基于多维时空的NPCA-PSR-IGM(1,1)组合模型的短时交通流预测

针对城市短时交通流序列非线性和混沌性的特点，为提高短时交通流的预测精度，该文提出一种基于多维时空的非线性主成分分析(NPCA)和相空间重构(PSR)的改进灰色(IGM(1,1))组合预测模型。首先，使用数据相关性的非线性主成分分析算法对多维交通流量序列进行时空降维，同时保留影响预测点的主要交通流量数据，从而提高建模的精确度；其次，利用多维时空交通流量序列相空间重构放大交通流量内部的细微特征，以使其内在规律得以充分展现，进一步提升预测精度；最后，结合背景值改进的灰色模型适应于线性、非线性以及所需数据少的特点，进行短时交通流预测。实验结果表明，NPCA-PSR-IGM(1,1)组合预测模型的平均相对误差相比NPCA-PSR-GM(1,1)组合预测模型减小3.12%，其标准偏差相对PCA-PSR-IGM(1,1)组合预测模型从15.7091下降到2.0589。同时与最新的预测模型相比，该组合预测模型也提高了预测精度，达到了较好的预测效果。

Short-term Traffic Flow Prediction Based on NPCA-PSR-IGM (1,1) Combined Model of Multi-dimensional Space-time

In view of the nonlinear and chaos of urban short-term traffic flow sequence, this article proposes a combined prediction model based on multi-dimensional spatio-temporal Nonlinear Principal Component Analysis (NPCA) and Phase Space Reconstructed (PSR) Improved Gray Model (IGM(1,1)) in order to improve its forecast accuracy. First, the data correlation NPCA algorithm is used to reduce the spatial and temporal dimensions of multi-dimensional traffic flow sequences, while preserving the main traffic flow data that affects the predicted points, so as to improve the accuracy of the modeling. Phase space reconstruction amplifies the subtle features inside the traffic flow, so that its internal laws can be fully displayed, and improve further the prediction accuracy. Finally, the gray model combined with the improved background value is adapted to the characteristics of linearity, non-linearity and less required data. Short-term traffic flow is predicted. The experimental results show that the average relative error of the NPCA-PSR-IGM (1,1) combination prediction model is 3.12% smaller than that of the NPCA-PSR-GM (1,1) combination prediction model, and its standard deviation is relative to the PCA-PSR-IGM (1,1) combination prediction model has dropped from 15.7091 to 2.0589. At the same time, compared with the latest prediction model, the combined prediction model also improves the prediction accuracy and achieves a better prediction effect.