灰色模型的病态问题研究

Study on morbidity problem in grey model

针对灰色模型在参数辨识过程是否出现病态问题利用矩阵条件数进行了研究,研究结果表明:只有在原始序列首项不为零其它各项近似为零的常数序列的情况下灰色模型才会发生病态性问题,对于这类序列在进行预测时是没有实际意义的.因此在灰色预测所建立的灰色GM(1,1)模型是不会存在病态问题.

Whether the model we have built has the morbidity problem is a key condition to judge its practicability. So this paper discusses if the morbidity problem will appear in the process of parameters differentiate in grey model, basing on the condition number of matrix. Results show that the morbidity problem could only exist in GM（ 1,1 ）when the first item of original sequence is unequal to zero while other items are equal to zero approximatively. Accordingly, there＇s no practical meaning to predict by this kind of sequence. Consequently, it also proves that the morbidity problem doesn＇ t exist in GM （ 1, 1） when making a grey prediction.