Heuristic Methods for Reservoir Monthly Inflow Forecasting: A Case Study of Xinfengjiang Reservoir in Pearl River, China
Abstract
:1. Introduction
2. Study Area and Data Sets
2.1. Study Area
2.2. Division of Data
Datasets | Statistic | ||||
---|---|---|---|---|---|
Xmean | Sd | Xmin | Xmax | Range | |
Training set | 204.1 | 14.3 | 9.3 | 1506.0 | 1496.7 |
Testing set | 192.1 | 13.9 | 24.5 | 1300.2 | 1275.7 |
Validation set | 176.3 | 13.3 | 22.3 | 1496.4 | 1474.1 |
Original data | 195.3 | 14.0 | 9.3 | 1506.0 | 1496.7 |
2.3. Data Preprocessing
3. Forecasting Methodology
3.1. Artificial Neural Network (ANN)
3.2. Support Vector Machine (SVM)
3.3. Genetic Algorithm (GA)
3.4. Hybrid Forecasting Method
4. Statistical Measures
5. Results and Discussion
5.1. Input Variables Determination
5.2. Development of Various Models
5.2.1. ANN Model A1 Development
5.2.2. SVM Model S1 Development
Trial No. | Optimal Parameters (C, ε, σ) | Training | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAPE | MAE | NS | R | RMSE | MAPE | MAE | NS | R | ||
1 | (10.653, 1.032, 0.078) | 151.00 | 59.19 | 87.85 | 0.49 | 0.70 | 153.90 | 70.23 | 93.03 | 0.42 | 0.64 |
2 | (9.827, 0.435, 0.064) | 144.82 | 54.29 | 85.60 | 0.53 | 0.73 | 133.07 | 61.87 | 82.54 | 0.56 | 0.75 |
3 | (2.783, 0.678, 0.125) | 152.46 | 61.54 | 88.08 | 0.48 | 0.69 | 152.51 | 66.38 | 89.44 | 0.43 | 0.65 |
4 | (9.425, 0.823, 0.081) | 118.66 | 70.48 | 82.44 | 0.68 | 0.83 | 96.60 | 75.73 | 74.36 | 0.77 | 0.89 |
5 | (11.803, 1.254, 0.708) | 147.80 | 64.17 | 88.98 | 0.51 | 0.71 | 154.22 | 74.28 | 94.58 | 0.41 | 0.65 |
5.2.3. ANN Model A2 Development
5.3. Comparison and Discussion
Models | Training | Validation | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAPE | MAE | NS | R | RMSE | MAPE | MAE | NS | R | |
SVM | 118.66 | 70.48 | 82.44 | 0.68 | 0.83 | 96.60 | 75.73 | 74.36 | 0.77 | 0.89 |
ANN | 118.60 | 55.20 | 79.73 | 0.68 | 0.83 | 102.09 | 63.68 | 73.49 | 0.74 | 0.87 |
Hybrid Method | 95.86 | 48.28 | 62.44 | 0.79 | 0.89 | 85.72 | 49.78 | 58.33 | 0.82 | 0.91 |
Peak No. | Date | Observed | Forecast Peak | Relative Error (%) | ||||
---|---|---|---|---|---|---|---|---|
Peak | SVM | ANN | Hybrid Method | SVM | ANN | Hybrid Method | ||
1 | 1999/9 | 362.0 | 327.9 | 346.9 | 369.5 | −9.4 | −4.2 | 2.1 |
2 | 2000/4 | 497.9 | 516.0 | 507.5 | 434.9 | 3.6 | 1.9 | −12.7 |
3 | 2001/6 | 618.1 | 530.3 | 488.4 | 492.9 | −14.2 | −21.0 | −20.3 |
4 | 2002/8 | 352.6 | 349.1 | 376.7 | 386.2 | −1.0 | 6.8 | 9.5 |
5 | 2003/6 | 336.2 | 272.0 | 285.6 | 334.4 | −19.1 | −15.1 | −0.5 |
6 | 2004/5 | 202.8 | 237.3 | 236.8 | 225.8 | 17.0 | 16.8 | 11.3 |
7 | 2005/6 | 1496.4 | 1355.5 | 1381.3 | 1405.7 | −9.4 | −7.7 | −6.1 |
8 | 2006/6 | 783.8 | 583.2 | 598.1 | 679.5 | −25.6 | −23.7 | −13.3 |
9 | 2007/6 | 687.5 | 555.7 | 581.4 | 592.1 | −19.2 | −15.4 | −13.9 |
10 | 2008/6 | 1066.0 | 776.5 | 792.3 | 840.5 | −27.2 | −25.7 | −21.2 |
11 | 2009/6 | 228.2 | 211.5 | 252.4 | 236.1 | −7.3 | 10.6 | 3.5 |
12 | 2010/6 | 867.5 | 701.4 | 626.7 | 677.5 | −19.2 | −27.8 | −21.9 |
13 | 2011/5 | 369.6 | 293.5 | 244.1 | 319.3 | −20.6 | −34.0 | −13.6 |
14 | 2012/6 | 442.3 | 315.6 | 348.7 | 419.6 | −28.6 | −21.2 | −5.1 |
15 | 2013/5 | 860.9 | 766.5 | 794.2 | 778.3 | −11.0 | −7.7 | −9.6 |
16 | 2014/5 | 616.2 | 544.8 | 567.0 | 584.9 | −11.6 | −8.0 | −5.1 |
Average (absolute) | 15.2 | 15.5 | 10.6 |
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Cheng, C.-T.; Feng, Z.-K.; Niu, W.-J.; Liao, S.-L. Heuristic Methods for Reservoir Monthly Inflow Forecasting: A Case Study of Xinfengjiang Reservoir in Pearl River, China. Water 2015, 7, 4477-4495. https://doi.org/10.3390/w7084477
Cheng C-T, Feng Z-K, Niu W-J, Liao S-L. Heuristic Methods for Reservoir Monthly Inflow Forecasting: A Case Study of Xinfengjiang Reservoir in Pearl River, China. Water. 2015; 7(8):4477-4495. https://doi.org/10.3390/w7084477
Chicago/Turabian StyleCheng, Chun-Tian, Zhong-Kai Feng, Wen-Jing Niu, and Sheng-Li Liao. 2015. "Heuristic Methods for Reservoir Monthly Inflow Forecasting: A Case Study of Xinfengjiang Reservoir in Pearl River, China" Water 7, no. 8: 4477-4495. https://doi.org/10.3390/w7084477