ahmad, F.; Hussain, A.; Ansari, M.A. Development of ANN model for the prediction of discharge coefficient of an arced labyrinth side weir. Model. Earth Syst. Environ.
**2022**, 1–8. [Google Scholar] [CrossRef] - Hameed, M.M.; AlOmar, M.K.; Khaleel, F.; Al-Ansari, N. An Extra Tree Regression Model for Discharge Coefficient Prediction: Novel, Practical Applications in the Hydraulic Sector and Future Research Directions. Math. Probl. Eng.
**2021**, 2021, 1–19. [Google Scholar] [CrossRef] - Jamei, M.; Ahmadianfar, I.; Chu, X.; Yaseen, Z.M. Estimation of triangular side orifice discharge coefficient under a free flow condition using data-driven models. Flow Meas. Instrum.
**2020**, 77, 101878. [Google Scholar] [CrossRef] - Gharib, R.; Heydari, M.; Kardar, S.; Shabanlou, S. Simulation of discharge coefficient of side weirs placed on con-vergent canals using modern self-adaptive extreme learning machine. Appl. Water Sci.
**2020**, 10, 50. [Google Scholar] [CrossRef] [Green Version] - Mehri, Y.; Soltani, J.; Khashehchi, M. Predicting the coefficient of discharge for piano key side weirs using GMDH and DGMDH techniques. Flow Meas. Instrum.
**2018**, 65, 1–6. [Google Scholar] [CrossRef] - Zaji, A.H.; Bonakdari, H.; Khodashenas, S.R.; Shamshirband, S. Firefly optimization algorithm effect on support vector regression prediction improvement of a modified labyrinth side weir’s discharge coefficient. Appl. Math. Comput.
**2016**, 274, 14–19. [Google Scholar] [CrossRef] - Göğüş, M.; Al-Khatib, I. Flow-Measurement Flumes of Rectangular Compound Cross Section. J. Irrig. Drain. Eng.
**1995**, 121, 135–142. [Google Scholar] [CrossRef] - Ozkandemir, V. Hydraulic Characteristics of Broad-Crested Weirs of Rectangular Compound Cross-Section. Master’s Thesis, Middle East Technical University, Ankara, Turkey, 1997. [Google Scholar]
- Henry, H.R. Discussion of diffusion of submerged jets by ML Albertson, YBDai, RA Jensen, H Rouse. Trans. ASCE
**1950**, 115, 687–694. [Google Scholar] - Safarzadeh, A.; Mohajeri, H. Hydrodynamics of rectangular broad crested porous weirs. J. Irrig. Drain. Eng.
**2018**, 144, 8–24. [Google Scholar] [CrossRef] - Hirt, C.; Nichols, B. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys.
**1981**, 39, 201e225. [Google Scholar] [CrossRef] - Rashid, M.A.; Abustan, I.; Hamzah, M.O. Numerical simulation of a 3-D flow within a storage areahexagonal modular pavement systems. In Proceedings of the 4th International Conference on Energy and Environment 2013 (ICEE 2013), Putrajaya, Malaysia, 20–22 December 2013. [Google Scholar] [CrossRef] [Green Version]
- Parsaie, A.; Haghyabi, A.; Moradinejad, A. CFD modeling of flow pattern in spillway’s approach channel. Water Resour. Manag.
**2015**, 1, 245–251. [Google Scholar] [CrossRef] [Green Version] - Bayon, A.; Valero, D.; Bartual, R.G.; Valles Moran, F.J.; Jimenez, P.A.L. Performance assessment of Open FOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environ. Model. Softw.
**2016**, 80, 322–335. [Google Scholar] [CrossRef] - Hirt, C.W.; Sicilian, J.M. A porosity technique for the definition of obstacles in rectangular cell meshes. In Proceedings of the 4th International Conference on Ship Hydro dynamics, Washington, DC, USA, 24–27 September 1985; National Academy of Sciences: Washington, DC, USA, 1985. [Google Scholar]
- Behbahani, S.D.; Parsaie, A. Numerical modeling of flow pattern in dam spillway’s guide wall. Case study: Balaroud dam, Iran. Alexandria Eng. J.
**2016**, 55, 467–473. [Google Scholar] [CrossRef] [Green Version] - Abbaspoor, A.; Yasi, M. Investigation of Flow in Combined Rectangular-Triangular Weir. Ph.D. Thesis, Urmia University, Urmia, Iran, 2002. [Google Scholar]
- Yakhot, V.; Orszag, S.A. Re normalization Group Analysis of Turbulence: Basic Theory. J. Sci. Comput.
**1986**, 1, 3–51. [Google Scholar] [CrossRef] - Cable, M. An Evaluation of Turbulence Models for the Numerical Study of Forced and Natural Convective Flow in Atria. Ph.D. Thesis, Queens University, Kingston, ON, Canada, 2009. [Google Scholar]
- Wilcox, D.C. Turbulence Modeling for CFD; DCW Industries Inc.: La Canada, CA, USA, 1998. [Google Scholar]
- Quinlan, J.R. Learning with continuous classes. In Proceedings of the 5th Australian Joint Conference on Artificial Intelligence, Hobart, Tasmania, 16–18 November 1992; Volume 92, pp. 343–348. [Google Scholar]
- Solomatine, D.P.; Xue, Y. M5 Model Trees and Neural Networks: Application to Flood Forecasting in the Upper Reach of the Huai River in China. J. Hydrol. Eng.
**2004**, 9, 491–501. [Google Scholar] [CrossRef] - Jothiprakash, V.; Kote, A.S. Effect of Pruning and Smoothing while Using M5 Model Tree Technique for Reservoir Inflow Prediction. J. Hydrol. Eng.
**2011**, 16, 563–574. [Google Scholar] [CrossRef] - Breiman, L. Bagging predictors. Mach. Learn.
**1996**, 24, 123–140. [Google Scholar] [CrossRef] [Green Version] - Breiman, L. Random forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef] [Green Version] - Liu, H.; Ong, Y.-S.; Shen, X.; Cai, J. When Gaussian Process Meets Big Data: A Review of Scalable GPs. IEEE Trans. Neural Netw. Learn. Syst.
**2020**, 31, 4405–4423. [Google Scholar] [CrossRef] [Green Version] - Pasolli, L.; Melgani, F.; Blanzieri, E. Gaussian process regression for estimating chlorophyll concentration in sub-surface waters from remote sensing data. IEEE Geosci. Remote Sens. Lett.
**2010**, 7, 464–468. [Google Scholar] [CrossRef] - Sihag, P.; Tiwari, N.K.; Ranjan, S. Modelling of infiltration of sandy soil using gaussian process regression. Model. Earth Syst. Environ.
**2017**, 3, 1091–1100. [Google Scholar] [CrossRef] - Shabani, S.; Samadianfard, S.; Sattari, M.T.; Mosavi, A.; Shamshirband, S.; Kmet, T.; Várkonyi-Kóczy, A.R. Modeling Pan Evaporation Using Gaussian Process Regression K-Nearest Neighbors Random Forest and Support Vector Machines; Comparative Analysis. Atmosphere
**2020**, 11, 66. [Google Scholar] [CrossRef] [Green Version] - Yu, Y.; Li, Y.; Li, J. Forecasting hysteresis behaviors of magnetorheological elastomer base isolator utilizing a hybrid model based on support vector regression and improved particle swarm optimization. Smart Mater. Struct.
**2015**, 24, 035025. [Google Scholar] [CrossRef] - Yu, Y.; Li, Y.; Li, J.; Gu, X. Self-adaptive step fruit fly algorithm optimized support vector regression model for dynamic response prediction of magnetorheological elastomer base isolator. Neurocomputing
**2016**, 211, 41–52. [Google Scholar] [CrossRef] [Green Version] - Sihag, P.; Jain, P.; Kumar, M. Modelling of impact of water quality on recharging rate of storm water filter system using various kernel function based regression. Model. Earth Syst. Environ.
**2018**, 4, 61–68. [Google Scholar] [CrossRef] - Haykin, S. Self-Organizing Maps. Neural networks—A Comprehensive Foundation, 2nd ed.; Prentice-Hall: Hoboken, NJ, USA, 1999. [Google Scholar]
- Taylor, K.E. Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res. Atmos.
**2001**, 106, 7183–7192. [Google Scholar] [CrossRef] - Nouri, M.; Hemmati, M. Discharge coefficient in the combined weir-gate structure. Flow Meas. Instrum.
**2020**, 75, 101780. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Definition sketch of compound BCW: (

**b**,

**c**) two diverse flow cases through the compound BCW segment.

**Figure 2.**(

**a**) Sketch for simultaneous flow over compound BCW and below gate: (

**b**,

**c**) are two diverse flow cases through the combined compound BCW gate.

**Figure 3.**Single broad-crested weir studied by Salmasi et al., [12].

**Figure 4.**Estimated C

_{dw}using numerical models; (

**a**) Broad crested weir with B/B

_{0}= 0.24, (

**b**)Broad crested weir with B/B

_{0}= 0.32.

**Figure 5.**Combined compound BCW gate and boundary conditions used; X

_{min}: P (specified pressure); X

_{max}: O (outflow); Y

_{min}, Y

_{max}and Z

_{min}: W (wall); Z

_{max}: S (symmetry).

**Figure 7.**Performance of M5P, RF, GP, SVM and MLR models in predicting C

_{dt}of BCW gate during model calibration and validation.

**Figure 9.**Agreement plot of multimode ANN prediction with observed C

_{dt}of BCW gate during training and testing.

**Table 1.**Variables and their range used in the study of Salmasi et al., [12].

Parameters | L (cm) | B_{0} (cm) | B (cm) | p (cm) | Z (cm) |
---|---|---|---|---|---|

Range of variables | 40 | 25 | 6, 8 and 12 | 10, 13 and 16 | 9 |

Parameters’ Values | Dimensionless Parameters |
---|---|

d/P | 0.36, 0.43, 0.52, 0.62 |

b/B_{0} | 0.28, 0.4 |

Z/P | 0.31, 0.56 |

B/B_{o} | 0.24, 0.32, 0.48 |

h_{1}/H | 0.15, 0.2, 0.33, 0.42, 0.45, 0.54 |

d/P | 0.36, 0.43, 0.52, 0.62 |

Range | Training Data Set | |||||
---|---|---|---|---|---|---|

d/p | b/B_{0} | Z/P | B/B_{0} | h_{1}/H | C_{dt} | |

Mean | 0.4657 | 0.3502 | 0.4722 | 0.3629 | 0.3332 | 0.7945 |

Median | 0.4375 | 0.4000 | 0.5625 | 0.3200 | 0.3333 | 0.8051 |

Standard deviation | 0.0996 | 0.0599 | 0.1203 | 0.1045 | 0.1309 | 0.0800 |

Kurtosis | −0.9827 | −1.9691 | −1.7536 | −1.7811 | −1.2383 | −0.1968 |

Skewness | 0.7604 | −0.3599 | −0.5784 | 0.0931 | 0.0572 | −0.6304 |

Minimum | 0.3684 | 0.2800 | 0.3158 | 0.2400 | 0.1579 | 0.6155 |

Maximum | 0.6250 | 0.4000 | 0.5625 | 0.4800 | 0.5429 | 0.9303 |

Confidence level (95.0%) | 0.0314 | 0.0189 | 0.0380 | 0.0330 | 0.0413 | 0.0252 |

Testing Data Set | ||||||

Mean | 0.4809 | 0.3520 | 0.4885 | 0.3600 | 0.3936 | 0.8188 |

Median | 0.4375 | 0.4000 | 0.5625 | 0.3200 | 0.4286 | 0.8329 |

Standard deviation | 0.1039 | 0.0603 | 0.1160 | 0.1054 | 0.1251 | 0.0748 |

Kurtosis | −1.4170 | −2.0180 | −1.2418 | −1.8330 | −0.5960 | −1.2048 |

Skewness | 0.5357 | −0.4421 | −0.9453 | 0.1533 | −0.4966 | −0.2163 |

Minimum | 0.3684 | 0.2800 | 0.3158 | 0.2400 | 0.1579 | 0.6915 |

Maximum | 0.6250 | 0.4000 | 0.5625 | 0.4800 | 0.5429 | 0.9235 |

Confidence level (95.0%) | 0.0486 | 0.0282 | 0.0543 | 0.0493 | 0.0586 | 0.0350 |

Approaches | Kernel Function | User-Defined Parameters |
---|---|---|

M5P | m = 4 | |

RF | m = 1 & K = 10 | |

SVM | RBF kernel | C = 2, $\gamma $ = 1 |

GP | RBF kernel | Gaussian noise = 0.01, $\gamma $ = 1 |

Approaches | CC | MAE | RMSE | Nash | SI |
---|---|---|---|---|---|

Training Data Set | |||||

M5P | 0.9550 | 0.0171 | 0.1492 | 0.9121 | 0.1878 |

RF | 0.9867 | 0.0106 | 0.0135 | 0.9706 | 0.0170 |

GP | 1.0000 | 0.0007 | 0.0009 | 0.9999 | 0.0012 |

SVM | 1.0000 | 0.0003 | 0.0005 | 1.0000 | 0.0007 |

MLR | 0.9465 | 0.0183 | 0.0255 | 0.8959 | 0.0320 |

Testing data set | |||||

M5P | 0.9148 | 0.0208 | 0.0408 | 0.8354 | 0.0498 |

RF | 0.9187 | 0.0240 | 0.0297 | 0.8339 | 0.0363 |

GP | 0.9581 | 0.0239 | 0.0277 | 0.8557 | 0.0338 |

SVM | 0.9585 | 0.0237 | 0.0276 | 0.8562 | 0.0337 |

MLR | 0.8549 | 0.0284 | 0.0380 | 0.7280 | 0.0464 |

Sr No. | Method | F | p-Value | F Crit | Variation between Groups |
---|---|---|---|---|---|

1 | M5P | 0.00483 | 0.944955 | 4.098172 | Insignificant |

2 | RF | 0.017288 | 0.896086 | 4.098172 | Insignificant |

3 | GP | 0.132998 | 0.717366 | 4.098172 | Insignificant |

4 | SVM | 0.124141 | 0.726533 | 4.098172 | Insignificant |

5 | MLR | 0.028042 | 0.867899 | 4.098172 | Insignificant |

Input Combination | Removed Parameter | Statistical Parameters (Testing Data Set) | ||||||
---|---|---|---|---|---|---|---|---|

d/p | b/B_{0} | z/p | B/B_{0} | h_{1}/H | CC | MAE | RMSE | |

None | 0.9585 | 0.0237 | 0.0276 | |||||

d/p | 0.6472 | 0.0456 | 0.0580 | |||||

b/B_{0} | 0.8553 | 0.0292 | 0.0381 | |||||

z/p | 0.9449 | 0.0212 | 0.0264 | |||||

B/B_{0} | 0.9006 | 0.0254 | 0.0330 | |||||

h_{1}/H | 0.3575 | 0.0671 | 0.0743 |

Statistic | M5P | RF | GP | SVM | MLR | Novel Multimode ANN |
---|---|---|---|---|---|---|

Minimum | −0.0460 | −0.0470 | −0.0420 | −0.0420 | −0.0468 | −0.0400 |

Maximum | 0.0960 | 0.0750 | 0.0500 | 0.0510 | 0.1130 | 0.0470 |

First Quartile | −0.0170 | −0.0295 | −0.0140 | −0.0140 | −0.0242 | −0.0118 |

Median | −0.0005 | −0.0045 | 0.0110 | 0.0095 | 0.0008 | 0.0090 |

Third Quartile | 0.0170 | 0.0153 | 0.0285 | 0.0278 | 0.0242 | 0.0263 |

Mean | 0.0016 | −0.0029 | 0.0076 | 0.0073 | 0.0037 | 0.0065 |

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## Share and Cite

**MDPI and ACS Style**

Nouri, M.; Sihag, P.; Kisi, O.; Hemmati, M.; Shahid, S.; Adnan, R.M.
Prediction of the Discharge Coefficient in Compound Broad-Crested-Weir Gate by Supervised Data Mining Techniques. *Sustainability* **2023**, *15*, 433.
https://doi.org/10.3390/su15010433

**AMA Style**

Nouri M, Sihag P, Kisi O, Hemmati M, Shahid S, Adnan RM.
Prediction of the Discharge Coefficient in Compound Broad-Crested-Weir Gate by Supervised Data Mining Techniques. *Sustainability*. 2023; 15(1):433.
https://doi.org/10.3390/su15010433

**Chicago/Turabian Style**

Nouri, Meysam, Parveen Sihag, Ozgur Kisi, Mohammad Hemmati, Shamsuddin Shahid, and Rana Muhammad Adnan.
2023. "Prediction of the Discharge Coefficient in Compound Broad-Crested-Weir Gate by Supervised Data Mining Techniques" *Sustainability* 15, no. 1: 433.
https://doi.org/10.3390/su15010433