特征自适应型GM(1,1)模型及对中国交通污染排放量的预测建模

Characteristic adaptive GM(1,1) model and forecasting of Chinese traffic pollution emission

兼顾精度与拟合趋势相似性是预测建模需要深入研究的重要问题.为提高模型对数据特征的适应能力,本文分析了GM（1,1）模型中灰微分方程和白化方程的一致性关系以及响应式还原方法问题,提出构建一种特征自适应型灰预测模型,即CAGM（1,1）模型.该模型采用含可变参数的背景值公式构建灰微分方程,并通过转化模型形式推导了参数估计过程,进而构建以背景值序列为基础的时间响应式;为提高模型预测能力,本文结合灰色关联度构建响应式还原过程中待定变量的适应度函数,采用粒子群算法取得其最优值.最后,案例研究了我国机动车污染排放预测问题,分别构建GM（1,1）和CAGM（1,1）模型对氮氧化合物排放量进行建模,通过比较二者拟合和预测结果验证新模型的改进效果,为管理实践提供有效工具.

Improvements of fitting precision and tendency similarity are of vital importance for forecasting analysis. To promote data characteristic adaptation of grey prediction model, this paper analyzes the relationship of grey differential equation and whitenization equation, and studies the restoring process of response function, then proposes a novel characteristic adaptive GM（1,1） model, namely CAGM（1,1） model. This model uses the novel background formula with quantile variable to construct grey differential equation, and employs the transformed model to derive the process of parameters evaluation. Further, we construct the time response formula based on background series; to improve forecasting performance, we propose a new fitness function according to grey incidence method and utilize the particle swarm algorithm to search optimal values of the variables in restoring process. The new model is used to analyze traffic pollution emission in China, and we construct GM（1,1） and CAGM（1,1） for comparison. The results confirm that the model proposed in this paper outperforms traditional GM（1,1） model and could be useful and effective in practice.