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

Xiaozhong Tang; Zhijun Zhu; Xiaomei Liu; Huibin Zhan; Xiaozhong Tang; Zhijun Zhu; Xiaomei Liu; Huibin Zhan

doi:10.3934/math.2025774

AIMS Mathematics

2025, Volume 10, Issue 8: 17305-17333. doi: 10.3934/math.2025774

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Research article

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

1.
School of Economics and Management, Huangshan University, Huangshan, China
2.
School of Economics and Management, Xi'an University of Technology, Xi'an, China
3.
College of Science, Jiujiang University, Jiujiang, China

Received: 03 June 2025 Revised: 16 July 2025 Accepted: 23 July 2025 Published: 01 August 2025
MSC : 65Q10, 62M10

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.
- nonlinear grey Bernoulli model,
- industrial electricity consumption,
- grey system theory,
- grey prediction model
Citation: Xiaozhong Tang, Zhijun Zhu, Xiaomei Liu, Huibin Zhan. A novel self-adaptive nonlinear grey Bernoulli model for forecasting China's industrial electricity consumption[J]. AIMS Mathematics, 2025, 10(8): 17305-17333. doi: 10.3934/math.2025774

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Abstract

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.

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