分数卷积灰色预测模型及其在信息传播中的应用

Grey model based on fractional sequence convolutionand its application in information communication

通过构造累加生成卷积序列的离散卷积运算实现了数据序列的累加生成,并推广到分数阶卷积幂以实现分数阶累加生成。离散序列卷积运算统一了累加生成和累减生成,给定阶数即可生成相应的卷积序列。引入离散卷积运算,可以从信号处理的角度来理解累加生成。累加生成系统可视为一个线性滤波器,累加卷积序列的本质是滤波器的单位冲击响应,卷积运算对应滤波过程。在分数累加卷积序列的基础上构建了分数阶灰色预测模型。最后给出数值实验和信息传播中的实际应用案例验证理论的正确性和方法的有效性。

The discrete convolution operation of accumulation generation convolution sequences was constructed to fulfill the accumulation generation of data sequence,and then was extended to the fractional order convolution power to implement the fractional accumulation generation.The discrete sequence convolution operation unified the accumulation generation and the reduction generation,and the corresponding convolution sequence could be generated as long as the order was given.The accumulation generation system could be viewed as a linear wave filter,and the essence of the convolution sequence was unit shock response of the filter,and the convolution operation corresponds to the filtering process.Then,a fractional order grey forecasting model was established based on the fractional accumulated convolution sequence.Finally,numerical experiments and practical application cases in information communication were given to verify the correctness of the theory and the effectiveness of the method.