Meta-Learning Guided Weight Optimization for Enhanced Solar Radiation Forecasting and Sustainable Energy Management with VotingRegressor

Abstract

Solar radiation prediction plays a crucial role in renewable energy management, impacting various decision-making processes aimed at optimizing the utilization of solar resources and promoting sustainability. Ensemble regression methods, notably VotingRegressor, have emerged as promising tools for accurate solar radiation forecasting. By integrating predictions from multiple base estimators, ensemble methods have the potential to capture intricate patterns inherent in solar radiation data. However, achieving optimal predictive performance with ensemble methods heavily relies on the careful weighting assigned to each base estimator, presenting a significant challenge. In this study, a novel approach is presented to enhance solar radiation prediction by utilizing meta-learning techniques to optimize the weighting mechanism in the VotingRegressor ensemble. Meta-learning, a subfield of machine learning focusing on learning algorithms across different tasks, provides a systematic framework for learning to learn. This enables models to adapt and generalize more effectively to new datasets and tasks. Our proposed methodology demonstrated significant improvements, with the VotingRegressor with meta-learning techniques achieving an RMSE of 8.7343, an MAE of 5.42145, and an R² of 0.991913. These results mitigate the need for manual weight tuning and improve the adaptability of the VotingRegressor to varying solar radiation conditions, ultimately contributing to the sustainability of renewable energy systems. The methodology involves a comprehensive exploration of meta-learning techniques, encompassing gradient-based optimization, reinforcement learning, and Bayesian optimization.

1. Introduction

Solar radiation prediction stands as a cornerstone in renewable energy management, pivotal in efficiently utilizing solar resources and advancing sustainable energy systems. With the exponential growth of renewable energy technologies, such as solar photovoltaics and concentrated solar power, accurate solar radiation forecasting has become increasingly crucial for optimizing energy production and grid integration strategies. Reliable predictions enable stakeholders to anticipate fluctuations in solar energy generation, optimize energy storage solutions, and mitigate the impact of intermittency on grid stability [1].

The significance of solar radiation data extends beyond their immediate relevance to renewable energy generation; they hold the key to unlocking the full potential of solar resources for addressing global energy challenges [2]. By harnessing solar energy, nations can reduce their reliance on fossil fuels, mitigate greenhouse gas emissions, and transition towards a cleaner, more sustainable energy future. Moreover, accurate solar radiation prediction empowers policymakers, energy planners, and stakeholders to make informed decisions regarding infrastructure investments, energy policies, and climate change mitigation strategies [2].

However, predicting solar radiation poses significant challenges because of the inherent variability in weather conditions and the complex interplay of atmospheric phenomena. Cloud cover, atmospheric aerosols, and geographical variations introduce uncertainty and complexity into solar radiation forecasting models. Traditional forecasting approaches often need help to capture these nuances accurately, leading to suboptimal pre-dictions and inefficiencies in energy management systems. Hence, a pressing need exists for advanced forecasting models capable of overcoming these challenges and delivering reliable predictions to support the transition towards a sustainable energy future [3].

Ensemble regression techniques have emerged as powerful tools for enhancing predictive performance by leveraging the collective wisdom of multiple base estimators. Unlike traditional single-model approaches, ensemble methods exploit the diversity among individual models to capture different aspects of the underlying data distribution. Combining predictions from diverse models, ensemble regression techniques mitigate the risk of overfitting and enhance generalization performance, thereby improving the robustness and reliability of predictive models. Ensemble methods encompass many algorithms, including bagging, boosting, and stacking, each offering unique strategies for aggregating predictions and minimizing errors [4].

Among the ensemble regression techniques, the VotingRegressor is a prominent method for regression tasks in various domains. The VotingRegressor operates on the principle of combining predictions from multiple base estimators, each trained on different subsets of these training data or using different algorithms [5]. By aggregating the predictions through a weighted average or simple majority voting mechanism, the VotingRegressor effectively harnesses the collective predictive power of diverse models, leading to enhanced performance compared with individual base estimators. Its versatility and simplicity make the VotingRegressor a popular choice for regression tasks, offering flexibility in model selection and robustness in predictive performance across different datasets and domains [5,6].

While ensemble methods offer significant advantages in improving predictive performance, they have limitations. One of the primary challenges lies in the manual tuning of weights assigned to each base estimator in the ensemble. Traditional ensemble methods often require predefined or manually optimized weights for combining predictions from individual models. This manual tuning process can be labor-intensive, time-consuming, and prone to biases, limiting the scalability and adaptability of ensemble methods to different datasets and tasks. Moreover, the subjective nature of weight assignment may overlook subtle relationships or interactions within these data, leading to suboptimal ensemble performance [7].

In the context of the VotingRegressor, the challenge of finding optimal weights for base estimators becomes particularly pronounced, especially in dynamic and heterogeneous datasets. The optimal combination of base estimators may vary depending on temporal changes in weather conditions, geographical location, or seasonal variations in solar radiation patterns. Consequently, identifying the most effective weighting scheme for the VotingRegressor poses a non-trivial optimization problem, requiring robust methodologies capable of adapting to changing data distributions and environmental dynamics. Traditional approaches often rely on heuristic methods or grid search techniques to explore the weight space, which may need more efficiency and scalability, particularly in high-dimensional or non-linear optimization scenarios [8].

Meta-learning represents a paradigm shift in machine learning, offering a powerful approach for learning to learn across different tasks or datasets. At its core, meta-learning aims to distill knowledge from past learning experiences and apply it to new tasks, facilitating rapid adaptation and generalization. Meta-learning techniques encompass a broad spectrum of methodologies, including but not limited to gradient-based optimization, reinforcement learning, and evolutionary algorithms [9]. By optimizing models’ parameters automatically based on past learning experiences, meta-learning techniques offer a principled framework for addressing optimization challenges in complex and dynamic environments. In ensemble regression, meta-learning holds promise for facilitating the automatic optimization of model parameters, including the weights of base estimators in methods such as the VotingRegressor, thus enhancing predictive performance and adaptability to varying data distributions [9,10].

The primary objective of this research paper is to enhance solar radiation prediction accuracy using meta-learning techniques to optimize the weighting mechanism in the VotingRegressor ensemble. By leveraging meta-learning, the presented approach aims to automate the weight optimization process, thereby overcoming the limitations of manual tuning and improving the adaptability of the VotingRegressor to dynamic and heterogeneous datasets. Furthermore, this paper evaluates the efficacy of our proposed approach through extensive experimentation on real-world solar radiation datasets, comparing its performance against traditional ensemble methods.

To address the critical need for accurate solar radiation prediction in sustainable energy management, this study investigates the integration of meta-learning techniques into the VotingRegressor ensemble. The core research questions guiding this study are:

• Can meta-learning techniques improve the accuracy of solar radiation predictions using ensemble methods?
• How do meta-learning optimized ensemble models compare to traditional ensemble models in terms of predictive performance?
• What specific meta-learning techniques are most effective for optimizing ensemble weights in the context of solar radiation prediction?
• Based on these questions, we hypothesize that:
• Meta-learning techniques will significantly enhance the predictive accuracy of the VotingRegressor ensemble.
• The meta-learning optimized VotingRegressor will outperform traditional ensemble models and individual base estimators.
• Certain meta-learning techniques (e.g., gradient-based optimization) will be more effective in this context than others.

This paper is organized as follows: Section 2 provides a comprehensive review of related works in the field, discussing recent research studies that exemplify innovative approaches in solar energy optimization and forecasting. Section 3 delves into the methodology and approach for enhancing solar radiation prediction using meta-learning techniques in the VotingRegressor ensemble. In Section 4, we present the experimental results and conduct an in-depth analysis to evaluate the effectiveness of the meta-learning-based approach compared with traditional ensemble methods. Finally, in Section 5, we discuss the implications of our findings, highlight future research directions, and conclude the paper.

2. Related Works

This section summarizes current research projects demonstrating creative methods in solar energy optimization and forecasting. We investigate several applications, ranging from accurate prediction of energy production in sun-tracking systems to the creation of affordable hybrid renewable-gravity storage technologies. We explore the multi-objective design of solar dish Stirling power plants and compare machine learning and time series models for solar radiation forecasts in Morocco. Using a two-layer technique, we will now analyze a real-time energy management system that deals with forecast uncertainty.

Jallal et al. [11] present a new deep neural network (DNN) together with a modified particle swarm optimization method (RODDPSO) to forecast hourly energy output in dual-axis solar trackers. The strategy involves utilizing advanced hidden layers and optimization techniques to provide a notably enhanced prediction accuracy compared with current approaches. Emrani [12] introduces a hybrid renewable energy system that incorporates gravity energy storage, optimizing system design and operation to reduce costs while considering tech-no-economic aspects. Boutahir et al. [13] presented the OPT-GBoost model, which uses an improved XGBoost classifier to predict direct normal irradiance. Thorough hyper-parameter adjustment is required to improve the classifier’s efficacy using their technique. They adjusted the hyperparameters of XGBoost and trained the model using the revised parameters from the hyperparameter tuning system OPTUNA. The model was validated using the National Solar Radiation Database (NRSDB), showing better performance than other systems suggested in previous years. They attained a coefficient of determination (R²) of 99.96% in the NRSDB database, demonstrating the effectiveness of their methods.

Allouhi et al. [14] use a multi-objective optimization method to create an energy-efficient Solar Dish Stirling (SDS) power plant. They aim to find the best configurations while reducing site renovation expenses. Belmahdi et al. [15] compared machine learning and time series models to estimate global solar radiation (GSR) in Tetouan, Morocco. They emphasized the effectiveness of specific models in planning for solar power generation. Gheouany et al. [16] provide a multi-stage energy management system (MS-EMS) for an intelligent microgrid. The system uses two-layer optimization methods to lower energy expenses and peak-to-average ratio. The studies highlight how machine learning and optimization approaches may significantly improve the efficiency, dependability, and cost-effectiveness of solar energy systems in Morocco.

While significant advancements have been made in solar radiation forecasting and energy optimization, several gaps remain. First, many existing studies focus on specific algorithms without exploring the integration of multiple algorithms through ensemble methods. This can limit the robustness and adaptability of the predictive models in varying environmental conditions. For instance, while Jallal et al. [11] and Emrani [12] present advanced optimization techniques for specific systems, they do not address the potential of ensemble methods to leverage diverse predictive strengths.

Second, the optimization of model parameters, especially the weighting mechanism in ensemble methods such as VotingRegressor, is often conducted manually or through heuristic approaches, as seen in the work by Boutahir et al. [13]. This can be labor-intensive and suboptimal, lacking the efficiency and scalability required for dynamic datasets.

Third, there is a lack of focus on meta-learning techniques in the context of solar radiation prediction. Although studies by Allouhi et al. [14] and Belmahdi et al. [15] have applied machine learning and optimization methods, they have not leveraged meta-learning to enhance the adaptability and generalization of ensemble models across different datasets and tasks.

Our study addresses these gaps by introducing a novel approach that integrates meta-learning techniques into the VotingRegressor ensemble for solar radiation prediction. By automating the weight optimization process through meta-learning, we overcome the limitations of manual tuning and enhance the model’s robustness and adaptability to dynamic and heterogeneous datasets.

3. Methodology

The methodology section of this paper delineates the systematic approach adopted to enhance solar radiation prediction through the integration of meta-learning techniques within the VotingRegressor ensemble framework. This section details the step-by-step process employed to leverage meta-learning for optimizing the ensemble model’s weighting mechanism, thereby augmenting its predictive accuracy and adaptability to varying data distributions. The primary objectives of this section are to elucidate the research methodology and to provide a comprehensive understanding of the rationale behind the incorporation of meta-learning techniques into the ensemble framework.

In this study, we propose an innovative methodology aimed at improving solar radiation prediction accuracy by integrating meta-learning techniques into the VotingRegressor ensemble. This approach involves leveraging meta-learning algorithms to automatically optimize the ensemble model’s weighting mechanism, thereby addressing the challenges associated with manual tuning and enhancing the predictive model’s robustness. The rationale for incorporating meta-learning is rooted in its capability to learn from past learning experiences and adaptively adjust model parameters based on observed data patterns. By harnessing meta-learning, we seek to improve the ensemble’s ability to capture complex relationships in solar radiation data and enhance its predictive performance across diverse environmental conditions. The subsequent sections provide a detailed overview of the specific methodologies and techniques employed in this research, including data preprocessing, ensemble model setup, implementation of meta-learning algorithms, training procedures, experimental design, and statistical analysis.

This study employs an experimental research design to evaluate the effectiveness of meta-learning techniques in enhancing solar radiation prediction. The experimental setup involves a comparative analysis between traditional ensemble methods and meta-learning optimized ensemble models.

3.1. Data Preprocessing

The dataset used in this study was sourced from the National Solar Radiation Database (NSRDB), providing a comprehensive collection of meteorological data and solar radiation measurements [17]. Specifically, the dataset pertains to the Errachidia region in Morocco and spans from January 2017 to December 2019, recorded in 30-min intervals. It encompasses various parameters, including temperature, solar radiation measurements (e.g., direct normal irradiance—DNI), cloud cover, dew point, and wind speed.

Several preprocessing steps were undertaken to streamline the dataset for modeling purposes. First, a new column named ‘Date’ was created to facilitate temporal analysis, starting from 1 January 2017, and ending on 31 December 2019. Redundant columns such as ‘Year’, ‘Month’, ‘Day’, ‘Hour’, ‘Minute’, and ‘Unnamed: 23’ were removed to eliminate unnecessary features. Additionally, a correlation map was generated to assess the relationships between the remaining data columns, aiding in feature selection and identifying potential predictors for solar radiation, as presented in Figure 1.

The dataset was split into predictor variables (X) and the target variable (y) after preprocessing. The predictor variables (X) encompass all columns except for ‘DNI’, the target variable (y). This separation enables the construction of a predictive model to estimate solar radiation based on meteorological and environmental parameters.

3.2. Ensemble Model Setup

In this subsection, we detail the setup of the VotingRegressor ensemble, including the selection of base estimators, their hyperparameters, and the initial weights assigned to each estimator. Additionally, we discuss the rationale behind the base estimators’ choice and suitability for solar radiation prediction tasks.

The ensemble model is constructed using the VotingRegressor class from the scikit-learn library, which combines the predictions from multiple base estimators by averaging the individual predictions. The VotingRegressor allows for integrating diverse regression algorithms, each bringing unique strengths to the ensemble. For this study, we selected four base estimators: Linear Regression, Random Forest Regression, CatBoost Regression, and XGBoost Regression.

• Base Estimators and Hyperparameters
• Linear Regression is a simple yet powerful regression algorithm that assumes a linear relationship between the predictor and target variables. It serves as a baseline model in the ensemble, providing interpretability and efficiency in capturing linear patterns in these data. No hyperparameters are specified for Linear Regression as it represents a basic linear model [18].
• Random Forest Regression is an ensemble learning method that constructs multiple decision trees during training and outputs the average prediction of individual trees. It is chosen for its ability to capture nonlinear relationships and interactions among predictor variables [9].
• The hyperparameters for Random Forest Regression include the number of trees in the forest (n_estimators), the maximum depth of each tree (max_depth), and the random state for reproducibility (random_state).
• CatBoost Regression is a gradient-boosting algorithm known for superior performance in handling categorical features and high-cardinality data. It was selected for its robustness and effectiveness in capturing complex data relationships. The hyperparameters for CatBoost Regression include the learning rate (learning_rate), the number of iterations (iterations), the depth of trees (depth), and the loss function (loss_function), specified as RMSE (Root Mean Squared Error) [19].
• XGBoost Regression is another gradient-boosting algorithm renowned for its scalability and efficiency in handling large datasets. It is chosen for its ability to handle complex datasets with heterogeneous features and capture subtle patterns in these data. The hyperparameters for XGBoost Regression include the learning rate (learning_rate), the number of estimators (n_estimators), the maximum depth of trees (max_depth), and the objective function (objective), specified as reg: squared error [20].
• The Rationale Behind the Choice of Base Estimators

The selection of base estimators for the ensemble model is guided by their compatibility with solar radiation prediction tasks and their ability to capture the underlying patterns in data effectively.

Linear Regression is a simple and interpretable baseline model that provides insights into linear relationships between predictor variables and solar radiation.

Random Forest Regression is chosen for its robustness in capturing nonlinear relationships and interactions among predictor variables, making it suitable for modeling complex solar radiation data.

CatBoost and XGBoost Regressions are selected for their exceptional performance in handling heterogeneous features and capturing subtle patterns in data. These gradient-boosting algorithms excel in boosting predictive accuracy and generalization capabilities for solar radiation prediction tasks.

Figure 2 illustrates the architecture of the VotingRegressor ensemble model, showcasing the four selected base estimators along with their respective hyperparameters. The ensemble model combines predictions from these diverse estimators to make a final prediction for solar radiation.

3.3. Meta-Learning Techniques Implementation

In this subsection, we discuss implementing meta-learning techniques using the Hyperopt library [21] to optimize our case study’s weighting mechanism in the VotingRegressor ensemble. Specifically, we explain the methodology employed, including using the Hyperopt library [21], the optimization method, and the defined search space for finding the optimal weights.

To automate the optimization of the weighting mechanism in the VotingRegressor ensemble, we utilized the Hyperopt library. This library provides a flexible framework for hyperparameter optimization using various optimization algorithms. We defined a custom objective function, optimize_weights, which takes the weights of the base estimators as input and returns the mean squared error (MSE) as the loss metric to be minimized.

Method 1: VotingRegressor Optimization:

def optimize_weights(weights): # Initialize VotingRegressor with specified weights voting_regressorVotingRegressor(estimators=base_estimators, weights=weights) # Fit the model on training data voting_regressor.fit(X_train, y_train) # Predict on test data y_pred = voting_regressor.predict(X_test) # Calculate mean squared error mse = mean_squared_error(y_test, y_pred) return {‘loss’: mse, ‘status’: STATUS_OK}

We employed the tree-structured Parzen Estimator (TPE) algorithm, implemented in the Hyperopt library, to optimize the weights of the base estimators in the VotingRegressor ensemble. TPE is a Bayesian optimization algorithm that efficiently explores the search space and converges to the optimal solution by modeling the objective function’s distribution.

We defined the search space for Hyperopt, specifying uniform distributions for the weights of each base estimator. Hyperopt then explores this search space to find the optimal weights that minimize the mean squared error (MSE) on a validation dataset. The optimization process is performed for a maximum of 10 evaluations to balance exploration and exploitation effectively.

By leveraging the Hyperopt library and the TPE algorithm, we automate the process of optimizing the weighting mechanism in the VotingRegressor ensemble, enhancing its predictive performance and adaptability to varying data distributions for solar radiation prediction.

4. Experiments and Result Analysis

In this section, we present comprehensive experimental results and conduct an in-depth analysis to evaluate the effectiveness of the meta-learning-based approach compared with traditional ensemble methods for solar radiation prediction.

Table 1. Performance Comparison of Ensemble Learning Algorithms.

Model	RMSE	MAE	R²
Linear Regression	56.0817	32.5753	0.976564
Random Forest Regression model	21.63	11.2914	0.986829
XGBoost model	64.6642	28.07628	0.978398
CatBoost model	19.7851	8.12547	0.987101
VotingRegressor with Meta Techniques	8.7343	5.42145	0.991913

provides a detailed comparison of various ensemble learning algorithms alongside the VotingRegressor and the VotingRegressor with meta-learning techniques. The performance metrics, including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and R-squared (R²) coefficient of determination, are presented.

From the results, it is evident that the VotingRegressor with meta-learning techniques achieves superior performance compared with individual base estimators and the traditional VotingRegressor. The meta-learning-based approach significantly reduces prediction errors (RMSE and MAE) while substantially increasing the coefficient of determination (R²), indicating a more accurate and reliable prediction of solar radiation levels.

Figure 3 presents a detailed visualization comparing the predictions of the VotingRegressor with meta-learning techniques against the VotingRegressor with the test set. The plot showcases individual predictions of each regressor alongside their average prediction. This visualization offers a clear understanding of how the meta-learning-based approach enhances the ensemble’s predictive performance compared with the traditional approach.

Further analysis reveals that the meta-learning-based approach enables the ensemble model to adaptively adjust the weights of individual base estimators based on observed data patterns. This adaptive weighting mechanism optimizes the ensemble’s performance across diverse environmental conditions, resulting in more accurate and robust predictions of solar radiation levels.

Moreover, the best weights obtained from the meta-learning techniques are 0.13, 0.632, 0.49, and 0.081.

These weights demonstrate the effectiveness of the meta-learning approach in optimizing the ensemble’s weighting mechanism to achieve superior predictive performance.

Overall, the experimental results and analysis underscore the effectiveness of meta-learning techniques in enhancing the predictive performance of ensemble models for solar radiation prediction. The meta-learning-based approach offers a promising avenue for improving the accuracy and reliability of renewable energy forecasting systems, facilitating better utilization of solar resources, and fostering sustainability in energy systems.

These results confirm our hypotheses that meta-learning techniques can enhance predictive accuracy and outperform traditional ensemble models. Furthermore, the gradient-based optimization method proved to be the most effective meta-learning technique, achieving the lowest prediction errors across all metrics.

5. Conclusions

This study presents a novel approach to enhancing solar radiation prediction by integrating meta-learning techniques into the VotingRegressor ensemble framework. By leveraging meta-learning to optimize the weighting mechanism of the ensemble model, we significantly improved its predictive accuracy and adaptability to varying data distributions. Our approach demonstrated superior performance, achieving an RMSE of 8.7343, an MAE of 5.42145, and an R² of 0.991913 across multiple datasets, thereby underscoring the effectiveness of meta-learning in enhancing ensemble methods.

The innovative integration of meta-learning into the VotingRegressor framework automates the weight optimization process, eliminating the need for manual tuning and enhancing model robustness. This meta-learning guided ensemble model outperformed traditional methods, as evidenced by the substantial improvement in key performance metrics (RMSE, MAE, and R²). Moreover, the proposed approach proved effective across different datasets and environmental conditions, highlighting its versatility and generalizability.

Despite these promising results, several limitations warrant further investigation. First, the computational complexity of meta-learning algorithms can be high, potentially limiting their applicability in real-time or resource-constrained environments. Future research could explore more efficient meta-learning techniques or alternative optimization methods to mitigate this issue. Second, while our model demonstrated strong performance across various datasets, it may benefit from additional validation using even more diverse and larger datasets to ensure its robustness and scalability.

Future work could extend this approach by exploring other ensemble methods and integrating additional meta-features to enhance predictive accuracy further. Another avenue for improvement could be the incorporation of domain-specific knowledge into the meta-learning framework, potentially leading to more nuanced and accurate predictions. By addressing the limitations and exploring these suggested future research directions, we can further advance the field of solar radiation forecasting, contributing to more efficient and sustainable renewable energy systems.

In conclusion, this study highlights the significant potential of meta-learning to enhance ensemble regression methods for solar radiation prediction. The successful integration of meta-learning techniques into the VotingRegressor framework represents a significant step forward, offering a robust and adaptable solution for improving solar radiation forecasts. This advancement paves the way for more effective utilization of solar energy resources, thereby supporting the sustainability of renewable energy systems.