Extrapolation optimization time power conformable fractional derivative non-linear grey Bernoulli model and its application

In order to address the structural limitations inherent in the current grey prediction model, this paper proposes the time power conformable fractional derivative non-linear grey Bernoulli model (CFNGBM(p,1) model) based on the traditional grey Bernoulli model, leveraging the theory of fractional calculus. Firstly, by utilizing the computational advantages of conformable fractional derivatives, the grey derivative of the traditional whitening equation is extended from first-order to fractional-order, making the model structure more flexible. Secondly, a time power term is introduced into the model structure to fully capture the non-linear relationship presented in real systems. Additionally, to address the overfitting phenomenon in grey models, an extrapolation optimization mechanism is incorporated into the traditional parameter optimization process by simulating future prediction scenarios. Finally, a case study of monthly production data of photovoltaic glass in the crystalline silicon industry chain demonstrates that the proposed CFNGBM(p,1) model outperforms three other grey Bernoulli models in terms of accuracy, and the use of extrapolation optimization mechanism significantly reduces overfitting.