Abstract
Weirs are often used to measure discharge and control upstream water levels. The accurate estimation of flow discharge from circular-crested oblique weirs depends on the accurate estimation of the discharge coefficient (Cd). Therefore, presenting a method that can provide an accurate output of this important parameter would be a significant aid to designers of hydraulic structures. Accordingly, in the first part of this study, new hybrid models using support vector machine (SVM) coupled with particle swarm optimization (PSO) and the genetic algorithm (GA) are developed for estimating the Cd of circular-crested oblique weirs. The ability of the hybrid developed models (SVM-PSO and SVM-GA) was compared with that of the single model (SVM). In the second part, the results of the intelligence models were compared with regression models, namely multiple linear regression (MLR) and multiple nonlinear regression (MNLR). To assess the performance of the proposed models, statistical indicators including R2, RMSE, RE%, and KGE, and graphical diagrams including Violin, RE%, Scatter, and Taylor plots were used. The results indicate that the performance of the SVM-GA model with R2 = 0.992, RMSE = 0.009, RE% = 1.43%, and KGE = 0.988 is better than the other intelligence models for estimating Cd for circular-crested oblique weirs. According to the Taylor plot, it is clear that the distance index obtained using the SVM-GA model is very close to the observed data, especially when compared with other methods. The SVM-GA model was also compared with regression models. The results indicate that the SVM-GA model estimates the Cd for circular-crested oblique weirs more accurately than the MLR and MNLR models.
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Abbreviations
- Q:
-
Discharge (m3/s)
- Cd :
-
Discharge coefficient (-)
- Re:
-
Reynolds number (-)
- Lc:
-
Weir crest length (m)
- He:
-
Total head above weir crest (m)
- P:
-
Weir height (m)
- D:
-
Weir crest diameter (m)
- \(\alpha\) :
-
Weir oblique angle (radian)
- g :
-
Acceleration due to gravity (m/s2)
- \({\uprho }\) :
-
Fluid mass density (kg/m3)
- \({\upmu }\) :
-
Fluid dynamic viscosity (kg/m·s)
- R2 :
-
Coefficient of determination
- RMSE:
-
Root mean square error
- RE%:
-
Relative error percent
- KGE:
-
Kling–Gupta efficiency
- MLR:
-
Multiple linear regression
- MNLR:
-
Multiple nonlinear regression
- SVM:
-
Support vector machine
- SVR:
-
Support vector regression
- GA:
-
Genetic algorithm
- PSO:
-
Particle swarm optimization
- ANN:
-
Artificial neural network
- BPNN:
-
Back-propagation neural network
- CFNN:
-
Cascade-forward neural network
- RBFN:
-
Radial basis function network
- GPR:
-
Gaussian process regression
- MLP:
-
Multilayer perceptron
- RF:
-
Random forest
- GEP:
-
Gene expression programming
- ANFIS:
-
Adaptive neural fuzzy inference system
- FF:
-
Firefly optimization
- WOA:
-
Whale optimization algorithm
- HHO:
-
Harris Hawks optimization algorithm
- SPSS:
-
Statistical package for social sciences
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Nourani, B., Arvanaghi, H., Pourhosseini, F.A. et al. Enhanced Support Vector Machine with Particle Swarm Optimization and Genetic Algorithm for Estimating Discharge Coefficients of Circular-Crested Oblique Weirs. Iran J Sci Technol Trans Civ Eng 47, 3185–3198 (2023). https://doi.org/10.1007/s40996-023-01110-0
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DOI: https://doi.org/10.1007/s40996-023-01110-0