When designing solar systems and assessing the effectiveness of their many uses, estimating sun irradiance is a crucial first step. This study examined three approaches (ANN, GA-ANN, and ANFIS) for estimating daily global solar radiation (GSR) in the south of Algeria: Adrar, Ouargla, and Bechar. The proposed hybrid GA-ANN model, based on genetic algorithm-based optimization, was developed to improve the ANN model. The GA-ANN and ANFIS models performed better than the standalone ANN-based model, with GA-ANN being better suited for forecasting in all sites, and it performed the best with the best values in the testing phase of Coefficient of Determination (R = 0.9005), Mean Absolute Percentage Error (MAPE = 8.40%), and Relative Root Mean Square Error (rRMSE = 12.56%). Nevertheless, the ANFIS model outperformed the GA-ANN model in forecasting daily GSR, with the best values of indicators when testing the model being R = 0.9374, MAPE = 7.78%, and rRMSE = 10.54%. Generally, we may conclude that the initial ANN stand-alone model performance when forecasting solar radiation has been improved, and the results obtained after injecting the genetic algorithm into the ANN to optimize its weights were satisfactory. The model can be used to forecast daily GSR in dry climates and other climates and may also be helpful in selecting solar energy system installations and sizes.

Previous research has demonstrated that green energy sources, particularly solar and wind, may serve as effective substitutes for conventional sources of energy in order to meet worldwide demand without harming the environment [

Artificial neural networks (ANNs) produce favorable outcomes with limited parameters; therefore, they are frequently used for solar radiation predictions. Using meteorological data from the province of Isparta [^{2}), mean absolute error (MAE), and root mean square error (RMSE) over initial forecasts. Also, reference [

A model that incorporates ANN and fuzzy inference is called the adaptive neuro-fuzzy inference system (ANFIS). To reduce the search space, the method splits a representation related to prior knowledge into subgroups. then the fuzzy parameters are adjusted using the backpropagation process. The end product is an adaptive ANN that has a linear relationship and functions exactly like a first-order Takagi-Sugeno inference system [^{2}) and (RMSE). The findings revealed that the suggested ANFIS could determine the daily Hd with accuracy in China. Reference [_{avg}) and (RH), hour angle (HA), along with the Gaussian membership function to estimate GSR models in four sites in Algeria.

GAs are widely employed in optimization problem solving, in both machine learning and research [

To the best of our knowledge, the use of optimizing algorithms such as GA to build hybrid models and comparing the use of fuzzy logic and genetic algorithms on the same multi-layer feed-forward neural network model in terms of enhancing prediction model accuracy have not yet been fairly included. Little is known about which method to inject into the model to get the best performance when trying to develop a hybrid model in arid areas. So far, it is not clear whether injecting optimization algorithms is better or whether the use of fuzzy logic is the best choice. The primary aim of our study is to systematically simulate daily GSR using our developed hybrid GA-ANN model, a combined machine learning approach, for forecasting global solar radiation. Subsequently, we evaluate its performance against two other approaches: A standalone ANN and an ANN-based method named ANFIS, using meteorological data from three chosen research regions (Adrar, Ourgla, and Bechar) in the Algerian desert.

The subject of the study region is located in Algeria’s desert (

Provinces | Latitude (°) | Longitude (°) | Altitude (m) |
---|---|---|---|

Adrar | 26.489 | −1.358 | 286 |

Ouargla | 30.998 | 6.766 | 178 |

Bechar | 31.386 | −2.012 | 785 |

The southern part of Algeria has the maximum insolation time at 3900 h [^{2} for the large part, or approximately 2263 kWh/m^{2}/year in the south of this country [

We build up a vast database that may be used for testing and training our model. Our research utilized daily data over 3 years (2019–2021) obtained from the Simple Ocean Data Assimilation Database (SODA) [

Parameters | Abbreviation | Unit | Type |
---|---|---|---|

Day of the year | D | Numerical | |

Average temperature | T_{avg} |
°C | |

Relative humidity | RH | % | |

Declination | DE | Degree (°) | |

Hour angle | HA | Degree (°) | |

Extraterrestrial solar irradiation | H_{0} |
Wh/m^{2} |

By correctly understanding the previous pattern, this technique could significantly reduce the issue of inadequate training as well as computation costs. As a result, preprocessing the inputs significantly improves the anticipating model’s efficiency. A variety of strategies can be used to preprocess the data that was provided to the forecasting approaches. In our paper, the normalizing [

The approach selects a subset of inputs out of a larger set. In consequence, regression inaccuracy could potentially be decreased by limiting the data to an interval of zero to one, increasing precision, and maintaining the relationship between the data sets’ correlation.

The neural activity of our brains is simulated by the ANN model [

The multi-layer feed-forward neural network (MLF), which has three layers (i, j, and k), which employs (BP) algorithm, is the most widely used ANN method for predicting solar radiation. The ability of this approach to represent issues which may not be separated by linearity makes it effective. Each of the layers is linked together by weights

The transformation in which each neuron adds a bias term to the sum before nonlinearity converts it into an output is known as the node activation function. Commonly used functions are the tangent-sigmoid transfer function (

With

In our approach, we design an ANN to anticipate daily GSR. The characteristics are illustrated in

Aspect | Description |
---|---|

Network architecture | With a “tansig” activation function for the hidden layer, this feedforward neural network has five hidden layers, each with five neurons. |

Data preprocessing | The mapminmax function is used to apply min-max normalization to the input (P) and target (T) data. |

Training parameters | ‘Levenberg-Marquardt Backpropagation’ is the training algorithm, with a maximum of 1000 epochs and a goal error of 0.000001. |

Training process | 80% of the provided data was used for training, and the remaining 20% was used for testing. |

Monitoring training | A training record (tr), which tracks both training and testing errors, is used to track the progress of the training process. |

For our MLP architecture, we used only one neuron (see

ANFIS integrates fuzzy and ANN algorithms; it involves fuzzy variables being handled by nodes in various feed-forward network layers. This is comparable to distributed variable fuzzy inference systems (FIS) [

The ANFIS is essentially built of five layers (see

1st Fuzzification Layer:

For adaptive nodes, make use of fuzzy C-means clustering.

Based on input values, membership grades for linguistic labels are generated.

Uses particular formulas to define the parameters of the premise.

Membership functions guarantee that outputs fall between 0 and 1.

2nd Rule Activation Layer:

Nodes multiply membership grades to determine the rule firing strength.

Determines rule products for every pair of linguistic labels.

3rd Normalization Layer:

Nodes normalize firing strengths that come from the layer before.

4th Consequent Layer:

The normalized firing strength is squared by each node and combined with the resulting parameters.

5th Output Layer:

The weighted products from the previous layer are aggregated by a single node to get the overall output [

We employed the following input and output Membership Functions Types, respectively:

Gaussian

Linear

{a.b.c.d} are MFs parameter sets where the maximum and minimum values are 1 and 0 [

These selection-based heuristic combinatorial methods of search are known as GAs. The major goal is to replicate the fundamental concepts of natural genetics in order to mimic the biological evolution processes of chromosomes, also known for their string structures. The GA procedure consists of:

• Determining which chromosomal sequencing should be utilized for testing or to represent a solution.

• Select a fitness function that will be utilized for testing GA solutions and determining if these results are suitable for use as solutions for the next generation.

The primary distinctions between GAs and conventional methods of optimization are [

- GAs encode parameter sets rather than the parameters themselves.

- A population of GAs is used to seek the local optimum, rather than a single point.

- GAs rely on objective function information rather than derivatives or other adjutant knowledge.

- GAs use probability-based evolution rules rather than deterministic rules.

The purpose of this hybrid model is to train the ANN using some data and then train it further using a GA to optimize its performance. This approach is summarized in

This model can be given in three main steps:

Create the data that will be set to train and test the developed ANN.

Then a hybrid training ANN-GA function is employed when training ANN using a hybrid approach that combines backpropagation with a GA. The function then sets the biases and weights of the developed model.

An apdated ANN is then used to make predictions on the input data.

The hybrid training ANN-GA function is a function that trains an ANN model using a GA optimization technique. The function takes in two inputs: The ANN model and the data to be used for training. The function first defines the optimization problem to be solved by setting the cost function.

The optimization problem in this case is to find the set of weights and biases that minimize the root mean squared error (RMSE).

The cost function is defined using another function that takes in the ANN weights and data to return the cost of the ANN model. The problem is then defined by setting the number of variables, the variable range, and the maximum and minimum values for each variable. Next, the GA parameters (the size of the population and the most iterations possible) are defined at the beginning. These parameters are used to set up the GA algorithm. The GA algorithm is then run using the defined problem and parameters. ANN-GA model parameters are given in

Number of hidden layers | Max iterations | Population size | Selection method | Crossover percentage | Mutation percentage |
---|---|---|---|---|---|

5 | 100 | 1000 | Roulette wheel | 0.6 | 0.4 |

Finally, the best solution found by this algorithm is employed to update the ANN weights, leading to an updated ANN, which is then used to make predictions on the input data.

Metrics frequently seen in evaluation scores were used to evaluate the effectiveness of the methodologies being investigated [

Indice | Ideal | Equation | |
---|---|---|---|

Zero | (7) | ||

Zero | (8) | ||

One | (9) |

Where _{Act}_{pre}

Daily GSR was anticipated by the developed ANN, ANFIS, and GA-ANN models across three Algerian localities.

City | Adrar | Ouargla | Bechar | ||||||

Model | ANN | ANFIS | GA-ANN | ANN | ANFIS | GA-ANN | ANN | ANFIS | GA-ANN |

R | 0.8909 | 0.9206 | 0.9008 | 0.8865 | 0.9304 | 0.9076 | 0.8839 | 0.9017 | 0.8877 |

rRMSE% | 10.33 | 9.05 | 10.05 | 13.11 | 10.76 | 12.32 | 13.88 | 13.07 | 13.85 |

MAPE% | 7.11 | 5.87 | 6.80 | 9.05 | 7.27 | 8.43 | 10.09 | 9.24 | 10.01 |

The ANN, ANFIS, and GA-ANN models are designed in order to predict daily GSR. It is obviously visible, as seen in

That is shown in the scatter plots (see

Based on statistical assessment measures, ANFIS is the most precise and accurate model when the results from the three approaches are compared. Following ANFIS, GA-ANN demonstrates relatively strong performance, while the stand-alone ANN model appears less accurate. This underscores the success of employing GA to optimize the stand-alone ANN, thereby enhancing its performance. Nevertheless, the other hybrid model (ANFIS) was able to perform even better in all locations.

We have now established that the two hybrid ANN-based approaches outperformed the stand-alone ANN model. To thoroughly investigate the effectiveness of the hybrid ANFIS and GA-ANN approaches. We can see in

The ANFIS model performs better than the GAANN model when it comes to daily solar radiation prediction. ANFIS has a stronger linear relationship and higher precision, especially for lower radiation values, as seen by

We can certainly establish that in this research, the hybrid ANFIS model resulted in the most accurate performance when anticipating the daily GSR according to the overall results. Therefore, we performed a deeper investigation to see how the two hybrid ANN-based (ANFIS and GA-ANN) models performed in the testing and training phases.

Training | Testing | ||||||
---|---|---|---|---|---|---|---|

City | Model | R | rRMSE% | MAPE% | R | rRMSE% | MAPE% |

ANFIS | |||||||

GA-ANN | 0.8971 | 10.21 | 6.86 | 0.9017 | 9.35 | 6.51 | |

ANFIS | |||||||

GA-ANN | 0.9095 | 12.26 | 8.43 | 0.9005 | 12.56 | 8.40 | |

ANFIS | |||||||

GA-ANN | 0.8894 | 13.61 | 9.92 | 0.8811 | 14.98 | 10.79 |

Despite the fact that fuzzy logic provides a mathematical foundation for handling imprecision and uncertainty, it is usually used in control systems and decision-making processes, and it is not an optimization algorithm like GAs, which find the best solution in fields like machine learning. Upon comparing the models developed in this work, it is clear that combining fuzzy logic with ANNs gave better results than the approach where ANN was combined with GA.

For forecasting solar radiation using the same input set, ANFIS emerges as a suitable approach. Its adaptability to rule-based and data-driven patterns, combined with improved interpretability via fuzzy logic, make it a favorable competitor. ANFIS effectively integrates language rules with data-driven learning and demonstrates abilities in dealing with the difficulties of nonlinear data relationships. Notably, it reduces the need for considerable manual tuning, making it ideal for scenarios involving both rule-based and complex data patterns. Although employing the same inputs, the hybrid GA-ANN model optimizes the weights of the artificial neural network (ANN) using genetic algorithms (GA). While it provides flexibility and customization in terms of ANN architecture and hyperparameters, its performance is primarily dependent on the evolutionary algorithm’s capacity to optimize weight. This model has the ability to excel in activities that need a high level of customization and optimization, particularly in complicated domains.

In our scenario, this model succeeds in outperforming the standalone ANN model by optimizing its weights. Consequently, it may be concluded that the application of optimization algorithms such as GA might not be the best option when developing a hybrid ANN model. It is undeniable that optimization algorithms do enhance the stand-alone model’s performance.

Reference | Model | Time step | Location | R |
---|---|---|---|---|

[ |
ANN | daily | France | 0.7800 |

[ |
ANN | daily | Iran | 0.8940 |

[ |
ANFIS | daily | Nigeria | 0.8540 |

[ |
PSO-BPNN | daily | Beijing, China | 0.9530 |

[ |
FFA-ANN | daily | ELoued city, Algeria | 0.9321 |

ANFIS | daily | Ouargla city, Algeria | 0.9304 | |

GA-ANN | Daily | Ouargla city, Algeria | 0.9076 |

The calculated assessment indice (R) is used to assess the predictability of the stated and current methodologies. When compared to other methodologies, the suggested investigation’s outcomes show comparable effectiveness in terms of predictability and forecasting proficiency.

In a study spanning three cities in southern Algeria (Adrar, Ouargla, and Bechar), the efficacy of three techniques (ANN, GA-ANN, and ANFIS) at forecasting daily global solar radiation (GSR) over a 3-year period (2019–2021) using six input variables has been assessed. Our hybrid GA-ANN model, which aims to improve the ANN technique by optimizing ANN weights, outperforms the standalone ANN according to the statistical metrics (rRMSE, R, and MAPE). Nevertheless, in comparison to the other approaches, the GA-ANN model required more computing time. Conversely, ANFIS demonstrated the effectiveness of fuzzy logic in conjunction with ANNs by outperforming GA-ANN in forcasting daily GSR across all locations. Furthermore, the usage of the GA is yet to be investigated for optimizing other aspects of the ANN model, such as the hidden layers number, and even using other optimizing algorithms before establishing that fuzzy logic is superior for constructing hybrid models. In conclusion, whenever data is available, the model that was developed may be used to anticipate daily GSR in regions that are dry as well as other locations with similar conditions. It may also be useful while deciding on the installation of solar power installations.

Global solar radiation

Genetic algorithm

Artificial neural networks

Adaptive neuro fuzzy inference system

The authors are grateful to the laboratory of Sustainable Development and Computer Science (LSDCS) for supporting this research, and to the Directorate-General for Scientific Research and Technological Development (DGRSDT).

The authors received no specific funding for this study.

Study conception and design: Djeldjli Halima, Ghasri Mehdi, Benatiallah Djelloul; data collection: Benatiallah Djelloul, Benabdelkrim Bouchra; analysis and interpretation of results: Djeldjli Halima, Benatiallah Djelloul; draft manuscript preparation: Djeldjli Halima, Tanougast Camel, Benatiallah Ali. All authors reviewed the results and approved the final version of the manuscript.

The data that support the findings of this study are available from the corresponding author, Djeldjli Halima, upon reasonable request.

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