A novel self-adaptive nonlinear grey Bernoulli model for forecasting China's industrial electricity consumption

The rigidity of subjectively preset adjustable parameters in the existing NGBM(1,1) model family restricts its ability to handle complex nonlinear time series. To address this issue, this paper proposed a self-adaptive nonlinear grey Bernoulli model [SANGBM(1, 1)] with enhanced predictive capabilities. Three key innovations were introduced. First, hyperparameterized functions were developed to dynamically optimize adjustable parameters, overcoming the rigidity of subjectively preset hyperparameters in the existing NGBM(1,1) model family and improving adaptability. Second, the derived implicit time response formula of the SANGBM(1,1) model fundamentally resolved the jump error inherent in the traditional NGBM(1,1) model. Third, based on the systematic deconstruction of the global sensitivity mechanism of the SANGBM(1,1) model's hyperparameters, a novel data-driven model structure selection algorithm that integrates the time series rolling cross-validation method with the firefly algorithm was designed to enhance generalization performance. Empirical results demonstrate the feasibility and effectiveness of the proposed model. Additionally, China's industrial electricity consumption for the next four years (2023–2026) was predicted, offering valuable references for formulating effective industrial electricity development planning.