A Novel Hybrid VMD-TCN-BiGRU Model for Solar Irradiation Prediction Using Long-Term Monthly Meteorological Data

Technical Summary: A Novel Hybrid VMD-TCN-BiGRU Model for Solar Irradiation Prediction

Problem Statement
Solar energy is a critical component of the global transition toward sustainable power, yet its integration into energy systems is hindered by the intermittent nature of solar irradiation (SI). Accurate forecasting of SI is essential for investment decisions, grid stability, and the efficient operation of photovoltaic (PV) systems. While various machine learning (ML) and deep learning (DL) methods have been applied to SI prediction, existing literature often relies on classical models or lacks powerful hybrid architectures capable of handling the high-order nonlinearity and non-stationarity inherent in long-term meteorological data. The challenge remains to develop a model that can effectively extract temporal dependencies and frequency components from complex weather datasets to achieve superior prediction accuracy.

Methodology
This study proposes a novel hybrid deep learning framework integrating Variational Mode Decomposition (VMD), Temporal Convolutional Networks (TCN), and Bidirectional Gated Recurrent Units (BiGRU). The model was applied to predict monthly SI for the Karapınar District in Konya, Turkey, using long-term meteorological data (January 1984 – December 2025) sourced from NASA POWER.

The proposed architecture operates through four sequential stages:

1. Data Preprocessing: Raw SI data undergoes a logarithmic transformation ($x(t) = \log(1+y(t))$) to mitigate the effects of sudden spikes and noise, followed by normalization to the $[0, 1]$ range.
2. VMD-Based Decomposition: The preprocessed signal is decomposed into $K=6$ unique Intrinsic Mode Functions (IMFs). This step isolates linear and non-stationary structures, allowing subsequent layers to identify unique periodic patterns within specific frequency bands.
3. Hierarchical TCN-BiGRU Engine: Each IMF component is processed in parallel by a deep learning block:
   • TCN Layer: Utilizes dilated causal convolutions to capture long-term temporal dependencies with an expanded receptive field, extracting hierarchical features from the IMFs.
   • BiGRU Layer: Processes the features from the TCN in both forward and backward directions to capture bidirectional temporal relationships, preventing data loss and mitigating gradient vanishing issues common in standard RNNs.
4. Aggregation and Reconstruction: The predictions for each of the six IMFs are summed to reconstruct the final signal. An inverse logarithmic transformation ($\exp(x) - 1$) is applied to convert the output back to the original units ($kW\cdot h/m^2/day$).

Benchmarking
The performance of the proposed VMD-TCN-BiGRU model was rigorously compared against eight established algorithms: XGBoost, Light Gradient Boosting Machine (LGBM), Convolutional Neural Network (CNN), Decision Tree (DT), Long Short-Term Memory (LSTM), Elastic Net (ENet), Extreme Learning Machine (ELM), and Histogram-Based Gradient Boosting (HGB). All models were trained on an 80/20 split of the dataset using identical hyperparameter optimization strategies.

Key Results
The study utilized multiple evaluation metrics, including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Coefficient of Determination ($R^2$), and Residual Prediction Deviation (RPD).

• Error Reduction: The proposed hybrid model achieved the lowest error rates among all nine models, with an MSE of 0.0593, RMSE of 0.2434, MAE of 0.1879, and MAPE of 4.14%.
• Explanatory Power: The model attained the highest $R^2$ value of 0.9849, indicating it successfully modeled nearly all variability in the dataset.
• Reliability (RPD): The model achieved an RPD value of 8.137, significantly outperforming the next best model (XGBoost at 6.037). An RPD above 8.0 suggests the model is highly reliable for practical applications.
• Stability and Generalization: A 10-fold cross-validation analysis confirmed the model's stability, with $R^2$ values ranging from 97.05% to 99.34% across folds, demonstrating robustness against overfitting.
• Error Distribution: Histogram and probability density analyses revealed that the proposed model's errors were most concentrated around zero with the least dispersion, whereas other models exhibited wider error tails and greater deviation.

Significance and Claims
The authors claim that the VMD-TCN-BiGRU hybrid model represents a significant advancement in SI prediction by addressing the limitations of single-architecture models. The study asserts that the integration of VMD effectively separates noise and complex signal components, while the TCN-BiGRU combination leverages both local feature extraction and bidirectional temporal learning.

The paper concludes that this hybrid approach offers higher accuracy and reliability than standard ML and DL methods (including CNNs and LSTMs) for long-term monthly SI forecasting. The authors position the model as a superior tool for energy management, grid planning, and PV system optimization, particularly in regions with high solar potential like Karapınar. The research highlights that the specific combination of signal decomposition and bidirectional deep learning is key to achieving the reported 98.5% accuracy level. Future work suggested by the authors includes testing the model in different climatic zones and exploring its application to other renewable energy sources like wind.