Modeling mechanism of a novel fractional grey model based on matrix analysis
Modeling mechanism of a novel fractional grey model based on matrix analysis
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基于矩阵分析的新型分数阶灰色模型的建模机制
DOI：
10.21629/jsee.2016.05.12
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发表时间：
2016-10-01
影响因子：
2.1
通讯作者：
Xiao, Xinping
中科院分区：
文献类型：
--
作者：
Mao, Shuhua;Zhu, Min;Xiao, Xinping
为了充分展示分数阶灰色模型(FGM(Q，1))的建模机理，本文将模型的数据矩阵分解为与分数阶累加灰色模型(FAGM(1，1))一致的均值生成矩阵、累计生成矩阵和原始数据矩阵。在此基础上，将累加数据差矩阵分解为累加生成矩阵、q阶约简累加矩阵和原始数据矩阵，并结合最小二乘法，发现差分阶数仅通过影响差分序列的形成来影响模型参数。然后总结了一些特殊序列的矩阵分解，如由增强和弱化算子生成的序列、跳跃序列和非等距序列。最后，将原始数据变换、累加序列变换、差分矩阵变换对模型参数的影响以矩阵的形式表达出来，并以非等距序列为例说明了其建模机理。
To fully display the modeling mechanism of the novel fractional order grey model (FGM (q,1)), this paper decomposes the data matrix of the model into the mean generation matrix, the accumulative generation matrix and the raw data matrix, which are consistent with the fractional order accumulative grey model (FAGM (1,1)). Following this, this paper decomposes the accumulative data difference matrix into the accumulative generation matrix, the q-order reductive accumulative matrix and the raw data matrix, and then combines the least square method, finding that the differential order affects the model parameters only by affecting the formation of differential sequences. This paper then summarizes matrix decomposition of some special sequences, such as the sequence generated by the strengthening and weakening operators, the jumping sequence, and the non-equidistance sequence. Finally, this paper expresses the influences of the raw data transformation, the accumulation sequence transformation, and the differential matrix transformation on the model parameters as matrices, and takes the non-equidistance sequence as an example to show the modeling mechanism.