A novel self-adaptive nonlinear discrete grey model based on non-homogeneous index sequence and its application

Abstract while NGBM(1,1) model has been successfully used in various fields,there are still some limitations in NGBM(1,1) model: First, the existing NGBM(1,1) model family is all based on the assumption that some adjustable parameters are known, which reduced the prediction performance of the NGBM(1,1) model family. Then, the leap error from the differential to difference still exists in many NGBM(1,1) models.Moreover, most of the existing NGBM(1,1) models were constructed on the hypothesis that the raw data obey the homogeneous exponential trend. To address these problem, this paper aims to construct a novel self-adaptive nonlinear discrete grey model based on nonhomogeneous index sequence by combining nonhomogeneous discrete grey model with NGBM(1,1) model (abbreviated as SNNDGM(1,1)). Improvements in the proposed model have the following features: Firstly, the new proposed model can effectively eliminate the discretization error of NGBM(1,1) model.Secondly, The new proposed model effectively improves the prediction accuracy of the NGBM(1,1) model by removing the aforementioned modeling assumptions. Thirdly, a new multi-parameter simultaneous optimization scheme based on the firefly algorithm is designed to improve the parameter estimation accuracy. Last but not least, Sobol’s method is used to investigate the mechanism of the adjustable parameters in the SNNDGM(1,1) model, which provides an important basis for model parameter calibration.Two classic numerical cases are introduced to confirm the effectiveness of the new proposed model. Comparisons show that SNNDGM(1,1) model has the highest prediction accuracy. Based on industrial electricity consumption from 2010 to 2019, SNNDGM(1,1) model is constructed to predict the industrial electricity consumption of Anhui Province in China from 2020 to 2024. The results show that industry electricity consumption in Anhui Province maintains a continuous increase, reaching 165.25568 billion kwh in 2024, while the annual growth rate decreases to 3.45%, which provides important information for the decision-making of Anhui electric power department.