基于扰动信息的连续区间灰数灰色预测模型

Grey prediction model of continuous interval grey number based on perturbation information

针对连续区间灰数的预测,提出了分数阶累加二次时变参数离散灰色预测模型(FQDGM(1,1)模型)。在不损失原始信息的前提下,将区间灰数转化为核序列和灰半径序列,然后分别对核序列和灰半径序列建立FQDGM(1,1)模型。新模型针对同时包含指数和二次曲线趋势的系统,通过二次时变参数的求解和阶数的调整,实现对于原始信息进行有效挖掘,避免扰动信息的干扰,提高模型的稳定性。最后,运用不同灰色预测模型,对于一个算例和一个实例进行建模,计算结果显示了所提方法的优越性,从而进一步拓展了灰色预测理论的应用范围。

In order to solve the prediction problem of continuous interval grey number,a fractional order cumulative quadratic time-varying parameter discrete grey prediction model (FQDGM (1,1) model) is proposed.On the premise that the original information is not lost,the interval grey number is transformed into kernel sequence and grey radius sequence,and then the FQDGM (1,1) model is established for kernel sequence and grey radius sequence respectively.The model can effectively mine the original information,avoid the disturbance of the perturbation information and improve the stability of the model by solving the quadratic time-varying parameters and adjusting the order for the system that contains both exponential and conic trend.In the end,a numerical example and a real case are modeled by using different grey prediction models.The results show the superiority of the method proposed.It further expands the application scope of grey prediction theory.