Improvement and application of GM(1,1) model based on multivariable dynamic optimization

For the classical GM(1,1) model, the prediction accuracy is not high, and the optimization of the initial and background values is one-sided. In this paper, the Lagrange mean value theorem is used to construct the background value as a variable related to k. At the same time, the initial value is set as a variable, and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error (MRE). Combined with the domestic natural gas annual consumption data, the classical model and the improved GM(1,1) model are applied to the calculation and error comparison respectively. It proves that the improved model is better than any other models.