基于Simpson公式改进的FAGM(1,1)模型及其应用研究

本文分析了传统FAGM（1，1）模型建模过程中存在的误差，提出了一种基于Simpson公式改进的FAGM（1，1）模型。首先，基于分数阶累加生成算子和分数阶累减生成算子建立分数阶FAGM（1，1）模型。其次，利用Simpson积分公式对FAGM（1，1）模型的背景值进行改进，建立SFAGM（1，1）模型。进一步，应用遗传算法确定SFAGM（1，1）模型的最优阶数以提高模型的预测精度。最后，以中国人均GDP为例，对比分析GM（1，1）模型、Simpson改进的GM（1，1）模型（SGM（1，1））、FAGM（1，1）模型、SFAGM（1，1）模型的模拟结果，并对"十三五"时期的人均GDP进行预测，其结果表明SFAGM（1，1）模型比GM（1，1）、SGM（1，1）、FAGM（1，1）在人均GDP的预测方面有更高的精度，"十三五"期间人均GDP年平均增长率为10.64%，到2020年达到83146.97元，是2010年人均GDP的2.69倍，以2010年的人均GDP为基准，到2020年将能够实现翻一番的目标。

The Improved FAGM(1, 1) Model Based on Simpson Formula and Its Applications

The errors in the traditional FAGM (1, 1) model are analyzed, and an improved FAGM(1,1) model with the Simpson formula is proposed. Firstly, the fractional FAGM (1, 1) model is developed based on the fractional order accumulating generation operator and the inverse accumulating generation operator. Secondly, employing the Simpson formula to construct the background value of the FAGM (1, 1) model to establish the SFAGM(1,1) model. Further, the genetic algorithm is used to determine the final optimal order of the SFAGM(1,1) model to improve the prediction accuracy of the model. Finally, taking China's per capita GDP as an example, the calculation results of the SFAGM(1,1) model are compared with the GM(1,1), the GM(1,1) model with Simpson formula (SGM(1,1)) and the FAGM(1,1) model, and then the GDP per capita in the "Thirteen-Five" period is predicted. The results show that the prediction accuracy of the SFAGM(1,1) is higher than GM(1,1), SGM(1,1), and FAGM(1,1) models, and the average annual growth rate of GDP per capita during Thirteenth Five-year plan is about 10.64%. The per capita GDP in 2020 will reach 83146.97 yuan,which is 2.69 times as much as that in 2010.And in ciew of 2010 per capita GDP in China, the double goal for 2020 per capita GDP will be achieved.