一种优化的高精度灰色GM(1,1)预测模型

尚军亮; 方敏

doi:10.3724/SP.J.1146.2009.00792

一种优化的高精度灰色GM(1,1)预测模型

doi: 10.3724/SP.J.1146.2009.00792

尚军亮,
方敏

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出版历程
- 收稿日期: 2009-05-22
- 修回日期: 2009-12-01
- 刊出日期: 2010-06-19

New Optimized Method of High-Precision Grey GM(1,1) Forecasting Model

摘要

摘要: 针对灰色GM(1,1)模型的建模方法存在偏差，模型不满足协调性条件，不具有变换一致性，且通过累加生成建模时，x(0)(1)没有起到高精度控制预测等问题。该文从重构GM(1,1)白化背景值出发，利用白化背景值的加权向前差商和向后差商平均值优化模型灰导数，根据新信息对认知的作用大于旧信息的原理，以x(1)(n)替换x(0)(1)作为模型的初始条件，对GM(1,1)预测模型进行了改进，从而使所建模型的预测精度大为提高，尤其是发展系数大于2时，新模型的拟合精度仍然很高。通过实例对比验证了新模型无论在低增长指数序列还是在高增长指数序列都有非常高的实用性和可靠性。
- 灰色系统理论; GM(1,1)模型; 背景值; 灰导数; 初始条件
Abstract: There are some problems in GM(1,1) model, such as, model method biased, compatibility condition not satisfied, transformation inconsistent and first number of the initial sequence not functioning high precision prediction in model after an accumulated generating operation. This paper deals with the GM(1,1) model improvement in reconstructing the GM(1,1) white background value, using white Background value weighted average of forward (backword) difference quotient as the new optimized models grey derivative, regarding the value of x(1)(n) replacement of x(0)(1) as the models initial condition. The new model improves the accuracy of the precision greatly. Even if the development coefficient is bigger than 2, the fitting precision of the new model is still high. The analysis of some examples indicates that the new optimized method using whether in low growth index series or in high growth index series has a very high practicability and reliability.

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参考文献(1)

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