为增强传统GM(1, 1)模型对系统动态变化的适应能力,有学者通过引入多项式时间项构建了时 变参数GM(1, 1)模型.在此基础上,首先从其白化微分方程推导得到一种新的时变参数灰色预测模型TGM(1, 1),然后给出了模型参数的最小二乘解,同时利用可变步长的复合$\frac{3}{8}$辛普森积分公式给出了可用于预测的离散时间响应式.最后通过实例表明新模型能显著提高预测精度,证实了新模型的有效性和实用性.

In order to enhance the adaptability of the traditional GM(1, 1) model to system dynamic change, the time-varying parameters of GM(1, 1) model was constructed by introducing a polynomial function of time. On this basis, the whitenization differential equation was derived to get a new time-varying parameters grey prediction model TGM(1, 1), and then the least squares solution of the model parameters was given. At the same time, the composite $\frac{3}{8}$ Simpson integral formula was employed to describe the discrete time response that can be used to predict. Finally, the example shows that the new model can significantly improve the prediction accuracy, which confirms the validity and practicability of the new model.