In order to achieve a highly accurate estimation of solar energy resource potential, a novel hybrid ensemble-learning approach, hybridizing Advanced Squirrel-Search Optimization Algorithm (ASSOA) and support vector regression, is utilized to estimate the hourly tilted solar irradiation for selected arid regions in Algeria. Long-term measured meteorological data, including mean-air temperature, relative humidity, wind speed, alongside global horizontal irradiation and extra-terrestrial horizontal irradiance, were obtained for the two cities of Tamanrasset-and-Adrar for two years. Five computational algorithms were considered and analyzed for the suitability of estimation. Further two new algorithms, namely Average Ensemble and Ensemble using support vector regression were developed using the hybridization approach. The accuracy of the developed models was analyzed in terms of five statistical error metrics, as well as the Wilcoxon rank-sum and ANOVA test. Among the previously selected algorithms, K Neighbors Regressor and support vector regression exhibited good performances. However, the newly proposed ensemble algorithms exhibited even better performance. The proposed model showed relative root mean square errors lower than 1.448% and correlation coefficients higher than 0.999. This was further verified by benchmarking the new ensemble against several popular swarm intelligence algorithms. It is concluded that the proposed algorithms are far superior to the commonly adopted ones.
The performance of photovoltaic or thermal energy conversion systems depends on the orientation and the inclination angle of their collection fields compared to the horizon. Usually (for technical and economic considerations), these systems are installed in a fixed tilted position according to the considered site location for maximum solar energy collection. On the other hand, the inclination angle of photovoltaic arrays or solar thermal collectors could also be adjusted few times a year according to optimum tilt angles defined for specific periods or seasons [
Hybrid-learning methods have attracted increasing attention amongst researchers. In recent years, various hybrid-learning techniques have been proposed and used to evaluate solar energy resources. Alrashidi et al. [
In most aforementioned papers, the climate variables are used to estimate solar radiation on a horizontal plane, or the horizontal solar radiation is used as an input variable to estimate radiation on a tiled surface [
Hourly solar radiation on tilted surfaces measured at the ground is processed in this study. Data were collected from two radiometric stations located in the southern region of Algeria.
Station ID | Lat. [°N] | Long. [°E] | Elev. [m] | Data periods | Tilt Angle [°] |
---|---|---|---|---|---|
ADR | 22.785 | 5.522 | 1378 | 2002–2006 | 23 |
TAM | 27.874 | −0.293 | 257 | 2009–2012 | 28 |
#Station | Statistic | GHI [Wh/m2] | Tmed [°C] | Hum [%] | WS [m/s] |
---|---|---|---|---|---|
ADR | Max. | 32.40 | 41.40 | 100.00 | 5.50 |
Min. | 0.00 | 0.00 | 7.50 | 0.00 | |
Mean | 15.04 | 21.22 | 60.04 | 1.69 | |
SD | 6.69 | 7.71 | 16.15 | 0.58 | |
TAM | Max. | 32.30 | 43.30 | 100.00 | 6.20 |
Min. | 0.00 | 0.00 | 16.20 | 0.00 | |
Mean | 15.11 | 22.13 | 61.95 | 1.37 | |
SD | 7.91 | 8.92 | 20.76 | 0.86 |
The Advanced Squirrel Search Optimization Algorithm (ASSOA) was first proposed in [
The initial locations of
The best solution value of the objective function indicates a hickory tree. The calculated values are sorted in ascending order. The first best solution is
where
The constant of seasonal,
The value of
The ASSOA algorithm is explained step-by-step in Algorithm 1. Steps 1 and 2 initialize the algorithm parameters. The objective function is then calculated for each agent to sort them and get the first, second, and third best agents and normal agents in Steps 3 and 4. From Step 5 to Step 44, the algorithm is working to update the agents’ positions. Steps from 45 to 50 calculate and update positions based on the seasonal constant to avoid local minima. The best solution is obtained by the end of the algorithm at Step 53.
The performance metrics used for the classification measurements are RRMSE, MBE, RMSE, MAE, and R. The mean absolute error (MAE) determines the average of absolute errors. The mean bias error (MBE) indicates whether the tested model is under-or over-predicting the actual measurements. The correlation coefficient (R) indicates the strength of the correlation between actual and estimated values. The root mean square error (RMSE) and the relative RMSE (RRMSE) provide estimates of the absolute and relative random error components [
The experiments are divided into two parts. First, the effectiveness of the five models is evaluated for technique selection based on the long-term measured meteo-solar datasets including mean air temperature, relative humidity, wind speed, and global horizontal irradiation, alongside extra-terrestrial horizontal irradiance, for the two Algerian stations. Second, an ensemble-learning method is selected to be used for the estimation of solar radiation. Each investigated dataset is divided randomly into three subsets for training, validation, and testing (60%, 20%, and 20%, respectively). The training set is used to train a k-nearest neighbors (KNN) classifier during the learning phase, the validation set is used when calculating the fitness function for a specific solution, and the testing set is used to evaluate the efficiency of the used techniques. For the KNN classifier, the number of k-neighbors is 5, and the k-fold cross-validation value is set to 10. The selected methods are Decision Tree Regressor (DTR), MLP Regressor (MLP), K-Neighbors Regressor (KNR), Support Vector Regression (SVR), and Random Forest Regressor (RFR). In addition, Average Ensemble (AVE) and Ensemble using SVR (SVE) are two new proposed ensembles for developing solar radiation estimators.
The evaluation of the accuracy of the five selected methods is provided based on the testing dataset, i.e., to determine their capability of handling input data.
Model | TAM | ADR | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
MAE | RMSE | RRMSE |
R | GPI | Rank | MAE | RMSE | RRMSE |
R | GPI | Rank | |
DTR | 0.0401 | 0.056 | 11.410 | 0.973 | −0.286 | 6 | 0.0301 | 0.0418 | 8.272 | 0.980 | −0.620 | 6 |
MLP | 0.0468 | 0.057 | 11.632 | 0.980 | −0.326 | 7 | 0.0336 | 0.0402 | 7.957 | 0.987 | −0.295 | 7 |
KNR | 0.040 | 0.053 | 10.756 | 0.982 | 0.000 | 4 | 0.0240 | 0.031 | 6.231 | 0.996 | 0.945 | 3 |
SVR | 0.039 | 0.048 | 9.715 | 0.984 | 0.213 | 3 | 0.0370 | 0.043 | 8.465 | 0.991 | −0.383 | 4 |
RFR | 0.0748 | 0.0867 | 17.679 | 0.938 | −2.617 | 5 | 0.0501 | 0.0631 | 12.487 | 0.978 | −2.591 | 5 |
AVE | 0.0343 | 0.0414 | 8.439 | 0.989 | 0.606 | 2 | 0.0238 | 0.0297 | 5.882 | 0.995 | 1.003 | 2 |
SVE | 0.0224 | 0.0278 | 5.650 | 0.994 | 1.383 | 1 | 0.0227 | 0.0257 | 5.080 | 0.998 | 1.409 | 1 |
Here,
The ability of the proposed SVR ensemble-based ASSOA algorithm for improving the accuracy is investigated
Parameter | Value | Parameter | Value |
---|---|---|---|
# Iterations | 50 | ||
# Agents | 10 | ||
SS | DF | MS | F (DFn, DFd) | P value | |
---|---|---|---|---|---|
Treatment (between columns) | 0.000134 | 3 | 4.48E-05 | F (3, 76) = 34.95 | P < 0.0001 |
Residual (within columns) | 9.74E-05 | 76 | 1.28E-06 | - | - |
Total | 0.000232 | 79 | - | - | - |
SS | DF | MS | F (DFn, DFd) | P value | |
---|---|---|---|---|---|
Treatment (between columns) | 0.000126 | 3 | 4.21E-05 | F (3, 76) = 77.12 | P < 0.0001 |
Residual (within columns) | 4.15E-05 | 76 | 5.46E-07 | - | - |
Total | 0.000168 | 79 | - | - | - |
To check the sensitivity of the proposed model to the weather conditions, different sky conditions (cloudiness) were considered. This time, the database was divided into three sub-databases according to the cloudiness index value, namely clear sky (CRS), partly cloudy sky (PCR), and complete overcast sky (OTS). The Box plots given in
This experimental test is used to investigate how the ASSOA optimization algorithm helps to improve the accuracy of solar radiation prediction models. To verify the effectiveness of the proposed prediction model, the following groups of comparative experiments are carried out using previously described ensembles models (AVE and SVE). The verification experiments are carried out based on measurement at ADR and TAM. The corresponding RMSEs are depicted in
Next, to verify the superiority of the proposed method, several other popular swarm intelligence algorithms including the genetic algorithm (GA), particle swarm optimization (PSO), and Grey Wolf Optimizer (GWO) are used as the benchmark algorithms. The configurations of the GA, PSO, and GWO algorithms, including the number of iterations (generations), population size, and other parameters, are shown in
The testing results of the selected swarm intelligence algorithms in this study are presented in
Algorithm | Parameter (s) | Value (s) |
---|---|---|
GA | #Generations | 50 |
#Population size | 10 | |
Ratio of mutation | 0.1 | |
Crossover | 0.9 | |
Mechanism of selection | Roulette wheel | |
PSO | Inertia |
|
GWO | #Iterations | 50 |
#Wolves | 10 | |
2 to 0 |
Optimizer | TAM | ADR | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
MAE | MBE | RMSE | RRMSE | R | MAE | MBE | RMSE | RRMSE | R | |
GWO | 0.00446 | −0.00028 | 0.00712 | 1.448 | 0.999 | 0.00438 | −0.00026 | 0.00693 | 1.369 | 0.999 |
GA | 0.00500 | −0.00213 | 0.01003 | 2.040 | 0.999 | 0.00510 | −0.00267 | 0.00993 | 1.962 | 0.997 |
PSO | 0.00510 | −0.00029 | 0.00998 | 2.031 | 0.999 | 0.00499 | −0.00030 | 0.00914 | 1.806 | 0.999 |
The variability of the RMSE indicators of the proposed approach, compared to the benchmark algorithms, is shown in
Another evaluation is conducted for further assessment of the proposed model against the state-of-the-art models. From
ASSOA | GA | PSO | GWO | |
---|---|---|---|---|
Theoretical median | 0 | 0 | 0 | 0 |
Actual median | 0.007122 | 0.01003 | 0.009982 | 0.008998 |
Number of values | 20 | 20 | 20 | 20 |
Wilcoxon Signed Rank Test | ||||
Sum of signed ranks (W) | 210 | 210 | 210 | 210 |
Sum of positive ranks | 210 | 210 | 210 | 210 |
Sum of negative ranks | 0 | 0 | 0 | 0 |
P-value (two tailed) | <0.0001 | <0.0001 | <0.0001 | <0.0001 |
Exact or estimate? | Exact | Exact | Exact | Exact |
P-value summary | **** | **** | **** | **** |
Significant (alpha = 0.05)? | Yes | Yes | Yes | Yes |
How big is the discrepancy? | ||||
Discrepancy | 0.007122 | 0.01003 | 0.009982 | 0.008998 |
ASSOA | GA | PSO | GWO | |
---|---|---|---|---|
Theoretical median | 0 | 0 | 0 | 0 |
Actual median | 0.006935 | 0.009934 | 0.009136 | 0.00988 |
Number of values | 20 | 20 | 20 | 20 |
Wilcoxon Signed Rank Test | ||||
Sum of signed ranks (W) | 210 | 210 | 210 | 210 |
Sum of positive ranks | 210 | 210 | 210 | 210 |
Sum of negative ranks | 0 | 0 | 0 | 0 |
P-value (two tailed) | <0.0001 | <0.0001 | <0.0001 | <0.0001 |
Exact or estimate? | Exact | Exact | Exact | Exact |
P-value summary | **** | **** | **** | **** |
Significant (alpha = 0.05)? | Yes | Yes | Yes | Yes |
How big is the discrepancy? | ||||
Discrepancy | 0.006935 | 0.0.009934 | 0.009136 | 0.00988 |
Model type | Ref. | Site of study | RMSE | RRMSE % |
---|---|---|---|---|
Present study | - | TAM | 0.00712 | 1.44817 |
Present study | - | ADR | 0.00693 | 1.36881 |
Olmo et al. | [ |
Granada | - | 27% |
Notton et al. | [ |
Ajaccio | - | 8.11–10.71% |
Padovan et al. | [ |
Padova | 39.43 | 6.4%–8.7% |
Notton et al. | [ |
Ajaccio | 18.23 | 5.28% |
In this paper, a novel combined approach using the ASSOA optimization algorithm is proposed. For this purpose, measurements of hourly solar irradiation on inclined surfaces covering 2002–2006 in Tamanrasset and 2009–2012 in Adrar, Algeria, were used. The proposed model accuracy was assessed based on MBE, MAE, RMSE, RRMSE, and R.
Different experiments are performed using the mentioned data; firstly, five models of technique selection were considered (DTR, MLP, KNR, SVR, and RFR) in developing solar radiation estimating models. The estimation is based on the long-term measured meteorological datasets, including relative humidity, mean air temperature, maximum air temperature, minimum air temperature, and daily temperature range. The performance is evaluated and compared to two new proposed ensembles known as Average Ensemble (AVE) and Ensemble using SVR (SVE). The identification of model performance rankings is then conducted based on the Global Performance Index (GPI). The results of the comparative analysis show the superiority of the AVE and the SVE models.
In the second experimentation, the ASSOA optimization algorithm effect on improving the accuracy results, in the estimation of the solar, was investigated. Comparative analyses were carried out using previously described ensembles models (AVE and SVE). It was concluded that the proposed is more successful than the two better ensemble-based models, AVE and SVE.
Thirdly, to check the proposed model's sensitivity to the climate condition, the proposed evaluation at different sky conditions is conducted. The results show that the ASSOA perform better in CRS condition than in PCR end OTS. The model achieves a quite similar accuracy for the PCR end OTS condition in the ADR site.
The proposed ASSOA algorithm was also compared to GA, PSO, and GWO optimizers for feature selection to validate its efficiency. Compared to the other swarm intelligence algorithms, the proposed ASSOA shows superior performance. When the proposed model in this study is compared against the state-of-the-art models, it can be said that the model offers high performance in the estimation of estimate the hourly solar radiation on tilted surfaces classified as arid climate.
The present work demonstrated the potential of estimating solar radiation on tilted surfaces while also considering the influential meteorological parameters. Thus, it will help in decision-making. Combining the proposed optimization algorithm with more accurate estimation models can be further improved in the future. Moreover, regional models can be established. This study can contribute to enhancing solar design and the facilitation of implementing solar technologies for remote areas.