A new adaptive grey prediction model and its application

In this study, a new fractional-order accumulation generation operation and a novel grey action quantity are designed to improve the grey prediction model. The design of the new accumulation generation operation emphasizes new information and stability, enabling the model to produce more robust prediction results. The new grey action quantity is designed based on a logarithmic function that reduces the dimensional differences in the coefficient matrix, making the model more stable. Additionally, the ridge regression mechanism is incorporated into the modeling process to improve the model’s robustness. Specifically, the Marine Predators Optimization algorithm is introduced to facilitate the model’s solution process. To validate the effectiveness of the model, the proposed method and several competitive algorithms are applied to model China’s annual GDP, population, and residential electricity consumption. The experimental results demonstrate that the proposed model outperforms the competing algorithms in all evaluation metrics, confirming its effectiveness.