GM(1,1) 模型的病态性问题再研究

针对GM(1,1) 模型参数辨识过程中的病态性和稳健性问题, 一方面通过不改变预测精度的数乘变换将模型参数辨识过程中的病态性矩阵转化为良态矩阵, 另一方面利用适当的正交矩阵对原始数据序列实施正交变换, 将模型的参数辨识过程转化为具有递归形式线性方程组的求解过程, 从而避免参数辨识过程中出现的病态性问题, 提高模型的适用性. 最后通过算例和Monte-Carlo 数值模拟进一步验证了所提出方法的有效性.

Morbidity problem of GM(1, 1) model

In order to improve the bad robustness and morbidity of parameter identification of GM(1,1) model, on one hand, the ill-conditioned matrix of parameter identification is transformed into the good-conditioned matrix by using the multiply transformation, which does not change the prediction precision of the model; on the other hand, the process of parameter identification is transformed into solving the linear equations with the recursive form by using the appropriating orthogonal matrix. By using the proposed methods, the morbidity problem of least squares is avoided, and the applicability of the model is improved. The numerical example and Monte-Carlo simulation show the effectiveness of the proposed methods.