A Novel Power-sum Time-varying Grey Prediction Model and Its Applications

The purpose of this paper is to propose an improved power-sum accumulation time-varying grey model (PATGM) to enhance the ability to mine the heterogeneity of sparse data. Firstly, a novel power-sum accumulation grey generating operator is introduced to smooth the observed values according to data fluctuations, mitigating the model's ill-conditioned property. Secondly, a time-varying function is introduced as a parameter structure to the traditional model, providing the model with flexibility in complex systems modeling. Finally, based on the Dingo Optimization Algorithm, a hyperparameter calibration strategy for PATGM is provided. The power-sum accumulation grey generating operator can amplify or minimize the nonlinear characteristics of the observations, thus significantly improving the adaptivity of the grey modeling approach to fluctuating sequences. Meanwhile, the elastic-net regression method is employed to obtain a more reasonable and stable parameter structure. The hyperparameters are calculated using the Dingo optimization algorithm, which effectively controls the noise resistance and nonlinearity in the prediction system. PATGM solves the data smoothing processing and model structure selection problems of the traditional grey model. This new model is suitable for processing data prediction tasks with complex characteristics, especially provides an effective prediction method for complex engineering and system modeling.