累加卷积变换及其在灰色预测模型中的应用  

The accumulative convolution transform and its application in grey forecasting model

作　　者：陈涛[1] CHEN Tao(Communication University of China,Beijing 100024,China)

机构地区：[1]中国传媒大学数据科学与智能媒体学院,北京100024

出　　处：《中国传媒大学学报（自然科学版）》2023年第2期76-84,共9页Journal of Communication University of China：Science and Technology

基　　金：中国传媒大学中央高校基本科研业务费专项资金(CUC220B005)。

摘　　要：基于数据序列卷积运算提出了一种构建累加生成算子的新途径。通过构造一种累加生成卷积序列来实现数据序列的累加生成。然后引入单边Z变换,得到累加生成卷积序列在频率域的形式,从而得到累加生成算子在频率域的表达式。对于逆累加生成算子,构造了相应的逆累加生成卷积序列,并导出它在频率域的表达式。通过构造累加生成卷积序列和单边Z变换得到其频率域的表达式,获得两个全新的视角来理解累加生成算子和逆累加生成算子之间的互逆关系。最后通过实际案例验证了理论的正确性和方法的有效性。Based on the convolution methods,this paper propose a new method to construct the accumulative generation operator.A data sequence called accumulative generation convolution sequence is constructed,which play the same role as accumulative generation operator.Through the single side Ztransform,the accumulative convolution sequence in the complex field is obtained,which is the expression of the accumulative generation operator in the frequency domain.The similar results of the inverse accumulative generation operator are also developed.Finally,we obtain two new points of view to interpret the mutually inversion relationships between the accumulating operator and the inverse accumulating generation operator.Finally,some real cases are demonstrated to verify the accuracy of the theoretical results and the effectiveness of the method.

关 键 词：灰色系统理论 灰色预测模型 微分方程 参数估计 Z变换 

分 类 号：N941.5[自然科学总论—系统科学]