Increasing global energy consumption has become an urgent problem as natural energy sources such as oil, gas, and uranium are rapidly running out. Research into renewable energy sources such as solar energy is being pursued to counter this. Solar energy is one of the most promising renewable energy sources, as it has the potential to meet the world’s energy needs indefinitely. This study aims to develop and evaluate artificial intelligence (AI) models for predicting hourly global irradiation. The hyperparameters were optimized using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton training algorithm and STATISTICA software. Data from two stations in Algeria with different climatic zones were used to develop the model. Various error measurements were used to determine the accuracy of the prediction models, including the correlation coefficient, the mean absolute error, and the root mean square error (RMSE). The optimal support vector machine (SVM) model showed exceptional efficiency during the training phase, with a high correlation coefficient (R = 0.99) and a low mean absolute error (MAE = 26.5741 Wh/m^{2}), as well as an RMSE of 38.7045 Wh/m² across all phases. Overall, this study highlights the importance of accurate prediction models in the renewable energy, which can contribute to better energy management and planning.

Increasing concern about the effects of climate change and the need to diversify energy sources has led to a significant increase in the development of renewable energy sources. Among these, solar energy has emerged as a viable option due to its abundance and potential to reduce carbon emissions. Moreover, as oil and gas resources become less available, developing renewable energy sources is becoming increasingly important for the country’s long-term energy security. According to the recent the intergovermental panel on climate change (IPCC) report, solar energy has the potential to meet a significant portion of the world’s energy needs, and Algeria is no exception [

Accurately estimating the amount of solar radiation hitting the Earth’s surface is critical for various applications such as photovoltaic systems, heating, medical research, agriculture, and architecture. This is usually done with solar measurement devices such as solarimeters or pyranometers. However, it is difficult to measure solar radiation in many places in Algeria because the meters are too expensive, and the systems are very complex. Even if there are several meteorological stations in different locations in Algeria, measurements may not always be available due to power outages or limitations on the number of variables that can be recorded [

To address these challenges, researchers have developed models that use readily available meteorological data to predict global solar radiation (GSR) more accurately. These predictive models are becoming more advanced daily, but results vary by location. Therefore, it is important to use sophisticated GSR prediction techniques to improve solar energy potential prediction accuracy in Algeria [

Many research efforts have been made to predict solar radiation (SR) in different areas of the world using various techniques such as artificial intelligence and empirical methods. One popular method is Multilayer Perceptron (ANN-MLP) artificial neural network technology. However, other methods, such as decision tree models, support vector machines (SVMs), and feed-forward radial basis functions (FF-RBFs), have also been used to estimate solar radiation. Researchers such as [

Solar energy is a focus of Algeria’s ambitious energy policy, which allocates significant resources to solar thermal and photovoltaic resources. Projections indicate that solar energy will account for more than 37% of the country’s electricity generation by 2030 [^{2} averages 5 KWh [

The main objective of this research is to develop a method to optimize the hyperparameters of traditional machine learning using the multilayer perceptron (MLP) and support vector machines, thus increasing the reliability of hourly predictions of global irradiance. We used the FNN-MLP and SVM models to produce a reliable forecast of global solar irradiance at one-hour intervals at stations with different climates in Algeria. The following overview provides the framework for this research work: the materials and processes are discussed in

In this investigation, two radiometric stations were used to compile the database. The first station, “Shems”, located in Bouzareah in Algeria, recorded experimental data using Kipp and Zonen pyranometers to measure the global horizontal irradiation (GHI). The second station, located in Tamanrasset in the Sahara Desert in southern Algeria, is equipped with an Eppley PSP pyranometer and has the highest solar energy resources in an arid desert environment.

Purpose | Station ID | Station name | Latitude (°) | Longitude (°) | Elevation (m) | Climate zone | Data and periods |
---|---|---|---|---|---|---|---|

Training | BOU | Bouzareah | 36.80 | 3.17 | 357 | Mediterranean climate | January 01, 14–December 31, 14 |

Testing | TAM | Tamanrasset | 22,78 | 5,51 | 1378 | Hot desert | July 01, 19–December 17, 20 |

^{2}. The TAM station has a maximum temperature of 38.5°C, a minimum humidity of 2%, a mean wind speed of 5.19 m/s, and a mean GHI of 678.76 Wh/m^{2}. The correlation between these variables and solar radiation is further explored in

#Station | Statistic | TMP (°C) | HUM (%) | WSP (m/s) | GHI (Wh/m^{2}) |
---|---|---|---|---|---|

BOU | Max. | 44.11 | 92.21 | 14.24 | 1027.00 |

Min. | 5.56 | 8.28 | 0.10 | 120.25 | |

Mean. | 24.67 | 40.55 | 4.63 | 517.89 | |

SD. | 7.79 | 16.61 | 2.39 | 244.72 | |

TAM | Max. | 38.50 | 99.00 | 13.90 | 1293.54 |

Min. | 1.50 | 2.00 | 0.00 | 35.50 | |

Mean. | 26.86 | 19.70 | 5.19 | 678.76 | |

SD. | 7.65 | 10.06 | 2.71 | 300.83 |

#Station | TMP (°C) | HUM (%) | WSP (m/s) | WID (°) | PRE (mbar) |
---|---|---|---|---|---|

BOU | 0.512 | −0.559 | −0.093 | 0.129 | −0.1567 |

TAM | 0.448 | −0.298 | 0.163 | – | – |

^{2}, with 508, 254, and 192 counts, respectively. In contrast, BOU has its highest frequency counts at the bin centers of 250, 450, and 550 Wh/m^{2}, with 508, 490, and 458 counts, respectively. These results indicate that TAM receives more GHI than BOU due to their different geographic locations and climatic conditions. Such analysis is valuable for understanding the variability of GHI and designing solar energy systems.

Feedforward Neural Networks’ multilayer perceptron, also known as FNN-MLP, is modeled on the human brain’s information processing. Their known ability to learn from their environment makes them ideal for nonlinear modeling systems that are difficult to characterize analytically. Even though the architecture allows for arbitrarily small approximation errors with related weight values, there is still an obstacle to their efficiency in some form of training. The multilayer perceptron, whose architecture defines multiple layers of neurons, is today’s most widely used supervised neural network for approximation problems.

The “FNN-MLP” consists of three layers: an input layer, a hidden layer, and an output layer. Each of these layers hides information from the other two layers. Synaptic weights,

The following

The instance outputs

The output “GHI”

The following mathematical formula, which accounts for all inputs and represents the global solar radiation, is produced when

The “FNN-MLP” framework was optimized for GHI prediction using MATLAB 2020b. The methods, database distribution, layer depth, neuron count, and activation functions are all included.

Training algorithm | Input layer | Hidden layer | Output layer | ||
---|---|---|---|---|---|

BFGS quasi-Newton (trainbfg) | Neurons number | Number of neurons | Activation function | Number of neurons | Activation function |

08 | 23 | The hyperbolic tangent sigmoid transfer function (tansig) | 1 | The linear transfer function (identity) |

The Support Vector Machine, commonly known as SVM, is a supervised learning method that has gained significant popularity recently for its ability to predict meteorological data such as temperature [

The dataset has a D-dimensional input vector

The following equations provide the SVM optimization model (for the training set):

The problem above can be solved in the same manner as a standard nonlinear restricted optimization problem by utilizing the concepts of Lagrange multipliers to generate a dual optimization problem:

Two models were used to develop an accurate prediction of hourly global solar irradiance: The FNN-MLP and the SVM. The process used to evaluate and improve the structure of the FNN-MLP and SVM models is shown in detail in

Several techniques were used to determine the most effective FNN-MLP model. The BFGS quasi-Newton training algorithm (trainbfg) was used, four activation functions (log sigmoid, tangent sigmoid, exponential, and sin) were used in the hidden layer, and a single transfer function (identity) was used. Experiments were performed with different sizes for the hidden layers (from 3 to 25 neurons) to obtain the most accurate model possible. An iterative testing process was performed to determine the FNN-MLP model with the best performance. An optimal SVM model was developed using the support vector machine learning strategy for the SVM technique. The selection of appropriate kernel features is critical to the success of the SVM model. The STATISTICA software provides a wide range of kernel functions for SVM models. The penalty term for the Gaussian radial basis function parameters was set to nu = 1.0000, C = 10.0000, and Gamma = 13.93. This process determined the optimal values for the target parameters of the SVM model.

In this study, various error measures were employed to determine the level of accuracy of the prediction models. These error measures include the Correlation Coefficient (R), mean percentage error (MPE), and Root Mean Squared Error (RMSE). These measures are mathematically represented by

This subsection presents the results of the models developed in the study to predict hourly global irradiation. Initially, data collected from the Bouzareah station generated two models: The FNN-MLP and SVM. The performance of these models was evaluated using three different data divisions for training, validation, and testing. The results were visualized in

The performance statistics of the optimal FNN-MLP model for the training, validation, testing, and overall phases in terms of R, MPE, and RMSE are presented in

Stat. | Training phase | Validation phase | Testing phase | Total phases |
---|---|---|---|---|

R (–) | 0.9543 | 0.9362 | 0.9567 | 0.9528 |

MPE (%) | 13.6706 | 17.3840 | 14.1855 | 14.0925 |

^{2}) |
72.9729 | 86.9887 | 71.4774 | 74.3451 |

Kernel functions | SVM number | Phase | RMSE (Wh/m^{2}) |
R (–) |
---|---|---|---|---|

Linear | 362 | Training | 193.312 | 0.625 |

Testing | 190.394 | 0.628 | ||

Total | 192.150 | 0.626 | ||

Polynomial | 474 | Training | 118.351 | 0.884 |

Testing | 120.717 | 0.873 | ||

Total | 119.303 | 0.880 | ||

Radial basis func | 1163 | Training | 32.414 | 0.991 |

Testing | 57.326 | 0.972 | ||

Total | 38.704 | 0.988 | ||

Sigmoid | 220 | Training | 229.925 | 0.414 |

Testing | 223.432 | 0.434 | ||

Total | 227.348 | 0.422 |

The linear SVM model with C = 10 and E = 0.1 achieved an RMSE of 193.312 Wh/m^{2} and R of 0.625 in the training phase, an RMSE of 190.394 Wh/m^{2} and R of 0.628 in the testing phase, and an overall RMSE of 192.150 Wh/m^{2} and R of 0.626. The polynomial SVM model with C = 10, nu = 1, Degree = 3, and Gamma = 0.125 achieved the lowest RMSE of 118.351 Wh/m^{2} and highest R of 0.884 in the training phase, an RMSE of 120.717 Wh/m^{2} and R of 0.873 in the testing phase, and an overall RMSE of 119.304 Wh/m^{2} and R of 0.880.

The RBF-SVM model with C = 10, nu = 1, and Gamma = 13.93 achieved the lowest RMSE of 32.414 Wh/m^{2} and highest R of 0.991 in the training phase but had a higher RMSE of 57.326 Wh/m^{2} and lower R of 0.972 in the testing phase, resulting in an overall RMSE of 38.706 Wh/m^{2} and R of 0.988. The sigmoid SVM model with C = 10, nu = 0.1, and Gamma = 0.125 had the highest RMSE of 229.925 Wh/m^{2} and lowest R of 0.414 in the training phase, an RMSE of 223.432 Wh/m^{2} and R of 0.434 in the testing phase, and an overall RMSE of 227.348 Wh/m^{2} and R of 0.422.

Overall, the RBF-SVM model with C = 10, nu = 1, and Gamma = 13.93 outperformed the other evaluated models, achieving the lowest RMSE and the highest R-value in the training phase, as well as the second-lowest RMSE and the second-highest R-value in the testing phase. This resulted in the lowest overall RMSE and the highest overall R-value. In comparison to the linear and sigmoid SVM models, the RBF-SVM model demonstrated a substantial improvement in both RMSE and R-values during the training and testing phases, indicating its efficacy in predicting hourly global horizontal irradiation. Furthermore,

Following a comprehensive verification process, we present the performance evaluation of the FNN-MLP and RBF-SVM models for solar radiation prediction at BOU and TAM stations in

Model | Phase | Station | R (−) | MPE |
RMSE^{2}) |
Station | R (−) | MPE |
RMSE (Wh/m^{2}) |
---|---|---|---|---|---|---|---|---|---|

FNN-MLP | Training | BOU | 0.9544 | 13.6706 | 72.9729 | TAM | 0.9322 | 14.7679 | 109.1829 |

Testing | 0.9568 | 14.1855 | 71.4774 | 0.9520 | 10.6584 | 87.2197 | |||

Total | 0.9528 | 14.0925 | 74.3451 | 0.9313 | 14.9170 | 109.5552 | |||

SVM-RBF | Training | 0.9914 | 6.9987 | 32.4142 | 0.9204 | 17.7120 | 119.0809 | ||

Testing | 0.9715 | 12.7947 | 57.3256 | 0.9351 | 13.8780 | 104.7578 | |||

Total | 0.9876 | 8.1586 | 38.7045 | 0.9231 | 16.9452 | 116.3575 |

Both models demonstrated reasonable accuracy in predicting solar radiation. However, the SVM-RBF model exhibited superior performance compared to the FNN-MLP model in terms of R and RMSE values for both stations, particularly during the testing phase. During the training phase, the FNN-MLP model achieved R values of 0.9544 and 0.9322 for the BOU and TAM stations, respectively. In contrast, the SVM-RBF model achieved notably higher R-values of 0.9914 and 0.9204 for the same stations.

Moreover, incorporating additional inputs such as MON, PRE, and WID did not yield improvements in the model’s performance. These findings indicate that the SVM-RBF model provides a more accurate GHI prediction than the FNN-MLP model.

The performance of the present work model in predicting hourly global solar radiation was compared with different techniques used in previous studies.

Models | Type of model | Prediction error “R, R^{2.}” |
---|---|---|

Present work | RBF-SVM | R = 0.9876 |

Al-rousan et al. [ |
Random forest | R^{2} = 0.9637 |

Benmouiza et al. [ |
K-means clustering-NAR | R = 0.93 |

Jallal et al. [ |
Artificial multi-neural | R = 0.9624 |

García-hinde et al. [ |
SVR-PLS | R = 0.94 |

Akarslan et al. [ |
Adaptive approach | R = 0.96 |

Guermoui et al. [ |
Machine learning | R^{2} = 96.68–98.52 |

Benali et al. [ |
Random forest | R = 0.95 |

The comparison results suggest that machine learning models have great potential in predicting hourly global solar radiation. However, the performance of these models can vary based on various factors, such as the quality and quantity of input data, feature selection, and the specific algorithm used. Therefore, it is important to carefully consider and test different models to achieve the best results for a particular application. The high accuracy achieved by the present work using RBF-SVM indicates that it could be a useful model for future predictions in this area.

This study aims to improve the accuracy of hourly global horizental irradiation prediction by using advanced machine-learning techniques. The main objective is to develop a method that optimizes the hyperparameters of conventional machine learning models, specifically multilayer Perceptron Feedforward Neural Networks (FNN-MLP) and Support Vector Machines (SVM). To achieve this, two models were used: the FNN-MLP and the SVM.

To create the most effective model FNN-MLP, the BFGS quasi-Newton method was used as the training algorithm, four activation functions were tested in the hidden layer, and a single transfer function was used. The dimensions of the hidden layers were also varied to obtain the most accurate model possible. Regarding power and performance, the SVM model with the radial basis function (RBF) kernel function gives significantly better results than the SVM models with other functions. The RBF kernel function also shows a superior capacity in characterizing the SVM model’s hourly global solar irradiance forecast.

The statistical error difference values between the RBF-SVM model and the FNN-MLP model are significant, indicating the higher accuracy of the proposed RBF-SVM model in predicting global solar irradiance compared to the FNN-MLP model. Moreover, all the machine learning methods discussed in this study provide highly accurate predictions of global solar irradiance at different temporal resolutions. However, our results show that the RBF-SVM model performs better than the FNN-MLP-BFGS model in predicting hourly global solar irradiance, with an R-value of 0.99 and an RMSE of 38.70 Wh/m^{2} over all phases. Moreover, this study also investigates the performance of the proposed models in different climatic regions of Algeria, which is crucial for accurately predicting solar radiation at a specific location. In this way, it could help in the design and installation of solar energy systems as well as in the evaluation of thermal conditions in building studies.

In summary, this study provides a promising alternative to the traditional methods currently used in Algeria to predict solar radiation. With its superior accuracy and performance, the RBF-SVM model can be a valuable tool for predicting global solar irradiance at any location, thus supporting the development and implementation of renewable energy sources in the country. In addition, the study opens the possibility of using these techniques in other countries with similar climate and energy needs.

The authors would like to thank the University of Relizane and the University of Dr. Yahia Fares-Laboratory Medea’s of Biomaterials and Transport Phenomena for their assistance with this work.

The authors received no specific funding for this study.

Study conception and design, Y. Ammi, N. Bailek, S. Hanini, L. Abualigah, E. El-kenawy; analysis and interpretation of results, A. Dahmani, Y. Ammi, S. Hanini, I. Colak, L. Abualigah; draft manuscript preparation, A. Dahmani, Y. Ammi, E. El-kenawy; writing—review and editing: N. Bailek, A. Kuriqi, N. Al-Ansari, I. Colak, L. Abualigah. All authors reviewed the results and approved the final version of the manuscript.

The authors confirm that the data supporting the reported findings are all available within the article.

The authors declare that they have no conflicts of interest to report regarding the present study.

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