Comparison of designed ANFIS scenarios
Model . | Input . | Output . | Iteration . | Sub-sets . | Membership function . | Training RMSE . | Test RMSE . | Training R2 . | Test R2 . |
---|---|---|---|---|---|---|---|---|---|
1 | Qt-1 | Qt | 1,000 | 5 | Gauss2mf | 15.03 | 12.97 | 0.48 | 0.40 |
2 | Qt-1, Qt-2 | Qt | 2,000 | 7-7 | Gauss2mf | 10.87 | 10.91 | 0.73 | 0.62 |
3 | Qt-1, Qt-2, Qt-3 | Qt | 100 | 4-4-4 | Gaussmf | 12.34 | 10.11 | 0.65 | 0.67 |
4 | Qt-1, Qt-2, Qt-3, Qt-4 | Qt | 5,000 | 2-2-2-2 | Trimf | 12.01 | 10.07 | 0.67 | 0.68 |
5 | Qt-1, Qt-2, Qt-3, Qt-4, Qt-5 | Qt | 100 | 3-3-3-3-3 | Gbellmf | 11.90 | 11.23 | 0.68 | 0.60 |
6 | Qt-1, Qt-2, Qt-3, Qt-4, Qt-5, Qt-6 | Qt | 2,000 | All 2 | Trimf | 11.82 | 10.64 | 0.68 | 0.64 |
7 | Qt-1, Qt-2, …, Qt-7 | Qt | 300 | All 2 | Trimf | 10,94 | 10.80 | 0.73 | 0.65 |
8 | Qt-1, Qt-2, …., Qt-8 | Qt | 50 | All 2 | Trimf | 10.95 | 12.19 | 0.76 | 0.58 |
9 | Qt-1, Qt-2, …, Qt-9 | Qt | 50 | All 2 | Trimf | 9.52 | 12.64 | 0.79 | 0.58 |
10 | Qt-1, Qt-2, …, Qt-10 | Qt | 10 | All 2 | Gaussmf | 10.85 | 11.21 | 0.73 | 0.62 |
11 | Qt-1, Qt-2, …, Qt-11 | Qt | 20 | All 2 | Trimf | 6.38 | 12.59 | 0.90 | 0.57 |
Model . | Input . | Output . | Iteration . | Sub-sets . | Membership function . | Training RMSE . | Test RMSE . | Training R2 . | Test R2 . |
---|---|---|---|---|---|---|---|---|---|
1 | Qt-1 | Qt | 1,000 | 5 | Gauss2mf | 15.03 | 12.97 | 0.48 | 0.40 |
2 | Qt-1, Qt-2 | Qt | 2,000 | 7-7 | Gauss2mf | 10.87 | 10.91 | 0.73 | 0.62 |
3 | Qt-1, Qt-2, Qt-3 | Qt | 100 | 4-4-4 | Gaussmf | 12.34 | 10.11 | 0.65 | 0.67 |
4 | Qt-1, Qt-2, Qt-3, Qt-4 | Qt | 5,000 | 2-2-2-2 | Trimf | 12.01 | 10.07 | 0.67 | 0.68 |
5 | Qt-1, Qt-2, Qt-3, Qt-4, Qt-5 | Qt | 100 | 3-3-3-3-3 | Gbellmf | 11.90 | 11.23 | 0.68 | 0.60 |
6 | Qt-1, Qt-2, Qt-3, Qt-4, Qt-5, Qt-6 | Qt | 2,000 | All 2 | Trimf | 11.82 | 10.64 | 0.68 | 0.64 |
7 | Qt-1, Qt-2, …, Qt-7 | Qt | 300 | All 2 | Trimf | 10,94 | 10.80 | 0.73 | 0.65 |
8 | Qt-1, Qt-2, …., Qt-8 | Qt | 50 | All 2 | Trimf | 10.95 | 12.19 | 0.76 | 0.58 |
9 | Qt-1, Qt-2, …, Qt-9 | Qt | 50 | All 2 | Trimf | 9.52 | 12.64 | 0.79 | 0.58 |
10 | Qt-1, Qt-2, …, Qt-10 | Qt | 10 | All 2 | Gaussmf | 10.85 | 11.21 | 0.73 | 0.62 |
11 | Qt-1, Qt-2, …, Qt-11 | Qt | 20 | All 2 | Trimf | 6.38 | 12.59 | 0.90 | 0.57 |
Note: Bold characters indicate the most successful ANFIS model.
Correlation coefficients of sub-series
Sub-series . | D1 . | D2 . | D3 . | A3 . |
---|---|---|---|---|
Qt-1 | −0.17 | 0.16 | 0.64 | 0.35 |
Qt-2 | −0.21 | −0.34 | 0.42 | 0.32 |
Qt-3 | 0.10 | −0.41 | 0.02 | 0.27 |
Qt-4 | 0.15 | −0.17 | −0.37 | −0.30 |
Qt-5 | −0.08 | 0.25 | −0.61 | 0.16 |
Qt-6 | −0.12 | 0.35 | −0.70 | 0.11 |
Qt-7 | 0.04 | 0.10 | −0.60 | 0.07 |
Qt-8 | 0.14 | −0.18 | −0.32 | 0.03 |
Qt-9 | 0.00 | −0.28 | −0.01 | 0.02 |
Qt-10 | −0.17 | −0.08 | 0.29 | 0.01 |
Qt-11 | −0.03 | 0.20 | 0.56 | 0.01 |
Sub-series . | D1 . | D2 . | D3 . | A3 . |
---|---|---|---|---|
Qt-1 | −0.17 | 0.16 | 0.64 | 0.35 |
Qt-2 | −0.21 | −0.34 | 0.42 | 0.32 |
Qt-3 | 0.10 | −0.41 | 0.02 | 0.27 |
Qt-4 | 0.15 | −0.17 | −0.37 | −0.30 |
Qt-5 | −0.08 | 0.25 | −0.61 | 0.16 |
Qt-6 | −0.12 | 0.35 | −0.70 | 0.11 |
Qt-7 | 0.04 | 0.10 | −0.60 | 0.07 |
Qt-8 | 0.14 | −0.18 | −0.32 | 0.03 |
Qt-9 | 0.00 | −0.28 | −0.01 | 0.02 |
Qt-10 | −0.17 | −0.08 | 0.29 | 0.01 |
Qt-11 | −0.03 | 0.20 | 0.56 | 0.01 |
Note: Bold characters indicate the sub-signals selected as input to the model.
Autocorrelation and partial autocorrelation functions of streamflow values.