Research Article
Spatial Approach of Artificial Neural Network for Solar Radiation Forecasting: Modeling Issues
Table 3
Radiation forecasting; spatial comparison of ANN models with time delay, neurons and transfer function.
| Number of inputs | %performance (MAE) | %training | %forecasting | Year | Delay | Neurons | Transfer function | Column | Row | Ranking | Training | Validation | Testing | MSE | RMSE | MSE | RMSE |
| 11* | 2.14* | 4.32* | 3.04* | 2.76* | 16.61* | 0.78* | 24.3* | 11* | 7* | 70* | satlins* | 1* | 2* | 1* | 7** | 2.86** | 4.22** | 3.08** | 3.18** | 17.83** | 0.73** | 24.51** | 12** | 3** | 130** | compet** | 3** | 1** | 2** | 6*** | 3.12*** | 3.41*** | 3.13*** | 3.18*** | 17.83*** | 0.63*** | 22.2*** | 12*** | 1*** | 10*** | hardlims*** | 2*** | 3*** | 3*** | 9 | 2.47 | 3.46 | 3.25 | 2.82 | 16.8 | 0.86 | 24.16 | 12 | 26 | 220 | hardlim | 3 | 3 | 4 | 15 | 2.14 | 3.6 | 3.29 | 2.66 | 16.31 | 1.35 | 27 | 11 | 2 | 100 | purelin | 2 | 3 | 5 | 29 | 1.63 | 4.76 | 3.33 | 2.6 | 16.12 | 0.69 | 25.05 | 9 | 7 | 40 | compet | 1 | 2 | 6 | 14 | 2.31 | 3.41 | 3.34 | 2.73 | 16.53 | 1.18 | 26.59 | 11 | 23 | 10 | purelin | 2 | 2 | 7 | 8 | 2.4 | 4.32 | 3.39 | 2.98 | 17.26 | 0.59 | 22.29 | 12 | 1 | 40 | satlin | 3 | 2 | 8 | 17 | 1.98 | 4.09 | 3.44 | 2.7 | 16.42 | 0.94 | 26.29 | 11 | 0 | 40 | poslin | 3 | 2 | 9 | 10 | 2.24 | 3.44 | 3.45 | 2.72 | 16.5 | 0.8 | 23.47 | 11 | 23 | 10 | logsig | 1 | 1 | 10 | 25 | 1.78 | 4.29 | 3.5 | 2.63 | 16.21 | 0.97 | 24.57 | 10 | 21 | 160 | purelin | 3 | 1 | 11 | 19 | 2 | 4.14 | 3.51 | 2.73 | 16.52 | 1.61 | 27.84 | 10 | 23 | 40 | tansig | 1 | 1 | 12 | 3 | 4.21 | 3.9 | 3.52 | 4.01 | 20.03 | 0.53 | 20.96 | 12 | 27 | 190 | poslin | 1 | 3 | 13 | 12 | 2.05 | 4.01 | 3.56 | 2.74 | 16.56 | 1.1 | 25.59 | 11 | 26 | 40 | hardlims | 1 | 3 | 14 | 5 | 2.79 | 4.52 | 3.59 | 3.29 | 18.15 | 0.44 | 21.05 | 12 | 1 | 250 | poslin | 2 | 2 | 15 | 26 | 1.82 | 4.31 | 3.6 | 2.68 | 16.36 | 1.6 | 29.29 | 10 | 19 | 190 | compet | 3 | 2 | 16 | 18 | 1.91 | 3.78 | 3.62 | 2.62 | 16.2 | 1.11 | 26.58 | 11 | 25 | 70 | satlins | 3 | 3 | 17 | 32 | 1.69 | 4.56 | 3.65 | 2.65 | 16.29 | 1.25 | 27.4 | 9 | 15 | 130 | satlins | 2 | 2 | 20 | 28 | 1.74 | 4.43 | 3.65 | 2.66 | 16.3 | 1.41 | 28.09 | 9 | 20 | 280 | purelin | 1 | 1 | 19 | 16 | 2.04 | 3.74 | 3.65 | 2.7 | 16.44 | 0.77 | 23.57 | 11 | 29 | 40 | purelin | 3 | 1 | 18 | 4 | 3.22 | 4.4 | 3.66 | 3.55 | 18.83 | 0.68 | 22.41 | 12 | 22 | 190 | satlin | 2 | 1 | 21 | 13 | 2.07 | 3.88 | 3.69 | 2.76 | 16.61 | 1.43 | 28.84 | 11 | 4 | 190 | poslin | 2 | 1 | 22 | 21 | 1.64 | 4.65 | 3.71 | 2.65 | 16.29 | 1.08 | 25.53 | 10 | 26 | 40 | logsig | 1 | 3 | 23 | 30 | 1.69 | 4.39 | 3.71 | 2.64 | 16.24 | 1.45 | 27.97 | 9 | 14 | 40 | tansig | 1 | 3 | 24 | 33 | 1.71 | 5.3 | 3.71 | 2.83 | 16.82 | 1.47 | 28.26 | 9 | 15 | 70 | satlin | 2 | 3 | 25 | 27 | 1.69 | 4.15 | 3.75 | 2.59 | 16.1 | 1.63 | 29.64 | 10 | 11 | 160 | hardlims | 3 | 3 | 26 | 34 | 1.69 | 3.98 | 3.86 | 2.58 | 16.07 | 1.1 | 25.55 | 9 | 23 | 10 | tansig | 3 | 1 | 28 | 23 | 1.72 | 4.29 | 3.86 | 2.67 | 16.33 | 1.35 | 26.66 | 10 | 26 | 10 | satlin | 2 | 2 | 27 | 35 | 1.68 | 4.36 | 3.94 | 2.67 | 16.34 | 1.24 | 27.56 | 9 | 21 | 70 | purelin | 3 | 2 | 29 | 20 | 1.64 | 4.4 | 3.96 | 2.66 | 16.3 | 0.99 | 25.71 | 10 | 7 | 10 | purelin | 1 | 2 | 30 | 31 | 1.65 | 4.15 | 4 | 2.62 | 16.2 | 1.39 | 28.13 | 9 | 27 | 70 | poslin | 2 | 1 | 32 | 22 | 1.7 | 4.1 | 4 | 2.64 | 16.25 | 1.41 | 28.43 | 10 | 8 | 160 | satlins | 2 | 1 | 31 | 38 | 1.7 | 5.8 | 4.03 | 2.98 | 17.27 | 2 | 30.4 | 8 | 10 | 190 | compet | 1 | 2 | 33 | 24 | 1.56 | 4.15 | 4.05 | 2.58 | 16.06 | 0.78 | 24.45 | 10 | 15 | 190 | compet | 2 | 3 | 34 | 37 | 1.62 | 4.39 | 4.1 | 2.67 | 16.33 | 1.83 | 29.63 | 8 | 2 | 70 | hardlims | 1 | 1 | 35 | 36 | 1.55 | 4.93 | 4.11 | 2.74 | 16.56 | 2.06 | 30.85 | 9 | 3 | 40 | tansig | 3 | 3 | 36 | 39 | 1.33 | 5.09 | 4.35 | 2.69 | 16.39 | 1.47 | 28.58 | 8 | 23 | 40 | hardlims | 1 | 3 | 37 | 40 | 1.29 | 5.51 | 4.54 | 2.78 | 16.68 | 1.48 | 30.01 | 8 | 7 | 130 | tansig | 2 | 1 | 38 | 44 | 1.24 | 5.79 | 4.56 | 2.81 | 16.77 | 2.06 | 32.39 | 8 | 3 | 10 | compet | 3 | 2 | 39 | 47 | 1.02 | 6.39 | 4.61 | 2.81 | 16.76 | 2.37 | 33.24 | 7 | 1 | 10 | logsig | 1 | 2 | 40 | 46 | 1.16 | 5.94 | 4.71 | 2.83 | 16.82 | 1.47 | 29.4 | 7 | 17 | 160 | poslin | 1 | 1 | 41 | 42 | 1.12 | 5.52 | 4.72 | 2.72 | 16.5 | 1.29 | 28.96 | 8 | 20 | 250 | hardlim | 2 | 3 | 42 | 41 | 1.21 | 5.62 | 4.75 | 2.8 | 16.73 | 0.99 | 28.11 | 8 | 25 | 40 | hardlim | 2 | 2 | 43 | 43 | 1.21 | 5.36 | 4.78 | 2.75 | 16.59 | 1.96 | 31.28 | 8 | 7 | 70 | tansig | 3 | 1 | 44 | 45 | 1.16 | 6.66 | 4.9 | 3.01 | 17.34 | 2.03 | 31.28 | 8 | 23 | 130 | hardlims | 3 | 3 | 45 | 52 | 1.09 | 5.36 | 5.04 | 2.74 | 16.54 | 1.71 | 31.25 | 7 | 5 | 10 | compet | 3 | 1 | 46 | 51 | 1.03 | 6.14 | 5.05 | 2.86 | 16.91 | 1.79 | 31.64 | 7 | 0 | 10 | satlin | 2 | 3 | 47 | 48 | 1.13 | 5.4 | 5.11 | 2.78 | 16.68 | 1.35 | 29.22 | 7 | 23 | 40 | compet | 1 | 3 | 48 | 57 | 0.88 | 6.31 | 5.12 | 2.82 | 16.78 | 2.15 | 32.84 | 6 | 8 | 100 | tansig | 1 | 3 | 50 | 50 | 1.16 | 5.7 | 5.12 | 2.86 | 16.92 | 2.65 | 33.98 | 7 | 12 | 40 | purelin | 2 | 2 | 49 | 49 | 1.12 | 5.89 | 5.19 | 2.89 | 16.99 | 2.77 | 33.92 | 7 | 7 | 10 | compet | 2 | 1 | 51 | 56 | 1.01 | 6.75 | 5.38 | 3.03 | 17.41 | 2.04 | 31.21 | 6 | 29 | 10 | compet | 1 | 2 | 52 | 55 | 0.9 | 6.13 | 5.45 | 2.86 | 16.91 | 2.77 | 33.86 | 6 | 8 | 10 | purelin | 1 | 1 | 53 | 54 | 0.98 | 6.54 | 5.48 | 2.99 | 17.29 | 2.48 | 33.87 | 7 | 4 | 100 | satlins | 3 | 3 | 54 | 59 | 0.96 | 6.58 | 5.51 | 3 | 17.31 | 2.08 | 32.38 | 6 | 15 | 40 | logsig | 2 | 2 | 55 | 53 | 1 | 9.49 | 5.62 | 3.62 | 19.02 | 1.2 | 27.62 | 7 | 22 | 40 | logsig | 3 | 2 | 56 | 61 | 0.83 | 6.91 | 5.63 | 3 | 17.33 | 3.46 | 36.2 | 6 | 1 | 100 | tansig | 3 | 1 | 57 | 60 | 0.91 | 6.52 | 5.75 | 3 | 17.32 | 3 | 36.7 | 6 | 0 | 10 | tansig | 2 | 3 | 58 | 2 | 5.85 | 6.76 | 5.91 | 6.05 | 24.59 | 1.34 | 25.05 | 12 | 1 | 40 | poslin | 1 | 2 | 59 | 58 | 0.9 | 6.48 | 6.03 | 3.04 | 17.43 | 3.16 | 35.41 | 6 | 10 | 10 | tansig | 2 | 1 | 60 | 62 | 0.75 | 8.21 | 6.09 | 3.31 | 18.19 | 2.5 | 34.12 | 6 | 25 | 100 | satlin | 3 | 2 | 61 | 65 | 0.67 | 6.9 | 6.44 | 3.07 | 17.53 | 3.46 | 36.21 | 5 | 25 | 40 | poslin | 1 | 2 | 63 | 63 | 0.71 | 6.49 | 6.44 | 3.01 | 17.36 | 3.31 | 35.07 | 6 | 5 | 40 | logsig | 3 | 3 | 62 | 66 | 0.69 | 7.08 | 6.45 | 3.12 | 17.66 | 2.52 | 34.33 | 5 | 28 | 10 | hardlim | 1 | 3 | 64 | 69 | 0.6 | 7.6 | 6.5 | 3.18 | 17.83 | 3.15 | 35.33 | 5 | 25 | 10 | logsig | 2 | 3 | 65 | 67 | 0.68 | 6.93 | 6.68 | 3.13 | 17.69 | 2.84 | 34.2 | 5 | 22 | 10 | satlins | 2 | 1 | 66 | 71 | 0.74 | 7.55 | 6.68 | 3.29 | 18.13 | 4.45 | 38.71 | 5 | 3 | 10 | tansig | 3 | 2 | 67 | 70 | 0.69 | 7.41 | 6.69 | 3.23 | 17.97 | 3.04 | 34.97 | 5 | 10 | 10 | logsig | 3 | 1 | 68 | 64 | 0.69 | 7.06 | 6.76 | 3.18 | 17.82 | 3.08 | 34.94 | 5 | 28 | 10 | hardlim | 1 | 1 | 69 | 68 | 0.74 | 6.56 | 6.9 | 3.14 | 17.71 | 3.39 | 36.01 | 5 | 23 | 40 | poslin | 2 | 2 | 70 | 72 | 0.79 | 6.72 | 7.31 | 3.28 | 18.11 | 2.77 | 34.86 | 5 | 5 | 40 | compet | 3 | 3 | 71 |
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