The comparison of the statistical criteria of the most suitable W-ANFIS models is presented in Table 3. When W-ANFIS models are compared, it is noteworthy that model 6 is the most successful. Accordingly, it is seen that the best estimation model can be established by separating the 400 iterations, the Gbellmf membership function, and the inputs into two sub-series.
Comparison of designed W-ANFIS scenarios
| Model . | Input . | Output . | Iteration . | Sub-sets . | Membership function . | Training RMSE . | Test RMSE . | Training R2 . | Test R2 . |
|---|---|---|---|---|---|---|---|---|---|
| 1 | Q(t–1)(D2+D3) | Q(t) | 1,000 | 3 | Gbellmf | 15.68 | 13.61 | 0.44 | 0.41 |
| 2 | Q(t–1)(D2+D3), Q(t–2)(D3+A3) | Q(t) | 1,000 | 5 5 | Gauss2mf | 13.70 | 14.57 | 0.57 | 0.35 |
| 3 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), Q(t–3)(A4) | Q(t) | 800 | 4 4 4 | Gbellmf | 9.92 | 12.09 | 0.78 | 0.53 |
| 4 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), Q(t–3)(A4), Q(t–4)(D1) | Q(t) | 100 | 3-3-3-3 | Gaussmf | 9.09 | 9.26 | 0.81 | 0.73 |
| 5 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), Q(t–3)(A4), Q(t–4)(D1), Q(t–5)(D2+A3) | Qt | 200 | 3-3-3-3-3 | Trimf | 6.59 | 10.35 | 0.90 | 0.66 |
| 6 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), Q(t–3)(A4), Q(t–4)(D1), Q(t–5)(D2+A3), Q(t–6)(D2+A3) | Qt | 400 | All 2 | Gbellmf | 7.49 | 9.13 | 0.87 | 0.73 |
| 7 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …, Q(t–7)(D2) | Qt | 100 | All 2 | Gaussmf | 6.58 | 9.58 | 0.90 | 0.71 |
| 8 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …., Q(t–8)(D1) | Qt | 50 | All 2 | Gaussmf | 5.40 | 10.19 | 0.93 | 0.69 |
| 9 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …, Q(t–9) | Qt | 20 | All 2 | Gbellmf | 4.67 | 11.63 | 0.95 | 0.63 |
| 10 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …, Q(t–10)(D3) | Qt | 10 | All 2 | Trimf | 38.72 | 31.07 | 0.10 | 0.02 |
| 11 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …, Q(t–11)(D2+D3) | Qt | 20 | All 2 | Trimf | 37.52 | 30.89 | 0.06 | 0.01 |
| Model . | Input . | Output . | Iteration . | Sub-sets . | Membership function . | Training RMSE . | Test RMSE . | Training R2 . | Test R2 . |
|---|---|---|---|---|---|---|---|---|---|
| 1 | Q(t–1)(D2+D3) | Q(t) | 1,000 | 3 | Gbellmf | 15.68 | 13.61 | 0.44 | 0.41 |
| 2 | Q(t–1)(D2+D3), Q(t–2)(D3+A3) | Q(t) | 1,000 | 5 5 | Gauss2mf | 13.70 | 14.57 | 0.57 | 0.35 |
| 3 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), Q(t–3)(A4) | Q(t) | 800 | 4 4 4 | Gbellmf | 9.92 | 12.09 | 0.78 | 0.53 |
| 4 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), Q(t–3)(A4), Q(t–4)(D1) | Q(t) | 100 | 3-3-3-3 | Gaussmf | 9.09 | 9.26 | 0.81 | 0.73 |
| 5 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), Q(t–3)(A4), Q(t–4)(D1), Q(t–5)(D2+A3) | Qt | 200 | 3-3-3-3-3 | Trimf | 6.59 | 10.35 | 0.90 | 0.66 |
| 6 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), Q(t–3)(A4), Q(t–4)(D1), Q(t–5)(D2+A3), Q(t–6)(D2+A3) | Qt | 400 | All 2 | Gbellmf | 7.49 | 9.13 | 0.87 | 0.73 |
| 7 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …, Q(t–7)(D2) | Qt | 100 | All 2 | Gaussmf | 6.58 | 9.58 | 0.90 | 0.71 |
| 8 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …., Q(t–8)(D1) | Qt | 50 | All 2 | Gaussmf | 5.40 | 10.19 | 0.93 | 0.69 |
| 9 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …, Q(t–9) | Qt | 20 | All 2 | Gbellmf | 4.67 | 11.63 | 0.95 | 0.63 |
| 10 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …, Q(t–10)(D3) | Qt | 10 | All 2 | Trimf | 38.72 | 31.07 | 0.10 | 0.02 |
| 11 | Q(t–1)(D2+D3), Q(t–2)(D3+A3), …, Q(t–11)(D2+D3) | Qt | 20 | All 2 | Trimf | 37.52 | 30.89 | 0.06 | 0.01 |
Note: Bold characters indicate the most successful model.