Research Article
Spatial Approach of Artificial Neural Network for Solar Radiation Forecasting: Modeling Issues
Table 1
Radiation forecasting; spatial comparison of ANN models with time delay.
| Number of inputs | Training | Forecasting | Year | Delay | Column | Row | Ranking | Input radiation | MAE | RMSE | MAE | RMSE |
| 10* | 7.81* | 16.55* | 3.85* | 19.63* | 11* | 23* | 1* | 1* | 1* | GHI* | 3** | 9.24** | 20.05** | 4.03** | 20.07** | 12** | 27** | 1** | 3** | 2** | GHI** | 9*** | 8.07*** | 16.88*** | 4.07*** | 20.17*** | 12*** | 26*** | 3*** | 3*** | 3*** | GHI*** | 11 | 7.68 | 16.47 | 4.27 | 20.66 | 11 | 7 | 1 | 2 | 4 | GHI | 22 | 7.81 | 16 | 4.29 | 20.71 | 10 | 8 | 2 | 1 | 5 | GHI | 21 | 7.79 | 16.06 | 4.4 | 20.98 | 10 | 26 | 1 | 3 | 6 | GHI | 26 | 7.88 | 15.96 | 4.47 | 21.14 | 10 | 19 | 3 | 2 | 7 | GHI | 24 | 7.89 | 15.92 | 4.6 | 21.44 | 10 | 15 | 2 | 3 | 8 | GHI | 8 | 8.49 | 17.22 | 4.73 | 21.75 | 12 | 1 | 3 | 2 | 9 | GHI | 4 | 8.96 | 19.01 | 4.79 | 21.89 | 12 | 22 | 2 | 1 | 10 | GHI | 12 | 7.93 | 16.51 | 4.85 | 22.02 | 11 | 26 | 1 | 3 | 11 | GHI | 31 | 8.26 | 15.94 | 4.85 | 22.03 | 9 | 27 | 2 | 1 | 12 | GHI | 6 | 8.77 | 17.94 | 4.85 | 22.03 | 12 | 1 | 2 | 3 | 13 | GHI | 5 | 8.74 | 18.21 | 4.89 | 22.11 | 12 | 1 | 2 | 2 | 14 | GHI | 1 | 12.28 | 29.34 | 4.95 | 22.25 | 12 | 24 | 1 | 1 | 15 | GHI | 23 | 7.91 | 15.88 | 4.95 | 22.25 | 10 | 26 | 2 | 2 | 16 | GHI | 7 | 8.5 | 17.47 | 4.96 | 22.27 | 12 | 3 | 3 | 1 | 17 | GHI | 28 | 8.29 | 15.94 | 5.03 | 22.43 | 9 | 20 | 1 | 1 | 18 | GHI | 30 | 8.31 | 15.82 | 5.18 | 22.77 | 9 | 14 | 1 | 3 | 19 | GHI | 18 | 8.04 | 16.08 | 5.26 | 22.94 | 11 | 25 | 3 | 3 | 20 | GHI | 19 | 8.31 | 16.09 | 5.27 | 22.95 | 10 | 23 | 1 | 1 | 21 | GHI | 14 | 7.86 | 16.28 | 5.29 | 23.01 | 11 | 23 | 2 | 2 | 22 | GHI | 44 | 8.93 | 15.72 | 5.4 | 23.24 | 8 | 3 | 3 | 2 | 23 | GHI | 15 | 8.16 | 16.31 | 5.42 | 23.29 | 11 | 2 | 2 | 3 | 24 | GHI | 16 | 7.9 | 16.23 | 5.42 | 23.29 | 11 | 29 | 3 | 1 | 25 | GHI | 33 | 8.35 | 15.81 | 5.45 | 23.35 | 9 | 15 | 2 | 3 | 26 | GHI | 42 | 8.81 | 15.72 | 5.49 | 23.43 | 8 | 20 | 2 | 3 | 27 | GHI | 20 | 7.76 | 16.1 | 5.51 | 23.46 | 10 | 7 | 1 | 2 | 28 | GHI | 13 | 8 | 16.33 | 5.55 | 23.56 | 11 | 4 | 2 | 1 | 29 | GHI | 52 | 8.56 | 15.68 | 5.62 | 23.72 | 7 | 5 | 3 | 1 | 30 | GHI | 39 | 8.42 | 15.75 | 5.63 | 23.74 | 8 | 23 | 1 | 3 | 31 | GHI | 40 | 8.74 | 15.79 | 5.64 | 23.75 | 8 | 7 | 2 | 1 | 32 | GHI | 41 | 8.41 | 15.65 | 5.65 | 23.77 | 8 | 25 | 2 | 2 | 33 | GHI | 51 | 8.92 | 15.74 | 5.71 | 23.89 | 7 | 0 | 2 | 3 | 34 | GHI | 32 | 8.19 | 15.88 | 5.72 | 23.91 | 9 | 15 | 2 | 2 | 35 | GHI | 17 | 7.8 | 16.16 | 5.73 | 23.95 | 11 | 0 | 3 | 2 | 36 | GHI | 47 | 8.78 | 15.75 | 5.83 | 24.14 | 7 | 1 | 1 | 2 | 37 | GHI | 25 | 8.14 | 15.9 | 5.9 | 24.29 | 10 | 21 | 3 | 1 | 38 | GHI | 70 | 9.06 | 15.83 | 5.91 | 24.3 | 5 | 10 | 3 | 1 | 39 | GHI | 36 | 8.38 | 15.71 | 5.95 | 24.38 | 9 | 3 | 3 | 3 | 40 | GHI | 38 | 8.44 | 15.76 | 6.02 | 24.54 | 8 | 10 | 1 | 2 | 41 | GHI | 27 | 8.55 | 15.83 | 6.03 | 24.56 | 10 | 11 | 3 | 3 | 42 | GHI | 50 | 9.2 | 15.64 | 6.22 | 24.95 | 7 | 12 | 2 | 2 | 43 | GHI | 48 | 8.93 | 15.74 | 6.25 | 25 | 7 | 23 | 1 | 3 | 44 | GHI | 45 | 8.74 | 15.65 | 6.3 | 25.09 | 8 | 23 | 3 | 3 | 45 | GHI | 62 | 8.57 | 15.78 | 6.31 | 25.12 | 6 | 25 | 3 | 2 | 46 | GHI | 46 | 9.03 | 15.78 | 6.43 | 25.35 | 7 | 17 | 1 | 1 | 47 | GHI | 34 | 8.31 | 15.75 | 6.44 | 25.37 | 9 | 23 | 3 | 1 | 48 | GHI | 2 | 12.02 | 24.59 | 6.44 | 25.38 | 12 | 1 | 1 | 2 | 49 | GHI | 37 | 8.39 | 15.66 | 6.51 | 25.52 | 8 | 2 | 1 | 1 | 50 | GHI | 71 | 8.87 | 15.77 | 6.65 | 25.79 | 5 | 3 | 3 | 2 | 51 | GHI | 55 | 8.75 | 15.73 | 6.69 | 25.87 | 6 | 8 | 1 | 1 | 52 | GHI | 29 | 8.48 | 15.8 | 6.74 | 25.96 | 9 | 7 | 1 | 2 | 53 | GHI | 59 | 8.94 | 15.64 | 6.75 | 25.98 | 6 | 15 | 2 | 2 | 54 | GHI | 35 | 8.57 | 15.88 | 6.82 | 26.11 | 9 | 21 | 3 | 2 | 55 | GHI | 73 | 9 | 15.63 | 6.83 | 26.13 | 4 | 28 | 1 | 1 | 56 | GHI | 83 | 9.16 | 15.99 | 6.9 | 26.27 | 3 | 15 | 1 | 2 | 57 | GHI | 49 | 8.62 | 15.57 | 6.91 | 26.28 | 7 | 7 | 2 | 1 | 58 | GHI | 53 | 9.06 | 15.68 | 6.94 | 26.34 | 7 | 22 | 3 | 2 | 59 | GHI | 58 | 8.8 | 15.77 | 7.03 | 26.52 | 6 | 10 | 2 | 1 | 60 | GHI | 63 | 8.79 | 15.81 | 7.05 | 26.56 | 6 | 5 | 3 | 3 | 61 | GHI | 57 | 9.14 | 15.71 | 7.09 | 26.62 | 6 | 8 | 1 | 3 | 62 | GHI | 61 | 8.83 | 15.63 | 7.11 | 26.66 | 6 | 1 | 3 | 1 | 63 | GHI | 56 | 9.21 | 15.86 | 7.21 | 26.86 | 6 | 29 | 1 | 2 | 64 | GHI | 65 | 9.06 | 16.02 | 7.26 | 26.95 | 5 | 25 | 1 | 2 | 65 | GHI | 43 | 8.94 | 15.75 | 7.29 | 27.01 | 8 | 7 | 3 | 1 | 66 | GHI | 66 | 9.15 | 15.79 | 7.3 | 27.02 | 5 | 28 | 1 | 3 | 67 | GHI | 82 | 9.47 | 15.96 | 7.31 | 27.03 | 3 | 11 | 1 | 1 | 68 | GHI | 85 | 9.27 | 16.05 | 7.37 | 27.15 | 3 | 17 | 2 | 1 | 69 | GHI | 75 | 9.01 | 15.74 | 7.41 | 27.21 | 4 | 12 | 1 | 3 | 70 | GHI | 79 | 9.28 | 16.07 | 7.43 | 27.26 | 4 | 28 | 3 | 1 | 71 | GHI | 54 | 8.93 | 15.59 | 7.44 | 27.27 | 7 | 4 | 3 | 3 | 72 | GHI | 76 | 9.27 | 15.9 | 7.48 | 27.34 | 4 | 5 | 2 | 1 | 73 | GHI | 69 | 9.06 | 15.58 | 7.49 | 27.37 | 5 | 25 | 2 | 3 | 74 | GHI | 64 | 8.76 | 15.75 | 7.51 | 27.41 | 5 | 28 | 1 | 1 | 75 | GHI | 81 | 8.99 | 15.97 | 7.53 | 27.44 | 4 | 24 | 3 | 3 | 76 | GHI | 74 | 9.41 | 15.71 | 7.54 | 27.45 | 4 | 15 | 1 | 2 | 77 | GHI | 67 | 8.99 | 15.78 | 7.58 | 27.53 | 5 | 22 | 2 | 1 | 78 | GHI | 87 | 9.19 | 16.04 | 7.67 | 27.7 | 3 | 12 | 2 | 3 | 79 | GHI | 80 | 9.26 | 15.99 | 7.69 | 27.73 | 4 | 12 | 3 | 2 | 80 | GHI | 77 | 8.9 | 15.92 | 7.87 | 28.05 | 4 | 25 | 2 | 2 | 81 | GHI | 78 | 9.21 | 15.84 | 7.96 | 28.22 | 4 | 4 | 2 | 3 | 82 | GHI | 60 | 9.04 | 15.86 | 8.25 | 28.72 | 6 | 0 | 2 | 3 | 83 | GHI | 72 | 9.17 | 15.76 | 8.43 | 29.03 | 5 | 5 | 3 | 3 | 84 | GHI | 84 | 9.3 | 16.25 | 8.47 | 29.1 | 3 | 24 | 1 | 3 | 85 | GHI | 68 | 9.43 | 15.96 | 8.54 | 29.22 | 5 | 23 | 2 | 2 | 86 | GHI | 88 | 9.2 | 16.13 | 8.78 | 29.63 | 3 | 0 | 3 | 1 | 87 | GHI | 86 | 9.02 | 15.85 | 9.35 | 30.57 | 3 | 6 | 2 | 2 | 88 | GHI | 89 | 9.25 | 16.26 | 10.2 | 31.93 | 3 | 6 | 3 | 2 | 89 | GHI | 90 | 9.52 | 16.15 | 10.39 | 32.23 | 3 | 5 | 3 | 3 | 90 | GHI |
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Stars () shows best three results in order.
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