Equivalent Discharge Coefficient of Side Weirs in Circular Channel—A Lazy Machine Learning Approach
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Setup
2.2. k Nearest Neighbor and K-Star
2.3. Random Forest
2.4. Support Vector Regression
2.5. Multilayer Perceptron
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Model | Number of Input Variables | Input Variables | No. of Hidden Layers | Number of Nodes |
---|---|---|---|---|
1 | 5 | Qo*, Γ, Ho/w, L/D, Lw/D2 | 3 | 6, 10, 6 |
2 | 4 | Γ, Ho/w, L/D, Lw/D2 | 2 | 40, 2 |
3 | 3 | Γ, Ho/w, Lw/D2 | 3 | 3, 100, 3 |
4 | 3 | Γ, Ho/w, L/D | 3 | 3, 100, 2 |
Nash–Sutcliffe Efficiency: It evaluates how the model fits experimental results and how well it predicts future outcomes. Hence, it represents a measure of the model accuracy. | |
Mean Absolute Error: It is the average of the absolute values of the errors, therefore it is an indicator of the distance between the predictions and the observed values. | |
Root Mean Square Error: It is the square root of the average of squared differences between predicted and experimental values. It has the advantage of penalizing large errors. | |
Relative Absolute Error: It represents a normalized total absolute error. |
Model | Input Variables | Algorithm | NSE | MAE | RMSE | RAE |
---|---|---|---|---|---|---|
1 | Qo* | k-NN | 0.863 | 0.0103 | 0.0159 | 29.8% |
Γ | K-Star | 0.912 | 0.0075 | 0.0119 | 21.7% | |
Ho/w | RF | 0.865 | 0.0089 | 0.0147 | 26.0% | |
L/D | SVR | 0.784 | 0.0128 | 0.0186 | 37.2% | |
Lw/D2 | MLP | 0.602 | 0.0232 | 0.0314 | 67.5% | |
2 | k-NN | 0.857 | 0.0105 | 0.0161 | 30.6% | |
Γ | K-Star | 0.845 | 0.0117 | 0.0166 | 34.1% | |
Ho/w | RF | 0.843 | 0.0110 | 0.0159 | 32.1% | |
L/D | SVR | 0.721 | 0.0150 | 0.0213 | 43.5% | |
Lw/D2 | MLP | 0.587 | 0.0218 | 0.0304 | 63.4% | |
3 | k-NN | 0.477 | 0.0229 | 0.0329 | 66.5% | |
Γ | K-Star | 0.185 | 0.0275 | 0.0387 | 79.9% | |
Ho/w | RF | 0.441 | 0.0225 | 0.0305 | 65.4% | |
Lw/D2 | SVR | 0.361 | 0.0270 | 0.0331 | 78.3% | |
MLP | 0.302 | 0.0334 | 0.0404 | 96.9% | ||
4 | k-NN | 0.462 | 0.0213 | 0.0334 | 61.8% | |
Γ | K-Star | 0.394 | 0.0202 | 0.0332 | 58.6% | |
Ho/w | RF | 0.529 | 0.0192 | 0.029 | 55.7% | |
L/D | SVR | 0.567 | 0.0179 | 0.0268 | 52.1% | |
MLP | 0.612 | 0.0338 | 0.0416 | 98.3% |
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Granata, F.; Di Nunno, F.; Gargano, R.; de Marinis, G. Equivalent Discharge Coefficient of Side Weirs in Circular Channel—A Lazy Machine Learning Approach. Water 2019, 11, 2406. https://doi.org/10.3390/w11112406
Granata F, Di Nunno F, Gargano R, de Marinis G. Equivalent Discharge Coefficient of Side Weirs in Circular Channel—A Lazy Machine Learning Approach. Water. 2019; 11(11):2406. https://doi.org/10.3390/w11112406
Chicago/Turabian StyleGranata, Francesco, Fabio Di Nunno, Rudy Gargano, and Giovanni de Marinis. 2019. "Equivalent Discharge Coefficient of Side Weirs in Circular Channel—A Lazy Machine Learning Approach" Water 11, no. 11: 2406. https://doi.org/10.3390/w11112406