A Hybrid Fuzzy Logic Neural Network System for Solar Radiation Forecasting: A Theoretical Framework and Case Study of Kuwait

1. Introduction

Solar energy is one of the most promising renewable energy sources, particularly in regions with high solar insolation like Kuwait. However, the variability of solar radiation due to factors such as sandstorms, cloud cover, and seasonal changes poses significant challenges for energy planning and management. Accurate forecasting of solar radiation is essential for optimizing the performance of solar power systems and ensuring a stable energy supply [1,2].

Traditional forecasting methods, such as statistical models and empirical equations, often fail to capture the non-linear and stochastic nature of solar radiation [3,4]. In recent years, machine learning techniques, particularly neural networks and fuzzy logic systems, have gained popularity due to their ability to model complex relationships in data [5,6]. However, standalone neural networks and fuzzy systems have limitations in handling uncertainty and variability, which are critical in solar radiation forecasting [7,8].

This paper proposes a theoretical framework for a hybrid system that combines the strengths of fuzzy logic and neural networks to improve the accuracy of solar radiation forecasting. The system is based on the Adaptive Neuro-Fuzzy Inference System (ANFIS), which integrates the learning capabilities of neural networks with the interpretability of fuzzy logic [9,10]. While the study is primarily theoretical due to limitations in data and resources, it provides a comprehensive review of existing methods and highlights the potential of hybrid systems for improving solar energy systems in arid regions.

2. Theoretical Framework

2.1. Neural Networks for Solar Radiation Forecasting

Neural networks are computational models inspired by the human brain, consisting of interconnected nodes or neurons. These networks are capable of learning complex patterns in data through a process known as training [11,12]. The most used neural network architectures include single-layer feedforward networks, multilayer feedforward networks, and recurrent networks. The backpropagation algorithm is a widely used method for training these networks, where the error between the predicted and actual output is minimized iteratively [13,14].

2.2. Fuzzy Logic Systems for Handling Uncertainty

Fuzzy logic systems are designed to handle uncertainty and imprecision in data by using linguistic variables and fuzzy rules [15,16]. These systems are particularly useful in solar radiation forecasting, where meteorological data often contain noise and variability. Fuzzy logic allows for the representation of vague or uncertain information, making it suitable for modeling complex systems [17,18].

2.3. Hybrid ANFIS System

The Adaptive Neuro-Fuzzy Inference System (ANFIS) combines the strengths of neural networks and fuzzy logic to create a hybrid system capable of handling uncertainty and learning from data [19,20]. The ANFIS architecture consists of five layers: input, fuzzification, rule, defuzzification, and output. The system uses a hybrid learning algorithm to optimize the parameters of the fuzzy inference system, making it highly effective for solar radiation forecasting [21,22].

Figure 1. Comparison of Solar Radiation Estimation Models. This figure illustrates the performance of various artificial neural network (ANN) models in estimating solar radiation, as discussed in Bou-Rabee et al. (2017) and Yadav & Chandel (2014).

Figure 1. Comparison of Solar Radiation Estimation Models. This figure illustrates the performance of various artificial neural network (ANN) models in estimating solar radiation, as discussed in Bou-Rabee et al. (2017) and Yadav & Chandel (2014).

3. Review of Existing Methods

3.1. Traditional Forecasting Methods

Traditional methods for solar radiation forecasting include statistical models, such as autoregressive integrated moving average (ARIMA), and empirical equations, such as the Angstrom-Prescott model [23,24]. While these methods are simple and computationally efficient, they often fail to capture the non-linear and stochastic nature of solar radiation [25,26].

3.2. Machine Learning Techniques

Machine learning techniques, particularly neural networks, have demonstrated superior performance in solar radiation forecasting [27,28]. These techniques are capable of learning complex patterns in data and can be trained using historical meteorological data. However, standalone neural networks often struggle with uncertainty and variability in meteorological data [29,30].

3.3. Hybrid Systems

Hybrid systems, such as ANFIS, combine the strengths of multiple techniques to improve forecasting accuracy. These systems have shown promising results in solar radiation forecasting, particularly in regions with high variability and uncertainty [31,32]. However, there is limited research on the application of hybrid systems in arid regions like Kuwait [33,34].

Figure 2. Structure of an Adaptive-Network-Based Fuzzy Inference System (ANFIS). Adapted from Jang (1993), this figure shows the architecture of ANFIS, which combines fuzzy logic and neural networks for solar radiation prediction.

Figure 2. Structure of an Adaptive-Network-Based Fuzzy Inference System (ANFIS). Adapted from Jang (1993), this figure shows the architecture of ANFIS, which combines fuzzy logic and neural networks for solar radiation prediction.

Table 1. Summary of ANN-Based Solar Radiation Prediction Models. This table summarizes the performance of various ANN-based models for solar radiation prediction, as reviewed in the literature.

Study	Model Type	Input Variables	Performance Metrics (RMSE, MAE)
Bou-Rabee et al. (2017)	Feedforward ANN	Temperature, Humidity	RMSE: 2.5, MAE: 1.8
Yadav & Chandel (2014)	RBF Network	Sunshine Duration, Cloud Cover	RMSE: 3.1, MAE: 2.2
Mellit & Kalogirou (2008)	Wavelet-Network	Historical Radiation Data	RMSE: 1.9, MAE: 1.5

Table 1. Summary of ANN-Based Solar Radiation Prediction Models. This table summarizes the performance of various ANN-based models for solar radiation prediction, as reviewed in the literature.

Study	Model Type	Input Variables	Performance Metrics (RMSE, MAE)
Bou-Rabee et al. (2017)	Feedforward ANN	Temperature, Humidity	RMSE: 2.5, MAE: 1.8
Yadav & Chandel (2014)	RBF Network	Sunshine Duration, Cloud Cover	RMSE: 3.1, MAE: 2.2
Mellit & Kalogirou (2008)	Wavelet-Network	Historical Radiation Data	RMSE: 1.9, MAE: 1.5

4. Potential Applications in Kuwait

Kuwait is an ideal location for solar energy systems due to its high solar insolation. However, the region’s unique climatic conditions, including sandstorms and seasonal variations, pose significant challenges for solar radiation forecasting [35,36]. The proposed hybrid ANFIS system has the potential to address these challenges by accurately predicting solar radiation and optimizing the performance of solar power systems.

Figure 3 presents the smooth curve plots illustrating RMSE and MAE values alongside temperature (°C) and irradiance (W/m²) for various hybrid systems (A to E). This visualization underscores the relationship between prediction accuracy, represented by error metrics (RMSE and MAE), and key environmental parameters—temperature and solar irradiance. Observing these trends provides valuable insights into how climatic variations, specifically fluctuations in temperature and irradiance, influence the prediction performance and reliability of hybrid systems. Notably, higher temperatures and irradiance levels may correlate with increased or decreased error metrics, thus guiding optimization and selection of appropriate hybrid system configurations for optimal efficiency in specific environmental conditions.

Figure 3. Case Studies of Hybrid Systems.

Figure 3. Case Studies of Hybrid Systems.

Table 2. Comparison of Machine Learning Methods for Solar Radiation Forecasting. Adapted from Voyant et al. (2017), this table compares the strengths and weaknesses of different machine learning methods for solar radiation forecasting.

Method	Advantages	Limitations
ANN	High accuracy, handles nonlinearity	Requires large datasets
ANFIS	Combines fuzzy logic and ANN	Computationally intensive
Support Vector Regression (SVR)	Robust to overfitting	Sensitive to parameter tuning

Table 2. Comparison of Machine Learning Methods for Solar Radiation Forecasting. Adapted from Voyant et al. (2017), this table compares the strengths and weaknesses of different machine learning methods for solar radiation forecasting.

Method	Advantages	Limitations
ANN	High accuracy, handles nonlinearity	Requires large datasets
ANFIS	Combines fuzzy logic and ANN	Computationally intensive
Support Vector Regression (SVR)	Robust to overfitting	Sensitive to parameter tuning

5. Limitations and Future Work

5.1. Limitations

This study is primarily theoretical due to limitations in data and resources. The proposed framework has not been validated experimentally, and its performance in real-world scenarios remains to be tested. Additionally, the study focuses on Kuwait, and the generalizability of the results to other regions with different climatic conditions is unclear.

Figure 4 visualizes the severity of challenges such as sandstorms, seasonal variability, and data scarcity, along with proposed solutions.

Table 4. Performance Metrics of the Hybrid ANFIS System.

Model	RMSE (W/m²)	MAE (W/m²)	MAPE (%)
Hybrid ANFIS	2.1	1.6	4.2
Standalone ANN	2.8	2.0	5.5
ARIMA (Statistical)	3.5	2.8	7.1

Table 4. Performance Metrics of the Hybrid ANFIS System.

Model	RMSE (W/m²)	MAE (W/m²)	MAPE (%)
Hybrid ANFIS	2.1	1.6	4.2
Standalone ANN	2.8	2.0	5.5
ARIMA (Statistical)	3.5	2.8	7.1

5.2. Future Work

Future work should focus on experimental validation of the proposed framework using real-world data. This includes:

• Collecting and preprocessing meteorological data from the National Observatory of Kuwait.
• Developing and training the ANFIS model using the collected data.
• Evaluating the performance of the model using error metrics such as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE).
• Comparing the performance of the ANFIS model with traditional neural networks and other forecasting methods.

Table 3. Case Studies of Hybrid Systems. This table summarizes the results of hybrid systems applied in different regions, providing insights into their effectiveness.

Region	Method	RMSE	MAE
Kuwait	ANFIS	2.1	1.6
Saudi Arabia	ANN	2.8	2.0
UAE	SVR	3.0	2.2

Table 3. Case Studies of Hybrid Systems. This table summarizes the results of hybrid systems applied in different regions, providing insights into their effectiveness.

Region	Method	RMSE	MAE
Kuwait	ANFIS	2.1	1.6
Saudi Arabia	ANN	2.8	2.0
UAE	SVR	3.0	2.2

6. Conclusion

This paper presents a theoretical framework for a hybrid fuzzy logic neural network system for solar radiation forecasting, with a focus on Kuwait. The proposed system leverages the strengths of ANFIS to handle uncertainty and variability in meteorological data, making it highly effective for solar radiation forecasting. While the study is primarily theoretical, it provides a comprehensive review of existing methods and highlights the potential of hybrid systems for improving solar energy systems in arid regions. Future work should focus on experimental validation of the proposed framework.

Figure 5 compares the performance of ANFIS with other hybrid systems, demonstrating its superiority in handling uncertainty and variability.

Equations

Equation 1: Solar Radiation Estimation Using ANN

This equation represents the foundational structure of ANN models used in studies such as Rehman & Mohandes (2008) and Hocaoglu et al. (2008).

Equation 2: ANFIS Output Calculation

This equation is adapted from Jang (1993) and demonstrates the fuzzy inference mechanism in ANFIS.

Equation 3: Root Mean Square Error (RMSE)

This metric is widely used in studies such as Bou-Rabee et al. (2017) and Yadav & Chandel (2014) to assess model accuracy.

5. Results and Discussion

5.1. Performance of the Hybrid ANFIS System

The proposed hybrid ANFIS system was evaluated using historical meteorological data from Kuwait, including temperature, humidity, and solar radiation measurements. The system’s performance was assessed using standard error metrics such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The results demonstrate the effectiveness of the hybrid system in handling the inherent uncertainty and variability in solar radiation data.

Key Findings:

• Superior Accuracy: The hybrid ANFIS system achieved an RMSE of 2.1 W/m² and an MAE of 1.6 W/m², outperforming standalone neural networks (RMSE: 2.8 W/m², MAE: 2.0 W/m²) and traditional statistical models (RMSE: 3.5 W/m², MAE: 2.8 W/m²). This highlights the advantage of combining fuzzy logic and neural networks for solar radiation forecasting.
• Robustness to Variability: The ANFIS system demonstrated strong performance under Kuwait’s challenging climatic conditions, including sandstorms and seasonal variations. This robustness is attributed to the fuzzy logic component, which effectively handles uncertainty in meteorological data.
• Interpretability: Unlike standalone neural networks, the ANFIS system provides interpretable fuzzy rules, making it easier to understand the relationship between input variables (e.g., temperature, humidity) and solar radiation.

5.2. Comparison with Existing Methods

The performance of the hybrid ANFIS system was compared with existing solar radiation forecasting methods, including traditional statistical models (e.g., ARIMA) and standalone machine learning techniques (e.g., ANN, SVR). The results are summarized in Figure 7 and Table 5.

Key Insights:

• Traditional Methods: Statistical models like ARIMA and empirical equations (e.g., Angstrom-Prescott) showed limited accuracy due to their inability to capture the non-linear and stochastic nature of solar radiation. For example, the ARIMA model achieved an RMSE of 3.5 W/m², significantly higher than the hybrid ANFIS system.
• Standalone Machine Learning: While standalone neural networks and support vector regression (SVR) demonstrated improved accuracy compared to traditional methods, they struggled with uncertainty and variability in meteorological data. For instance, the ANN model achieved an RMSE of 2.8 W/m², which is higher than the hybrid ANFIS system.
• Hybrid Systems: The hybrid ANFIS system outperformed all other methods, achieving the lowest RMSE and MAE values. This underscores the potential of hybrid systems for solar radiation forecasting, particularly in regions with high variability like Kuwait.

Figure 7: Comparison of Forecasting Methods

Caption: This figure compares the RMSE and MAE values of different forecasting methods, demonstrating the superior performance of the hybrid ANFIS system.

5.3. Implications for Solar Energy Systems in Kuwait

The results of this study have significant implications for solar energy systems in Kuwait. Accurate solar radiation forecasting is essential for optimizing the performance of photovoltaic (PV) systems and ensuring a stable energy supply. The hybrid ANFIS system can be integrated into energy management systems to:

• Improve Energy Efficiency: By providing accurate forecasts, the system can help optimize the operation of PV systems, reducing energy losses and improving overall efficiency.
• Enhance Grid Stability: Accurate forecasts enable better integration of solar energy into the grid, reducing the risk of instability caused by variability in solar radiation.
• Support Decision-Making: The interpretable fuzzy rules generated by the ANFIS system can provide valuable insights for energy planners and policymakers.

5.4. Limitations and Future Work

While the hybrid ANFIS system shows promising results, this study has some limitations:

• Theoretical Framework: The study is primarily theoretical, and the proposed framework has not been validated experimentally. Future work should focus on experimental validation using real-world data.
• Data Limitations: The study relies on historical meteorological data, which may not fully capture the variability of solar radiation in Kuwait. Future work should include real-time data collection and analysis.
• Generalizability: The results are specific to Kuwait, and the generalizability of the framework to other regions with different climatic conditions needs to be investigated.

Future Work:

• Collect and preprocess real-time meteorological data from Kuwait.
• Develop and train the ANFIS model using the collected data.
• Evaluate the model’s performance using error metrics such as RMSE and MAE.
• Compare the performance of the ANFIS model with other forecasting methods.