GM（1，1）改进模型及其应用

Modified GM(1,1) model and its application

田敏 赵永军 颛孙鹏程

1．中国石油大学地球资源与信息学院，山东 东营 257061 胜利油田钻井工程技术公司，山东 东营 257064

传统GM（1，1）模型实质上是用指数规律来模拟原始序列的变化，因此需要对原始数据序列的累加生成序列进行准指数规律的检验。但对本身已具有准指数规律的原始序列进行累加生成不但不能提高预测精度，反而会增加数据的灰度，影响预测效果。针对传统GM（1，1）模型的这一缺陷，GM（1，1）改进模型根据最小二乘法原理对本身已具有准指数规律的原始序列直接建立模型，克服了传统GM（1，1）模型在建模过程中的盲目性；并在产油量预测中获得了较高的模拟精度，使平均相对误差由5.6％下降至3.8％。较理想的预测效果也验证了GM（1，1）改进模型的正确性和有效性，从而为提高GM（1，1）模型的预测精度提供了一条新的途径。

The essence of the original GM (1,1) model is to simulate the change of the original data sequence with the index law. So it is
necessary to verify the quasi-index law of the 1-AGO data sequence. But generating the 1-AGO data sequence of the original data
sequence with the quasi-index law would not get higher precision and even become worse. The uncertainty degree of the data could
be increased and the forecasting result could be affected. Regarding the limitation of the original GM (1,1)model, the modified GM
(1,1) model is directly established with original data sequence possessing quasi-index law and according to the least square method,
which overcomes the blindness of the original GM (1,1) model. The modified GM (1,1) model can improve the simulation precision
and forecasting precision, making average relative error reduce from 5.6% to 3.8%. The correction and effectiveness of the modified
GM(1,1) model have been verified, which can provide a new way for improving forecasting precision