振荡序列的分数阶离散GM(1,1)幂模型及其应用

Fractional order discrete grey GM(1,1) power model based on oscillation sequences and its application

针对GM(1,1)幂模型从离散的参数估计到连续的预测函数所产生的固有误差,提出一种新的分数阶离散GM(1,1)幂模型,并针对可能存在的病态性,利用正则化算法替代最小二乘法估计部分参数以提高参数估计的精度;为了提高模型的预测精度,提出新的累加阶数及幂参数的确定方法.对工业废水排放率及城市用水量两个实例的预测结果表明,所提出的模型及确定参数的方法对于振荡时间序列有着很好的预测精度.

To overcome the system errors of the grey GM（1, 1） power model, in which the parameters estimation is discrete and the forecast function is continuous, a new fractional order grey discrete GM（1, 1） power model is constructed, and the method of regularization is used in stead of the least square method in some parameters＇ estimation because of the problem of ill-condition to improve the accuracy of parameters estimation. A new method is proposed to determine the optimization values of accumulation order and power exponential so as to increase the forecast precision. The tests on the forecast of industrial waste emissions rate and urban water consumption show that the proposed model and the methods of parameters estimation have higher forecast accuracy in oscillation sequences.