Ameliorating GM (1, 1) Model Based on the Structure of the Area under Trapezium

Abstract

According to the research on the structure of background value in the GM(1,1) model, the structure method of background value, a exact formula about the background value of χ ⁽¹⁾(t) in the region [k,k + 1],which is used when establishing GM(1,1), is established by integrating χ ⁽¹⁾(t) from k to k + 1 .The modeling precision and prediction precision of the ameliorating background value can be advanced. Moreover, the application area of GM(1,1) model can be enlarged. At last, the model of Chinese per-power is set up. Simulation examples show the effectiveness of the proposed approach.