Modeling Average Grain Velocity for Rectangular Channel Using Soft Computing Techniques
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Setup and Data Observation
2.1.1. Methodology
2.1.2. Input Parameters
2.2. Multiple Linear Regression—MLR
2.3. Artificial Neural Network—ANN
2.4. Support Vector Machine-SVM
2.5. Performance Evaluation
3. Results and Discussion
3.1. Statistical Parameters
3.2. Trial Selection
3.3. Quantitative Performance Evaluation
3.4. Qualitative Performance Evaluation
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations and Nomenclature
References
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Variables | Mean | Median | Minimum | Maximum | Std. Dev. | C.V. | Skewness |
---|---|---|---|---|---|---|---|
All Data | |||||||
λ | 0.9707 | 1.000 | 0.5700 | 1.000 | 0.0823 | 0.0848 | −3.283 |
W | 51.733 | 49.60 | 32.200 | 73.40 | 16.966 | 0.32795 | 0.1874 |
U* | 0.0754 | 0.0731 | 0.0529 | 0.1030 | 0.0120 | 0.1598 | 0.4072 |
y/d | 0.8573 | 0.7142 | 0.2500 | 2.352 | 0.4281 | 0.4994 | 1.220 |
Vp | 0.5473 | 0.600 | 0.0 | 1.174 | 0.3352 | 0.6124 | −0.2776 |
Training Data | |||||||
λ | 0.9793 | 1.0 | 0.6 | 1.0 | 0.0706 | 0.0721 | −3.964 |
W | 51.476 | 49.6 | 32.2 | 73.4 | 17.035 | 0.3309 | 0.2091 |
U* | 0.0696 | 0.0688 | 0.0529 | 0.0862 | 0.008 | 0.1150 | 0.0828 |
y/d | 0.7894 | 0.6667 | 0.25 | 2.222 | 0.4031 | 0.5106 | 1.295 |
Vp | 0.4070 | 0.474 | 0.0 | 0.8440 | 0.2793 | 0.6863 | −0.3741 |
Testing Data | |||||||
λ | 0.9503 | 1.0 | 0.57 | 1.0 | 0.1035 | 0.1089 | −2.368 |
W | 52.344 | 49.6 | 32.2 | 73.4 | 17.05 | 0.3258 | 0.1369 |
U* | 0.0892 | 0.0903 | 0.0774 | 0.103 | 0.0081 | 0.0914 | 0.1011 |
y/d | 1.0185 | 0.8012 | 0.5714 | 2.352 | 0.4489 | 0.4407 | 1.1701 |
Vp | 0.8806 | 0.8855 | 0.333 | 1.174 | 0.1901 | 0.2159 | −0.6570 |
Model | Training | Testing | ||||
---|---|---|---|---|---|---|
RMSE (m/s) | PCC | WI | RMSE (m/s) | PCC | WI | |
MLR | 0.1340 | 0.8756 | 0.7532 | 0.1459 | 0.8375 | 0.6789 |
ANN | ||||||
Trial-1 | 0.1266 | 0.8911 | 0.8106 | 0.3109 | 0.1509 | 0.3420 |
Trial-2 | 0.0873 | 0.9502 | 0.8756 | 0.2154 | 0.3636 | 0.4579 |
Trial-3 | 0.0689 | 0.9692 | 0.8799 | 0.1721 | 0.5176 | 0.5012 |
Trial-4 | 0.0663 | 0.9728 | 0.8999 | 0.2302 | 0.1945 | 0.3666 |
Trial-5 | 0.0699 | 0.9678 | 0.8916 | 0.1906 | 0.4365 | 0.4751 |
Trial-6 | 0.0759 | 0.9625 | 0.9439 | 0.1821 | 0.4900 | 0.5058 |
SVM | ||||||
Trial-1 | 0.1423 | 0.8595 | 0.7475 | 0.1208 | 0.8852 | 0.7231 |
Trial-2 | 0.1381 | 0.8675 | 0.7531 | 0.1341 | 0.8688 | 0.7022 |
Trial-3 | 0.1431 | 0.8577 | 0.7479 | 0.1195 | 0.8877 | 0.7243 |
Trial-4 | 0.1408 | 0.8622 | 0.7513 | 0.1247 | 0.8795 | 0.7150 |
Model/Trial | Architecture |
---|---|
ANN | |
Trial-1 | 4-1-1 |
Trial-2 | 4-4-1 |
Trial-3 | 4-5-1 |
Trial-4 | 4-7-1 |
Trial-5 | 4-5-5-1 |
Trial-6 | 4-4-4-4-1 |
SVM | |
Trial-1 | C = 10, = 0.25, ε = 0.01 |
Trial-2 | C = 10, = 0.25, ε = 0.1 |
Trial-3 | C = 10, = 0.45, ε = 0.01 |
Trial-4 | C = 10, = 0.45, ε = 0.05 |
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Kumari, A.; Kumar, A.; Kumar, M.; Kuriqi, A. Modeling Average Grain Velocity for Rectangular Channel Using Soft Computing Techniques. Water 2022, 14, 1325. https://doi.org/10.3390/w14091325
Kumari A, Kumar A, Kumar M, Kuriqi A. Modeling Average Grain Velocity for Rectangular Channel Using Soft Computing Techniques. Water. 2022; 14(9):1325. https://doi.org/10.3390/w14091325
Chicago/Turabian StyleKumari, Anuradha, Akhilesh Kumar, Manish Kumar, and Alban Kuriqi. 2022. "Modeling Average Grain Velocity for Rectangular Channel Using Soft Computing Techniques" Water 14, no. 9: 1325. https://doi.org/10.3390/w14091325