数据驱动的分数阶灰色预测模型及其应用研究

Due to the low quality and the higher volatility of air quality in haze day, to excavate the potential information of new sample and adjacent region data as much as possible, a new fractional order grey modeling techniques is put forward by taking the "in between" idea from fractional order as the main line. Firstly, for the time series with medium size sample, fractional order adjacent accumulation operator is proposed. The grey model can get the output of interval number by the input of grey information. Secondly, the conflict that exists between our desire for minimal variance and desire to use the freshest data is addressed via fractional accumulated generating operator. And grey Holt-Winters model with fractional season accumulation operator is developed for the cyclic data. Thirdly, for the memory of time series and non-locality of spatial data, set the goal of new information priority and adjacent data priority, fractional order error pooled operator is discussed. The forecasting result of the intersection point in panel data can be obtained by GM(p,N) with fractional order derivative and GM(0,M) with the fractional accumulation. Fourthly, grey forecasting model system is introduced. The priority of recent information and the other mathematical properties of the new model are investigated further. Finally, these grey models will be used to forecast haze time in Han-Xing district. It will help the Han-Xing government to control and prevent the environmental pollutions.

以分数阶的“in between”思想为研究主线，实现新信息和邻近区域数据的最大挖掘为目标，提炼一套与数据相匹配的分数阶灰建模技术。首先，针对中等规模的时间序列，提出分数阶邻近累加生成算子，使灰信息输入能够得到区间数输出，构建适用于中等规模样本的灰色预测模型。其次，将分数阶累加算子引入指数平滑，解决指数平滑不能兼得最小拟合误差和数据理想权重的问题，进而针对周期性数据提出含有同期累加算子的灰色Holt-Winters模型。再针对面板数据，借助分数阶在时间序列的记忆性和空间数据的非局域性，提出分数阶误差合并算子，构建含分数阶导数的GM(p,N)和分数阶GM(0,M)模型，得出面板数据在交叉点的预测结果。然后，构建数据驱动的灰色预测模型体系，探讨新模型稳定性与样本量的关系、模型的新信息优先性等一些数学性质。最后，运用新模型解决邯邢地区大气污染灾变预测难题，提出可操作的对策建议。

本课题从雾霾重灾区的空气质量数据入手，以分数阶的“in between”思想为研究主线。首先，针对中等规模的时间序列，提出分数阶邻近累加生成算子，构建适用于中等规模样本的灰色预测模型。其次，提出含有同期累加算子的灰色Holt-Winters模型，解决指数平滑不能兼得最小拟合误差和数据理想权重的问题。再构建含分数阶导数的GM(p,N)和分数阶GM(0,M)模型，基于耦合模型得出面板数据在交叉点的预测结果，解决灰色预测模型不适用于面板数据的问题。然后构建数据驱动的灰色预测模型体系，并探讨了新模型稳定性与样本量的关系等一些数学性质。本项目研究成果对夯实灰色预测的基础理论，拓展模型应用范围具有重要意义。课题组在《Socio-Economic Planning Sciences》、《Sustainable Cities and Society》、《Energy》、《Sustainable Production and Consumption》、《Applied Mathematical Modelling》、《Communications in Nonlinear Science and Numerical Simulation》和《中国管理科学》等国内外期刊发表论文48篇，其中SCI/SSCI检索36篇，EI期刊检索4篇，4篇入选ESI高被引，项目主持人以第一作者/通讯作者发表40篇。研究成果获省级自然科学二等奖。