A novel fractional time-delayed grey Bernoulli forecasting model and its application for the energy production and consumption prediction

Energy affects the stable and sustainable development of social economy. Energy prediction plays an important role in the process of China's energy market transformation. Scientific and reasonable energy predicting method can help government to make decisions effectively, and then adjust energy structure and industrial layout. The energy field is full of fractional order phenomenon and nonlinear disturbance. Aiming at the energy data sets with the characteristics of scarcity, complexity and nonlinear, a mathematical model including time delay term and Bernoulli equation can be used to fit this trend. A new fractional time-delayed grey Bernoulli model is proposed, and the new model has a wider application in the nonlinear field. The model is discretized by integral, and the least square estimation of the linear parameters and the approximate time response equation are obtained. The Grey Wolf Optimizer (GWO) is used to search the optimal parameters of the model. In addition, the energy prediction model is established from the perspective of renewable energy and fossil energy, and the effectiveness of the model is verified by three actual cases of renewable energy, crude oil and fossil fuel. Compared with the other seven grey models, the results show that the new model has higher prediction performance. Finally, the energy development trend in the next few years is predicted by using the proposed model, and relevant conclusions are drawn according to the prediction results.