Abstract: On the basis of the novel kernel and grayscale, the mechanism of the delayed action of the GM(1,N) model on the driving term is still unclear. Under the circumstances, time delay parameters are introduced into the driving term of GM(1,N) model, and a time delay GM(1,N) model based on the new kernel and gray scale is constructed. Meanwhile, the identification method of time lag parameters and the modeling mechanism of the new model are analyzed and discussed respectively. To better verify the validity of the model, the optimized time-lag GM(1,N) model is used to predict and analyze the haze in Nanjing, and the GM(1,N) model and the one-dimensional regression model are selected to compare with the optimized model in the paper. The results show that the optimized model fits the PM₁₀ concentration with higher accuracy and the errors are all controlled within 5%, thus verifying that the proposed optimized model is suitable for simulation and prediction of data with time lag characteristics.

Key words: grey system theory, GM(1,N)model, time-lag effect, new kernel and degree of greyness, forecasting smog

摘要： 为了解决GM(1,N)模型在新型核与灰度的基础上,对驱动项的延迟作用机理不明确的问题,将时滞参数引入到GM(1,N)模型的驱动项中,构建了基于新型核与灰度的时滞GM(1,N)模型,分析了时滞参数的辨识方法,讨论了新模型的建模机理。为了更好地对该模型的有效性进行验证,将优化的时滞GM(1,N)模型对南京市的雾霾进行预测分析,选择GM(1,N)模型、一元回归模型与文中的优化模型进行对比。结果显示,优化模型对PM₁₀浓度的拟合精度更高,且误差均控制在5%之内,从而验证了提出的优化模型适用于具有时滞特征数据的模拟和预测。

关键词: 灰色系统理论, GM(1,N)模型, 时滞效应, 新型核与灰度, 雾霾预测