Interval forecasting of solar irradiation using LSTM, XGBoost and bandwidth optimization of KDE by differential evolution

Accurately predicting solar irradiation intervals remains a critical challenge for decision-making in the energy management of solar-powered smart microgrids. To cope with the resulting uncertainties, models capable of providing accurate and reliable prediction intervals are essential. This paper proposes a novel hybrid approach combining long short-term memory (LSTM), extreme gradient boosting (XGBoost), and an adaptive kernel density estimator (AKDE), whose bandwidth is optimized via differential evolution (DE). By optimizing both the local and global bandwidths of the kernel density estimator, the proposed method generates highly accurate and reliable prediction intervals, demonstrating enhanced robustness. Comparative analyses across multiple evaluation sites reveal that the hybrid model (LSTM–XGBoost–DE–AKDE) outperforms existing models reported in the literature. Specifically, the average PINAW value achieved by the proposed model is substantially lower than that of the KDE–PSO–LSTM model. At the 95% confidence level, the proposed model achieves a PINAW of 0.122 compared to 0.301; at the 90% level, 0.101 versus 0.256; and at the 85% level, 0.083 versus 0.258.