A novel damped conformable fractional grey Bernoulli model and its applications in energy prediction with uncertainties

Energy resources, such as oil, coal are important to people's life and the development of the economy. Predicting the energy consumption and production with uncertainties can help the government and policymakers make the reasonable energy strategy and give constructive guidance. In this paper, a novel damped conformable fractional accumulation operator with two parameters are proposed to have control of both accumulation generation and new information involvement. The new accumulation can be adjusted from linear approximation to high order accumulation. A structure adaptive grey Bernoulli model based on proposed accumulation method is established, with the parameters optimized by particle swarm optimization algorithm. For testifying the effectiveness and the robustness of the model, two validation cases and two application cases are used to build the prediction model of diverse series with unexpected trends or fluctuations in energy fields. Compared with other existing fractional grey models and non-grey models, the proposed model has best prediction accuracy, better model stability and greatly improved applicability. The global coal consumption by industry is predicted as 30.85×106 TJ in 2025 and 30.81×106 TJ in 2026. The world coal production could be 182.93-187.73 exajoules in 2025 and 180.85-182.16 exajoules in 2026.