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今天小编为大家带来《灰色预测GM(1,1)模型在MATLAB中的代码实现》，一起来看看吧！
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【1】基础概念
灰色系统理论是由我国著名学者邓聚龙教授创立，是中国原创学科，是确定性理论和系统科学领域的重要学科。我们称部分信息已知，部分信息不明确的系统为灰色系统，通过对少量信息的累加、累减等计算处理，获取有价值的部分，实现对灰色系统变化趋势的预测，或者对当前系统状况的准确监控。如今灰色系统理论已经进过了将近40年的发展完善，成果丰硕，在理论体系和模型框架方面已经比较完善，参数优化和计算方法等方面都有了相当大的改进，已形成包含了系统分析、预测、优化等技术体系，在许多学科领域得到了广泛的应用。
GM(1,1)模型作为灰色系统理论重要组成部分，适合于小样本数据的预测，在样本缺乏导致信息不足的情况下能充分利用所观察到的决策信息，给出较高精度的预测结果。GM(1,1)模型的思想是对最开始的数据进行一次累加生成数据序列，新的数据序列相应的曲线可以应用特定曲线无限逼近，把逼近曲线作为基础模型，将预测值做几次滚动累加还原，以预测出发展趋势。
【2】方法步骤
令不完全信息非负序列为X(0)，生成1-AGO(1-Accumulating Generation Operational)序列X(1)。
则X(1)的连续相邻序列Z(1)可表示为：
构建GM(1,1)模型，并求出模型参数。
最后得到预测序列。
【3】代码详解
本文构建非负实数序列X(0)=(6.45 7.78 9.99 10.03 14.28)，并通过GM(1,1)模型对原始序列进行预测，得到后三期的结果。
原始序列在MATLAB中的编码如下所示。
1-AGO序列为：
相应的连续相邻序列为：
GM(1,1)内参数表示的代码如下：
将预测次数设定为8(5+3)，则时间响应序列表示为：
最后可得到原始序列的预测值：
【英语学习】
Grey system theory was founded by the famous Chinese scholar Professor Deng Julong. It is an original subject in China and an important subject in the field of deterministic theory and systems science. We call a system with some known information and some unclear information as a gray system. By accumulating and subtracting a small amount of information, we can obtain valuable parts to predict the changing trend of the gray system or the current system status. Accurate monitoring. Now the grey system theory has been developed and perfected for nearly 40 years, with fruitful results. It has been relatively complete in terms of theoretical system and model framework, and considerable improvements have been made in parameter optimization and calculation methods, and it has been formed to include system analysis. Technical systems such as, forecasting, and optimization have been widely used in many disciplines. As an important part of gray system theory, GM(1,1) model is suitable for the prediction of small sample data. It can make full use of the observed decision information when the lack of samples leads to insufficient information, and give high-precision prediction results . The idea of the GM(1,1) model is to accumulate the initial data once to generate a data sequence. The corresponding curve of the new data sequence can be approximated infinitely by a specific curve. The approximate curve is used as the basic model and the predicted value is rolled several times. Accumulate reduction to predict the development trend.
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[1] Yao T , Wang Z . Crude oil price prediction based on LSTM network and GM (1,1) model[J]. Grey Systems Theory and Application, 2020, ahead-of-print(ahead-of-print).
[2] Liu S , Yin C , Cao D . Weapon equipment management cost prediction based on forgetting factor recursive GM (1,1) model[J]. Grey Systems Theory & Application, 2019, 10(1):38-45.