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针对灰色GM(1,1)幂模型存在的缺陷,从背景值和初始条件两个方面对GM(1,1)幂模型进行参数寻优。首先分析传统模型背景值的误差来源,从定义出发,构建优化后的背景值公式;其次指出传统预测公式中默认的已知条件是不合理的,从原始序列与其预测值的误差平方和最小原则出发,建立初始条件的选取方法;最后以等维新息原则对预测模型的构建步骤进行优化改进,并以我国天然原油产量案例验证所述模型的有效性。结果表明,基于背景值、初始条件以及等维新息原则共同改进的优化方法能够有效提高GM(1,1)幂模型的模拟精度和预测精度。
Aimed at the defects of gray GM (1,1) power model, the parameters of GM (1,1) power model are optimized from the background value and the initial condition. Firstly, the source of the error of the background value of the traditional model is analyzed. From the definition, the optimized background value formula is constructed. Secondly, it is unreasonable to point out that the default known condition in the traditional prediction formula is not reasonable. Then, the selection method of the initial conditions is established. Finally, the construction steps of the prediction model are optimized and improved based on the principle of equal dimensionality and the validity of the model is verified by the case of natural crude oil production in our country. The results show that the optimization method based on background values, initial conditions and the principle of equal dimensionality and innovation can effectively improve the simulation accuracy and prediction accuracy of GM (1,1) power model.