含有时间幂次项的灰色预测模型病态特性

Morbid property of grey prediction model with time-power

为了准确揭示含时间幂次项灰色预测模型的解在系统原始特征序列存在微小扰动下的变化规律,对该模型背景值和时间幂系数在不同取值下的系数矩阵谱条件数值进行分类计算.研究结果表明,一般情况下该模型不存在严重病态性.研究结论认为,在系统建模预测过程中,该模型的预测值不会因系统原始特征序列存在一定误差而产生显著振荡现象.

Aiming to reveal the change law of modeling parameters of the grey model with time-power resulted from a small perturbation of primitive sequence, the spectrum condition number of the matrix is taken as a tool of measuring the morbidity of this model, and the value of conditions of the coefficient matrix with the background value and time-power item of this model in different cases, respectively. The research result shows that this grey model has no unusually severe morbidity. The research conclusion suggests that, in the grey prediction modeling process, while using this grey model with time-power, the solution of this model will not occur significant drift for the original data series of systems existing minor errors.